Keywords: Semiconductor measuring transducers, Piezoresistive effect in p-type silicon, silicon sensor, pressure, LF-acceleration Inertial Accelerometer with Piezoresistive Transducer

The main part of scientific material of PhD thesis "Silicon Integrated Mechanical Sensors of Control, Monitoring, Regulation Systems for Temperature Range (0 ÷ 300) • C" in the specialty 05.13.05 "Elements and devices of computer engineering and control systems" is presented. The main results: the regular influence of physical and geometrical parameters on the temperature dependence of the insulating properties of p-n-junctions, allowing to expand the working temperature range up to +210 • C, has been established; the way of further expansion of the temperature range up to 300 • C by eliminating the insulating p-n junction has been proposed, grounded and experimentally evaluated; the methods of improving the accuracy of silicon integrated converters have been developed and experimentally evaluated. On the basis of this work, total pressure and low-frequency acceleration transducers were created, meeting the requirements and operating conditions for model tests of modern and advanced rocket engines. The efficiency and great practical importance of the work were confirmed by the results of the introduction into the experimental and design work of the organizations of the Ministry of General Machine-Building

MLTI (now Mytischi Branch of Bauman Moscow State Technical University)

Space Faculty

LIST OF FIGURES

2.1 Block diagram of the conversion of a mechanical quantity into an electrical signal using a sensor with an integrated piezoresistor transducer (IPT). 1 -for inertial sensors; 2 -for IPT with distributed parameters. . .

Introduction

The introduction substantiates the relevance of the topic of the dissertation work, formulates scientific novelty and the provisions submitted by the author for defense.

Relevance of problem

At the present stage of development of our industry, the parameters of control system elements (CS), system control (MS), system regulation (RS) largely depend on the quality of products, improvement of their technical characteristics. Depending on the purpose of the system, the elements divide into four functional groups of devices: (1) for receiving information about processes and objects; (2) to receive, transform and transmit information;(3) for processing, storing information, and forming control commands;(4) devices for using command information.Information acquisition tools (1) are the largest group and usually make up more than half of the assortment of all technical means of the system. When solving industrial problems, the main components of this group of elements are primary transducers (sensors) of mechanical quantities (pressure, acceleration, impact, etc.). Typical for the industry sensors of mechanical quantities VT, LH, ANS, etc. They have significant disadvantages: high weight and overall dimensions, low sensitivity, the high labor intensity of manufacture, driving during operation. Their constructive-technological solutions probably will not allow to significantly improve technical indicators in the future. For this reason, existing primary information transducers do not fundamentally solve a number of current industrial problems, especially in the creation of new products. One of these tasks relates to the management of research tests of the RD-170 (11D521) and RD-171 (11D520) reusable LPRE units. The problem here comes from obtaining accurate information about the pressure fields in LPRE units. Ranges of measured pressures from 0 -1 atm to 0 -10 atm. In this case, the intrinsic error of the pressure sensors should not exceed ±1%. The second problem includes obtaining accurate information about vibration modes, parameters of dynamic stability, dynamic overloads on nodes, and power elements. Measured acceleration ranges from 0 ± 1 g to 0 ± 10 g, frequency spectrum 0 -300 Hz. The intrinsic error of accelerometers should not exceed ±5%.

Methods of research

Theoretical studies use methods of mathematical modeling, the theories of transport phenomena, contact phenomena, and the piezoresistive effect in semiconductors. The author experimentally determined the electrophysical characteristics of the piezoresistive channels, the material of the elastic element, the insulating p-n junction, and the metrological characteristics of the integrated piezoresistive transducer (IPT). The methods of probability theory and mathematical statistics confirmed the results of the experiments.

Scientific novelty.

The scientific novelty of the work consists in the development of physical and functional models and principles of constructing monolithic silicon integrated strain resistor transducers of small sensors mechanical values for the operating temperature range 0 -300 • C.

The new results:

the natural influences of physical and geometric parameters on the temperature dependence of the insulating properties of the IPT p-n junctions at temperatures more than 0 -+100 • C; a physical and functional model of the primary deformation transducer with a part of the elastic element material electrically connected to the bridge measuring circuit; the principles of designing precision monolithic IPT of small-sized pressure and acceleration sensors for the operating temperature range of 0 -300 • C, including minimization of the intrinsic error of the IPT by the identity of the electrical parameters of the bridge measuring circuit; minimization of the complementary temperature error of the IPT with an insulating p-n junction in the 0 -+200 • C range by using the regular temperature changes of the electrophysical characteristics of silicon piezoresistive p-type channels and passive regulating resistive elements; minimization of the complementary temperature error of IPT by using a part of the elastic transducer element as a regulating element of the output signal temperature dependence for the 0 -300 • C range.

Practical value and implementation of results

Developed unified series of microminiature IPT SIAP 408854.001 for small pressure sensors from 0 -0.1 atm to 0 -10 atm, small-sized LF-accelerometers (LF-Low Fre-quency) ANPPE SIAP.402139.001 for measurements of low-frequency accelerations from 0 ± 1 g to 0 ± 30 g in the frequency range 0 -300 Hz.

Approbation

The All-Union Conference "Methods and means of tensometry and their application in the national economy" in Sverdlovsk 1989 ; Scientific conferences of faculty and postgraduate students of the MSFU (Moscow State Forest University) 1983, 1984, 1985.

Publications

The author outlined the main content and results of the work in 9 articles and defended three certificates of authorship.

The volume of work

The thesis work consists of an introduction, four chapters, and a conclusion, on 83 pages of typescript, 6 tables, 35 figures, a list of literature comprising 84 titles and applications.

1.9 The main provisions: extension of the upper limit of the working temperature range of silicon integrated strain gauge transducers of mechanical quantities, with an insulating p-n junction, to values over +200 • C by reducing the area, the transition perimeter, and the number of angles in the topological structure of the elements;

the physical and functional model of the transducer of mechanical quantity without insulating p-n junction, allowing at the expense of selection of electro-physical characteristics of Si piezoresistive channels and Si elastic element to extend the upper limit of a range of working temperatures to values more than 300 • C; a method to compensate for the complementary temperature error in the temperature range -60 -325 • C of silicon mechanical magnitude sensors by electrically connecting part of the resilient element material to a bridge circuit and selecting the resistivity of the resilient element material in the range (0.5 ÷ 10)Ω • cm.

CHAPTER 2

Analysis of Silicon Integrated Piezoresistor Transducers for the Temperature Range 0 ÷ 300°C

Introduction

The physical and functional models of mechanical sensors with silicon integrated piezoresistor transducers IP T are described in detail in 1 2 3 4 5 . Fig. 2.1 show a generalized structural diagram of the transducer and parameters that characterize the conversion of the input mechanical quantity ϕ in into the output electrical signal V out . The input mechanical quantity ϕ in is perceived by the elastic element (EE) directly or, as in inertial sensors, through a preliminary mechanical transducerthe inertial mass. In this case, ϕ in is converted into functionally related to it distributed relative strain of the EE ε ee . In turn, the deformed state of the EE is functionally related to the deformed state of the insulation layer of the piezoresistor channels, characterized by the value of relative strain ε il . In the body of the channels, ε il is converted into the relative change in electrical resistance ∆R/R. The constant electrical stabilized supply voltage through the thermal compensation circuit is fed to the input of the sensor bridge circuit.

In Fig. 2.1, in the conversion circuit, the conversion function of each of the transducers is represented by the expression:

y = y 0 (x 1 , x 2 , . . . , x n ) + K (x, x 1 , x 2 , . . . , x n ) • x (2.1)
where x is the input quantity; y is the output quantity; K (x, x 1 , x 2 , . . . , x n ) is the conversion coefficient for the transducer, which is a function of the input quantity x and the set of influencing quantities x 1 , x 2 , . . . , x n ; y 0 is the initial value of the output quantity y (at x = 0), and also a function of influencing quantities x 1 , x 2 , . . . , x n .

When analyzing designs, temperature effects on the elements of the sensor structure are considered the only influencing factor. Design parameters related to the influence of temperature on the characteristics of the sensor are divided into two groups.

The first group includes parameters that define the upper limit of the operating range: • temperature T per , at which the insulation resistance value R i decreases to the critical value R i min and the layer softening temperature T sof t for electrical insulating, masking and connecting elements of the structure;

• intrinsic conductivity temperature T int , related to the impurity concentration of the majority carriers N CH , N EE , N RB for the semiconductor elements of the structure, in which the conversion and transfer of the electrical signal occurs. According to 6 T int (ρ) = 273 10 4, 5 + log ρ -1 ;

(2.2)
where, ρ is the resistivity of the semiconductor material depending on the concentration of the majority carriers impurity.

The second group contains parameters that determine the complementary temperature error of the sensor:

• temperature dependences of resistances R T C (T ) of elements of regulation and compensation structure of IP T ;

• temperature dependences of the elements of the measuring circuit structure: input and output resistances R in (T ) and R out (T ), resistance of contact pads R c (T );

• temperature dependencies of piezoresistive channels R ch (T ) and their gauge factor K ch (T );

• temperature coefficients of linear expansion IP T of materials of structural elements determining deformed state of α l , i.e. transducers of mechanical parameters into mechanical ones, mechanical into electric ones, as well as the oxide layer, rigid base connecting layer of IP T with a housing part, the housing part itself.

A brief description of the elements of the IP T structure shown in the block diagram (see Fig. 2.1): [T CC] with passive thin-film elements 7 converts the constant stabilized supply voltage V input to a temperature-dependent electrical signal V in (T ) , which compensates for the temperature dependence of the output signal V output .

[IL], designed to electrically isolate electrical signal transducers from EE, is one of the main elements in the operation of high-temperature sensors. Two types of isolation are used: dielectric and p-n junction. For most designs, dielectric is still SiO 2 5 .

[P CH] are piezoresistive conducting silicon channels of p-type with contact areas that form a symmetrical 4-shoulder bridge circuit. Two variants are used:

• with lumped parameters, where contact pads connect separate, electrically isolated from each other [P CH] 8 ;

• with distributed parameters, where the contact areas are located directly on the elastic element EE, similar to the Hall transducer 9 .

[RB]+[EE] is, for most IP T , the monolith that sets the required mechanical stress epuplus for converting pressure or force to strain.

[CL], the layer connecting IP T to the body parts ([BP ]) is used as:

• eutectic bonding 10 • electrostatic coupling through glass when α cl l ≈ α rb l ≈ α bp l 11 ;

• adhesive bonding 12 .

The requirement for the material of the structural part [BP ] of the sensor is to have the least effect on the conversion characteristic of the sensor, i.e. α bp l ≈ α rb l ≈ α ee l . For silicon IP T is covar or titanium 12 .

With "perfect" channel isolation, when at any temperature values R IL i = ∞, the temperature characteristics of the sensors are primarily determined by the temperature dependences of the material parameters P CH -R ch (T ) and K ch (T ). The temperature error of the sensor when M C is thermally compensated by the T CC signal V in (T )

increases as the nonlinearity of these dependencies increases. The thermocompensation mechanism extends to the region of temperatures in which there are no extremes or sharp drops in the dependence 13 . It is known that the electrical resistances of silicon P CH R ch (T ) and M C R in (T ) have two extremes: 1 -the minimum due to the change of the charge carrier scattering mechanism at temperature T = T min 14 , 2 -the maximum due to the appearance of intrinsic conductivity at temperature T = T max 15 6 .

Then the temperature interval (T min ; T max ) can be considered as the operating range and range of thermal compensation IP T . Fig. 2.2 shows a graph of the dependence of T min and T max on the resistivity ρ of silicon layers, from which it follows that with ρ ⩽ 0, 1 Ω • cm (typical values for silicon IP T ) T min < 0 • C; T max > 400 • C 15 . However, if inside the range (T min ; T max ) values R IL i become commensurate with R ch (T ) [START_REF] Tikhomirov | Ehksperimental'nye issledovaniya kharakteristik datchikov davleniya novogo pokoleniya [Experimental studies of the characteristics of the new generation of pressure sensors[END_REF] , the temperature characteristics depend on the current distribution in the body EE, RB, etc., and changes in the temperature dependence of parameters IP T will determine another upper limit of the sensor operating temperature. As an example, Fig. 2.3 shows a graph of temperature dependences of parameters of the industrial sample IP T , made according to 17 , with the average resistance of diffusion piezoresistive channels P CH ρch = 2, 3 • 10 -3 Ω • cm. Here the p -n junction isolates M C from EE . Obviously, the method of isolation, which largely determines the operating temperature limit, is an important characteristic of high-temperature sensor design. Based on this, the following technical solutions for IP T designs are considered:

• M C or P CH are "perfectly" electrically isolated from EE by dielectric layers;

• M C or P CH electrically isolated from EE by p-n junction layers depleted of charge carriers; High-temperature mechanical sensors with heteroepitaxial IPTs (SOS-IPT) are successfully developed 18 and serially produced 19 , for which

• intrinsic error ±0.5%;

• complementary temperature error (5 -8)%;

• dielectric isolation resistance from EE more than 1 • 10 8 Ω;

• upper limit of operating temperature range 300 • C;

• dimensions greater than ∅30 mm.

A typical SOS-IPT (D-16, D-100) [START_REF] Perepelitsyn | Mikroehlektronnaya tekhnologiya izgotovleniya preobrazovatelei fizicheskikh velichin[END_REF] pressure sensor design contains a monolithic profiled membrane EE and a rigid base (RB+EE) of titanium alloy (VT-9) with α ee l = 8.3

• 10 -6 • C -1 . A sapphire substrate (α il l = 5 • 10 -6 • C -1
) is attached to the RB+EE structure and is an insulating layer for a heteroepitaxial silicon PCH p-type (α

ch l = 3 • 10 -6 • C -1 ).
The operating temperature of IPT also increases significantly if P CH is insulated with a dielectric layer of SiO 2 , as, for example, in SON OS-IPT sensors. Kulite (USA) manufactures XCEL series sensors [START_REF]Product Advisor -Kulite -The Leader in Pressure Transducer Technology[END_REF] capable of operating at temperatures up to 500°C with a temperature error of less than 0.1%/ • C . . The PCHs are isolated from each other and from EE by silicon dioxide up to 2 µm thick. The sensor has an overall size of 30 × 15 × 15 mm and weighs 30 g. In SON OS-IPT, the PCH material is monocrystalline silicon, while EE -RB is polycrystalline. For the design, the equality of α ch l ≈ α il l ≈ α ee l ≈ α rb l ; which reduces the residual mechanical stresses in the elements of the IPT structure. A design feature of Kulite sensors is that the EE-RB monolithic structure is formed of silicon.

Silicon is a material with ideal mechanical properties. A silicon elastic element is characterized by fast, predictable and reproducible conversion of mechanical quantities into electrical quantities 22 . But all of the above applies to monocrystals. Polycrystalline EE are characterized by deterioration of mechanical characteristics and significant errors in the reproduction of geometrical dimensions during their production 1 .

A promising design of IPT type "silicon-glass-silicon" (SGS-IPT) is considered in [START_REF] Yerman | Dielectrically isolated integral silicon diaphram or other semiconductor product[END_REF] . In SGS-IPT material P CH and EE-RB is monocrystalline silicon, and the insulating layer is silicon heat-resistant glass with a coefficient of thermal expansion close to silicon. The P CH material is highly alloyed p-type silicon with ρch = 2 • 10 -2 Ω • cm. This means that thin silicon wafers 50 ÷ 100 µm thick must be used to single out piezoresistors with a nominal resistance greater than 50 Ω . The difficulty of working with such wafers and the additional thickness reduction technology (wafers over 200 thick are available) greatly reduces the yield of good sensors. The variation in resistivity in modern silicon wafers of up to ±20% leads to differences in the physical properties of P CH and greatly increases the intrinsic and complementary temperature errors of the sensor.

Based on the reviewed works and the analysis of IPT with dielectric insulation, the following conclusions can be made:

1. The sensor designs are characterized by large overall dimensions, more than ∅15 mm, and weight, more than 30 g. Decrease of mass-habarrent characteristics of sensors at satisfaction of requirements to elements of reception of the information in systems of the control, management and regulation of units of branch products will considerably increase both labour input of their manufacture and bias component of a intrinsic error:

• due to high-temperature gas profiling of sapphire (α -Al 2 O 3 ) before forming piezoresistive channels and measuring and thermocompensation elements in SOS -IP T ;

• due to the non-reproducibility of the geometric dimensions of the elastic element and the base in the isotropic etching of polysilicon in SON OS-IPT;

• due to the non-reproducibility of the geometric dimensions of the glass insulation layer during sintering of silicon wafers in SGS-IPT;

• due to the low accuracy of reproduction of the geometric dimensions of the channels of resistive mesa-structures.

2. In heterogeneous SOSand SON OS-IPT structures, there are residual mechanical tensions in P CH and EE due to differences in thermal expansion coefficients.

In the SOS-IPT, cubic crystal lattice silicon is grown on an insulating layer of αmodified sapphire with a hexagonal lattice, and the insulating layer is connected to a elastic element and a base of titanium alloy. SON OS-IPT has significantly different coefficients of thermal expansion of silicon, α Si l = 3 • 10 -6 1/ • C and oxide α SiO2 l = 6 • 10 -7 1/ • C . Residual stresses largely determine the magnitude and temperature dependence of the additive error components ε ee0 (T ), ε il0 (T ), r 0 (T ) in the IPT design element conversion functions, and also require additional restrictions on the relative values of the elastic elements, insulating layer and meza-P CH thicknesses.

