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Keywords: SiGe HPT, microwave-photonics, Silicon-based photodetectors, phototransistor, opto-microwave performances, OM-SNOM

The influence of the lateral scaling such as emitter width and length on the frequency behavior of SiGe bipolar transistor is experimentally studied.Electrical transistors of different emitter sizesare designed and fabricated by using a commercial bipolar transistor technology. The effect of peripheral current and collector current spreading on electrical bipolar transistor performances are analyzed in regards to the state of the art. Furthermore, the lateral scaling effect on SiGe phototransistor electrical and opto-microwave frequency behavior is studied. The impact of the lateral flow of photo-generated carriers toward the optical opening in phototransistor structure is investigated. Moreover, the two dimensional carrier flow effect on the opto-microwave frequency behavior of the phototransistor is characterized through opto-microwave Scanning Near-field Optical Microscopy (OM-SNOM)measurements, in the course of which the intrinsic parameters such as transit time and junction capacitances are extracted over the surface of the phototransistor.An intrinsic optical transition frequency of 6.5 GHz is measured for 10x10 μm 2 .

I. INTRODUCTION

Short distance optical-communication systems encourage the development of optoelectronic components on a Silicon platform. In particular, ultra-low-cost silicon based optoelectronic devicesare highly desirable for Radio-over-Fiber (RoF) applications within buildings and houses [START_REF] Viana | Hybrid photo-receiver based on SiGe heterojunction photo-transistor for low-cost 60 GHz intermediatefrequency radio-over-fibre applications[END_REF] [START_REF] Guillory | 60GHz Intermediate Frequency over Fiber using a passive Multipoint-to-Multipoint architecture[END_REF]. SiGe Heterojunction bipolar Phototransistors (HPT) is one of the optoelectronic device that are recently proposed for a direct integration with a high speed SiGe technologies using standard bipolar transistors [START_REF] Tegegne | Substrate diode effect on the performance of Silicon Germanium phototransistors[END_REF][4] [START_REF] Polleux | An SiGe/Si Heterojunction Phototransistor for Opto-Microwave Applications: Modeling and first Experimental Results[END_REF][6] [START_REF] Egels | Design of an optically frequency or phase-controlled oscillator for hybrid fiber-radio LAN at 5.2 GHz[END_REF][8] [START_REF] Lai | High-Responsivity Photodetector in Standard SiGeBiCMOS Technology[END_REF].

Phototransistors, which incorporate a PIN photodiode and a transistor in a single device, benefit from both photo-detection and internal amplification of the structure. Thus, it avoids the need of a Trans-impedance Amplifier (TIA) as Manuscript received November 27, 2017.This work was partially supported by the French government in the framework of the FUI8 ORIGIN project (Optical-Radio Infrastructure for Gigabit/s Indoor Networks). Z.G. Tegegne and J.L.Polleuxare with the Université Paris Est -ESYCOM laboratory (EA2552), ESIEE Paris, UPEM, Le Cnam,Cité Descartes, BP 99, 93162 Noisy-le-Grand Cedex, France (e-mail: tegegnez@esiee.fr, jl.polleux@esiee.fr).

previouslystudied based on InP/InGaAs HPTs [START_REF] Kim | InP/InGaAsunitravelling carrier heterojunction phototransistors[END_REF] [START_REF] Leven | InP-based double-heterostructure phototransistors with 135 GHz optical gain cutoff frequency[END_REF] and recently with SiGe HPTs [START_REF] Egels | Design of an optically frequency or phase-controlled oscillator for hybrid fiber-radio LAN at 5.2 GHz[END_REF][12] [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. SiGe HPTs were recently successfully used in a 3 Gbps signal radio-over-fiber transmission of IEEE 802.11.3c signals at 5 GHz [START_REF] Viana | Hybrid photo-receiver based on SiGe heterojunction photo-transistor for low-cost 60 GHz intermediatefrequency radio-over-fibre applications[END_REF].

To fabricate the HPT, the heterojunction bipolar transistor (HBT) structure is mostly enlarged, with the emitter contact limited to its original size, thus creating an optical window opening for a vertical [START_REF] Rosales | Design and implementation of SiGe HPTs using an 80GHz SiGe bipolar process technology[END_REF] [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. The optical window can be designed either by extending only the base and collector layers [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF] or by extending thebase, emitter and collector layers [START_REF] Rosales | Design and implementation of SiGe HPTs using an 80GHz SiGe bipolar process technology[END_REF]. Thus, from the geometrical point of view, the lateral dimensions of the HBT are modified to fabricate the HPT. Therefore, the frequency behavior of the HPT is modifiedversus its active layers length and width.

In general the speed of semiconductor devices tends to improve as the device dimensions shrink [START_REF] Rieh | SiGe Heterojunction Bipolar Transistors and Circuits Toward Terahertz Communication Applications[END_REF]. However, according to [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF], at a given minimum emitter width, the reduction of the emitter length leads to a significant reduction of speeddue to the difficulties of the electron flow whereas doubling the emitter width significantly increases the speed.Our laboratory presented the first single layer SiGe HPT in 2003 [START_REF] Polleux | A Strained SiGe layer Heterojunction BipolarPhototransistor for Short-Range Opto-Microwave Applications[END_REF] and we have illustrated the impact of the substrate photo-current on the speed of the HPT in [START_REF] Tegegne | Substrate diode effect on the performance of Silicon Germanium phototransistors[END_REF] by using the same SiGe HPT topology. This paper is a furtherance of our previous works that explores further the frequency response limitations of the device. The main focus of this work is to envisage the lateral scaling of SiGe HPTs in order to improve their frequency behavior; and to analyses thesources of discrepancyto electrical HBT.

This paper is organized as follows. In section II describes the phototransistor structure under study, andSection III presents both vertical and lateral scaling impacts on the speed performance of the HPT. Then, Section IV focuses on the investigation of the 2-D carrier flow effects on the optomicrowave frequency behavior of the HPT via experimental results. Phototransistor scaling limitations and design rules are presented in Section V. The final section draws a conclusion on phototransistor design aspects to improve its optomicrowave frequency behavior.

II. SIGE/SI HPT STRUCTURE UNDER TEST

The SiGe HPT is fabricated using standard SiGe2RF HBT technology from Telefunken [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. This heterojunction bipolar transistor technology is used in wireless communication systems. The minimum emitter size on the layout of 0.8x1. [START_REF] Polleux | A Strained SiGe layer Heterojunction BipolarPhototransistor for Short-Range Opto-Microwave Applications[END_REF] HBT of this technology attain electrical f f max up to 90 GHz. This enables circuits working above 10 GHz and potentially up to 60 GHz in some [START_REF] Liu | 33-43 GHz and 66-86 GHz VCO With High Output Power in an 80 GHz SiGe HBT Technology[END_REF]. The general scheme of the HBT cross in Figure 1.

Figure 1: Schematic cross-section of SiGe2RF technology from Telefunken

The process parameters of the standard SiGe2RF HBT technology are not modified to fabricate This ensures compatibility with the technological process and potential integration of circuits including opto radio-frequency parts.

The basic HPT structure is designed by extending simultaneously the emitter, base and collector layers of the reference HBT [START_REF] Rosales | Design and implementation of SiGe HPTs using an 80GHz SiGe bipolar process technology[END_REF]. A cross-section of the photo structure is given inFigure 2. This HPT is essentially one large HBT with emitter contactrestricted to the edge side of the emitter. Several phototransistorshave been study with square optical windows of 10x10 μm 2 , 20x20 µm², 30x30 µm², 40x40 50x50 µm². The base is made of ~40-80 nm thin abrupt SiGe layer with Ge content in the range of 20-25 doping in the range of 10 19 cm -3 as inferred from static measurements and physical simulation comparison with earlier 50 GHz SiGe HBT generation [START_REF] Polleux | An SiGe/Si Heterojunction Phototransistor for Opto-Microwave Applications: Modeling and first Experimental Results[END_REF] [START_REF] Moutier | Frequency response enhancement of a single strained layer SiGe phototransistor based on physical simulations[END_REF] typically 300-400 nm thick and low doped. A p+ guard ring connected to the ground is surrounding the substrate region and creates a homo-junction at the interface with the silicon substrate.

Figure 2: Simplified schematic cross-section of an extended Emitter Base Collector HPT

In this paper, HBTs and HPTs are emitter configuration. All RF measurements under 50Ω load conditions on the base and coll through 100µm GSG RF probe.