3. The Joule heat release is significant in SON OSand SGS-IPT with M C insulated by Si02 film and glass, respectively. The thermal conductivity of the SiO 2 film is 50 times less than silicon and 10 times less than sapphire [START_REF] Petersen | Kremnii Kak Mekhanicheskii Materia [Silicon As A Structural Material[END_REF] . At standard values of nominal resistance P CH R ch0 = 1000 Ω and supply voltage 12 V overheats will be 20-30 °C higher than in monolithic silicon IPTs. the IPT error compared to the constructions discussed in Section 2.1:

ε ee = ε ee0 (T ) + K ee (T, ϕ in ) • ϕ in ; (2.3) ∆R R = r 0 (T ) + K ch (T, ε ee ) • ε ee ;
(2.4)

V out = V in (T ) K mc0 (T ) + K mc T, ∆R R • ∆R R ; (2.5)
where K ch is the gauge factor of the piezoresistor; K mc0 is the normalized null output; K mc -is the gauge factor (bridge sensitivity) of the bridge measuring circuit M C

It has already been noted that silicon, as a material, has excellent physical properties. Although brittle, the silicon elastic element in the IPT has a wider range of elasticity than the stainless steel elastic element in traditional sensors. Unlike most metals and polycrystalline silicon, monocrystalline silicon can be repeatedly exposed to mechanical stresses without exhibiting fatigue effects. In 22 the following limits of silicon monocrystals of integrated circuits (ICs) are noted :

• frequency range up to several megahertz;

• pressure range up to 350 mPa;

• Acceleration range up to 100,000 g.

A clear advantage for IPT development is the compatibility of precision multilevel profiling of monocrystalline silicon (silicon wafers) of crystallographic orientation (100) by anisotropic chemical etching with microelectronic IC manufacturing technology 1 25 . This technology is quite capable of accurately reproducing all geometric dimensions and ratios in miniaturized IPT when developing small-size sensors [START_REF] Petersen | Kremnii Kak Mekhanicheskii Materia [Silicon As A Structural Material[END_REF] .

The upper limit of the working temperature range of silicon EE, which is determined by the temperature of the appearance of plastic deformation of the material, according to 26 27 is 500-600°C. However, in 5 it is noted that most of the known sensors with monolithic IPT, due to the loss of insulating properties of the p-n junction, are operable up to +125 °C. It is known that the isolation resistance of P CH from EE in an ICP is characterized by the parameters of the common I-V characteristic of p-n junctions at reverse bias 4 . In this case for MC

R IL i = R p-n i = V rev n i=1 I rev i = V rev n i=1 J rev i • A p-n i (2.6)
where V rev is the applied voltage to the MC p-n junction at reverse bias; I rev i is the reverse current of the p-n junction of one of the elements IPT; J rev i is the current density of the p-n junction of one of the IPT elements at reverse bias; A p-n i -is the area of p-n junction of one of the IPT elements.

In modern IPTs, the total p-n junction area is usually defined by the following elements: diffusion or ion-alloy P CHs, diffusion control and compensation resistors, diffusion, so-called "tunnel" junctions for the connection sections with the body part, etc. . For such IPTs, typically n i=1 A p-n i ⩾ 1 • 10 -2 cm 2 , and the sharp exponential increase in I rev with increasing temperature will at T IL per = (+100 ÷ +130) 0 C 6 . If the design is based only on the P CH regions and the balancing resistors, as in the IPT samples with ρch = 2.3 • 10 -3 Ω • cm 17 , the upper operating temperature value will correspond to (+150 ÷ +160) °C (see graph in Figure 3). It is reported in [START_REF] Kim | Temperature sensitivity in silicon piezoresistive pressure transducers[END_REF] that a silicon IPT "RB-EE-IL-PCH" structure using only diffusion piezoresistors and a total p-n junction area of 2.5 • 10 -4 cm 2 can extend the operating temperature range of the sensor to +180 °C.

Thus, reducing the total p-n junction area in the IPT, where the MC elements are electrically insulated from EE by a p-n junction layer, leads to an extension of the upper limit of the operating range to temperatures above +125 °C.

In the 60's a monolithic deformation IPT design was proposed in 8 , in which M C with concentrated parameters contains four contact regions located in the vertices of the square and connected by single-band P CH. The contact regions in P CH are formed by diffusion impurity doping in a thin silicon wafer-body elastic element. The surface resistance of the diffusion layers, the H ee thickness and the resistivity ρ ee should provide at least 10 times more conductivity in the P CH layers than in the EE body. At the same time, the current distribution of the charge carriers in the EE body does not yet have a noticeable effect on the characteristics of the full-symmetric M C in the transducer. A restriction imposed on the design parameters:

1 10R in ⩾ 1 R ee (2.7)
where R in is the input resistance of the bridge circuit, and R ee is the resistance EE between the M C input contacts, must be met over the entire operating temperature range of the transducer.

Let us estimate the values of the volume resistances for the piezoresistive channels ρch and the elastic element ρ ee , at which the relation (2.7) is fulfilled. We will consider the elastic element as a flat plate of thickness H ee . The value of H ee usually ranges from 1 • 10 -3 cm to 1 • 10 -2 cm. Consider a bridge circuit connected in parallel with the square part of the elastic element EE by the common contact pads K 1 and K 3 (see Fig. 2.5). For configuration (b) R ee = 1.383 ρee Hee , and for configuration (a) R in = 10 • ρch X j , where X j is the P CH thickness (calculation was done numerically using the 2D model, so Fig. 2.5 shows the relative dimensions of the configuration). If the thickness of the piezoresistor is taken as X j = 0.35•10 -4 cm, which is a charecteric value for ion-alloyed P CH and use the value H ee = 10 -3 ÷ 10 -2 cm, then the constraints for configurations

ρ ee = (2, 1 ÷ 21) • 10 -3 • ρch (2.8)
The smallest value ρch used in diffusion piezoresistors is 1 • 10 -3 Ω • cm 1 . Then, R in of a bridge circuit with configuration (a), would be 100 Ω. In this case, for the thickness of the elastic element to vary within 1 • 10 -3 cm ⩽ H y ⩽ 1 • 10 -2 cm, its resistivity must be ρ ee ⩾ 20 Ω • cm. As shown in Fig. 2, the temperature T int at which the impurity semiconductor EE turns into intrinsic is +150°C. Thus, the upper limit of the IPT operating temperature range described in 8 cannot exceed +150°C. The reason for limiting the operating temperature range is the sharp decrease of the resistance EE connected in parallel to the MC input and output, resulting in a decrease of sensitivity to the input value by the law

V out = V oc • Ree Ree+R in 12 (V oc is open circuit voltage of the bridge)
A IP T design in which the M C with distributed parameters is not isolated from the elastic element has been considered in the aggregate of a number of papers.The articles 29 30 4 describe an IPT design for measuring mechanical quantities using a "shear" piezoresistive sensing element, which is the piezo analogue of a Hall sensor (x-ducer). In a silicon monolith EE-RB n-type is formed P CH of p-type. Inside the P CH region, two pairs of contacts are created on orthogonal axes. When measuring the mechanical quantity, a direct current passing through the longitudinal axis of the element generates a strain-dependent potential difference on the pair of contacts located on the transverse axis. For this case, the temperature limit is the same as for IP T with an insulating p-n junction layer. However, in 31 a technical solution was proposed for the design of IP T whose measuring circuit is created in the EE body without forming P CH layers, i.e., by forming contacts directly on the material of the elastic element.

In this case, the mechanical value is converted into electrical value by the material EE and the upper boundary of the working temperature is determined only by the temperature of intrinsic conductivity of the elastic element material. It can reach values of T EE int > 400 • . But for IP T , where M C with distributed parameters are characterized by significant disadvantages. The advantage of reducing the value of the normalized null output of the bridge measuring circuit K mc0 and its temperature dependence K mc0 (T ), does not lead to a significant reduction in the additive component of the complementary temperature error, since the strain-sensitivity is 2-3 times smaller compared to M C with lumped parameters. In addition, in the design of the transducer without P CH a significant decrease in sensitivity for IP T with bending elastic elements (membranes, beams) associated with the distribution of charge carrier current and mechanical stresses in the section EE in the direction Z , normal to its planar surface is obvious.

For IP T without isolating its M C from EE, the measurement conversion of the input mechanical quantity ϕ in to the electrical output signal V out is shown in Fig. 2.4 (b) . In this case, the conversion functions are defined by only two relations:

ε ee = ε ee0 (T ) + K ee (T, ϕ in ) • ϕ in (2.9) V out = V in (T ) [K mc0 (T ) + K mc (T, ε ee ) • ε ee ] ; (2.10)
and is characterized by the smallest number of factors affecting the sensor error. And so, for monolithic silicon IP T structure, where M C is isolated from P CH by p-n junction layer depleted in carriers and without isolating layer:

• the advantages of monocrystalline silicon being the material of elastic element and piezoresistive channels are widely used;

• monolithic monocrystalline silicon structure IP T does not require matching the mechanical properties of base, elastic element, insulating layer and piezoresistive channels materials (but in miniature and high-sensitive constructions the mechanical properties of masking layer SiO 2 should be considered 32 );

• the intrinsic error of the sensors is significantly reduced due to the joint use of modern group technology processes of silicon micromachining and formation of resistive elements and conductors with high reproducibility of geometric dimensions and ratios in the monolithic silicon structure IP T ;

• the operating temperature range is considerably extended if a measuring circuit with distributed parameters is created in a part of the resilient element material without forming insulating layers.

On the basis of the analysis the following design solutions are identified for further research:

1. IP T with isolating p-n junction, where a monolithic monocrystalline silicon element contains a rigid base, elastic element, isolating p-n junction layer, piezoresistive channels and contact pads of a full bridge circuit with lumped parameters.

2. IP T with distributed parameters, where a monolithic monocrystalline silicon element contains a rigid base an elastic element and contact pads of a full bridge circuit with distributed parameters.

3. IP T "silicon-glass-silicon (SGS -IP T ). Silicon construction with a monocrystalline silicon "elastic element-rigid base" and silicon piezoresistive channels connected to each other and electrically isolated from each other by a layer of glass matched to the temperature coefficient of linear expansion.

Analysis of Physical and Functional Models of Monolithic IPT 2.3.1 Electrophysical Properties of Piezoresistor Channels of the IPT Bridge Circuit

In IP T for mechanical sensors, the strain-to-electrical output signal conversion is carried out by the piezoresistive channels of the four resistors of a full bridge measuring circuit 33 12 (P CH -M C). The conversion characteristic for IP T with insulating p-n junction from Fig. 2.1 can be represented as:

V out (T, r 1 , . . . , r 4 , ε x ) = V in (T ) • [K mc0 (T ) + K mc (T, r 1 , . . . , r 4 , ε x ) • K ch (T, ε x ) • ε x ]
(2.11) where, K mc0 (T ) is the normalized null output IP T ; K mc (T, r 1 , . . . , r 4 , ε x ) is the conversion coefficient M C; K ch (T, ε x ) is the load sensitivity of one of P CH; r 1 , . . . , r 4temperature-dependent values of relative strain changes of resistances of P CH of four arms of M C, caused by changes in the input value ϕ in ; ε x -strain area at the location of one of P CH.

The value and temperature dependence of the normalized null output K mc0 (T ) is mainly determined by :

• the variation of P CH resistances and their temperature dependences;

• the temperature-dependent local mechanical strains of P CH due to the difference in the coefficients of α Si l and α SiO 2 l 24 27 ;

• temperature-dependent strain state EE also because of the difference in the coefficients α Si l and α SiO 2 l 24 27 .

Three possible feeding conditions of M C should be determined:

• from a stabilized voltage source when V input = V in = const;

• from a stabilized voltage source through T CC with passive thin-film resistive elements, when

V in (T ) = K tcc T, R ch1 , . . . , R ch4 , R T C 1 , . . . , R T C n • V input ,
where

K tcc T, R ch1 , . . . , R ch4 , R T C 1 , . . . , R T C n
is the conversion factor for T CC, which depends on the temperature and resistance values of the four arms M C R ch1 , . . . , R ch4 , and thermoresistors, adjustment resistors

R T C 1 , . . . , R T C n in T CC • from a stabilized current source when V in (T ) = I in • R in (T ), where R in (T ) is the temperature-dependent input resistance of M C.
If we assume that K mc0 (T ) = 0, then the temperature and strain dependences of the bridge sensitivity IP T (equal to the ratio of the output signal V out to the nominal value of supply voltage V in or current I in ) are determined by the temperature dependences of both resistance R ch (T ) and the value of relative strain change of resistance r ch (T, ε).

As already noted, the electrical resistance function P CH on temperature has two extremes: at T min ; T max . Inside the temperature interval T min ÷ T max resistance of semiconductor material, the value of which increases with increasing temperature, is determined by the dependence [START_REF] Levshina | Ehlektricheskie izmereniya fizicheskikh velichin: (Izmeritel'nye preobrazovateli)[END_REF] :

R ch (T ) = R ch0 1 + A 1 (T -T 0 ) + A 2 (T -T 0 ) 2 (2.12)
where T 0 , is the initial operating range temperature; R ch0 is the resistance P CH at T = T 0 ; A 1 and A 2 are the linear and quadratic resistance temperature coefficients.

According to [START_REF] Lenk | Electromechanishe systeme[END_REF] , the positive strain change of the pezoresistance r ch can be calculated by the formula

r ch = ∆R R = K 1 ε + K 2 ε 2 + . . . (2.13)
where, K 1 is the linear strain coefficient; K 2 is the quadratic strain coefficient; ε is the relative strain of P CH.

The dependence of the coefficients K 1 and K 2 on temperature has a complex character 3 36 , the study of which cannot be considered complete 4 . For comparison of the literature data and results of researches we will represent the relation (2.13) as

∆R R = K A1 + K B1 T 0 T + K C1 T 0 T 2 ε x + K A2 + K B2 T 0 T + K C2 T 0 T 2 ε 2 x (2.14)
Then the gauge factor of the piezoresistive channel is equal:

K ch (ε, T ) = ∆R R • ε = (K A1 + K A2 • ε x ) + (K B1 + K B2 • ε x ) T 0 T + + (K C1 + K C2 • ε x ) T 0 T 2 .
(2.15)

The electrophysical characteristics of strain-sensitive channels P CH are integral functions of the distribution of impurity concentration in the direction Z normal to the planar surface IP T . In 37 38 , the electrophysical characteristics are related to the surface concentration N , which is calculated from the known values N (z = X j ) at the depth X j of the p-n junction and the surface resistance R s of the channel, assuming a Gaussian or additional error function erfc(z) for distribution. In some cases, for example at N ≈ 10 20 cm -3 , this assumption can lead to an error of N s determination of half an order, in connection with which in [START_REF] Kiss | Dimensioning of Temperature Compensated Silicon Pressure Gauges[END_REF] the integration of known electrophysical characteristics for uniformly doped silicon by real distribution of impurity is assumed. The results of the study of piezoresistive coefficients (π) in uniformly doped silicon are given in 3 40 41 .

In work [START_REF] Tikhomirov | Temperature Dependence of Sensitivity of Silicon Integrated Mechanical Transducer in The Temperature Range from -60°C to +200°C[END_REF] it is shown that in the established technological process of formation P CH of p-type in n-type substrate in a small interval of variation of average resistivity ρch , equal to ρch = R s • xj , connection of electrophysical characteristics with this value on informativity is equivalent to the similar connection in homogeneously alloyed silicon. In the future, our studies of the electrophysical characteristics of piezoresistive layers will be related to the parameter of the layer resistivity ρ l .

From the data [START_REF] Vaganov | Integral'nyitenzopreobrazovatel[END_REF] , the gauge factor associated with the orientations (001) (011) can be represented by the relations:

K (100)[011] = ∆R R • ε x 0 = ±0.5 (1 -ν 12 ) • E 12 π 44 ± (π 11 + + π 12 ) 1 + ν 12 1 -ν 12 = = ±7.9 [π 44 ± 1.13 • (π 11 + π 12 )] (2.16
)

K (011)[111] = ∆R R • ε x 0 = 0.667 (1 -0.5 • ν 12 ) • E 12 π 44 + (π 11 + 2 • π 12 ) 1 + ν 12 2 -ν 12 = = 1.138 [π 44 + 0.65 • (π 11 + 2 • π 12 )]
(2.17)

K (011)[110] = ∆R R • ε x 0 = 0.5 • E 12 [π 44 + π 11 + π 12 • (1 + 2 • ν 12 )] = = 0.844 [π 44 + π 11 + 1.72 • π 12 ]
(2.18)

where the " + " sign corresponds to the longitudinal coefficient (K ∥ ), the " -" sign corresponds to the transverse one (K ⊥ ); E 12 , ν 12 are Young's modulus (P a) and Poisson's ratio in silicon along the crystallographic direction [110]; π 44 is the main shear piezoresistive coefficient, Pa -1 .