III. SCALING EFFECT ON ELECTRICAL

In this section, we studythe impact of the emitter length and width on the radio-frequency (RF) performance of HPT. For this purpose,we have fabricated seven different HBTs GHz in some configurations The general scheme of the HBT cross-section is shown

section of SiGe2RF technology from

The process parameters of the standard SiGe2RF HBT fabricatethe phototransistors. This ensures compatibility with the technological process and of circuits including opto-electronic and

The basic HPT structure is designed by extending simultaneously the emitter, base and collector layers of the section of the phototransistor . This HPT is essentially one large restricted to the edge side of the have been fabricated for this 3x3 µm², 5x5 µm², µm², 40x40 µm² and nm thin abrupt SiGe 25 % and with high pas inferred from static s and physical simulation comparison with [START_REF] Moutier | Frequency response enhancement of a single strained layer SiGe phototransistor based on physical simulations[END_REF]. The collector is nm thick and low doped. A p+ guard ring connected to the ground is surrounding the substrate region junction at the interface with the p-doped section of an extended Emitter are used in common . All RF measurements are performed load conditions on the base and collector ports EFFECT ON ELECTRICAL PERFORMANCES the impact of the emitter length and performance of HPT. For we have fabricated seven different HBTs having an emitter width (along x-axis) of lengths (along y-axis). We have also fabricated s with square optical window having a)

The impact of emitter length on the speed Emitter length variation m Therefore, looking for the optimum emitter length is design high speed HBT. The emitter delay (τ EC ) can effectively represent scaling on f T and f max as they are linked .

1 1 2 2 T EC f π τ π τ = = ⋅ ⋅ ⋅ ⋅ ⋅ + With τ F =C BC .(R E +R C )+ τ b + τ max 8 T BC B f f C R π =
where τ F is the forward transit time, voltage at low injection, C EC emitter-base and collector-base capacitances the depletion and parasitic capacitance dynamic emitter and collector resistances, respectively base, emitter and base time delay. These parameters are highly affected by both vertical and lateral scaling of the transistor.

The HBT can be viewed as an emitter and a peripheral transistor arou in Figure 3. According to [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF] is the sum of the intrinsic component I carriers within the emitter window) and external component I (due to lateral injection of carriers at the emitter periphery). Reducing the emitter size leads to an increase in the peripheral length-to-area ratio as shown in of the emitter periphery on the transistor behavior increases as the perimeter-to area ratio increases due to the contribution of the peripheral carriers in the total current particular it can highly influence the transistor properties as the total transit time, the junction capacitance and resistance and hence f T . axis) of 0.9 µm and different emitter axis). We have also fabricated seven HPTs square optical window having different dimensions.

Figure 3: Schematic a) cross-section and b) top view of the length L and width l to illustrate the influence of the peripheral region over the extension ξ.

The impact of emitter length on the speed

variation modifies the HPT/HBTspeed. , looking for the optimum emitter length is crucial to T. The emitter-to-collector transit time represent the effect of the device they are linked by equations( 1)and (3) [START_REF] Viana | Hybrid photo-receiver based on SiGe heterojunction photo-transistor for low-cost 60 GHz intermediatefrequency radio-over-fibre applications[END_REF] 1

EC F C k T C q I π τ   ⋅ ⋅ ⋅ ⋅ +   ⋅   (1)
+

τ e + τ bc (2) (3)
is the forward transit time, k.T/q is the thermal EC = C BE +C BC, withC BE and C BC are base capacitances (which includes parasitic capacitances), R E and R C are the dynamic emitter and collector resistances, τ b , τ e and τ bc are base, emitter and base-collector depletion transit time delay. These parameters are highly affected by both vertical and lateral scaling of the transistor.

The HBT can be viewed as an intrinsic transistor under the a peripheral transistor around the emitter as shown [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF][20] [START_REF] Walkey | Predictive Modelling of Lateral Scaling in Bipolar Transistors[END_REF], the collector current I C component I i (due to the injection of in the emitter window) and external component I e (due to lateral injection of carriers at the emitter periphery). Reducing the emitter size leads to an increase in the peripheral area ratio as shown in Figure 5. Hence the influence of the emitter periphery on the transistor behavior increases as to area ratio increases due to the contribution of al carriers in the total current [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF][20] [START_REF] Walkey | Predictive Modelling of Lateral Scaling in Bipolar Transistors[END_REF]; in particular it can highly influence the transistor properties such as the total transit time, the junction capacitance and resistance

section and b) top view of the HBT of length L and width l to illustrate the influence of the peripheral

Figure 4shows the experimental result of the maximum values of f T and f max versus the emitter length. We recall the emitter width is kept constant at l=0.9 µm. The emittercollector voltage is fixed Vce=3.5 V in this measurement. Indeed, both frequency characteristics are extracted by extrapolating respectivelythe device current and power gain. A significant improvement of f T could be achieved through vertical scaling of the base, emitter and collector layers, as it leads to a significant reduction of transit time [START_REF] Hafez | Vertical Scaling of 0.25-"m Emitter InP/InGaAs Single Heterojunction Bipolar Transistors with fT of 452 GHz[END_REF]. Indeed, in this study all the fabricated HBTs have the same vertical stacks, doping levels, vertical dimensions and material concentrations. Thus, only the lateral dimensions impactthef T values.

For a given emitter width of 0.9µm, the cut-off frequency f T increases with the emitter length from 3 µm to 20 µm before keeping constant from 20 µm to 50 µm (Figure 4). This augmentation can be attributed to the lower emitter perimeterto-area ratio for longer emitter size (shown in Figure 5) that minimizes the relative contribution of the peripheral transit time to the total transit time.The peripheral carriers are far from the metal contacts as compared to the areal carriers and hence its transit time is larger.Thus, the peripheral component is more influent for a smaller emitter length as presented in Figure 5. In other words, the reduction of the emitter length L increases the ratio between the external and intrinsic current components, and as the path of peripheral carriers to the collector is longer, the associated transit time is higher.

The decrease of f max as the emitter length increases, as shown in Figure 4, can be ascribed to the increase of the capacitance with emitter size. Itis larger than f T at low emitter length; according to equation(3), this indicates a low value of R B .C BC product that is explained by a low surface capacitance.On the other hand, theR B .C BC product is supposed to be constant with emitter length variation, but the experimental result shows that the variation of the device capacitance is indeed faster than the base resistance. f max is smaller for emitter length equal to 3 µm than the one for 5 µm. This is due to the lower value of f T for 3 µm long HBT compared to 5 µm HBT.

Figure 6represents

the variation of f T as a function of the collector current density for different emitter length HBTs. At high injection level (current densities above 1.5 mA.cm -2 ) all the curves are overlaid; this confirms that the injection level is mostly controlled by the doping levels which are the same for all HBTs. The maximal f T values are all obtained in the same medium current density region (around 0.7 mA.cm -2 )and increase with the emitter length.Indeed, the level of f T peak value is controlled by peripheral carrier contribution leading to a significant f T reduction for small emitter length.

5: The perimeter to area ratio of various size HBTs versus emitter length with a constant emitter width l = 0.9 µm

Figure 6: f T versus collector current density for different emitter length HBTs with a constant emitter width of 0.9 µm

Three regions can be distinguished inFigure 6: 1. Low current densities:at a very lowcurrent density, f T quicklyincreases with the collector current density as the junction capacitance reduces withthe dc supply. As the transit time of the electrons injected at the peripheryis larger than the internal injected electron transit time, the value of f T at low current density is lowerfor smaller emitter size (smaller emitter length has more peripheral electrons than the internal electrons). 2. Medium current densities:this is the region before the critical current density which is defined as the onset of high injection in [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF] where f T reaches its peak.As the intrinsic conductance decreases, the capacitance charging time becomes smaller than the forward transit time. As a consequence, the device speed is mainly limited by both areal and peripheral transit times. The effect of the peripheral transit timeis predominating in device whose emitter length is smaller than 20 µmas the peripheral carriers are numerous [15][20].In larger emitter size HBTs (L>= 20µm), the peripheral carriers are negligible and hence the speed is limited by areal transit time. 3. High current densities:in this region, not only the peripheral injection is responsible for the quick roll-off of f T , but also the emitter current crowding and the current spreading in the collector region (shown in Figure 7) [14] [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF]. At high current densities (above 1.5 the reduction inf T is observed for all transistors and similar values are obtained whatever the emitter length is

b) Impact of optical window size on

An HPT is a transistor with an optical opening for light injection,as described in section II. The extended part of the phototransistor (optical window) modifies the electrical behavior of the transistor due to additional parasitic related to the increasein emitter width.

Figure 8:f T-HPT , f T-HBT and f max-HPT as a function of emitter length L for a constant emitter width of l=0.9 µm. For HPTs, the optical window W and emitter length L as shown in dimension whereas for HBTs W=0 µm along x

Figure 8 shows f T-HPT , f T-HBT and f max-HPT emitter length L. f T-HPT and f T-HBT are extracted from the HPT (where the optical window W=L along x and y axes see 9) and HBT (where W=0 µm along x-axis for the same L respectively. The maximum of f T-HPT appears for a width of 10 µm. In the HPT case, the increase in emitter length is connected to the increase in the optical window a square shape. The electron path from th collector contact is then increased by the width W. The related R C resistance is thus almost constant (the path is wider also longer) and the capacitances increase decrease of f T-HPT as the optical window widens is due R C .C EC term influence which become predominant structure. The smaller values for width below 10 explained by the influence of the peripheral carriers, including lateral path region Δ and collector current spreading effect HPT as a function of the are extracted from the HPT along x and y axes see Figure axis for the same L) appears for a width of In the HPT case, the increase in emitter length is connected to the increase in the optical window size W, as it is a square shape. The electron path from the emitter to the collector contact is then increased by the width W. The related the path is wider but increase. Therefore, the as the optical window widens is due to the predominant in HPT . The smaller values for width below 10 µm are nce of the peripheral carriers, including lector current spreading effect (see Figure 9), whose impact is higher with smaller window size.

On the other hand, f max-HPT size increases. This is due to the base resis collector junction capacitance increase with the optical window size.

In the HPT structure, we believe that the total optical window size (see Figure 9) may not act electrically as an active transistor. We believe that the area under the emitter contact may be the only active area of the transistor with however a partial spreading of the electrical active region in its vicinity into the optical window. H area of the transistor is modulated in size due to the dc supply bias. That means due to the dc bias the effective active region of the transistor could be extended into the optical window as shown inFigure 9 by the lateral extension region region is actually a consequence ofthe inhomogeneity of the base-collector potential due to the asymmetrical design of emitter-base-collector contacts. The extension of the electrical region, ∆, is also dependent on the optical window size increases as the size decreases. As a result, the peripheral carrier effect mentioned for HBT structure is increased in HPT case due to this additional lateral path Δ and the increase of the collector current spreading angle α towards the optical window ( 9. In this region, the carriers move both vertically and laterally hence the transit time to reach their respective contacts is increased. At the same time, the collector curren also enhanced compared with HBT having the same length. The junction capacitances increase along with the extended active layers. Hence the cutoff frequency could decrease. whose impact is higher with smaller window HPT decreases as the optical window size increases. This is due to the base resistance and basecollector junction capacitance increase with the optical In the HPT structure, we believe that the total optical ) may not act electrically as an active transistor. We believe that the area under the emitter contact may be the only active area of the transistor with however a partial spreading of the electrical active region in its vicinity into the optical window. Hence the effective active area of the transistor is modulated in size due to the dc supply bias. That means due to the dc bias the effective active region of the transistor could be extended into the optical window as by the lateral extension region Δ. This region is actually a consequence ofthe inhomogeneity of the collector potential due to the asymmetrical design of cts. The extension of the electrical , is also dependent on the optical window size [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. It increases as the size decreases.

cross-sectional and b) top view of the transistor that indicates the impact of the peripheral region ξ, the collector current spreading region θ and lateral extension into the

As a result, the peripheral carrier effect mentioned for HBT structure is increased in HPT case due to this additional lateral and the increase of the collector current spreading towards the optical window (α>θ) as shown in Figure . In this region, the carriers move both vertically and laterally hence the transit time to reach their respective contacts is increased. At the same time, the collector current spreading is also enhanced compared with HBT having the same length. The junction capacitances increase along with the extended active layers. Hence the cutoff frequency could decrease. decreases versus emitter length below unlike the τ EC-HBT , the τ EC-HPT increases length higher than 10 µm. This is explained term becomes predominant. The junction capacitance also increases with optical window size increases.

Comparing HBT and HPT: According to

forward transit time should decreased for a given emitter length. In other words, the forward transit time in HPT should be smaller than in HBT as the emitter width of the HPT is enlarged to create the optical window for a given emitter length. However, the forward transit time in HPT is larger than in HBT. This can be explained by the fact that, in a phototransistor structure addition to the peripheral current and collector current spreading effects, the lateral extension result the lateral path length for the electrons emitter to the sub-collectordominates path length, which thusincreasesthe overall transit time HPT structure. These values can be easily extracted from a collector time delay (τ EC ) versus the junction capacitanceis and the forward transit time isgiven . The extracted values of the HBT and HPT as a Figure 10. We recall by keeping the emitter width to whereas for HPTsthe the emitter length L are Figure 10, we draw the rapidly decreases for hus, it indicates that the carrier is higher with forward transit time slightly decreases as the emitter length increases from 10 µm to he junction capacitance increases as the size Similar to the HBT, the transit time (τ EC-HPT ) itter length below 10µm. However, increases further for emitter . This is explained by the R C .C BC The junction capacitance also increases with optical window size increases.

According to [START_REF] Schroter | PhysicalModelingof Lateral ScalinginBipolar Transistors[END_REF], the should decreased versus emitterwidth

In other words, the forward sit time in HPT should be smaller than in HBT as the emitter width of the HPT is enlarged to create the optical However, the forward transit time in HPT is larger than in HBT. This can be phototransistor structure,in rent and collector current extension Δ takes place. As a for the electrons between the dominates over the vertical the overall transit time in

: The extracted electrical transit time and junction length L for HBT (with

For the HPT structure, the extracted capacitance is supposed to have a parabolic shape with respect to the emitter length (due to the square optical window square of the emitter length). However, the electrical area of the HPT is restricted to the area situated emitter contact (which is 0.9µm extension towards the optical window (indicated by Figure 9). Thus, the capacitance is directly related by (0.9+∆)*L and varies linearly

IV. 2-D CARRIER FLOW EFFECT ON THE MICROWAVE FREQUENCY

Theopto-microwave gain (Gom) of the HPT ratio of the HPT output signal power to the output power of a photodiode with a 1A/W responsivity and loaded by 50 [5][13].This is of particular use as it is equal to the square of the HPT responsivity (so the same loading condition.It can be deduced from the S measurement [5][13]. To characterize the opto behavior of the HPTwe follow the measurement test bench set up described in [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. Figure 11 shows the Gom versus frequency of 10x10 optical window size HPT. The mode) is obtained by setting the photodiode mode (PD mode) 0 V and Vce=3 V. The substrate contribution is removed according to [START_REF] Tegegne | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF].

Optical transition frequency (f the Gom of the HPT in phototransistor mode is equal to the low frequency Gom in photodiode mode as shown in 11. Compared tof T , f Topt is influenced by additional terms related to the photo-detection mechanism. pure electrical effects (such as the peripheral carrier effects), theopto-microwave limited by the transit time of the photo the increase injunction capacitance mechanism. Under illumination condition the photo electrons and holes take long time to reach to their respective contacts; and the active region extended to all region of the CLICK HERE TO EDIT) < 5

For the HPT structure, the extracted capacitance is supposed to have a parabolic shape with respect to the emitter length (due to the square optical window whose surface is the the emitter length). However, the electrical active restricted to the area situated under the emitter contact (which is 0.9µm wide) and the lateral the optical window (indicated by ∆ in . Thus, the capacitance is directly related by ly as shown in Figure 10.

FLOW EFFECT ON THE HPT OPTO-MICROWAVE FREQUENCY RESPONSE microwave gain (Gom) of the HPT represents the ratio of the HPT output signal power to the output power of a photodiode with a 1A/W responsivity and loaded by 50Ω This is of particular use as it is equal to the square of the HPT responsivity (so the same value in dB) under a 50 Ω loading condition.It can be deduced from the S-parameter

To characterize the opto-microwave behavior of the HPTwe follow the measurement test bench set microwave gain inthe photodiode (Vbe=0 V, and phototransistor (Vbe=0.857 V,Vce=3 V) modes HPT.

shows the Gom versus frequency of 10x10 µm² size HPT. The phototransistor mode (HPT is obtained by setting Vbe=0.857 V and Vce= 3 V and photodiode mode (PD mode) is obtained by settingVbe=

The substrate contribution is removed requency (f Topt )is the frequency at which of the HPT in phototransistor mode is equal to the in photodiode mode as shown in Figure is influenced by additional terms detection mechanism. In addition to the pure electrical effects (such as the peripheral ξ and lateral Δ microwave cutoff frequency is mainly sit time of the photo-generated carriers and capacitancesdue to photo-detection Under illumination condition the photo-generated electrons and holes take long time to reach to their respective and the active region extended to all region of the device as shown in Figure 12. Therefore expand equation ( 1) by expressing the increase in capacitance and transit time terms of the HPT that affects the frequency response as follows:

( )

_ _ _ 1 1 2 2 Topt EC opt EC EC opt F F opt C f k T C C q I π τ π τ τ = = ⋅ ⋅   ⋅ ⋅ ⋅ + + +   ⋅  
whereτ F is the electrical forward transit time from emitter to collector, C EC is theelectrical junction capa light effect), τ F_opt andC EC_opt arethe additional forward transit time and junction capacitance due to mechanism.