The data on the concentration and temperature dependences of the main longitudinal (π 11 ) and transverse (π 12 ) piezoresistive coefficients given in the literature are insufficient to correctly take them into account in the calculations. It is known that the value of π 11 decreases with increasing impurity concentration from 2 • 10 -11 P a -1 at N = 3 • 10 18 cm -3 to 1 • 10 -11 P a -1 at N = 1 • 10 21 cm -3 , and the all-round compression factor (π 11 + π 12 ) has a positive sign and is ∼ (1 ÷ 2) • 10 -11 P a -1 for these concentrations [START_REF] Tufte | Piezoresistive Properties of Silicon Diffused Layers[END_REF] . The authors 1 44 45 believe that due to the small (relative to π 44 ) values of the coefficients π 11 ; π 12 , they can be neglected, that is, In Fig. 2.6, according to data 1 3 4 36 40 41 46 plots the dependences of linear (K 1 ) and quadratic (K 2 ) strain sensitivity coefficients on resistivity. For convenience of comparison of dependences, K 2 are represented by products of their values by the boundary (when used in tensometry) relative deformation of silicon, equal to 1 • 10 -3 . The graphs show that K 2 • 10 -3 will not exceed 10% of the smallest values of K 1(001) [110] . If we assume ∆R/R = 0.01, then for the minimum value in the graph K 1(100)[011] the deformation ε y will be 3 • 10 -4 . Therefore, in further studies we will assume that in formulas (2.14) and (2.15) the values K 2 • ε are negligibly small compared to K 1 , then

K ∥ = |K ⊥ |, if the plane EE (001).
K ch (T ) = K A + K B T 0 T + K c T 0 T 2 (2.19)
where K A , K B , K C are approximation coefficients of the temperature dependence of the gauge factor P CH. Using high impedance diffusion layers with ρl = (2÷8)•10 -2 Ω•cm will reduce the insulating p-n junction area. In addition, when making P CH with given values of ρl and supplying IP T with stabilized current, when the input signal V in (T ) = I in • R in (T ), thermal compensation of the output signal V out 1 is possible. Ion implantation will provide a high impurity concentration and reduce the p-n junction area. According to the results obtained in [START_REF] Borshchev | Ehlektrofizicheskie kharakteristiki tenzorezistivnykh struktur, legirovannykh implantirovannym borom. [Electrophysical characteristics of tensoresistive structures alloyed with implanted boron[END_REF] , the study area of ion-alloyed layers should be limited to one value -the ligation dose 2 • 10 15 cm -2 (R s = (80 ÷ 100) Ω/□). This will allow for the smallest variation in resistance values P CH at fixed process parameters and thus reduce the temperature drift K mc0 (T ).

The electrical properties of P CH are influenced by metal-semiconductor contact junctions, which have been thoroughly studied in the temperature range -60 ÷ +300 • as early as during the research and development of the first semiconductor devices and integrated circuits 49 50 . But in IP T the contacts of thin-film conductive tracks M C with P CH have special requirements: transient resistances and their temperature dependences should not have a noticeable effect on the sensor conversion characteristic. Obviously, the contact resistance R c increases with decreasing contact area A c . The results of studies of the dependence of R Al-Si c on the resistivity of the silicon p-type layers and the area A c are given in work [START_REF] Mazel | Planarnaya Tekhnologiya Kremnievykh Priborov [Planar Technology for Silicon Devices[END_REF] . However, as already noted, the additive component of the error IP T due to the presence of the normalized null output K mc0 is largely determined by the technological variation of resistance P CH, including series-connected contact R c and their temperature dependences. Therefore, experimental studies of the influence of contact area A c on the value of K mc0 and its temperature dependence are necessary within a stable manufacturing technology IP T . Such data in scientific and technical information was not found.

Isolating Properties of the P-N Junction

The upper bound of the temperature range of IP T with isolating p-n junction depends on the p-n junction leakage currents (reverse current VAC ) and the shunt effect of the wafer, i.e. EE. The temperature dependence of the input resistance of the bridge circuit according to 4 13 is determined by the temperature changes of the resistive layer resistance R ch and the shunt resistance "p-n junction -elastic element" R sh which depends on the insulation resistance of p-n junction

R IL i and resistance EE R EE i , i.e. R in (T ) = R ch (T ) 1 + R ch (T ) R sh (T ) (2.20)
As the temperature increases, the resistance of the tensoresistive layer increases, and R sh , due to the exponential increase in the reverse current of the p-n junction decreases, which leads to a maximum in the temperature dependence of the input resistance M C R in (T ) (see Fig. 2.

3).

At temperatures when R sh = (R IL I + R EE I ) becomes less than 200 • R in due to redistribution of current carriers in P CH and body EE is observed:

• a sharp change in the temperature dependence of the normalized null output K mc0 due to the symmetry violation of the electrophysical characteristics of the arms of the full bridge circuit;

• a sharp drop in the sensitivity coefficient K M C due to the shunt effect of resistance R sh by the law

V out = V oc R sh
R sh +R ch , and also because in the body of the elastic element the current, first, is directed along the non-tensosensitive crystallographic directions, second, is distributed along the section EE along the axis Z with deformations of contraction and stretching.

Leakage current of p-n junction or reverse current J rev is divided into three components 52 :

• I 0gen -current of generation of carriers in the carrier poor p-n junction region in the body of elastic element;

• I Sgen -charge carrier generation current in the carrier poor p-n junction region on the surface of the elastic element;

• I d is the diffusion component of the reverse current, i.e.

I rev = I 0gen + I Sgen + I d , (2.21)
I 0 gen = 1 2 q n i τ 0 d p-n • A p-n , (2.22)
where n i is the carrier concentration in the native semiconductor; τ 0 is the carrier lifetime in the p-n junction region; d p-n is the width of the p-n junction region; q is the elementary charge;

I Sgen = 1 2 qS 0 • n i • d p-n • P p-n , (2.23)
where S 0 is the surface recombination rate; P p-n is the perimeter of the p -n junction;

I d = qn 2 i L p τ p N n • A p-n , (2.24)
where L p is the diffusion length of minority charge carriers in the EE body; N n is the concentration of the impurity in the EE body; n i -concentration of free charge The temperature dependence of the parameter τ p is determined by the change in the concentration of "traps" n t . When n t becomes comparable to the concentration of the majority charge carriers n 0 the time of life begins to increase, and under the condition n t > n 0 the dependence τ p (T ) coincides with the exponential function n t (T ). The rapid growth of τ p slows down near T int . In this case, the concentration of n t increases already slower than the concentration of its intrinsic charge carriers n i 6 .

The graph in Fig. 2.9 shows the dependence of τ p on material resistivity EE and on temperature 6 .

If we use known physical constants and parameters of silicon, the temperature dependence of the concentration of intrinsic charge carriers is determined by the relation:

n i (T ) = n i0 • e 21.3(1-T 0 T ) , (2.25)
where n i0 is the concentration of intrinsic charge carriers charge carriers at T = T 0 . The near-surface layer has a special zone structure and qualitatively different parameters than in the volume, which must be taken into account when analyzing and designing IP T with p -n junction. As a rule, due to the large concentration of "traps" near the surface, the lifetime of charge carriers at the surface τ s < τ p . τ s is difficult to calculate and measure. To characterize the surface recombination it is accepted to use a parameter -surface recombination rate S 0 . S 0 depends significantly on the method and quality of crystal surface treatment and has typical values of 100 ÷ 10 4

cm/s 6 .

The upper temperature limit of IP T operation depends on the voltage V in 4 . As V in increases, R sh increases and therefore its influence decreases. However, this is under limited conditions, depending on the magnitude of the breakdown voltage of the p -n junction. Increasing R sh results in a T max shift toward higher temperatures. According to 4 13 , the highest value of T max corresponds to the circuit in which there is no reverse bias p -n junction M C -EE.

Influence of Temperature on Physical Properties of Monocrystalline Silicon Elastic Elements

Silicon EE, due to the directional covalent nature of the bonds, has a very low ductility.

From the graph in Fig. 2.10 (a), based on the data [START_REF] Runyan | Silicon Semiconductor Technology[END_REF] , it follows that up to a temperature of 550 • C silicon fractures without appreciable plastic deformations at ε = 1 • 10 -2 .

In the higher temperature range, plastic deformation is found and the elastic limit is limited to deformation values ε = 8 • 10 -3 and ε = 2 • 10 -3 respectively at 600 • C and

850 • C.
The temperature variations of the linear geometric dimensions of monocrystalline silicon EE can be represented by the dependence:

ℓ(T ) = ℓ 0 1 + α l 1 (T -T 0 ) + α l 2 (T -T 0 ) 2 (2.26)
where ℓ 0 is the linear size of the silicon EE at the initial temperature T = T 0 ; α l 1 is the linear coefficient of thermal expansion ; α l 2 is the quadratic coefficient of thermal expansion.

Then the differential temperature coefficient of linear expansion of silicon α si l is:

α Si l (T ) = 1 ℓ(T ) • dℓ(T ) dT = α l 1 + 2α l 2 (T -T 0 ) 1 + α l 1 (T -T 0 ) + α l 2 (T -T 0 ) 2
(2.27) Fig. 2.10 (b) shows the temperature dependence α Si l (T ) (based on data from [START_REF] Runyan | Silicon Semiconductor Technology[END_REF] ), from which two temperature regions are defined: The first -170

• C ÷ -50 • C, when ℓ(T ) = ℓ 0 1 + 8.8 • 10 -9 (T + 155) , (2.28) second 0 • C ÷ 600 • C, when ℓ(T ) = ℓ 0 1 + 2.5 • 10 -6 (T -25) + 2.1 • 10 -9 (T -25) 2 .
(2.29)

The thermal resistance R t and the thermal conductivity coefficient of the material EE in the heat sink circuit "P CH-EE-RB" are related by the relation 4 :

R t = δ S c • λ t , (2.30)
where δ is the distance from P CH to RB; S c is the contact area between EE and RB. Based on the results of [START_REF] Runyan | Silicon Semiconductor Technology[END_REF] , Fig. 2.10 (c) plots the temperature dependence λ t (T), from which, taking into account ( 2.30 ), it follows that in the temperature region -200 • C ÷ 600 • C the thermal resistance is:

R t (T ) = R t0 1 + 5.4 • 10 -3 (T -25) .
(2.31)

Methods for Minimizing Errors in the IPT Conversion Characteristic

The problems of improving the accuracy of small-size sensors with silicon resistor integrated transducers are mainly related to the non-reproducibility of geometrical dimensions EE and significant temperature variations of the electrical output signal 7 28 .

The standard bias of the intrinsic error, depending on the sensor type and accuracy class, is set from ±0.02% to ±10% 51 53 . The absolute error of reproducing the thickness of the elastic element H ee during the deep etching process when using silicon wafers of thickness H w = 300 µ as blanks is given in 5 and is ±7.5 µ. The error of other geometrical dimensions, taking into account the etching angle of the wafer with orientation (001), is ±10 µ. Then the limiting value of the relative error of the sensitivity coefficient of, for example, beam EE with inertial mass, δ kee due to non-reproducibility of geometrical dimensions is determined by the ratio:

δ kee = ∆K ee K ee = ∆A A + ∆B B + ∆H w H w + ∆(A + L) A + L + 2 ∆H ee H ee (2.32)
where A, B, H w are the geometric dimensions of the inertial mass, L is the length EE, W is the width EE.

For example, the integral beam accelerometer [START_REF] Roylance | A miniature integrated circuit accelerometer[END_REF] in Fig. 2.11, with H ee = 50 µ; A × B × C = 3 mm × 3 mm × 0.3 mm; L = 0.3 mm and W = 0.4 mm, will have error δ kee = ±40%. For EE with smaller geometric dimensions, the error can be much larger.

The ability of the sensor to reproduce the specified conversion characteristic in the working temperature range, in addition, is estimated by the complementary temperature error of the device. To a greater extent, the temperature error is related to the temperature variation of the normalized null output K mco (T ) of the bridge circuit at the technological variation of the temperature dependences of resistances R ch (T ) and gauge factor K ch (T ) 7 . In an IPT with H ee < 100 µ, K mc0 (T ) is affected by marked differences in the internal mechanical stresses in P CH and the initial stress state EE [START_REF] Kim | Temperature sensitivity in silicon piezoresistive pressure transducers[END_REF] . The error in the transducer conversion characteristic associated with changes in the output signal in the presence of a significant temperature gradient is reduced by minimizing the transducer, bringing the temperature-dependent internal thermocompensation elements closer to P CH. The main source of temperature hysteresis in most silicon transducers is the RB-CL-BP base structure. For monocrystalline IP T this error is negligible, as Fig. 2.11 Reverse side of the silicon beam element of an accelerometer with silicon inertial mass [START_REF] Roylance | A miniature integrated circuit accelerometer[END_REF] is the temperature aging error 7 . When designing a sensor, it is necessary to know the parameters of the heat sink circuit elements. Joule heating irregularity of piezoresistors in asymmetric M C also affects the temperature dependence of K mco (T ) [START_REF] Tikhomirov | Vliyanie nagreva rezistorov mostovykh tenzoizmeritelnykh skhem na koehffitsienty peredachi[END_REF] .

complementary temperature error is reduced:

• by optimizing the design and choosing the necessary technology;

• by non-electrical compensation, for example, using the differential-temperature invariance phenomenon of piezoresistance in SOS -IP T s 26 ;

• by electrical compensation using T CC.

There are many methods of adjusting the sensors by internal adjustment elements by changing the parameters of the piezoresistors conversion function and the measuring circuit. It is necessary to use the regulating elements capable of working at temperatures above +100 • C and not affecting the upper limit of the operating temperature range.

The following T CC can be used when powered from a stabilized voltage source: (a) with a resistor M C in series with a temperature dependence of the form:

R T C (T ) = R T C 0 1 + A 1 (T -T 0 ) + A 2 (T -T 0 ) 2 (2.33)
where R T C 0 is the resistance value at T = T 0 ; A 1 is the linear temperature resistance coefficient with negative sign; A 2 is the quadratic resistance coefficient; (b) power is supplied through a voltage divider, in which the resistance in series with respect to M C is independent of temperature, and in parallel with the temperature dependence of the form (2.33) when A 1 with a positive sign.

For circuits (a) it is reasonable to use thin-film resistors made of RS 1004 alloy [START_REF] Tikhomirov | Issledovanie i razrabotka novoi tekhnologii sozdaniya mikrominiatyurnykh preobrazovatelei dlya datchikovoi apparatury[END_REF] , whose fabrication technology on an insulating layer of SiO 2 silicon EE is described in 56 57 . In order to form temperature-dependent resistances in circuits (b) it is reasonable to use traditional diffusion resistors with ρ ⩾ 4 • 10 -2 Ω • cm.

Conclusions and Problem Statement

Based on the analysis of the state of the art of silicon integral piezoresistor measuring transducers of mechanical quantities, the following conclusions can be drawn:

1. A monolithic monocrystalline silicon structure containing a base, an elastic element, piezoresistive p-type conduction channels and contact pads of a complete DC bridge circuit, in the aggregate of its qualities:

• advantages of monocrystalline silicon as a material of the elastic element and resistive channels;

• consistency of mechanical properties of the elements of the measuring conversion circuit;

• the possibility of using modern group technological processes of silicon micromachining and formation of resistive elements with high reproducibility of electrophysical parameters and geometrical dimensions; is most suitable for creating miniature integrated piezoresistive measuring transducers of small-sized sensors of mechanical quantities for the working temperature range of 0 ÷ 300 • C.

2.

In known designs of IP T isolating properties of p -n-junctions at temperatures above +100 • are not sufficiently studied. The temperature limit +125 • indicated in the literature is not the limit for operation of monocrystalline silicon IP T with insulating p -n junction. The upper limit of the operating temperature range increases as the total area of insulating p -n junctions decreases. At temperatures where the R IL i isolation resistance of the p -n junction decreases to a value of R IL i ⩽ 200R in , abrupt changes in the temperature dependences of IP T parameters are observed.

3. The use of monolithic monocrystalline IP T without an insulating p -n junction allows the operating temperature range to be extended. The upper temperature limit rises:

• Up to +150 • C for IP T with M C, where the P CH conductivity is more than 10 times that of EE (need ρ ⩾ 20 Ω • cm). The reason for the range limitation is the decrease in sensitivity due to the sharp decrease in resistance of the part of the material connected in parallel to the input and output of M C when the silicon's intrinsic conductivity appears;

• up to 400 • C for IP T with M C, where contact areas are formed directly on EE without P CH. In this case, the sensitivity of IP T is more than 3 times less due to the fact that in the EE body the current is firstly directed along the non-piezosensitive crystallographic directions and secondly distributed in the Z direction normal to the planar surface (for bending EE).

4. The upper limit of the working temperature range of the elastic element made of monocrystalline silicon is 600 • C. When selecting and calculating the IP T design, it must be considered that in the temperature range of 0 ÷ 300 • C the relative linear geometric expansion of silicon is determined by the ratio:

∆ℓ(T ) ℓ 0 = 2.5 • 10 -6 (T -25) + 2.1 • 10 -9 (T -25) 2 (2.34)
5. The magnitude of the relative change in thermal resistance of a silicon elastic element over a temperature range of 0 ÷ 300 • C is determined by the relation:

∆R t ( T) R t0 = 5.4 • 10 -3 ( T -25) (2.35)
6. The known electrophysical characteristics of diffusion P CH layers differ significantly from each other, which seems to be due to inconsistencies of real impurity distributions with idealized ones. Significant differences in the electrophysical characteristics of uniformly alloyed silicon piezo layers do not allow accurate IP T calculations to be performed by integrating over the real impurity distribution. The calculation of the IP T design must be based on data obtained within a stable fabrication technology. In studies of the electrophysical characteristics and calculations of the IP T design, it is reasonable to characterize the alloying level of P CH by the value of the average resistivity ρch = R s • Xj . 8. In silicon IP T , workable in the operating temperature range of 0 ÷ 300 • C is advisable formation of aluminum-silicon ohmic contacts. The ranges of contact resistances and their temperature dependences on the average values should increase with a decrease in the area of the contact areas. In the known studies there are no data on the influence of the area of contact areas on the normalized null output M C.

9.

It is reasonable to adjust IP T by correction with internal regulating passive resistive elements located near the piezoresistive channels. It is advisable to use RS-1004 thin-film alloy, which is operable at temperatures above +100 • and is characterized by a negative temperature coefficient of resistance, 1

R T C (T ) dR T C (T ) dT < 0.
In accordance with the analysis of the state of the issue, to achieve the goal of the work it is necessary to solve the following basic design and technological problems:

1. to study the model of isolation of piezoresistive channels of p-type conductivity of monolithic IP T bridge circuit from an elastic element by a p-n junction layer depleted of charge carriers at temperatures above +100 • in order to determine the upper value of the operating temperature range;

2. to study the effect of minimizing the geometric dimensions of the topological structure of the IP T bridge circuit at values of the total of insulating layer area of p-n junction less than 2•10 -3 cm 2 on the upper value of operating temperature range, the value of temperature dependence of normalized null output;

3. to investigate in the temperature range of 0 ÷ 300 • C the regularities of changes in the electrophysical characteristics of P CH monolithic IP T with an insulating p-junction, where the formation of piezoresistive channels is carried out by a steady-state technological process:

• boron diffusion with average channel resistivity values (2 ÷ 8) • 10 -3 Ω • cm;

• boron ion implantation with doping doses of 2 • 10 15 cm -2 ;

4. to investigate the principles of modeling IP T with distributed parameters without isolating p -n junctions, where the conductivity of piezoresistive channels is 2 ÷ 10 times the conductivity of the elastic element;

5. to investigate the electrophysical characteristics of IP T with distributed parameters in the temperature range of 0 ÷ 300 • C;

6. to develop methods to minimize the intrinsic and complementary temperature errors of IP T in the operating temperature range of 0 ÷ 300 • C;

7. to investigate and develop small-size pressure sensors with intrinsic error ±1% and acceleration sensors with intrinsic error ±5% of control, management and regulation systems for testing industry products in order to obtain information about processes and objects when the ambient temperature changes in the range of 0 ÷ 300 • C.

CHAPTER 3

Principles of Monolithic IPT Modeling for the 0÷300°C

Temperature Range

The upper limit of the operating temperature range T max of a monolithic IP T with an insulating p -n junction is determined by the conditions when the insulating resistance R p-n i of the junction reaches the critical value R p-n i min . At R p-n i min , the shunt effect of the EE resistance on one of the M C arms changes the transfer coefficient value K mc by 1% relative to the nominal value, equal to K mc = 10 mV V . From [START_REF] Tikhomirov | characteristics of the measuring circuit of the silicon integrated mechanical magnitude transducer at temperatures above +100°C]. Ehlektronika i Schetno-Reshayushchaya Tekhnika v Lesnoi i Derevoobrabatyvayushchei Promyshlennosti[END_REF] , where IP T with a resistance P CH equal to R ch = 1000 Ω was investigated, the upper value of the range corresponds to a temperature T max = T per when the reverse bias voltage p -n junction of the U rev = 5 V has a reverse current VA of I rev = 2 • 10 -6 A. For this IP T design, it is assumed that in the temperature range T min ⩽ T ⩽ T max M C has lumped parameters, and the physical principle of conversion of mechanical matter to electrical signal is studied and undeniable. Therefore, modeling and experimental studies are related to the study of the temperature dependences in the range (0 ÷ 300) • C of the V AC parameter of the isolating p -n junction, which determines R p-n i -the reverse current density J rev (T ).

For IP T without insulating p -n junction, where in M C with distributed parameters P CH conductivity is 1÷10 times higher than EE conductivity, i.e. elastic element is electrically connected to the bridge circuit, the physical principle of conversion is not studied. Here, modeling and experiments have been performed both to determine the upper bound of the operating temperature range and to study the change in IP T parameters as the EE resistance values change at ρ ee ⩽ 20 Ω • cm in the range (0 ÷ 350) • C.

To simplify modeling and increase the accuracy of experimental studies of miniature monolithic IP T with extended to 300 • C operation temperature range, their inherent design solutions are defined. In domestic practice, the highest accuracy of geometric dimensions is achieved for monolithic designs IP T of weakly and medium alloyed silicon wafers with orientation in the plane (001) [START_REF] Kanischeva | Poluchenie vypuklykh i vognutykh ploskostei anizotropnym travleniem Si (100)[END_REF] . This anisotropic etching method can be used to perform most of the EE types in use. In such IP T tensometric channels doped with an acceptor impurity are arranged parallel and perpendicular to the boundaries of the elastic element along the species directions [110]. The same stress state of the regions in which the longitudinal and transverse P CH are located causes, at small deformations, proportional changes in the resistances, which are close in magnitude and opposite in sign [START_REF] Bogatov | Kremnievyi chuvstvitel'nyi ehlement dlya datchikov sil, uskorenii, vibratsii.[The silicon sensing element for sensors of forces, accelerations, vibrations]. Tekhnologiya. Tekhnologiya Priborostroeniya: Nauch.-Tekhn.Sb. TSNTI "Poisk[END_REF] .

Reducing the complementary temperature error IP T by approaching to zero the value and temperature dependence of the normalized null output K mc0 is possible if the following design requirements are met:

• minimizing the deviations of the electrical resistance IP T from the average values and the identity of their temperature characteristics;

• minimization of values and variances of the initial deformations of the elastic element in the areas of P CH placement; identity of the temperature dependences of these values;

• equality of all thermal resistances in the heat sink chain P CH -EE -BR;

• minimization of temperature gradient in the plane of P CH placement on EE.

The deformation transducer design, which provides the above requirements, contains identical square contact pads M C of size b with centers at the vertices of a square of size a, connected by four single-band P CH width d ch longitudinal (R 1,3 ) and transverse (R 2,4 ) piezoresistors (Fig. 3.1). Contact pads and piezoresistive channels are formed by local doping (boron doping) of the planar surface with orientation (001) of the monolithic monocrystalline silicon structure BR -EE. The M C elements are located in the EE body H ee thick at a distance C from the H w thick base boundary.

Assuming K 0 (T ) = 0, the transformation characteristic for any mechanical

V out V in = K mc • K ch • ε = = 2 • K ∥ • ε x 0 •    1 -K ⊥ K ∥ (εx 4 +εx 2 ) 2εx 0 2 + K ∥ • ε x 0 • 1 + K ⊥ K ∥ • εx 2 εx 0 • 2 + K ∥ • ε x 0 • 1 + K ⊥ K ∥ • εx 4 εx 0   
(3.1) where K ∥ , K ⊥ are the longitudinal and transverse gauge factor of the silicon channel P CH, respectively; ε x 0 is the amount of strain EE at the geometric centers of piezoresistors R 1 ; R 3 channels; ε x 2 , ε x 4 -deformation values in the geometric centers of piezoresistors R 2 ; R 4 channels.

For the selected M C, the total area A p-n and perimeter P p-n of the insulating p-n junction are determined by the relations:

A p-n = 4 b 2 + d ch (a -b) ; (3.2)
P p-n = 8[a + b -d ch ] (3.3)
The standard value of R in for piezoresistive mechanical sensors is in the range (95÷ 1520) Ω) 60 . In this case, at d ch = 1 • 10 -3 cm and the surface resistance of the ion-alloy layer equal to 85 Ω/□, the channel length (a -b) is within (10 ÷ 200) • 10 -4 cm and the total p -n junction area, at b = 40 • 10 -4 cm, is A p-n = (0.5 ÷ 2) • 10 -4 cm 2 . M C with such miniature dimensions can be composed on small-sized diaphragm, beam, and other elastic elements in mechanical IP T . When the size of the elastically deformable part EE is greater than 0.2 cm × 0.2 cm, we can assume that the equality ε x 2 ≈ ε x 4 ≈ ε x 0 holds, then for IP T , where |K ∥ | ≈ |K ⊥ |, from (3.1) the transformation characteristic will be:

V out V in = 0.5 • K ∥ • ε x 0 1 - K ⊥ K ∥ . (3.4)

Monolithic IPTs with Isolating P-N Junction

In deriving the calculated dependence of the inverse current density J rev on temperature to determine the upper limit of the operating temperature range of monolithic IP T , where P CH p-type in EE n-type are isolated by a layer of carrier-poor p -n junction, the following conditions, initial data and calculation relations were chosen.

(1) The dependence of I rev (T ) is determined by relations (2.21)-(2.25) and temperature changes of parameters:

• of free charge carriers n i (T ) from relation (2.25);

• the lifetime τ p (T ) for the minority charge carriers in the body EE from the graph in Fig. 2.9;

• the lifetime of µ p (T ) for the minority charge carriers in the EE body from the relation 6 :

µ p (T ) = µ p0 T 0 T 2.5 (3.5)
where µ p0 (T ) is the hole mobility at temperature T 0 = 293 K;

• the diffusion length L p (T ) for the minority charge carriers in the body EE from the relation:

L p (T ) = µ p (T ) • τ p (T ) • k • T q 1/2 (3.6)
• S 0 -does not change with temperature and is equal to the maximum value S 0 = 1 • 10 4 cm/sec.

(2) P -N junction is a sharp, asymmetric, stepped, p-n -type junction (i.e., ρch ≪ ρ ee )

with the width of the bulk charge region in the EE body equal to

d p-n ≈ 3.65 • 10 3 (Vrev) Ne EE 1/2 (3.7)
and a uniform distribution of bulk charges along the metallurgical junction boundary.

( The ratio of the perimeter p -n junction P p-n to the area A p-n is a constant value equal to Taking into account the selected initial data and calculated relations, the temperature dependence of the reverse current density VAC of the isolating p -n-junction IPT is determined by the following expression:

K p-n = P p-n A p-n = 500 cm -1 (3.8) (4
J rev = q • a p-n • 1 τp(T ) + S 0 • K p-n • e 22.2•( T -293 T ) + + q • k•µ p0 q•τp(T ) 1/2 • 113.7 T 3 • P n • e 22.2•( T -293 T ) • e 22.2•( T -293 T ) (3.10)
where A p-n = 500 cm -1 . P CH were formed by boron ion implantation technology with a doping dose of 2 • 10 15 cm -2 . The surface resistivity of the ion-doped piezoresistive layers R s = 85 Ω/□. Fig. 3.4 shows experimental for IP T samples and calculated from the graph in Fig. 3.2 for this topological structure M C dependences of the reverse current I rev V AC on temperature, by which the upper limit of the temperature range (value T per at I rev = 2 µA) is determined:

a p-n = d p-n •n i0
• for samples IP T values +180 • C ÷ +200 • C
• for the value +210 • C calculated from formula (3.10).

The experimentally measured temperature dependences K mc0 (T ), K u mc (T ) and K i mc (T ) in Fig. 3.4(b) are characterized by smooth changes over the whole range up to the limiting research temperature +260 • C.

The performed calculations and experimental studies give grounds to assert that monolithic silicon integral piezoresistive transducers with isolation of piezoresistive channels of p-type conductivity from EE by p -n junction layer are workable up to temperatures +180 • C ÷ 300 • C. The specific boundaries of the operating range will be determined by the values of the resistivity and geometrical parameters of the topological structure M C selected during the design.

Monolithic IPT with Distributed Parameters

The physical meaning of the modeling and research was to find the relations between the electrophysical characteristics of EE and P CH, allowing to calculate and design IP T with extended beyond the critical temperature T per = 150 • C=150 C, operating range, provided that the conductivity (2 ÷ 10) times the conductivity of EE, that is at ρ ee < 20 Ω • cm. Determination of the computational relationships is related to the problem of constructing and investigating the M C model with distributed parameters P CH, which are formed in the volume of an equal-thick silicon wafer.

For the modeling, the strain transducer design shown in Fig. 3.1 and Fig. 3.5, consisting of a silicon elastic element 1 p-type with orientation in the plane (100) and thickness H ee , in which equal square contact pads 8, 9,10, 11 with sides b with centers at the vertices of a square with sides (a + b), are connected by four single-band piezoresistive channels p + -type 2,3,4,5 oriented along crystallographic directions [011] with width equal to b and thickness -x j .

The problem is solved under the following conditions and assumptions:

• -a ≫ H ee ;

• the strain component ε y is directed along the crystallographic trajectory [011];

• the bridge circuit is fed from the stabilized voltage source V in through the diagonal contacts 9,11;

• current I r is evenly distributed with respect to the plane of cross section of channels 2,3,4,5; its distribution is similar in neighboring channels 2,3 and 4,5 with common contacts 11,9, respectively;

• the current in the elastic element 1 is evenly distributed in the cross section in the direction Z along the normal to the flat surface of the elastic element 1; currents are absent outside the circuit area bounded by channels 2,3,4,5; inside the area are characterized by components I c and I e ; the direction of components I c is normal relative to the sides of neighboring channels 4,5 with a common power contact 11; current component I e is directed along the diagonal connecting power contacts 9,11;

• distribution of concentration of majority carriers in the channels 2,3,4,5 is uniform; the level of doping is characterized by the value of resistivity equal to the mean value of resistivity at real non-uniform distribution of impurity;R Sc = ρch

x j
where R Sc -values of surface resistance of channels 2,3,4,5 , Ω/□; x j -doping depth of channels 2,3,4,5,cm, equal to depth of p-n junction, if elastic element 1 of silicon n-type;

• the level of doping of elastic element 1 is characterized by the value of resistivity of the initial material ρ ee .

As a discrete analogue of the transducer model, we use the equivalent circuit of a long line with parameters distributed along the X-axis, shown in Fig. 3.5. c), for which

I r1 (x) = -dφ 1 (x) dx • b R Sc1 ; I r2 (x) = -dφ 2 (x) dx • b R Sc4 ; I c (x) = -dI r1 (x) dx ; I c (x) = -dI r2 (x)
dx ;

I e (x) = - dV in (x) dx • b • H ee √ 2 • ρ ee ; dI e (x) dx = 2I c (x).
(3.11)

After transformations (3.11), the differential equations look like

d 2 Υ 1 (x) dx 2 = x -1 C 1 • Υ 1 (x); d 2 Υ 2 (x) dx 2 = x -1 C 2 • Υ 2 (x), (3.12)
where

Υ 1 (x) = φ 1 (x) -V in (x); Υ 2 (x) = φ 2 (x) -V in (x); C 1 = 2 √ 2 + R Sc1 ρ ee H ee ; C 2 = 2 √ 2 + R Sc4 ρ ee H ee .
The solution of equations (3.12) has the form [START_REF] Kamke | Differentialgleichungen Lösungsmethoden und Lösungen[END_REF] :

Υ(x) = √ xZ 1 (i • 2 √ Cx) (3.13)
where Z 1 (i • 2 √ Cx) is a Bessel function with an imaginary unit. The following boundary conditions were used: at

x = 1 : Υ 1 (1) = Υ 2 (1) = 0; φ 1 (1) = φ 2 (1) = V in ; V in (1) = V in ; at x = a : Υ 1 (a) = φ 1 ; Υ 2 (a) = φ 2 ; V in (a) = 0; φ 1 (a) = φ 1 ; φ 2 (a) = φ 2 ; I r 1 (a) = φ 1 b R Sc2 •a ; I r 2 (a) = φ 2 b R Sc3 •a ; I in = I e (a) + 2I c (a); I e (a) = I in -φ 1 b R Sc2 •a -φ 2 b R Sc3
•a ; with which, the solution of equations (3.12) determined the following relations for circuit parameters:

V dp out = φ 1 -φ 2 = = V in • R 2 R 1 + R 2 + R 1 •R 2 •b ρee•a H ee • Φ - R 3 R 4 + R 3 + R 3 •R 4 •b ρee•a H ee • Φ ; (3.14) R dp in = 1 + 2 R 2 •b ρee•a H ee • Φ R 1 + R 2 + R 1 •R 2 •b ρee•a H ee • Φ + 1 R 3 + R 4 + R 3 •R 4 •b ρee•a H ee • Φ + b • H ee ρ ee • a √ 2 -1
;

(3.15) where V out is the value of the output of the bridge circuit, V; R in -value of input resistance of the bridge circuit, Ω; R 1 , R 2 , R 3 , R 4 -resistance values of piezoresistive channels 5,4,3,2 electrically isolated from each other in the four shoulders of the bridge circuit, Ω; Φ is a dimensionless coefficient for the strain transducer model, which characterizes the redistribution of the charge carrier current in the channels and the elastic element.