Figure 12:The simplified cross-sectional view of the phototransistor that indicates the peripheral region ξ and its enlargement Δ, the collector current spreading region photo-generated carrier flow.

To study the opto-microwave frequency behavior, we focus on the 10x10 µm² optical window size HPT as it highest f T value among other HPTs 13shows the extracted optical transition frequenciesf collector current (I C ). The presented optical transition frequency are measured after displacing the illuminating optical fiber above the optical window in order to maximize this frequency; thus the plotted values correspond to optimal ones in regard to the illuminating fiber position. maximum value of f Topt reaches 6.5 GHz which is very small compared to f T value obtained with the same transistor (namely 52 GHz). This, obviously, demonstrates the impact of the photo-generated carriers on HPT frequency performance under opto-microwave operation. However, this f Topt value still indicates that this HPT could optical applications operating up to 6.5 GHz.

  ⋅ ⋅ + + +     (4)
is the electrical forward transit time from emitter to electrical junction capacitance (without additional forward transit the photo-detection sectional view of the phototransistor and its dissymmetric , the collector current spreading region θ, and the microwave frequency behavior, we focus HPT as it reaches the (Figure 9).

Figure shows the extracted optical transition frequenciesf Topt versus

The presented optical transition frequency are measured after displacing the illuminating optical fiber above the optical window in order to maximize this frequency; thus the plotted values correspond to optimal ard to the illuminating fiber position. The GHz which is very small obtained with the same transistor demonstrates the impact of on HPT frequency performance microwave operation. However, this maximal could be implemented in GHz. We have also explicitly explored the influence of lateral structure on thefrequency performance by performing opto-microwave Scanning Near (OM-SNOM) by translating window surface. Figure 14 shows the microscopic picture o 10x10 µm² optical window is performed. Figure 15presents the intrinsic versus the fiber positionabove the superimposed layout of the designed HPT cartography at Y=0 µm is shown in is symmetrical with respect to the symmetric with respect to X axis as its peak appears close to the base and emitter. A maximum f at X=-5 µm and Y=0 µm. We recall the illumination position corresponding to f Topt peak has been chosen measurement results given in f Topt peakisshiftedfrom the center of the optical window towards the base and emitter contact dimensionalpath for photo-generated emitter junction in the electrical extended active region where they will initiate the transistor effect injected close to the base and emitter contact, the distance travelled by the holes to reach the bas become very short, whereas when the optical beam is injected at the center of the optical window the distance travel the holes to reach the base and emitter contact related transit time. intrinsic optical transition frequency above the HPTalong with the layout of the designed HPT.A slice curveof this µm is shown inFigure 16. The f Topt curve is symmetrical with respect to the Y axes; however it is not symmetric with respect to X axis as its peak appears close to the base and emitter. A maximum f Topt of 6.2G Hz is measured

We recall the illumination position peak has been chosen for the ent results given in Figure 13.

shiftedfrom the center of the optical window towards the base and emitter contactsdue tothe 2 generated holes to reach the baseemitter junction in the electrical extended active region where they will initiate the transistor effect. When the optical beam is injected close to the base and emitter contact, the distance to reach the base and emitter contacts hereas when the optical beam is injected at the center of the optical window the distance travelled by the holes to reach the base and emitter contactsis longer as the To complete this analysis, we extracted the opto capacitances and transit times while displacing the optical fiber over HPT surface. Figure 17 a) and b) respectively show the slice curves of the opto-microwave transit time and junction capacitance at Y=0, -2 and 2 µm. Important variationson the OM transit time ( observed over the HPT optical window. ofτ F-OM is obtained when the optical beam is close to the collector contact (atX=5µm), i.e. farfrom the emitter and base contacts. In this region the transit time is mainly controlled by the photo-generated holes traveling towards emitter contacts. The minimum transit time close to the base contact, i.e. farfrom the coll area the transit time of the electrons to reach the collector contact is responsible for the measuredOM To complete this analysis, we extracted the opto-microwave while displacing the optical a) and b) respectively show microwave transit time and µm.

ical transition frequency f Topt at

Important variationson the OM transit time (τ F-OM )are window. The highest value when the optical beam is close to the from the emitter and base . In this region the transit time is mainly controlled by traveling towards the base and The minimum transit time value is obtain from the collector ones. In this the transit time of the electrons to reach the collector measuredOM transit time value.

microwave a) forward transit time ctor junction capacitance at different optical injection positions over the phototransistor optical window. The ) and emitter-collector ) are plotted in figures a) and b) respectively.

The optimal transit time away from the center of the optical window towards the base and emitter contacts. This opto is much higher than the electrical transit time ( This confirms that the photo region under the optical window electrical contacts.

The opto-microwave junction capacitance lotover the optical window as shown in compared to the electrical junction capacitance (C it is increased by a factor of more than 3.

V. SCALING LIMITATIONS A

The speed of a phototransistor could be improved through properly designing regarding different layers. However, the main focus of this work is to use the existing HBT technology to phototransistor or photodiode cost. As a result, the HPT fabrication process HBT technology byusing the existing masks and follow industrial fabrication process layers and other properties of the However, the designer can optimize the speed of the targeted HPT by properly designing the optical window. As demonstrated above, both the length and width of the emitter highly influence the speed of the transistor due to the presence of the emitter peripheral current, the collector current spreading and effects have to be minimize structure.

To minimize the influence collector current spreading, the optimum determined through a proper physical or electrical modeling of the structure that could be done Besides, the 2-D carrier flow effect can be minimized through proper design of the structure be considered: o Design a symmetrical contactsas it will lead to more vertical o Fragmentation of the HPT in as the electrical extension fragmented device size limit.

o Considering laterally illuminated structure improve the HPT opto-microwave speed.

VI. C

The influence of lateral scaling on the important bipolar transistor characteristics such as transit time and junction capacitance is shown through intensive experimental re The impact of emitter width and length are independently. During this study it is demonstrated that the HBT cutoff frequency, f T decreases as the emitter length decreases from 20 µm to 3 µm for a given emitter width due to the predominance of the peripheral current for smaller size HBT.

For the opto-microwave applications, the phototransistor is 20 30

CLICK HERE TO EDIT) < 7 transit time value is reached 2 µm to 4 µm away from the center of the optical window towards the base This opto-microwave transit time (τ F-OM ) the electrical transit time (τ F = 1.5ps). o-carriers generated in the active region under the optical window need longer time to reach the junction capacitance does not vary a over the optical window as shown in Figure 17b). However, compared to the electrical junction capacitance (C EC =0.7 pF), it is increased by a factor of more than 3.

CALING LIMITATIONS AND DESIGN RULES

The speed of a phototransistor could be improved through regarding the vertical thickness of its layers. However, the main focus of this work is to use the existing HBT technology to fabricate the phototransistor or photodiode in order to minimize the total fabrication process is adapted to the the existing masks and following the industrial fabrication process without modifying the vertical properties of the technological process. However, the designer can optimize the speed of the targeted HPT by properly designing its lateral dimensions and optical window. As demonstrated above, both the length and width of the emitter highly influence the speed of the transistor due to the presence of the emitter peripheral current, collector current spreading and the 2-D carrier flow. These minimized through proper design of the To minimize the influence of the peripheral current and collector current spreading, the optimum HPT size has to be through a proper physical or electrical modeling of done using commercial software's. D carrier flow effect can be minimized esign of the structure. Several solutions can al collector, base and emitter lead to more vertical carrier flow.

the HPT into smaller individual HPTs, as the electrical extension region ∆may reach to the limit. illuminated structures [START_REF] Tegegne | Edge illuminated SiGe Heterojunction Phototransistor for RoF applications[END_REF][23] to microwave speed.

CONCLUSION influence of lateral scaling on the important bipolar transistor characteristics such as transit time and junction shown through intensive experimental results. The impact of emitter width and length are studied independently. During this study it is demonstrated that the decreases as the emitter length µm for a given emitter width due to the predominance of the peripheral current for smaller size microwave applications, the phototransistor is fabricated by using the existing SiGe HBT technology without modifying the vertical stacks and layers. Instead, the lateral dimensions of the active layer are increased by extending the emitter-base-collector layers with the emitter contact kept at its original position in order to create the optical access. We choose a square optical window in order to minimize the influence of the peripheral current. It is experimentally demonstrated that the optimum cutoff frequency f T appears when the optical window is of 10x10 µm². The asymmetry between base and collector contacts generates the lateral flow of carriers which reduces the phototransistor speed. This effect is more predominant for HPTs of small optical window. For HPTs having optical window larger than 10x10 µm², the f T decreases as the junction capacitances and resistances increase with the size.

We focused on 10x10 µm² optical window size HPT to show the dependency of the opto-microwave frequency behavior on the 2-D carrier flow effect. For that purpose, an OM SNOM analysis is performed over the surface of the HPT window in order to identify the fastest and the slowest regions. It is observed that the peak of the optical transition frequency appears close to the base-emitter. We observed that there is small variation of the OM junction capacitance value over the optical window. However, the transit time quickly increases as the optical beam moves towards the collector contact and its optimum smallest value appears towards the emitter-base contact.

To improve the frequency response, proper design rules areproposed that are to get symmetric collector, base and emitter contacts so that the electrical field is more vertical, to fragment the HPT into smaller individual HPTs as the electrical extension may reach a limit in its increase. Laterally illuminated HPT structure could also improve the optomicrowave speed.

VII. ACKNOWLEDGEMENT

This work was partially supported by the French government in the framework of the FUI8 ORIGIN project (Optical-Radio Infrastructure for Gigabit/s Indoor Networks).

Figure 4 :

 4 Figure 4: f T andf max of HBTs as a function of emitter length L with a constant emitter width l = 0.9µm and for Vce=3.5 V.

Figure 7 :

 7 Figure 7: The simplified cross-sectional view of the transistor that indicates the impact of the peripheral current and the collector current spreading. The θ is the angle of current spreading in the collector.

  LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < (above 1.5 mA.cm -2 ), observed for all transistors and similar values are obtained whatever the emitter length is.sectional view of the transistor that current and the collector is the angle of current spreading in the dow size on HPT'sspeedHPT is a transistor with an optical opening for light . The extended part of the phototransistor (optical window) modifies the electrical behavior of the transistor due to additional parasitic effect as a function of emitter length L µm. For HPTs, the optical window W and emitter length L as shown in Figure9have equal µm along x-axis.

Figure 9 :

 9 Figure 9: The simplified a) cross transistor that indicates the impact of the peripheral region collector current spreading region optical windowΔ.

W

  To demonstrate this assumption, the forward transit time and junction capacitance of the HPT and HBT are extracted experimentally. These values can be easily extracted from a plot of the emitter-collector time delay ( 1/I C according to equation (1): the junction extracted from the slope and the forward transit time byy-intercept. The extracted values of the HBT and HPT as a function of the emitter size are shown in Figure that HBTsare fabricated by keeping the emitter width l=0.9 µm with various emitter lengths L, whereas extended optical windows size W and the equal and take several values. From Figure following observations: 1. HBT: The transit time (τ EC-HBT ) rapidly emitter length below 10 µm. Thus, it contribution of the peripheral carrier smaller HBT. Then the forward transit time slightly decreases as the emitter length increases from 10 50 µm. The junction capacitance increases keep increasing. 2. HPT: Similar to the HBT, the transit time (

Figure 10 :

 10 Figure 10: The extracted electrical transit time and junction capacitances as a function of emitter length L l=0.9 μm) and HPT (with l=L) structures.

  LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < he forward transit time on capacitance of the HPT and HBT are extracted

Figure 11 :

 11 Figure 11: Opto-microwave gain Vce=3 V) and phototransistor of10x10 µm 2 optical window HPT

  LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < herefore, we propose to by expressing the increase in capacitance the HPT that affects the frequency

Figure 13 :

 13 Figure 13:The optical transition current when the optical beam is injected frequency.

Figure 14 :

 14 Figure 14: The microscopic picture of the top view of the transistor.

Figure 15 : 6 :

 156 Figure 15: The topological map of the optical transition frequency f Topt at various locations of optical light illumination.

  The topological map of the optical transition frequencyof optical light illumination.

Figure 16 :

 16 Figure 16: The slice curve of the optical transition frequency f Y=0µm

Figure 17 :>

 17 Figure 17:The extracted opto-microwave a) forward transit time and b) emitter-collector junction capacitance at different optical injection positions over the phototransistor optical window. The electrical forward transit time (τ F ) and emitter capacitance (C EC ) are plotted in figures a) and b) respectively.

  μm 2 for vertical NPN HBT transistors leads to actual Study of lateral scaling impact on the frequency performance of SiGe Heterojunction Bipolar Phototransistor Zerihun Gedeb Tegegne, Carlos Viana, Jean-Luc Polleux, Marjorie Grzeskowiak, and Elodie Richalot Université Paris-Est, ESYCOM (EA2552), ESIEE-Paris , UPEM, Le CNAM, 93162 Noisy-le-Grand, France size after processing of 0.5x1.1 μm 2 due to lateral spacers.

Optical window Base contact Emitter contact

	> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <
					due to lateral spacers.
					f T up to 80 GHz and
			This enables circuits working above
			poly Si	Emitter contact
			Base
	z		contact
	x	TiSi & poly-SiGe			Si n
	y	SiO 2		Si n -	SiGe p
					Si n ++ sub collector
		Si	p-Substrate
	z		poly Si
		x
	y	TiSi & poly-SiGe SiO 2		Si n -	SiGe p +
					Si n ++ sub collector
		Si	p-Substrate


Zerihun Gedeb Tegegne

Carlos Viana

Jean-Luc Polleux
email: jl.polleux@esiee.fr

Marjorie Grzeskowiak

Elodie Richalot

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1

Keywords: Silicon-based photodetectors, microwavephotonics, SiGe phototransistor, OM-SNOM, Substrate effect I

Theintrinsic frequency response of Silicon-Germanium Heterojunction bipolar Photo-Transistors (HPT) at 850nm is studied to be implemented in multimode fiber systems. The experimental analysis of an HPT with an optical window size of 10x10µm 2 is presented. An Opto-Microwave Scanning Near-Field Optical Microscopy (OM-SNOM) is performed to observe the variation of the HPT dynamic behavior versus the illumination location of the phototransistor. The photocurrent generated by the photodiode at the interface between the n++ sub-collector and the p+ guard ring is analyzed and its impact on the performance of the HPT is investigated. Then, we propose a technique to remove the substrate photocurrent effect on the optical transition frequency (f Topt ): the f Topt value of 4.1GHz given by raw measurement results increases up to 6GHz after removing the substrate response. The influence of the twodimensional carrier flows on the HPT intrinsic Opto-Microwave (OM) behavior is also studied. Design aspects of SiGe/Si HPT structures are finally discussed as a conclusion.

There is a continuous interest to develop phototransistors from newer standard SiGe HBT technologies that offer faster operating frequencies to improve the performances of the HPTs without modifying the vertical stack of layers imposed by the technological process. To optimize the phototransistor speed, Moutier el al [START_REF] Moutier | Frequency response enhancement of a single strained layer SiGe phototransistor based on physical simulations[END_REF]performed physical simulationsto observe the fastest and slowest regions of the HPTs' structure. Other authors [START_REF] Helme | Analytical modeling of speed response of heterojunction bipolar phototransistors[END_REF] and [START_REF] Yuan | MEXTRAM modeling of Si-SiGe HPTs[END_REF]investigated the phototransistor performances through opto-electronic compact circuit modeling. The existence of substrate photocurrent was demonstrated in [START_REF] Yuan | MEXTRAM modeling of Si-SiGe HPTs[END_REF] [14][15]. This paper develops amathematical procedure to remove the substrate response and to extract the core performances of SiGe HPT such as the optical transition frequency (f Topt ). Concerning these core performances, the intrinsic electrical parameters such as the junction capacitance and transient time are deduced and thenthe influence of the two-dimensional carrier flow (near the metal contacts) on the device speed is demonstrated. A conclusion is then drawn on the design aspects of SiGe/Si HPTs to improve their performances. The measurement of the phototransistor frequency characteristics is performed under multimode optical fiber illumination. While measurement under single mode fiber illumination would bring clear information on the physics of the device, it is also essential to include the impact of the distribution of the multimode fiber optical beam on such characteristics with a view to commercial implementation.