We assume that

R 1 = R 2 = R 3 = R 4 = R ch = ρch • a b • x j ; dR 2 dε x = - dR 1 dε x = dR 4 dε x = - dR 3 dε x = R ch • K ch ; (3.16)
where K ch is the gauge factor of electrically isolated piezoresistive channels 2,3,4,5.

Then the gauge factor of the transducer and the input resistance of the bridge circuit are equal:

K dp mc (T, ε y ) = 1 V in dV out dε y = 2K ch (T ) 2 + ρch (T ) ρee(T ) • Hee•Φ x j ; (3.17) R dp in (T ) = 0.5 • R ch (T ) 1 + R ch (T ) ρee(T ) • Hee•Φ•b a 2 + R ch (T ) ρee(T ) • Hee•Φ•b a + 0.354 R ch (T ) • H ee • b ρ ee (T ) • a -1 (3.18)
where

K ch (T ) = K 0 + K 1 T 0 T + K 2 T 0 T
2 is the gauge factor of electrically isolated piezoresistive channels 2,3,4,5 with temperature dependence determined according to 62 by second degree polynomial in case the temperature parameter t, t = T 0 T . This is true for silicon piezoresistors [START_REF] Osipovich | Datchiki fizicheskikh velichin[END_REF] ; α ch [1/K], β ch [1/K 2 ] are approximation coefficients; ρch0 -is the resistivity at T = T 0 ;

R ch (T ) = ρ ch (T ) • a b • x j = R ch0 1 + α ch (T -T 0 ) + β ch (T -T 0 ) 2
-resistance value of electrically isolated piezoresistive channels 2,3,4,5; R ch0 -is the resistance at T = T 0 ; ρ ee (T ) = ρ ee0 1 + α ee (T -T 0 ) + β ee (T -T 0 ) 2 -is the resistivity of the initial silicon wafer 7 with the temperature dependence defined by the polynomial of the second degree; α ee [1/K], β ee [1/K 2 ] are approximation coefficients.

For any transducer design, the condition a ≤ H ee is possible. Then the assumptions about the uniformity of current distribution in the elastic element along the direction Z will not be adequate to the nature of the distribution in the real object. Therefore, instead of H ee its effective value H ef is used. The redistribution parameter of the current of charge carriers in the channels and the elastic element in this case is equal to:

Λ = H ef • Φ • b a . (3.19)
The numerical value of the parameter Λ is determined by joint measurements [START_REF] Kulikovskii | Metody i sredstva izmereniya[END_REF] . With known values of temperatures inside the selected operating range T 1 and T 2 , the values R inT 1 and R inT 2 are measured. For the same temperature values, the values R chT 1 , R chT 2 are calculated. If α ch and β ch are unknown a priori, R chT 1 and R chT 2 are measured on specially designed test samples . The same is true for ρ eeT 1 and ρ eeT 2 . Using the system of 2 equations derived from (3.18), we obtain the ratio for calculating Λ. The test IP T were made of silicon wafers of KDB-0.5, KDB-1 and KDB-10 types with resistivities ρ 0 (at T 0 = 293 K) equal to 0.50 Ω•cm, 1 Ω•cm, 10 Ω•cm respectively. The unification of the sensor design by the input mechanical quantities will be related to changing the slope of the conversion characteristic by selecting the thickness of the elastic element. An important condition is the independence of the circuit parameters from the thickness H ee . From the graph in Fig. 3.6, which shows the experimental dependence of the change in the input resistance R in on the calculated parameter Hee a , it can be seen that this condition will hold at Hee a ⩾ 0.3 . The dependence of the parameter Λ on the resistivity ρ ee was determined by measuring test samples of thickness H EE = 1 • 10 -2 cm. The change in Λ values for ρ ee = (0.5 ÷ 10) Ω • cm was within the measurement error. For samples in which piezoresistive channels were formed by boron ion implantation with a doping dose of 2 • 10 15 cm -2 ,Λ = (9.1 ± 0.5) • 10 -3 cm .

Conclusions

1. The topological structure of the bridge circuit is chosen, where equal square contact areas of size b with centers in the vertices of the square of size a are connected to each other by four single-band piezoresistive channels of width d of longitudinal and transverse piezoresistors; such a scheme will allow: -approximate to zero the magnitude and temperature variations of the normalized null output, K mc0 (T ) = 0; -reduce the total area of the insulating p-n junction to A p-n ≤ 2 • 10 -4 cm 2 .

2. The main regularities of the influence of physical factors on the temperature dependence of the insulating properties of p -n-junctions at temperatures above 100 • C have been established. The upper value of the working temperature range T per for IP T (in which the insulation of piezoresistive channels and contact pads of p + -type conductivity bridge circuit from the elastic element is performed by the depleted charge carriers layer p -n-junction) is determined by the condition when the insulation resistance value p -n-junction decreases to the value R p-n i = 2.5 • 10 6 .

3. The calculated ratio is obtained and the temperature changes of reverse current density p + -n-transition for IP T with resistivities EE from 0.5 Ω•cm to 20 Ω•cm are calculated.

4. For ITPs with specific resistances of the elastic element ρ ee ⩽ 10 Ω • cm and the area of insulating p-n junction A p-n ⩽ 1.28 • 10 -4 cm 2 the calculated upper limit of the operating temperature range is determined by the values T per ⩾ 210 • C. The discrepancy between the experimentally obtained values of T per and the calculated values was not more than 15 %.

5.

The relations are obtained for calculating the parameters of a strain IP T with distributed parameters (in which the piezoresistive channels and contact areas of the bridge circuit are doped with an impurity that increases the concentration of the majority charge carriers of p-type silicon elastic elements with a resistivity from 20 Ω•cm to 0.5 Ω•cm) defining the upper limit of the operating temperature range from +150 • C to 300 • C. For a force sensor with a beam elastic element, where the design parameter H EE a ⩾ 0.3, the values of the Λ parameter characterizing the redistribution of charge carrier current in the channels and volume of the elastic element were experimentally measured. Changes of Λ parameter values for IP T with resistances of 0.50 Ω • cm, 1 Ω • cm, 10 Ω • cm were within the measurement error. For IP T where EE were formed by boron ion implantation with a doping dose of 2 • 10 15 cm -2 the Λ parameter is (9.1 ± 0.5) • 10 -3 cm.

CHAPTER 4

Principles of Monolithic IPT design for the 0÷300°C temperature range From the results of the analysis in Chapter 1, the design problems arise for which additional studies of the electrophysical, metrological and operational characteristics of IP T elements in the range of temperatures (0 ÷ 300) • C are necessary. The practical use of the results of the studies performed in Chapter 2 under certain conditions and assumptions also requires experimental refinements. Therefore, the purpose of this chapter is to experimentally investigate and determine the initial data required for further design of specific IP T designs.

Designing an IPT with an Isolating P-N Junction

Minimization of the geometrical parameters of the topological structure M C in Fig. 3.1 depends on the constraints on the minimum values of the contact areas b , length (a -b) and width d ch of the piezoresistive channels. The determination of the minimum size constraints b min is related to the experimental dependence of the temperature instability parameter γ mc0 of the normalized null output K mc0 , equal to

γ mc0 = K mc0 (T per ) -K mc0 (T 0 ) K mc0 (T 0 ) • (T per -T 0 ) • 100%. ( 4
R in R s = a -b d ch (4.2)
The value of R in is determined by the standard values (95-1520) Ω 53 60 . According to [START_REF] Borshchev | Ehlektrofizicheskie kharakteristiki tenzorezistivnykh struktur, legirovannykh implantirovannym borom. [Electrophysical characteristics of tensoresistive structures alloyed with implanted boron[END_REF] , R s for ion-alloyed P CH is determined by the value R ion s = 85 Ω/□, and for diffusive (if the value x j = 2.5 • 10 -4 cm) R dif s = (85 ÷ 320) Ω/□ . Decreasing the width of P CH, provided that d ch < b min , leads to an increase in the parameter K p-n = P p-n A p-n (which is obvious from relations (3.2),(3.3)) in relation (3.8). In this case, finding the upper bound of the operating temperature range for the real design IP T using the dependences in Fig. 3.3 would be incorrect. Restrictions on the minimum values d ch min will be determined by experimental studies of the dependence of the temperature change of the inverse current density on the parameter K p-n .

For the idealized structure of an isolating p -n junction it is assumed that the concentration of ionized atoms determining the area of the volume charge and the related electric field strength are uniformly distributed in the direction of the y-axis coinciding with the metallurgical boundary of the transition. In real p -n junctions in the corners of rectangular elements M C should increase the concentration of ionized atoms, which, apparently, will lead to changes in the parameters determining the generative surface and volume components of the reverse current, and thus to dependence of J rev on the number n of these corners in the topological structure. The breakdown voltage of an idealized p-n junction from relation (3.9) was calculated without taking into account the influence of the surface on the electrical insulation strength, where adsorbed ions are always present, creating conditions for avalanche development earlier than in the volume [START_REF] Trutko | Metody rascheta tranzistorov [Transistor Calculation Methods[END_REF] . From the results obtained in 66 , V br depends on EE resistivity, transition type, environment, and surface condition. The real breakdown stresses for the experimental IP T samples were found to be (5÷10) V and (20÷50) V if the resistivity of the elastic element region is 0.5 Ω • cm and 4.5 Ω • cm respectively ( P CH doping was done by boron ion implantation). It is likely that for most IP T with ρ ee1 = 0.5 Ω • cm, where the breakdown voltages are commensurate with standard sensor supply voltages, the insulating properties will not be satisfactory. Therefore, single-crystal silicon of p-type orientation (001) with resistivity ρ ee1 = 4.5 Ω • cm was chosen to make the IP T experimental samples.

The beam test-IP T forces 5E.2251.130.00.00.000 contain specially designed ( according to the stated research objectives ) test M C with different geometrical parameters. Fig. 4.1 shows the general view of the force IP T , and the table (Fig. 4.2) shows the investigated topological structures of M C and their geometrical parameters. • boron ion implantation with a doping dose of 2 • 10 15 cm -2 and surface resistivity R s ee = 85 Ω/□;

• diffusion of boron with average resistivity values P CH (where we can expect in the range (0 ÷ 300) • C "auto-compensation" of temperature sensitivity changes when feeding M C with stabilized current) 0.02 Ω•cm, 0.03 Ω•cm and 0.06 Ω•cm For all IP T variants, formed diffusion low-resistance contact areas with surface resistivity (10 ÷ 12) Ω/□.

To evaluate the electrophysical characteristics of IP T with an insulating p -n junction, the following parameters and computational relationships have been used:

• input resistance M C, R in = V in I in (4.3)
• normalized null output M C,

K mc0 = V out 0 V in (4.4)
• reverse current I rev when the insulating p -n junction is reverse biased by a 5 V voltage;

• sensitivity coefficient of the P CH at the assumed equality K ∥ = |K ⊥ |, equal to

K ch = V in F -V out 0 V in • ε x 0 (4.5)
where V in F is the output of M C when the console of the elastic element is loaded with a load F ; ε x 0 is the strain at the location of M C;

• intrinsic error for pressure sensors not more than ±1%; for sensors of vibration acceleration (acceleration sensors) not more than ±5%;

• approximation coefficients of temperature dependence of input resistance

M C R in = R in 0 1 + A 1 (T -T 0 ) + A 2 (T -T 0 ) 2 , A 1 and A 2 were determined by joint measurements 64 R in 1 , R in 2 ,R in 0 at temperatures respectively T 1 = 300 K, T 2 = 500 K, T 0 = 400 K ;
• approximation coefficients of the temperature dependence of the gauge factor P CH (2.19) K A , K B , K C were determined by joint measurements K ch 1 , K ch 2 , K ch 0 at temperatures T 1 = 300 K, T 2 = 500 K, T 0 = 400 K respectively. intrinsic error ±1%, according to 53 , the limit value of the complementary temperature error should not be more than 0.06%/ • C. When selecting the boundary value γ mc0 , it was taken into account that the experimentally obtained dependence in the graph of Fig. 4.3 gives an estimate of the influence of contact resistances only. For this purpose, during the measurements IP T were not fixed in the case and had a thickness EE H ee ⩾ 100•10 -4 cm. As shown in 32 67 , at real values of H ee = (10÷100)•10 -4 cm the temperature-dependent initial stress state of the transducer due to the difference in the α ch l (= α Si l ) α SiO 2 l ; α il l ; α ee l (= α si l ); α rb l increases the γ mc0 by (0.02 ÷ 0.03)%/ • C. The boundary value of γ mc0 is taken to be (0.03)%/ • C. Then the minimum contact dimensions b c min (from the graph in Fig. 4.3) and the diffusion contact region b min at 5-micron process gap between the contact and p -njunction are b c min = 20 • 10 -4 cm, b min = 30 • 10 -4 cm. Fig. 4.4 shows a graph of the temperature dependence of the reverse current density of insulating p-n junctions with ion-alloyed and diffusion P CH for the test structure M C#5 with A p-n = 3 • 10 -4 cm 2 . The noticeable difference in the variation for the experimental samples at temperatures below +150 C can be explained by the influence of the variation in the surface recombination rate S 0 . The temperature dependence of the diffusion component of the reverse current at temperatures above +150 • C becomes determinative, and the dependences for the experimental samples approach each other.

The results of the investigation of the influence of the geometrical parameters of the topological structure of MS K p-n and n on the insulating properties of the p -n- (A) The high-level region of reverse current density "A" is formed by dependencies for structures where the number n is maximal (n = 32), and K p-n is in the range 800 -1400(#1, #2). In this case, the extension of the upper bound of the operating temperature range to the values T per ⩾ 200 • C is unlikely. The areas of insulating p -njunctions should be A p-n ⩽ 2•10 -5 cm 2 , i.e., more than 3 times less than the previously defined limit value of the total area of the four M C contact sites.

(B) The J rev "B" plot of mean values belongs to the MC dependence of structures where the number of n angles is 32 and 8, but K p-n is in the range (500 ÷ 700)cm -1 (#4, #5, #7). Here, a realistic design for high temperatures is MC #7 with parameters K p-n = 500 cm -1 and n = 8 with p -n transition area A p-n ≤ 2 • 10 -4 cm 2 .

(C) The "C" cross section, for a M C #10 ring structure with K p-n = 500 cm -1 , at temperatures T > 180 • C, is in good agreement with the calculated J rev (T ) dependence. The differences at temperatures T < 180 • C can be explained by the fact that the calculated dependence J rev (T ) selected a maximum limiting value S 0 equal to S 0 = 1 • 10 4 cm/s. It is possible that in a real MC the value of S 0 could be 100 times smaller 6 .

To determine the values of approximation coefficients of temperature dependences of the sensitivity coefficients K A , K B , K C and resistance A 1 , A 2 at the previously selected values of average resistivity of diffusion alloyed P CH samples with the structure 4.1 Values of approximation coefficients of temperature dependences of PCH strain-sensitivity K mc (T ) and input resistance R in (T ) for topological structures of test-IPT with ion-doped PCH.

K A K B K C A 1 , 1/K A 2 , 1/K 2 #4 10 ± 5% 60 ± 8% -(14 ± 3.6) (1.14 ± 0.03) • 10 -3 (1.5 ± 0.4) • 10 -6 #10 5 ± 2% 60 ± 7% -(16 ± 4) (1.14 ± 0.03) • 10 -3 (1.5 ± 0.4) • 10 -6
current in P CH and EE. For this purpose, the P CH and contact regions are formed by locally doping the impurity that increases the concentration level of the majority charge carriers in the silicon elastic element, for example in EE of P -type silicon by ion implantation or boron diffusion.

As shown in Chapter 2, the redistribution effect of charge carrier current in M C begins to show on the characteristics when the resistivities of the silicon elastic element ρ ee < 20 Ω • cm. For this case, the design parameters IP T , where Hee a ⩾ 0.3, can be found from relations (3.14), (3.17) and (3.18):

V dp out (T ) V in = R 2 (T ) R 1 (T ) + R 2 (T ) + 9.1 • 10 -3 • R 1 (T )•R 2 (T ) ρee(T ) - - R 3 (T ) R 4 (T ) + R 3 (T ) + 9.1 • 10 -3 • R 3 (T )•R 4 (T ) ρee(T ) (4.6)
K dp mc = K ch (T ) 1 + 4.55 • 10 -3 • R ch (T ) ρee(T ) (4.7)
R dc in = R ch (T ) 2+18.2•10 -3 • R ch (T ) ρee(T ) 2+9.1•10 -3 • R ch (T ) ρee(T ) + 0.707 • R ch (T )•H ef •b ρee(T )•a (4.8)
To confirm the obtained calculation ratios, to determine the design constraints for the placement of M C in the EE body and the pressure range of the working temperatures, a design of a pressure test transducer with a beam elastic element 5E.2251.205.00.00.000 was developed. The topological structure and geometric parameters are shown in Fig. 4.8. The coordinates of the M C location in the EE volume relative to the x and y axes are changed by aligning the topological layers with specially formed signs in the oxide layer of the silicon plate. This solution significantly simplified the design of the test transducer and reduced the error in reproducing the specified geometric dimensions of the bridge circuit.