II. SIGE/SI HPT STRUCTURE AND TECHNOLOGY

The SiGe HPTis fabricated using the conventional SiGe2RF Telefunken GmbH process for bipolar SiGe transistors. Indeed, the phototransistor fabrication respects the vertical stack of layers used in standard SiGe2RF HBT technology. This guarantees the compatibility with this technological process and enables the potential integration of photonic and electronic circuits.

The phototransistor is designed by extending the emitter, base and collector layers of the reference HBT [START_REF] Shi | Performance enhancement of high-speed SiGe based heterojunction phototransistor with substrate terminal[END_REF]. The optical injection is made vertically through the emitter. A cross-section of the phototransistor structure is given in Figure 1. The light path goes through the oxide and polysilicon of the emitter before entering the Si emitter, SiGe base and Si collector regions. This HPT is essentially one large HBT whose emitter metallization only partially covers the emitter Intrinsic frequency response of Silicon-Germanium phototransistor associated with 850nm multimode fiber We have designed phototransistors with a optical opening. The base region consists of a 40 SiGe layer with Ge content of 20-25 % and high p doping i the range of 10 19 cm -3 as presented in [START_REF] Pei | A High-Performance SiGe-Si Multiple-Quantum-Well Heterojunction Phototransistor[END_REF] typically 300-400 nm thick with low doping and the emitter region is less than 100nm thick. The doping levels of each region are estimated in [START_REF] Polleux | An SiGe/Si Heterojunction Phototransistor for Opto-Microwave Applications: Modeling and first Experimental Results[END_REF].

III. EXPERIMENTAL RESULTS AND DISCUSSION

A. Substrate photodiode current analysis

The Gummel plots under illumination (at 850 wavelength) and dark conditions are shown current at low base-emitter voltage (Vbe photocurrent which is far lower than the current the transistor effect observed at higher base Under illumination condition, the base current represented by its absolute value. At low Vbe, t Ib has a negative sign and hence flows out of the base contact.Its sign changes at Vbe=0.82 V where it minimal. Under dark condition and at low Vbe, the collector current Ic and the base current Ib are equal, whereas for the same biasing condition with the light magnitude of Ic and Ib are different. This behavior is not encountered with phototransistors such HPTs [START_REF] Schiellein | Analysis of opto-microwave paths into a InP/InGaAs UTC-HPT[END_REF] (for which the magnitude of Ib and Ic are low base-emitter voltage and under illumination condition)where the InP substrate is optically transparent at region. The substrate is grounded through a p+ guard ring phototransistors with a 10x10 μm 2 opening. The base region consists of a 40-80 nm thin % and high p doping in in [START_REF] Pei | A High-Performance SiGe-Si Multiple-Quantum-Well Heterojunction Phototransistor[END_REF].The collector is m thick with low doping and the emitter less than 100nm thick. The doping levels of each section of HPT with extended Emitter, Base and Collector regions.

AND DISCUSSION

current analysis

under illumination (at 850 nm shown inFigure 2. The Vbe) corresponds to the is far lower than the current induced by at higher base-emitter voltage. he base current in Figure 2is At low Vbe, the base current negative sign and hence flows out of the base where its amplitude is mW optical power

Under dark condition and at low Vbe, the magnitude of the base current Ib are equal, whereas ondition with the light "ON", the magnitude of Ic and Ib are different. This behavior is not such as InGaAs/InP magnitude of Ib and Ic are equal at emitter voltage and under illumination where the InP substrate is optically transparent at the wavelength of interest. As holes (h+) generated in the substrate diode is effetely grounded via the substrate contact. However, the electrons ( generated in the substrate diode is combined which are generated in the active region (emitter collector) of the HPT toreached measured as collector current, I 0.7V, most parts of the holes generated at the junction attract electrons from the emitter for transis amplification and some parts contact. Whereas, when Vbe less than generated holesgenerated within the out into the base contact and can be measured Ib.Thus, the difference between collector and base photocurrent magnitudes shown in corresponds to the photocurrent generated by the substrate diode called substrate photocurrent computed using the equation below To locate the source of this extra photocurrent in the phototransistor structure and to study its impac Microwave (OM) behavior of the HPT, we perform and an opto-microwave mapping Near Field Optical Microscopy (SNOM) measurement setup described VCSEL (of 12GHz cutoff frequency) illuminate the HPT through a lensed (MMF)moved over the HPT surface.

Figure 4-a) shows the microscopic photography of the 10x10 µm² phototransistor (over which the topological mapping is performed) where the ground (emitter contact) and signal (base and collector) line contact is taken from the left side, collector contact from the right side and the emitter contact is connected at its top and bottom sides to the ground (common emitter configuration).

CLICK HERE TO EDIT) < 2

As it is indicated in Figure 3, the holes (h+) generated in the substrate diode is effetely grounded via the substrate contact. However, the electrons (e-) generated in the substrate diode is combined with theelectrons which are generated in the active region (emitter-basereached the collector contact and measured as collector current, I C . When Vbe is greater than of the holes generated at the base-collector from the emitter for transistor s are however escaped to the base Vbe less than 0.4V, all photowithin the active regionis flowing to the base contact and can be measured as base current, Thus, the difference between collector and base photocurrent magnitudes shown in Figure 2at Vbe=0V corresponds to the photocurrent generated by the substrate diode called substrate photocurrent (I sub ) [START_REF] Tegegne | Substrate diode effect on the performance of Silicon Germanium phototransistors[END_REF]. This can be ation below:

) ( ) , , , _ _ _ sub C PD C PD dark b PD b PD dark I I I I I = - - - (1)
are respectively the dark base and photodiode (PD) mode (at Vbe=0V). I C,PD are the collector and base currents under illumination : the schematic that indicates the flow of photo-generated carriers that are generated at different region of the HPT.

To locate the source of this extra photocurrent in the phototransistor structure and to study its impact on the Optobehavior of the HPT, we performed a DC microwave mapping of the devicesusing Scanning Near Field Optical Microscopy (SNOM) with the measurement setup described in [START_REF] Tegegne | An 850nm SiGe/Si HPT with a 4.1GHz maximum Optical Transition Frequency and 0.805A/W Responsivity[END_REF] [START_REF] Zerihun | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF],where a 850 nm cutoff frequency) is directly modulated to illuminate the HPT through a lensed Multi-Mode Fiber over the HPT surface.

a) shows the microscopic photography of the µm² phototransistor (over which the topological mapping is performed) where the ground (emitter contact) and signal (base and collector) lines are clearly visible. The base contact is taken from the left side, collector contact from the right side and the emitter contact is connected at its top and bottom sides to the ground (common emitter configuration).

The layout is accordingly sketched in Figure 4-b) which defines the coordinates of the optical fiber center; its origin is fixed at the center of the optical window. We performed the experimental mapping (consisting of displacing the illuminating optical fiber) on HPT at two different bias conditions i.e. at Vbe=0V and Vbe=0.857V for Vce=3V. The phototransistor mode (HPT mode) is obtained by fixing the collector-emitter voltage at 3 V and a fixed baseemitter voltage at 0.857 V. These biasing conditions correspond to the optimal ones in terms of opto-microwave responsivity. In this mode, there is an internal amplification of photo-generated carriers due to transistor effect (current gain β). The photodiode mode (PD mode) is obtained by setting the collector-emitter voltage at 3 V and the base-emitter voltage at 0 V. In PD mode, as the base-emitter junction is electrically inactive, there is no amplification in the deviceso that the purely photo-generated currents can be extracted. The DC current and opto-microwave frequency response of the HPT is then measured at each location of the illuminating optical beam in both modes.An injected optical power level of 2.38mW is used in the subsequent experimental results.