Model samples of IP T were made from silicon wafers KDB-0.5(P -T ype 0.5 Ω• cm), KDB-10(P -T ype 10 Ω•cm), KDB-4.5(P -T ype 4.5 Ω•cm), using boron ion implantation with a doping dose of 2 • 10 15 cm -2 to form P CH (with a sheet resistance of R Sch = 85 Ω/□). IP T with elastic elements of N-type silicon wafers KEF - To calculate the parameters of IPT, the following input data were used:

• temperature variations of the specific resistance ρ ee (T ) up to the temperature of intrinsic conductivity obtained from the temperature dependencies of the differential temperature coefficients of specific resistance α ρee = 1 ρee(T ) dρee(T )

dT , calculated in [14] for uniformly doped layers of p-type silicon: for ρ ee1 = 0.5 Ω • cm (KDB -0.5)

ρ ee1 (T ) = 0.5 1 + 6.6 • 10 -3 (T -T 0 ) + 1.4 • 10 -5 (T -T 0 ) 2 ; for ρ ee2 = 1 Ω • cm (KDB -1) ρ ee2 (T ) = 1 + 7.6 • 10 -3 (T -T 0 ) + 1.6 • 10 -5 (T -T 0 ) 2 ; for ρ ee1 = 10 Ω • cm (KDB -10) ρ ee3 (T ) = 10 1 + 7.83 • 10 -3 (T -T 0 ) + 1.68 • 10 -5 (T -T 0 ) 2 ;
• values of the temperature of intrinsic conductivity T int , calculated in 14 (α ρee = 0):

# Resistivity Intrinsic Conductivity Temperature

1 ρ ee 1 325 • C 2 ρ ee 2 300 • C 3 ρ ee3 200 • C
• temperature variations of the resistance R ch and the piezoresistive coefficient K ch of electrically isolated ion-implanted PCH, determined in Chapter 4 (see Table 4.1).

• effective thickness H ef determined from the graph in Fig. 3.6, under the condition of appearance of the input resistance M C dependence on the thickness EE (H ee , Hee a ⩽ 0.3) for IP T 5.EH.2251.205.00.00.000, where a = 200 • 10 -4 cm, equal to H ef = 60 • 10 -4 cm;

• allowable variations of IPT parameters when changing the location of M C for the normalized null output ∆K mc0 ⩽ ±0.2 mV V and the temperature instability coefficient of the normalized null output ∆γ mc0 ⩽ ±0, 01 %/ • C.

The calculated and experimental dependencies of changes in the input resistance M C relative to its value for electrically insulated P CH on the specific resistance EE Fig. 4.12 shows the calculated and experimentally obtained temperature changes in the piezoresistive coefficients for IP T with specific resistances EE of 0.5 Ω • cm, 1 Ω • cm, 10 Ω • cm. The temperature ranges of operation for IP T are determined from the graphs as follows:

# Resistivity Operating Temperature Ranges 1 ρ ee 1 = 0.5 Ω • cm (0 ÷ 325) • C 2 ρ ee 2 = 1 Ω • cm (0 ÷ 300) • C 3 ρ ee3 = 10 Ω • cm (-60 ÷ +200) • C

Study of Methods to Minimize the Intrinsic and Temperature Errors IPT

As shown in Chapter 1, the systematic component of the intrinsic error δ kee for microinertial IPTs with H ee < 100•10 -4 cm, which is associated with the reproducibility of the transformation characteristic under the technological dispersion of the geometric sizes EE, can reach values up to δ kee = ±40%. In this case, for low-frequency accelerometers with a intrinsic error of 5%, assuming that the error of modern low-frequency vibration measurement devices is ±3%, the error value should not exceed ±3% 68 69 , and the yield of acceptable products in serial production should be less than 5%.

The identity of the conversion characteristic slope is achieved by additional adjustment with internal adjustment elements 5 70 . However, most known adjustment methods have their drawbacks: they change the electrical parameters of the sensor and limit the range of operating temperatures to values of (+100 ÷ +150) • C.

A method for adjusting beam transducers for low-frequency accelerometers of inertial action by changing the conversion coefficient EE K ee has been developed and studied [START_REF] Tikhomirov | Malogabaritnyi kremnievyi akselerometr s termokompensirovannym vykhodnym signalom v diapazone temperatur ot 0 do +150°C[END_REF] . The adjustment method is carried out as follows (see Fig. into groups of parallel bands with piezoresistors D 1 and regulating n bands D 2 without piezoresistors. The control of the parameters marked on the wafer IPT determines the systematic error component δ kee , and the resonance frequency f 0 72 . To adjust, it is necessary to determine the total width value of the adjustable strips m • D 2 , which can be expressed by the equation:

m • D 2 = δ kee • (2 • D 1 + n • D 2 ) (4.9)
Then m adjustment strips are torn without violating the symmetry of the elastic element. For the design of a low-frequency accelerometer SIAP 402.139.001, where

D 1 = 400 • 10 -4 cm, D 2 = 40 • 10 -4 cm, n = 32,
the required number of tear strips is determined by the equation:

m = δ kee 2 • D 1 + n • D 2 D 2 = 52 • δ kee (4.10)
The following results were obtained during the tuning of the low-frequency accelerometers: The adjustment of the slope of the transfer characteristic of membrane pressure sensors, where the intrinsic error should not exceed ±1%, is carried out by changing the thickness during the formation of the transducer [START_REF] Tikhomirov | Method of batch production of semiconductor strain transducer elements[END_REF] .

Periodically, during pauses in the etching process, the silicon plate with the IPT is placed on a probe setup, a control transducer (one or more) is loaded with a constant mechanical value, and the output electrical signal is measured. Etching is stopped when the desired output signal is reached.

Advantages of the methods considered: electrical parameters and the working temperature range of the sensor remain unchanged; the output of usable parts increases by more than 10 times; the systematic component of the intrinsic error decreases by more than 10 times.

Monolithic IPT with a p-n junction isolating the measurement circuit

Based on the results of studies of temperature changes in the normalized null output K mc0 , the additive component of additional temperature error is determined by the value Fig. 4.13 Tuning methods for integral piezoresistive transducers (IPT) of γ 0 ⩽ 0.04 %/ • C. The standard value of the additive temperature error for pressure sensors with an intrinsic error of ±1% is 0.06% • C (for low-frequency accelerometers with an intrinsic error of ±5%, 0.1% • C). Thus, the allowable value of the multiplicative error component during temperature changes of the bridge sensitivity K mcV (T ) should be γ mc = 0.04% • C (γ mc = 0.07% • C for accelerometers). The error parameter γ for the temperature range (T 1 , T 2 ) is estimated by the change in the output signal as a percentage of its nominal value when the ambient temperature changes (the temperature instability of the output signal) 53 60 :

V outmax -V out min V out (T 0 ) • 1 T 2 -T 1 • 100% ≤ γ; %/ • C
where V outmax and V out min are the maximum and minimum values of the output signal when the temperature changes. When analyzing the conditions for implementing compensation of temperature changes in the conversion characteristic (multiplicative component), the differential temperature coefficient of sensitivity [START_REF] Tikhomirov | Temperature Dependence of Sensitivity of Silicon Integrated Mechanical Transducer in The Temperature Range from -60°C to +200°C[END_REF] is used, which is equal to

Γ mc = 1 K mc (T ) • dK mc (T ) dT (4.11)
where

K mc = 1 V in (T ) dVout(T ) dT
is the M C sensitivity IP T . The temperature dependence of the characteristics of the conversion with an isolated p-n junction in the case of supplying the MC from a stabilized voltage source (V in = V input = const) is characterized by the coefficients obtained from relations (2.19) and (3.4), provided that K ∥ = -K ⊥ , as follows:

Γ mcV = Γ V 2 T 0 T 2 + Γ V 3 T 0 T 3 (4.12)
where

Γ V 2 = - K B T 0 K A + K B T 0 T + K C T 0 T 2 ; (4.13) Γ V 3 = - 2K C T 0 K A + K B T 0 T + K C T 0 T 2 , (4.14)
then

Γ mcV = - K B •( To T ) 2 +2K C •( To T ) 3 T 0 • K A +K B • T 0 T +K C •( T 0 T ) 2 (4.15)
The compensation condition for the temperature dependence of the conversion characteristics is possible at In articles 17 22 76 , the results of research on the physical and functional models of the IP T with an isolating p -n junction are presented for the case of powering the M C from a stabilized current source in the temperature range of (-60÷+80) • C. When analyzing the conditions for implementing compensation for temperature changes in the conversion characteristic, the differential temperature sensitivity coefficient [START_REF] Tikhomirov | Temperature Dependence of Sensitivity of Silicon Integrated Mechanical Transducer in The Temperature Range from -60°C to +200°C[END_REF] is used, which is given by

T = T 0 if K B = K C = 0 (a) or K B = -2K C (b). Condition (a)
Γ mcI = 1 KmcI 0 dK mcI (T ) dT , (4.23)
where

K mcI (T ) = V out (T ) I in • ε x 0 = R in 0 • 1 + A 1 • (T -T 0 ) + A 2 • (T -T 0 ) 2 × × K A + K B • T 0 T + K C • T 0 T 2
is the sensitivity coefficient of the M C when supplied with stabilized current. The differential temperature sensitivity coefficient for this case is given by:

Γ mcI = Γ I0 + Γ I1 • T + Γ I2 • T 0 T 2 + Γ I3 • T 0 T 3 (4.24)
where

Γ I1 = 2 • K A •A 2 K A +K B +K C (4.25) Γ I2 = K B A 1 -A 2 •T 0 -1 T 0 -K C •(A 1 -2A 2 •T 0 ) R A +R B +R C (4.26) Γ I3 = 2 • K B • A 1 -A 2 •T 0 -1 T 0 K A +K B +K C (4.27)
The choice of optimal average resistivity values in the range of ρch = (2 • 10 -2 ÷ 8 • 10 -2 ) Ω • cm determines the conditions for IPT compensation in the temperature range of (0 ÷ +300) 0 C 42 . For the given values of γ mc ⩽ 0.04%/ 0 C, the temperature working ranges for IPT with an isolated p-n junction are given in Table 4 (+50 ÷ +210) 0 C Fig. 4.18 shows the experimentally obtained temperature dependences of the sensitivity change for the IPT without TCC with power supply of the measuring circuit from a stabilized current source. For IP T with ion-alloyed P CH at a dose of 2 • 10 15 cm -2 the temperature range is defined from 0 • C to 210 • C. One significant difference in the construction of a distributed parameter IP T is the electrical connection of the elastic element to the measurement circuit. In such a design, the elastic element is not only a converter of mechanical quantity into deformation but also a means of regulating the temperature dependence of the output signal with precise information about changes in the ambient temperature, as it combines the functions of heat transfer on the sensor's P CH. This design increases the reliability of the sensor at high temperatures above +200 • C since it does not require any elements to adjust its characteristics, and the parametric failure of the elastic element can occur only simultaneously with its mechanical failure. Determining the compensation conditions Γ dp mc = 0 for a distributed parameter IP T is a complex technical task related to the optimal selection of various design and technological parameters: specific resistance of the elastic element, average specific resistance of the P CH, thickness of the elastic element, geometric dimensions and shape of the IP T 's topological structure, etc. In this case, we consider the sensor's construction described in section 3.2.

1 ρch1 = 3 • 10 -2 Ω • cm (-20 ÷ +180) 0 C 2 ρch2 = 3.5 • 10 -2 Ω • cm (0 ÷ +210) 0 C 3 ρch3 = 4 • 10 -2 Ω • cm (+50 ÷ +210) 0 C
When powering the distributed parameter sensor from a stabilized voltage source, the differential temperature coefficient of the sensitivity, taking into account the empirical temperature dependencies of K mc (T ) and R ch (T ) and relationships (4.7) and (4.11), is equal to:

Γ dp mc = Γ mcV - - Λ• A ch 1 +2A ch 2 •(T -T 0 ) 1+A ch 1 •(T -T 0 )+A ch 2 •(T -T 0 ) 2 - A ee 1 +2A ee 2 •(T -T 0 ) 1+A ee 1 •(T -T 0 )+A ee 2 •(T -T 0 ) 2 • R ch (T ) ρee(T ) 2+Λ• R ch (T ) ρee(T ) (4.28)
where

Γ mcV = - K B ( T 0 T ) 2 +2Kc( T 0
T ) 3 T 0 K A +K B T 0 T +K C ( T 0
= 10Ω • cm (-50 ÷ +200) • C 2 ρ ee 2 = 1Ω • cm (0 ÷ +300) • C 3 ρ ee3 = 0.5Ω • cm (0 ÷ +325) • C
The graph of Fig. 4.19 shows the dependence of the temperature T tc , when Γ dp mc = 0, on the specific resistance of the elastic element, calculated using formula (4.28) for the IP T design, in which P CH is formed by ion implantation of boron with a doping dose of 2•10 15 cm -2 and a parameter Hee a ≥ 0.3. The graph of Fig. 4.12 shows the calculated and experimentally obtained temperature dependences of the sensitive coefficient for designs with ρ ee 2 = 1Ω • cm, selected for the design of miniature pressure sensors. The parameter characterizing the additional temperature error in the temperature range (0 ÷ 300) • C is γ mc = 0.04 %/ • C.

Conclusions

1. The influence of minimizing the geometric dimensions of monolithic IPTs with a total area of the isolating p -n junction A p-n < 2 • 10 -3 cm 2 on the upper limit of the operating temperature range and the temperature dependence of the normalized null output M C has been studied. It has been experimentally confirmed that the upper limit of the operating temperature range depends on the design parameters: the perimeter-to-area ratio of the isolating p -n junction K p-n and the number of corners in the topological structure of p-type regions of M C, n p-n . Provided that A p-n < 2 • 10 -4 cm 2 , K p-n = 500 ÷ 700, n p-n ⩽ 8, the upper limit of the operating temperature range for IPTs with an isolating p -n junction corresponds to (+250 ÷ 300) • C.

2. The temperature changes of the electrophysical characteristics of P CH required

(T ) = R ch 0 1 + A 1 (T -T 0 ) + A 2 (T -T 0 ) 2 .
The approximation coefficients of the temperature changes K ch (T ) and R ch for the diffusional P CH with the average material resistance in the range ρch = (2 • 10 -2 ÷ 8 • 10 -2 ) Ω • cm and for boron implanted P CH with doping dose 2 • 10 15 cm 2 .

3. The electrical and constructional characteristics of IP T with distributed parameters were investigated to design small-sized sensors with a working temperature range of -60 • C to 325 • C, where the construction parameter Hee a ⩾ 0.3. The experimental dependencies of the sensitivity coefficient and input resistance of M C on the specific resistance of the material EE in the range of ρ ee = (0.1÷10) Ω•cm differ by no more than 10% from those calculated from the relations obtained during modeling in Chapter 2. The construction parameter ∆L, which determines the allowable approximation to the edge of EE, was experimentally determined to be △L ⩾ 200 µ. The working temperature ranges were determined based on the temperature changes of the electrical characteristics as follows:

ρ ee 1 = 0, 5Ω • cm 0 ÷ 325 • C ρ ee 2 = 1Ω • cm 0 ÷ 300 • C ρ ee 3 = 10Ω • cm -60 ÷ +200 • C 4.
To minimize the intrinsic error of small-sized sensors with a temperature working range of (0 ÷ 300) • C, a tuning method has been developed and experimentally studied, in which the adjustment of the conversion characteristic of IP T is carried out by changing the conversion coefficient of EE. The advantages are as follows: the electrical parameters of M C and the temperature working range of the sensor are not changed; the systematic component of the intrinsic error is reduced by more than 10 times.

5. The principles of minimization of additional temperature error of IP T with insulating p -n junction are formulated:

• for the case of sensor power supply from stabilized voltage source using experimentally obtained regular temperature changes of strain-sensitivity, input resistance MC, resistance of thin-film resistive elements made of RS -1004 material; developed thermal compensation scheme allowing IP T adjustment with high accuracy (less than 0.05%/ 0 C) in temperature range (0 ÷ 300) • C

• for the case of sensor feeding from stabilizing current source, using the regular temperature changes of electro-physical characteristics, the possibilities of "auto-thermal compensation" were investigated experimentally by using the selection of optimal values of specific resistance of material (1 ÷ 5)%; the following temperature ranges of the sensors with intrinsic error (1 ÷ 5)% were determined for the design of sensors: with diffusion

ρch1 = 3 • 10 -2 Ω • cm (-20 ÷ +180) 0 C ρch2 = 3.5 • 10 -2 Ω • cm (0 ÷ +210) 0 C ρch3 = 4 • 10 -2 Ω • cm (+50 ÷ +210) 0 C
with ion-doped boron implantation doping 2 • 10 15 cm 2 (0 ÷ 300) • C.

6. The method of thermocompensation sensitivity is proposed and tested experimentally, when the element adjusting the temperature dependence of the output signal IP T with distributed parameters are elastic elements with perfectly accurate information on the change in ambient temperature. Advantages of the method: high reliability in the range of high temperatures, because no additional regulating element is required, and parametric failure of the EE section is possible only simultaneously with its mechanical destruction.