B. Substrate photocurrent effect on opto-microwave behavior

The opto-microwave (OM) power gain represents the ratio of the HPT microwave output signal power to the output power of a photodiode with 1A/W responsivity [START_REF] Zhu | Resonant Cavity SiGe/Si MQW Heterojunction Phototransistor Grown on the SIMOX Substrate for 1.3pm Operation[END_REF]. It is equal to the square of the responsivity under 50Ω load condition but may change as a function of the load as described in depth in [START_REF] Polleux | Optimization of InP-InGaAs HPT Gain: Design of an Opto-Microwave Monolithic Amplifier[END_REF].OM gain is extracted from S-parameter measurement as a function of frequency. Figure 5-a) and -b) show the low frequency (50 MHz) OM responsivity of a 10x10 µm² optical window size HPT (loaded by 50 Ω) as a function of the optical fiber position in HPT and PD modes, respectively. In HPT mode, the peak of the responsivity appears inside the optical window, whereas in PD mode, the responsivity is maximal when the optical fiber is around the optical window according to a ring shape as shown in Figure 5-b).

The ring shape of the maximal responsivity in PD mode is due to the illumination of the substrate diode; we can observe the responsivity of the substrate diode is clearly stronger than the one of the photodiode created by the base and collector in the active region. As shown in Figure 5-a) the ring shape does not appear in phototransistor mode as the substrate diode effect is hidden by the transistor amplification. Figure 6presents the OM gain (Gom)as a function of the frequency at different optical fiber locations extracted from Figure 5-b) (in photodiode mode). The Gom at X=2 µm and Y= -16 µm (outside the optical window) is higher than the Gom at the center (X=Y=0 µm) at all frequencies. From this result, we can deduce that the substrate diode is clearly dominating over the intrinsic diode (the diode created by the base and collector) even at the central position despite the optical beam is attenuated by the layer vertical stack. When the optical fiber moves further away from the optical window, the low frequency Gom decreases until reaching the noise level as the substrate diode becomes slower and then non effective to detect the 50 MHz signal. The Gom curves at (X=24 µm, Y= -12 µm) and (X=28 µm, Y= -3 µm) illustrate this evolution in Figure 6.

The substrate responsivity can be isolated from the intrinsic behavior by the mathematical model as described in the following section. The photodiode mode intrinsic responsivity (R PD,i ), substrate responsivity (R sub ) and raw responsivity (R om,PD ) for an illuminated beam displacing along Y axis(X=0) are presented in Figure 7. Indeed, the R om,PD curve corresponds to the variation along the line X=0 of the PD mode responsivity measured at 50 MHz and presented in Figure 5-b. To extract the substrate responsivity at 50 MHz we use the definition of OM power gain in [START_REF] Polleux | A Strained SiGe layer Heterojunction BipolarPhototransistor for Short-Range Opto-Microwave Applications[END_REF], and considering the 50 Ω load, it comes:

where I C,PD is the total current measured at the collector contact in PD mode, I C,PD,ph is the photocurrent generated in the HPT active area in PD mode, I C,PD,dark is the dark current measured at the collector contact, I sub is the substrate photocurrent, R om,PD is the raw OM responsivity in PD mode, α cal is a 1 A/W normalization factor and P opt,RF is the illuminating optical power expressed as the equivalent current I opt,RF . Then we deduce the intrinsic responsivity:

( )

2 2 2 2
,PD , ,PD ,PD ,dark , , , ,

C ph C C sub om P D sub PD i opt R F opt R F R R I I I I R I I     - -     = = = -         (4)
,PD ,P D,dark , , , ,

C C sub P D i om PD sub opt RF opt R F I I I R R R I I - = - = - (5)
To extract the substrate responsivity (R sub ) at low frequency, we assume that the intrinsic DC responsivity (R PD, i, DC ) is equal to the intrinsic responsivity at low frequency (R PD,i,LF ), this assumption being valid for Vce=3 V with no amplitude variation atlow frequency. Hence: ,PD , ,

C ph C ph P D i PD i D C opt RF opt I I R R I I = ≅ = PD , , ,LF , , , ,D C
Thus the substrate responsivity (R sub ) at low frequency is calculated from equation ( 5) and [START_REF] Pei | A High-Performance SiGe-Si Multiple-Quantum-Well Heterojunction Phototransistor[END_REF].

, , ,

sub om PD PD i LF R R R = - (7)
As presented in Figure 7, the peak of intrinsic responsivity (R PD, i, DC )appears at the center of the optical window (X=Y=0 µm) whereas at the same location the substrate photodiode responsivity is weaker than the intrinsic photodiode responsivity.However, the substrate response becomes stronger when the optical beam moves outside the optical window (around Y=±10 µm). The substrate responsivity is low in the HPT's active region, but it is not null due to the optical light penetration through the HPT to the substrate, underneath the active region.

The dynamic behavior of the phototransistor can be analyzed through the optical transition frequency (f Topt ). The latter is defined as the frequency at which the 50 Ω OM gain in HPT mode is equal to the 50 Ω low frequency gain in PD mode (Vbe=0 V). Indeed, it is the frequency at which the phototransistor stops amplifying as shown in Figure 9. As it has been demonstrated in [START_REF] Tegegne | Substrate diode effect on the performance of Silicon Germanium phototransistors[END_REF], the substrate photocurrent in SiGe HPT has a huge impact on the frequency response of the phototransistor mainly in PD mode. To observe the intrinsic properties of the HPT (that can be used for future SiGe HPT modeling), one needs to remove (deembed) the substrate response from the raw measured data at each position of the optical fiber and atallfrequencies. The substrate response at low frequency computed by equation ( 7) is extrapolated to all frequencies using the transfer function presented in equation [START_REF] Rosales | Full area emitter SiGe phototransistor for opto-microwave circuit applications[END_REF].

0 0 (f ) ( ) 1 f sub sub R R f f j α =   +     (8)
wheref 0 is 50 MHz and ∝ is the order of the transfer function to model the frequency slope of the substrate photodiode. Figure 8 shows the fitting of the model with the experimental OM gain measured by illuminating the structure at X=5 µm and Y=15 µm where the substrate photocurrent amplitude is maximum. The model well fits with the measurement results for ∝=0.4 corresponding to an The substrate diode influence is then removed at all frequencies from the phototransistor responsivity to intrinsic responsivity in phototransistor mode ( intrinsic optical transition frequency (f Topt,int at which R HPT,i is equal to the intrinsic DC responsivity in photodiode mode (R PD,i,DC ).

The complete and intrinsic OM gains PD and HPT modes when the optical beam center of the optical window (X=0 µm, Y=0 inFigure 9. The model of substrate photodiode frequency response at X=Y=0 µm is also presented in the same figure. The raw and intrinsic Gom are equal at all frequencies mode operation. This indicates that the frequency response of the substrate photodiode is hidden by the amplification effect. However, in PD mode, the substrate photodiode contributes to its OM gain and reduces its The variation of f Topt at X=0 µm along Y Figure 10-a) before and after removing the substrate diode effect. The a flat f Topt,int peak appears over the optical window (the peak width is about 10 µm), anditdrops to zero outside the optical window. Whereas, along X-axis, the intrinsic f Topt,int the optical window (Figure 10-b). The intrinsic f > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

The substrate diode influence is then removed at all frequencies from the phototransistor responsivity to obtain the intrinsic responsivity in phototransistor mode (R HPT,i ). The Topt,int ) is the frequency is equal to the intrinsic DC responsivity in versus frequency in when the optical beam focuses at the m, Y=0 µm) is presented substrate photodiode frequency µm is also presented in the same figure .  at all frequencies in HPT mode operation. This indicates that the frequency response of the substrate photodiode is hidden by the internal transistor amplification effect. However, in PD mode, the substrate gain and reduces its speed.

gain in photodiode and phototransistor modes for =0 µm.The level of the µm along Y-axis is shown in before and after removing the substrate diode over the optical window drops to zero outside the cy before and after the substrate diode effect with the optical beam f Topt,int is not flat over b). The intrinsic f Topt,int peak is shifted from the center of the optical window towards the base and emitter contacts. This is because when the optical beam is injected close to the base an travelled by the holes to reach the base and emitter contacts become very short, whereas when the optical beam is injected at the center of the optical window, the distance travelled by the holes to reach the base and emitt related transit time. The f Topt to 6 GHz while extracting substrate diode effect.

Figure 11 shows the intrins f Topt,int versus collector current (I transition frequency has been optical fiber location to obtain the higher f value of f Topt,int reaches 6.5 could be implemented in optical applications operating up to 6.5 GHz.

1) Low current region:

In this region f Topt quickly increases with the collector current due to the junction capacitance reduction as the dc supply increases.

2) Medium current region:

The peak of f Topt is reached between I The frequency behavior in this region is mainly limited by the carrier time to reach the metal contacts. Photo generated carrier transit time is the main limiting factors of the peak f Topt .