CHAPTER 5

Creation of Samples of Small-Size Pressure and Low-Frequency

Acceleration Sensors

For rocket propulsion test systems designed for reusable complexes, there is a lack of means of obtaining information about mechanical parameters. In many cases, test conditions require obtaining information about processes and objects when the ambient temperature changes in the range of 0 -300 • C.

Obtaining accurate information about pressure fields is considered a problem . The range of measured pressures is from 0 ÷ 0.01 M P a to 0 ÷ 1 M P a. The intrinsic error of the sensor should not exceed ±1%.

The second problem is to obtain accurate information about the parameters of dynamic stability, dynamic overloads on nodes and force elements for strength assessment, as well as vibration modes of devices and systems. Range of measured accelerations from 0 ± 10g to 0 ± 30g. Frequency spectrum (0 ÷ 300) Hz. The intrinsic error of the LF accelerometer is less than ±5%.

Important requirements to the test execution conditions are considered to be the lowest level of perturbing mechanical impacts by the system elements on the conditions in the units and obtaining information about the processes and objects when the ambient temperature changes in the range (0 ÷ 300) • C. To solve such problems, hightemperature sensors with overall dimensions of 15 mm×15 mm×15 mm and weighing less than 10 grams are needed.

On the basis of the results of the studies stated earlier in Chapter 2 and Chapter 3, the designs were designed, prototypes were made and metrological characteristics of small-sized pressure and acceleration sensors, the appearance of which is shown in Fig. 5.1 and Fig. 5.2 were investigated for unit test systems.

Small-Sized High-Temperature Pressure Sensors

The sensors are designed to measure static and dynamic pressure from 0÷1 atm to 0÷10 atm at ambient temperatures (air, oxygen, naphthyl, etc.) in the range of (0 ÷ 300) • C. In calculating IP T P , the temperature changes R in (T ) and K ch (T ) were determined by dependences (4.22;77) and (2.19;19), where K A , K B , and K C from Table 4.1 are equal to K A = 10, K B = 60, and K C = -14. The temperature dependence of the specific resistance for KDB-1.0 plates (material EE) does not have sharp drops up to a temperature of 300 • C and at T 0 = 150 • C is determined as

ρ ee (T ) = 2.2 1 + 5.2 • 10 -3 (T -150) + 8.2 • 10 -6 (T -150) 2 [Ω • cm] (5.1)
Using the manufacturing method proposed in [START_REF] Tikhomirov | Research, development and improvement of manufacturing technology of integral transducers and sensors of energy parameters, including for control and regulation of parameters of technological processes of MEA production (Flexible manufacturing systems (FMS), Flexible manufacturing modules (FMP), etc[END_REF] , batches of model and experimental samples of IP T P SIAP 408 854.001 were produced at the enterprise P/Ya R-6668. Assembly of small-sized high-temperature sensors was carried out jointly by the enterprises P/Ya A-1891 and P/Ya R-6668.

Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer

The principle of operation and construction of the device (an inertial element that performs double differentiation of [elastic] displacement and a resistive element of resistance, made in the form of a monolithic silicon monocrystal) are well known [START_REF] Roylance | A miniature integrated circuit accelerometer[END_REF] . The new design, shown in Fig. 5.2 to Fig. 5.5, improves the metrological and operational characteristics of the known devices. The accelerometer consists of (Fig. 5.2) a measuring module (IP T M ) installed on a thermal expansion-matched elongation housing (BP α ) made of Kovar alloy 29NK. Electrical connection to the next device of the information-measuring system is provided by a flexible flat cable (F C) on a polyamide base with an electrical connector RPS1-7. The structural elements (DE) are made of monocrystalline silicon plates oriented in the (100) plane. The elastic element (EE) (see Fig. 4.13) consists of 28 cantilever beams with a length L, width D i , and thickness H ee , rigidly fixed on a ring The first part of the design, aimed at expanding the range of operating temperatures, is associated with the electrical insulation of the piezoresistive element (M C) using a p -n junction in the temperature range up to 200 • C while maintaining satisfactory conversion characteristics. In this formulation, the insulation failure criterion for M C is defined as a 1% change in sensitivity K mc due to shunting of the output resistance by the elastic element. This criterion can be met by designing M C with a sufficiently small area of the p -n junction. Chapter 4 shows the temperature behavior of the reverse current of the insulating p-junction as a function of the ratio of the perimeter to the surface area of the junction. Option #4 was chosen. Areas of M C were constructed for two options:

-Boron diffusion with average specific resistance values of P CH (where "autocompensation" of temperature changes in sensitivity can be expected in the range of (0 ÷ 200) • C when M C is powered by a stabilized current) of 0.035 Ω • cm; -For The second part consists of compensating for the strong influence of temperature on the coefficient of piezoresistive sensitivity without deteriorating the insulation of M C. At temperatures up to +200 • C, two compensation forms were chosen. One is compensation using the T CC scheme in the power supply circuit located on a separate DE. The second option is compensation of the temperature drift of the current bridge sensitivity, called "auto-compensation". Both options are discussed in Chapter 4.

To compensate for the sensitivity change of the accelerometer, a circuit (see Fig.

The surface resistance of diffusion-doped layers is 300 Ω/□, so they can be made with a small area of p-n junctions. The resistor circuit with such characteristics reduces the sensitivity compared to uncompensated M C by a factor of 1.5 for IP T with ion-doped piezoresistors and by a factor of 1.8 for diffusion-doped piezoresistors.

Self-compensation of IP T powered by a stabilized current is achieved at temperatures of 0 -200 • C. Fig. 5.2 shows the temperature behavior of the error parameter γ when compensated by the T CC thermistor bridge (curve 2), self-compensation with ion-doped piezoresistive channels (P CH) (curve 3) and diffusion-doped (curve 1). As can be seen from Fig. 2, when self-compensating, the error of the accelerometer for both types of IP T does not exceed 0.04%/ • C.

In a wide range of temperatures, air damping is preferable. For small sensors, damping should be provided in narrow gaps between the planes of the inertial element and the internal surfaces of the housing components SC (covers). In this accelerometer, silicon covers with internal cavities were used. For a specific design, the damping coefficient θ * , which characterizes the level of damping, is related to the geometric gap size w = (20 ÷ 80) • 10 -6 m by the empirical relationship θ * = 2 • 10 -11 (H ee -11 • 10 -6 ) (w -16 • 10 -6 ) , (5.4) where H ee = (15 ÷ 25) × 10 -6 m is the thickness of the elastic element.

The mechanical strength of the deformable component of the sensor element MSS is determined by two factors. The first factor is the reduction of geometric dimensions to values corresponding to [START_REF] Runyan | Silicon Semiconductor Technology[END_REF] . The second factor is the treatment of the surface of silicon by chemical etching in the process of manufacturing the elastic element [START_REF] Tikhomirov | Issledovanie, razrabotka perspektivnykh konstruktorsko-tekhnologicheskikh reshenii, obespechivayushchikh uluchshenie metrologicheskikh ehkspluatatsionnykh kharakteristik datchikov apparatury [Research and development of promising design and technological solutions that improve the metrological and operational characteristics of instrumentation sensors[END_REF] . The strength of the elastic element of such a configuration and with such surface treatment is on average 25 times higher than the level of working deformation (ε x = 4 • 10 -4 ).

Sensitivity adjustment is achieved by destroying strips with a laser. With this method, it is possible to independently adjust sensitivity to the mechanical input parameter and sensitivity to temperature changes. The method is also convenient in that after adjusting the elastic elements of the entire series of accelerometers for a certain input nominal, they are characterized by the same amplitude-frequency responses.

The sensitivity to acceleration components acting in the plane perpendicular to the measured component is due to the displacement of the center of mass of the inertial element in the MSS relative to the midplanes of the elastic element plates (see Fig. 5.2). This sensitivity can reach 15% relative to the measured component. Partial compensation of this error is achieved by installing IPTM on the wedge-shaped holder BP α , the angle α between the upper and lower surfaces of which is equal to the angle between the surface of the elastic element and the plane passing through the centers of the inertial element Ci and the plates Cp. The error caused by these acceleration components is reduced to 3%.

The carrier also performs the function of a mechanical separator of the silicon IPTM, protecting it from stresses caused by the attachment of the accelerometer and deformation of the object.

Specifications for the small silicon accelerometer are as follows: dimensions = 10 × 8 × 3 mm; weight = 1.5 gramm; acceleration ranges = 0 ± 15 g, 0 ± 30 g; sensitivity = 6.6 mV /g and 3.3 mV /g; transverse sensitivity 3%; operating frequency range = 0÷150 and 0÷300 Hz; basic error ⩽ 3%; operating temperature range = -60 to +200 • C; temperature compensation range = 0 ÷ +200 • C; additional temperature error components: temperature drift of initial output signal < 0.04%/ • C, temperature sensitivity drift < 0.04%/ • C; supply voltage = 10 V ; circuit input resistance = 800 ÷ 1000Ω.

Conclusions

1. Based on the physical and functional models of IPT developed in this work and the principles of their design identified, constructions were created, prototype samples were manufactured, and metrological characteristics of pressure and acceleration sensors were measured [START_REF] Tikhomirov | Ehksperimental'nye issledovaniya kharakteristik datchikov davleniya novogo pokoleniya [Experimental studies of the characteristics of the new generation of pressure sensors[END_REF] . The obtained technical characteristics meet the requirements imposed on the elements of control, monitoring, regulation sys-tems for research and development testing of products by the Ministry of General Machine Building.

2. Static-dynamic pressure sensors ranging from 0 ÷ 1 atm to 0 ÷ 10 atm with dimensions of ∅13 × 11 and weighing less than 10 g, containing monolithic IPTs with distributed parameters without isolating p -n junctions, are characterized by the intrinsic error of less than 1% and additional temperature error of less than 0.05 %/ • C in the temperature range of (0 ÷ 300) • C.

3. Low-frequency (0 ÷ 300Hz) acceleration sensors (0 ± 100 . . . 0 ± 300)M/c 2 with dimensions of 10mm × 8mm × 3mm and weighing less than 2g, containing a monolithic IPT A with an isolating p -n junction, are characterized by the intrinsic error of less than ±5% and additional temperature error from 0.06 %/ • C to 0.13 %/ • C. The temperature operating range is (0 ÷ 200) • C.

CHAPTER 6

Conclusion

1. The isolation model of M C elements of monolithic IP T with a depleted charge carrier layer p -n junction was studied, and the majority of regularities of the influence of physical and geometric parameters on the temperature dependence of insulation properties at temperatures above +100 • C were established. It was experimentally confirmed that due to the reduction of the p -n junction area, the ratio of perimeter to junction area, and the number of angles in the topological structure of M C elements, the upper limit of the working temperature range is determined by values above +200 • C. In the temperature range from 0 to 250 • C, the electro-physical characteristics of monolithic IP T elements with an insulating p -n junction manufactured by established technological processes were experimentally studied, and regular temperature dependencies of strain-sensitivity and resistance were determined.

2.

A physical and functional model of a deformation transducer with distributed parameters in the measuring circuit and elastic element is proposed, where P CH and CA are doped with impurities that increase the concentration level of major charge carriers EE, providing an upper limit of the working temperature range from 150 • C to 350 • C. Using the results of modeling and the experimentally obtained parameter Λ, which characterizes the redistribution of charge carrier current in the channels and volume of EE, the principles of designing transducers for other mechanical quantities were determined using the calculated parameter

H EE a ⩾ 0.3.
3. The effectiveness of minimizing intrinsic and additional temperature errors of small-sized sensors with a working temperature range of 0 -300 • C has been investigated and experimentally evaluated. To minimize the systematic component of intrinsic error, a precise tuning method has been developed and experimentally studied, in which the tuning of the IP T conversion characteristic is performed by changing the conversion coefficient EE. For the case of powering a sensor with a p -n junction (isolating M C from EE) from a stabilized voltage source, a temperature compensation scheme was developed using experimentally obtained regular temperature variations of the piezoresistive coefficient, M C input resistance, tuning diffusion resistance and tuning thin-film resistance (RS-1004 alloy), which allows the IP T to be fine-tuned over the 0 -+210 • C temperature range with high accuracy (less than 0.05%/ • C). For the case of powering a sensor with a p -n junction (isolating M C from EE) from a stabilized current source, the possibilities of "auto-temperature compensation" have been studied by selecting the average value of the specific resistance P CH and establishing temperature ranges of operation in the range of -20 -+210 • C using experimentally obtained regular temperature changes of the piezoresistive coefficient and output resistance M C. A precise method of sensitivity temperature compensation has been proposed and experimentally verified for temperature ranges of operation in the range of -60 -320 • C, where the element regulating the temperature dependence of the output signal IP T with distributed parameters is a part of the EE material with ideal information about temperature changes in the surrounding environment.

4. On the basis of the physical and functional models of IPTs substantiated in the work and the identified principles of their design, the designs, prototypes and measured metrological characteristics of pressure and acceleration sensors were created. The obtained technical characteristics meet the requirements for the elements of control, management and regulation systems for research and designbuild tests of the industry products.

2. 2 3 . 6

 236 Graph of dependence of T min and T max on resistivity ρ of silicon layers . 2.3 Temperature dependence of parameters of IP T on made according to 17 :(a) R in -input resistance M C; R IL - i isolation resistance p-n junction at V rb = 5V ; R EE i -series resistance of elastic element body;(b) K mc0normalized null output; K v mc -bridge sensitivity when supplied MC with stabilized voltage V in = 5V ; K i mc -bridge sensitivity when supplied MC with stabilized current I in = 5 mA . . . . . . . . . . . . . . . . . . 2.4 Schemes of conversion of input mechanical quantity into output electric signal for monolithic IPT: a) MC with lumped parameters; b) MC with distributed parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Configurations of the bridge circuit layers and elastic element in Fig.4 in 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Graph of the dependence of the gauge factor on the resistivity of uniformly doped P-type silicon layers . . . . . . . . . . . . . . . . . . . . 2.7 Dependence of the approximation coefficients of the temperature dependences of resistance on the resistivity (ρ l ) for silicon p-type: ✖diffusion-doped layers 43 (experimental data); ❍-diffusion-doped layers 38 (experimental data); -uniformly doped layers 15 (calculated data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Dependences of approximation coefficients (K A , K B , K C ) of temperature dependences of strainsensitivityfrom resistivity (ρ l ) for p-type silicon layers: • -uniformly doped layers 3 (calculated data); ▲ -uniformly doped layers 40 (experimental data) ✖ -diffusion layers) 38 (experimental data). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Temperature dependence of the lifetime of the majority carriers 6 . . . . 2.10 Temperature dependences of physical parameters of silicon elastic elements; (a) -deformation limits ε(T ) 27 ; (b) -differential temperature coefficient of linear expansion of silicon α Si l (T ), glass 7740 PYREX α IL l ( T) and oxide α S 1 O 2 l ( T); (c) -thermal conductivity coefficient of silicon λ T ( T) 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Reverse side of the silicon beam element of an accelerometer with silicon inertial mass 54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Topological structure of a symmetric four-branch bridge circuit. 1piezoresistive channel; 2-diffusion contact pad of p-type; 3-contact "Al-Si (p-type)". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Calculated dependences of reverse current density J rev of p-n junction IPT on temperature for different values of resistivity of elastic element ρ ee 3.3 Calculated dependences of permissible temperature T per values on the area of insulating p-n junction A p-n for different values of resistivity of elastic element ρ ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Temperature dependences of IPT sample parameters: a) I rev reverse current: -experimentally, -calculated ; b) K mc0 -normalized null output, K v mc -IPT bridge sensitivity when V in = 5 V stabilized voltage is fed to the MC, K i mc -IPT bridge sensitivity when I in = 5µA stabilized current is fed to the MC . . . . . . . . . . . . . . . . . . . . 3.5 Deformation transducer along the X-axis, selected for modeling the characteristics of the transducer with distributed parameters: a) topological structure of the IPT; b) -also, second projection, section along A -A; c) -equivalent diagram of the analog of the discrete model. . . . v Experimentally obtained dependences of the change in the coefficient Φ and the input resistance R dp mc on the design parameters for IPT with distributed parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 View of the beam force Test-IPT 5.E.2251.130.00.00.000. . . . . . . . . 4.2 Topological structures and geometrical parameters of MC on test-IPT force transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Dependence of the temperature instability parameter γ mc0 of the initial MC transfer coefficient on the contact size b c . . . . . . . . . . . . . . . 4.4 Dependence of insulating p-n junction reverse current density for MS #5: ✖ -with diffusion PCHs; ❍with ion-alloyed PCHs. . . . . . . . . 4.5 Temperature dependences of the reverse current density of p-n junction insulating ion-alloyed and diffusion contact areas MC: -calculated from (3.10) ■ -#1 ; ✚ -#2; ▲ -#4 ; • -#5; ✖ -#7 ; ❍ -#10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Dependences of approximation coefficients of temperature dependences of input resistance on average resistivity PCH, obtained from the research of diffusion channels PCH . . . . . . . . . . . . . . . . . . . . 4.7 Dependences of the K A ; K B ; K C approximation coefficients of the temperature dependences of the gauge factor PCH on the average resistivity PCH ρch , obtained from the research of the diffusion channels PCH . . 4.8 Topological structure and geometrical parametries Test-IPT pressure with distributed parameters 5.E.2251.205.00.00.000. . . . . . . . . . . 4.9 Dependences of variations of input resistance of MC with distributed parameters R dp in relative to its value for isolated R lp in on the resistivity EE -calculated; -experimental . . . . . . . . . . 4.10 Dependences of variations of strain factor of MC with distributed parameters K dp mc relative to its value for isolated K ch on the resistivity EE -calculated; -experimental . . . . . . . . . . . . . 4.11 Graphs of changes in the magnitude K mc0 (a) and temperature instability coefficient γ mc0 (b) of the initial transfer coefficient of the MC depending on the arrangement of the circuit on the elastic element. . . . the bridge sensitivity for the IPT with spaced parameters K dp mc (T ) and electrically isolated from the elastic element (K mcV (T )) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Tuning methods for integral piezoresistive transducers (IPT) . . . . . . 4.14 IPT wiring diagram with TCC . . . . . . . . . . . . . . . . . . . . . . 4.15 Calculated graph of resistance values TCC providing thermal compensation condition at temperature T = T 0 = 150 • C . . . . . . . . . . . . 4.16 Calculated graph of K tc0 values for different values of R tc rs , R tc si . . . . 4.17 Temperature dependences of the coefficient γ mcV when supplied powered from a stabilized voltage source:1-IPT without compensation circuit; 2 -IPT with TCC containing regulating resistors with TCR of different sign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.18 Temperature dependences of the bridge sensitivity K mcI when powered from a stabilized current source for the MC: -with diffusion channels; -with ion-alloy channels . . . . . . . . . . . . . . 4.19 Calculated dependence of the temperature, when Γ dp mc = 0, on the resistivity of the elastic element for an IPT with distributed parameters, where PCHs are formed by ion implantation of boron . . . . . . . . . . 5.1 Static-dynamic pressure sensor . . . . . . . . . . . . . . . . . . . . . . 5.2 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer. Mechanical Silicon Sensor (MSS). Topological drawing (Design Documentation SIAP.402139.001) . . . . . . . . . . . . . . . . 5.4 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer. Silicon covers (SC) perform the functions of thermocompensating circuits (T CC). Topological drawing (Design Documentation SIAP.402139.001) . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer. Silicon bottom cover (SC). Topological drawing (Design Documentation SIAP.402139.001) . . . . . . . . . . . . . . . . . . . . CHAPTER 1

Fig. 2 . 1

 21 Fig. 2.1 Block diagram of the conversion of a mechanical quantity into an electrical signal using a sensor with an integrated piezoresistor transducer (IPT). 1 -for inertial sensors; 2 -for IPT with distributed parameters.

Fig. 2 . 2

 22 Fig. 2.2 Graph of dependence of T min and T max on resistivity ρ of silicon layers

Fig. 2 . 3

 23 Fig. 2.3 Temperature dependence of parameters of IP T on made according to 17 :(a) R in -input resistance M C; R IL - i isolation resistance p-n junction at V rb = 5V ; R EE i -series resistance of elastic element body;(b) K mc0 -normalized null output; K v mc -bridge sensitivity when supplied MC with stabilized voltage V in = 5V ; K i mc -bridge sensitivity when supplied MC with stabilized current I in = 5 mA

Fig. 2 . 4

 24 Fig. 2.4 Schemes of conversion of input mechanical quantity into output electric signal for monolithic IPT: a) MC with lumped parameters; b) MC with distributed parameters.

Fig. 2 . 5

 25 Fig. 2.5 Configurations of the bridge circuit layers and elastic element in Fig.4 in 8

  (a) and (b) will take the form of the relation:

Fig. 2 . 6

 26 Fig. 2.6 Graph of the dependence of the gauge factor on the resistivity of uniformly doped P-type silicon layers

Fig. 2 . 7

 27 Fig. 2.7 Dependence of the approximation coefficients of the temperature dependences of resistance on the resistivity (ρ l ) for silicon p-type: ✖-diffusion-doped layers 43 (experimental data); ❍-diffusion-doped layers 38 (experimental data); -uniformly doped layers 15 (calculated data)

Fig. 2 . 8

 28 Fig. 2.8 Dependences of approximation coefficients (K A , K B , K C ) of temperature dependences of strainsensitivityfrom resistivity (ρ l ) for p-type silicon layers: • -uniformly doped layers 3 (calculated data); ▲ -uniformly doped layers 40 (experimental data) ✖ -diffusion layers) 38 (experimental data).

Fig. 2 . 9

 29 Fig. 2.9 Temperature dependence of the lifetime of the majority carriers 6

Fig. 2 .

 2 Fig. 2.10 Temperature dependences of physical parameters of silicon elastic elements; (a) -deformation limits ε(T ) 27 ; (b) -differential temperature coefficient of linear expansion of silicon α Si l (T ), glass 7740 PYREX α IL l ( T) and oxide α S 1 O 2 l ( T); (c) -thermal conductivity coefficient of silicon λ T ( T) 27

7 .

 7 The temperature range of the known experimental studies of the electrophysical characteristics of IP T is limited for diffusion +125 • C for ion-alloyed +100 • C. Using diffusion layers with ρch = (2 ÷ 8) • 10 -2 Ω • cm will reduce the P CH geometric dimensions and additional IP T temperature error when feeding M C with stabilized current. The study area of ion-alloyed layers should be limited by the doping dose 2 • 10 15 cm -2 , which provides the smallest variation of the P CH electrical resistivity.

Fig. 3 . 1

 31 Fig. 3.1 Topological structure of a symmetric four-branch bridge circuit. 1piezoresistive channel; 2-diffusion contact pad of p-type; 3-contact "Al-Si (p-type)".

)

  In the topological M C structure in Fig. 3.1, the geometrical parameter b is given a constant value equal to b = 40•10 -4 cm. For the calculations it is chosen that b = d ch , then changing the area of the insulating p-n junction is possible only by changing the length of P CH l ch = (a -b).

)( 5 ) 6 )

 56 The reverse bias voltage p -n junction and supply voltage M C is V rev = V in = 5V . The boundary values of the resistances EE are determined by the values: ρ ee1 = 20 Ω • cm, from the graph in Fig.9 the intrinsic conductivity temperature +150 • C; ρ ee1 = 0.5 Ω • cm is the calculated value of the breakdown voltage p -n transition in the EE volume, chosen equal to V br = 10 • V in from the ratio: V br = 10 • V in = 86 • ρ ee (3.9) ρ ee1 = 4.5 Ω • cm is the standard resistivity value of silicon wafers in IP T production. (Initial temperature value T 0 = 293K.

2

  is a parameter characterizing the concentration of the intrinsic charge carriers n i0 in the p -n junction region at temperature T = 293 K ; of minority charge carriers in the EE body at T = 293 K ; k = 1.38 • 10 -23 J/K -Boltzmann constant. Fig.3.2 shows the calculated dependences of J rev (T ) for the selected values of ρ ee on which dependences of the allowable temperature values T per on the area of insulating

Fig. 3 . 2

 32 Fig. 3.2 Calculated dependences of reverse current density J rev of p-n junction IPT on temperature for different values of resistivity of elastic element ρ ee

Fig. 3 . 4

 34 Fig. 3.4 Temperature dependences of IPT sample parameters: a) I rev reverse current:-experimentally, -calculated ; b) K mc0 -normalized null output, K v mc -IPT bridge sensitivity when V in = 5 V stabilized voltage is fed to the MC, K i mc -IPT bridge sensitivity when I in = 5µA stabilized current is fed to the MC

Fig. 3 . 5

 35 Fig. 3.5 Deformation transducer along the X-axis, selected for modeling the characteristics of the transducer with distributed parameters: a) topological structure of the IPT; b) -also, second projection, section along A -A; c) -equivalent diagram of the analog of the discrete model.

Fig. 3 . 6

 36 Fig. 3.6 Experimentally obtained dependences of the change in the coefficient Φ and the input resistance R dp mc on the design parameters for IPT with distributed parameters

. 1 )

 1 from the change in "Al-Si" contact area A c , equal to A c = b 2 c . At the known values of b min , a further decrease in the geometric dimensions of M C (i.e., the insulating p -n junction area) is associated with a decrease in the geometric parameters ((a -b) and d ch , which are related by the input resistance rating R in and the surface resistance R s of the P CH layer by the relation

Fig. 4 . 1

 41 Fig. 4.1 View of the beam force Test-IPT 5.E.2251.130.00.00.000.

Fig. 4 . 2

 42 Fig. 4.2 Topological structures and geometrical parameters of MC on test-IPT force transducer

Fig. 4 .

 4 Fig. 4.3 shows the dependence of the temperature instability coefficient of K mco on the value of b c when feeding M C with stabilized voltage. For pressure sensors with a

Fig. 4 . 3

 43 Fig. 4.3 Dependence of the temperature instability parameter γ mc0 of the initial MC transfer coefficient on the contact size b c .

Fig. 4 . 4

 44 Fig. 4.4 Dependence of insulating p-n junction reverse current density for MS #5: ✖with diffusion PCHs; ❍with ion-alloyed PCHs.

Fig. 4 . 5 10 Fig. 4 . 6

 451046 Fig. 4.5 Temperature dependences of the reverse current density of p-n junction insulating ion-alloyed and diffusion contact areas MC: -calculated from (3.10) ■ -#1 ; ✚ -#2; ▲ -#4 ; • -#5; ✖ -#7 ; ❍ -#10

Fig. 4 . 8

 48 Fig. 4.8 Topological structure and geometrical parametries Test-IPT pressure with distributed parameters 5.E.2251.205.00.00.000.

Fig. 4 . 9

 49 Fig. 4.9 Dependences of variations of input resistance of MC with distributed parameters R dp in relative to its value for isolated R lp in on the resistivity EE -calculated; -experimental

Fig. 4 .

 4 Fig. 4.10 Dependences of variations of strain factor of MC with distributed parameters K dp mc relative to its value for isolated K ch on the resistivity EE -calculated; -experimental

4

 4

  .13): by anisotropic etching of the silicon wafer on the flat side elastic elements and inertial mass regions are formed. By anisotropic etching of the wafer on the flat side the EE regions are divided

Fig. 4 .

 4 Fig. 4.11 Graphs of changes in the magnitude K mc0 (a) and temperature instability coefficient γ mc0 (b) of the initial transfer coefficient of the MC depending on the arrangement of the circuit on the elastic element.

Fig. 4 .

 4 Fig. 4.12 Calculated ( ) and experimentally obtained () temperature changes of the bridge sensitivity for the IPT with spaced parameters K dp mc (T ) and electrically isolated from the elastic element (K mcV (T ))

Fig. 4 .

 4 Fig. 4.15 Calculated graph of resistance values TCC providing thermal compensation condition at temperature T = T 0 = 150 • C

Fig. 4 .

 4 Fig. 4.17 Temperature dependences of the coefficient γ mcV when supplied powered from a stabilized voltage source:1-IPT without compensation circuit; 2 -IPT with TCC containing regulating resistors with TCR of different sign.

Fig. 4 .

 4 Fig. 4.18 Temperature dependences of the bridge sensitivity K mcI when powered from a stabilized current source for the MC:-with diffusion channels; -with ion-alloy channels

Fig. 4 .

 4 Fig. 4.19 Calculated dependence of the temperature, when Γ dp mc = 0, on the resistivity of the elastic element for an IPT with distributed parameters, where PCHs are formed by ion implantation of boron

Fig. 5 .

 5 Fig. 5.1 Static-dynamic pressure sensor

Fig. 5 . 2

 52 Fig. 5.2 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer

Fig. 5 . 3 Fig. 5 . 4

 5354 Fig. 5.3 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer. Mechanical Silicon Sensor (MSS). Topological drawing (Design Documentation SIAP.402139.001)

Fig. 5 . 5

 55 Fig. 5.5 Integral Single-Component Inertial Accelerometer with Piezoresistive Transducer. Silicon bottom cover (SC). Topological drawing (Design Documentation SIAP.402139.001)

4 .

 4 14 and Fig.5.2) is applied, which is constructed as a thermosensitive bridge with two arms with positive T CR and two arms with negative T CR, connected in the diagonal with M C. The arms of the thermosensitive circuit are characterized by the following relationships: diffusion dopingR p 1 (T ) = R p 1 0 1 + 3.4 • 10 -3 ( T -T 0 ) + 2.3 • 10 -6 ( T -T 0 ) 2 (5.2) thin film from RS1004 R p 2 (T ) = R p 2 0 1 -2.7 • 10 -3 ( T -T 0 ) + 7.3 • 10 -6 ( T -T 0 ) 2

  Then the conversion functions of the input mechanical quantity ϕ in to the output electrical signal V out are defined by relations in which there are fewer factors influencing

	4. A promising design for small-size high-temperature sensors is an IPT design with
	monocrystalline silicon EE-RB and piezoresistive channels connected and elec-
	trically insulated from each other by a layer of glass matched to the silicon by
	the coefficient of thermal expansion. However, to develop SGS-IPT with satis-
	factory metrological characteristics new design and technological solutions are
	required.
	2.2.2 Monolithic IPTs with Isolation of MC Elements by a P-N Junction Layer and
	without an Isolation Layer
	Most monolithic p-n junction isolated IPT structures contain a monocrystalline silicon
	sensor (M SS) consisting of a base, elastic element, channel isolation layer, piezoresis-
	tive channels, resistive channels, control and compensation elements, i.e. "RB -EE -
	IL -P CH". On the planar side, the silicon structure "RB -EE -IL -P CH"
	is protected by a masking layer SiO 2 , on which aluminum contact pads and conduc-
	tive tracks are formed. Considering that in the conventionally accepted IPT structure
	(see Fig. 2.1) the RB, EE, IL, PCH elements are a conventional silicon monolith, the
	measurement conversion should be considered as shown in Fig. 2.4.(a).

Table 4 .

 4 .2 and Table 4.3. 2 IPT with lumped parameters for diffusion channels.

	#	Resistivity	Operating Temperature Ranges

Table 4 .

 4 3 IPT with lumped parameters for Ion-alloyed channels.

	#	Dose of doping	Operating Temperature Ranges
	1 N id = 2 • 10 15 cm -2

Table 4

 4 -n junction. Operating temperature ranges for IP T with distributed parameters without isolating p -n junction are presented in Table4.4

	T ) 2	(4.29)

LIST OF TABLES

Based on the results of statistical processing of the measurements on undivided silicon wafers, the smallest scatter of input resistances R in , less than ±2.5% and normalized null output K mc0 less than ±1.2 mV /V are determined for M C#7 and M C#10. These structures are also characterized by the lowest average values of K mc0 , equal to +1.2 mV /V and -1.2 mV /V , respectively. The values of approximation coefficients of temperature dependences of sensitivity and resistance for topological structures M C with ion-alloyed P CH are given in the table 4.1.

Monolithic IPT with Distributed Parameters

A characteristic feature of monolithic IP T design with distributed parameters is electrical connection of elastic element volume to M C by redistribution of charge carrier for diffusion PCH is expected at ρ ee < 1 • 10 -3 Ω • cm, but due to physical limitations in the form of the maximum solubility of boron, it is not achievable. Condition (b) is not realized (as can be seen from the graph in Fig. 4.7). Similar conclusions apply to IPT with ion-implanted PCH (see Table 4.1). The minimum calculated values of γ obtained from experimental data from the graph in Fig. 4.7 and in Table 4.1 are: for diffusion channels 0.13% • C, for ion-implanted channels 0.12 %/ 0 C.

The experimental temperature dependence for the diffusion resistor R looks as follows:

The transformation function of the IP T with T CC input mechanical value ε x 0 into the output electrical signal V out is determined by the relationship:

K tc (T ) is the coefficient of transformation of the stabilized voltage of the source V input into the temperature-dependent power supply voltage M C V in (T ). For the IP T circuit in Fig. 4.14 from [START_REF] Levshina | Ehlektricheskie izmereniya fizicheskikh velichin: (Izmeritel'nye preobrazovateli)[END_REF] , the conversion coefficient is equal to:

If the temperature dependence K mc (T ) is defined by a second-degree polynomial (2.19), then the conversion function (4.18) for the IP T circuit with T CC in Fig. 4.14 is:

Given relations (4.12), (4.18), and (4.19), the differential temperature sensitivity coefficient for IP T with T CC, from (4.11) is

The design of a beam force transducer 5E.2251.130.00.00.000 (see Fig. 4.1) was selected for the calculation and modeling of the IP T circuit with T CC. The input resistance of the IP T with ion-implanted P CH at T = 25 • C is R in = 1000 Ω. Taking into account the parameters in Table 4.1, the temperature changes of R in (T ) are determined by the experimentally obtained dependence:

The values of the parameters R tc * rs , R tc * si , and K * tc0 at normal conditions (T = 25 • C) providing thermocompensation Γ tc mcV = 0 at temperature T = T 0 = 150 • C are determined by the "golden section" method of minimization [START_REF] Rekleitis | Optimizatsiya v tekhnike[END_REF] . Fig. 4.15 shows the calculated graph of T CC resistance values that satisfy the condition Γ tc mcV = 0 at temperature T = T 0 = 150 • C. From equation (4.18) and the graph in Fig. 4.16, which presents the calculated values of K tc0 for different values of R tc rs , R tc si , it can be seen that when using