3) High injection current region:

For I C greater than 12 mA, f injection of a large number of carriers ( device which limits the speed of HPTs.

The peak value of the f compared to its equivalent electrical transition fr 47.3GHz) as shown in Figure by additional terms related to the such as additional transit time and junction capacitances introduced by the injected optical power shifted from the center of the optical window towards the base and emitter contacts. This is because when the optical beam is injected close to the base and emitter contacts, the distance travelled by the holes to reach the base and emitter contacts become very short, whereas when the optical beam is injected at the center of the optical window, the distance travelled by the holes to reach the base and emitter contacts is longer as the Topt peak is improved from 4.1 GHz GHz while extracting substrate diode effect. intrinsic optical transition frequencies versus collector current (I C ). The presented optical has been measured after optimizing the optical fiber location to obtain the higher f Topt,int . The maximal reaches 6.5 GHz, indicating that this HPT could be implemented in optical applications operating up to

The optical transition frequency f Topt as a function of

The injected optical power is 2.38mW.

Figure 11) can be divided into three quickly increases with the collector e to the junction capacitance reduction as the dc is reached between I C =6 mA and 12 mA. The frequency behavior in this region is mainly limited by the carrier time to reach the metal contacts. Photogenerated carrier transit time is the main limiting factors current region: mA, f Topt quickly drops, due to the injection of a large number of carriers (Kirk effect) in the device which limits the speed of HPTs.

The peak value of the f Topt (6.5GHz) is very small electrical transition frequency (f T = Figure 12. Unlike f T , f Topt is influenced by additional terms related to the photo-detection mechanism onal transit time and junction capacitances introduced by the injected optical power. The intrinsic parameters of the HPT such as the capacitances and transit time can also be deduced experimentally from optical transition frequency. These parameters could be used in optical system modeling to implement the HPT as a photodetector as well as for future study of the HPT structures. The opto-microwave transition time delay τ F_OM is the time required by the opto-microwave photo-generated carriers to reach any contact and is calculated from f Topt according to τ F_OM =1/(2πf Topt ) [START_REF] Zerihun | SiGe/Si Microwave Photonic Phototransistors and Interconnects towards Silicon-based full Optical Links[END_REF]. Figure 13 shows the opto-microwave transition delay versus 1/I C . The totalcapacitance (including base-emitter and base-collector depletion, diffusion and parasitic)and the transit time of the phototransistor can be extracted from the slope and y-intercept of the transition time delay curve respectively. Table 1 compares the extracted electrical (τ F , C E ), opto-microwave (τ F_OM , C OM ) and optical (τ F_opt , C opt ) transit times with the related capacitances. The first two parameters (electrical and opto-microwave) are extracted from f T and f Topt respectively. The optical terms are deduced by removing the electrical terms from the opto-microwave ones. Larger values of capacitance and transit time under optomicrowave operation mean that photo-generated carriers cover a longer path than the electrically generated ones. Indeed, the active region of the electrical transistor corresponds to the vertical region of the emitter contact, whereas the transistor effect (active area of the HPT) under opto-microwave operation is distributed along the whole device with additional lateral paths of photo-carriers to reach the electrical contacts. Similarly, capacitance is larger under opto-microwave operation, when compared with under electrical operation, as the active surface of the structure increases related to the photo-detection process. Thisimplies both the junction and diffusion capacitancesincrease related to the injected optical power.

We deduce the "optical" capacitance and transit time by removing the electrical parameters from the opto-microwave ones. These values correspond to the additional capacitance and transit time due to the additional path length and the equivalent active surface area increase encountered by photogenerated carriers compared to the electrical ones. "Optical" capacitance is higher than the half of the total opto-microwave one. Such variation of the equivalent capacitance may correspond to a corresponding double surface. Optical transit time is much larger than the electrical one. Considering that the vertical stack is unchanged, this may be attributed to a lateral path required for holes to be amplified or for electrons injected from the emitter to reach the photo-generated holes in the base region.

IV. CONCLUSION

This paper considered a SiGe/Si phototransistor developed by using the industrial SiGe HBT technology without modifying the vertical stack of layers. The OM SNOM analyse is shown to be crucial to understand the behavior of such SiGe HPTs. It allows the extraction of the DC and dynamic behaviors of the device for all the positions of the illuminating optical fiber. As slow carriers from the substrate diode affect the dynamic response of the SiGe/Si HPTs, an extraction method has then been developed to isolate the substrate effect and then deduce the intrinsic behavior of the HPT; an intrinsic optical transition frequency of 6 GHz has been obtained. Thus, the impact of the two dimensional carriers flow in the intrinsic phototransistor structure is demonstrated. The speed increases when we illuminate the HPT close to the base contact and it gradually decreases when the optical beam moves away from the base-emitter contact. This is due to the speed of holes which are collected at the base-emitter region.

1/2πf

Topt (ns)

The internal electrical parameters such as transit time and capacitances of the phototransistor are extracted and can be an input for future modeling of the phototransistor. Further studies using a single mode optical fiber would be interesting for a more precise modeling of the SiGe HPT and for a reduction of the substrate diode effect when illuminating the optical window.

Several alternatives exist to eliminate the substrate contribution, as the design of metallic diaphragms around the optical window to hide the substrate photodiode, or through lateral illumination of the HPT. Alternatively, taking advantage of the substrate effect could be envisaged for a combined HPT-PD structure.The influence of the 2D carriers flow effect can also be avoided or minimized via a proper designof the metal contacts to get a symmetric contact of the collector, base and emitters that will make the electrical field more vertical.

V. ACKNOWLEDGEMENT

This work was partly supportedby the French DGCIS FUI8 ORIGIN project.

Figure 1 :

 1 Figure 1: Simplified schematic cross-section of HPT with extended Emitter, Base and Collector regions

Figure 2 :

 2 Figure 2: Gummel plot under 2.28 mW optical power illumination and dark conditions.

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(

  I b_PD_dark and I C,PD,dark are respectively the collector currents in photodiode (PD) and I b,PD are the collector and base current condition.

Figure 3 :

 3 Figure 3: the schematic that indicates the flow of photo carriers that are generated at different region of the HPT.

Figure 4 :

 4 Figure 4: a) Top view of the phototransistor; b) Layout of the 10x10 µm² optical window phototransistor and optical fiber coordinate axes centered at the center of optical window.

Figure 5 :

 5 Figure 5: Low frequency (50 MHz) opto-microwave responsivity of HPT with 10x10 µm 2 in a) HPT mode (Vbe=0.857 V), b) PD mode (Vbe=0 V) for Vce=3 V loaded by 50 Ω.

Figure 6 :

 6 Figure 6: Gom as a function of frequency in photodiode mode at different positions of optical fiber extracted from figure 9-b).

Figure 7 :

 7 Figure 7: The raw (R om,PD ), substrate (R sub ) and intrinsic responsivity (R PD, i, DC ) of HPT with 10x10 µm 2 optical window size in PD mode operation (Vbe=0 V) and for an optical beam along Y axis ( X=0) axis.

Figure 8 :

 8 Figure 8: The transfer function model fitted to the measured OM gain of the substrate photodiode (optical fiber located at X=5 µm, Y=15 µm and biases Vbe=0 V, Vce=3 V).The level of the injected optical power is 2.38mW.

Figure 9 :

 9 Figure 9: OM gain in photodiode and phototransistor modes an optical beam located at X=0 µm and Y=0 injected optical power is 2.38mW.

Figure 10 :

 10 Figure 10: Optical transition frequency before and after removing the substrate diode effect with centered at X=0 μm (a) and Y=0 μm (b).

Figure 11 :

 11 Figure 11: The optical transition frequency f the collector current.The injected optical power is 2.38mW. The f Topt versus I C curve (Figure mean regions:

Figure 12 :

 12 Figure 12: The electrical transition frequency f T as a function of the collector current.

Figure 13 :

 13 Figure 13: The opto-microwave transit time delay versus 1/Ic to extract the junction capacitances from the curve slop and the opto-microwave transit time from y-intercept.

Table 1 : The extracted junction capacitances and forward transit times of the HPT illuminated at the position corresponding to the optimal f Topt .

 1

	Electrical	Total(Opto-	Optical
			microwave)
	C E (pF) τ F (ps) C OM	τ F_OM	C opt (pF) τ F_opt
			(pF)	(ps)		(ps)
	0.798	1.5	1.7	18.7	0.902	17.2

partially supported by the French government in the framework of the FUI8 ORIGIN project (Optical-Radio Infrastructure for Gigabit/