P Virostko

Z Hubička

M Čada

M Tichý

Ion current to a substrate in the pulsed DC hollow cathode plasma jet deposition system

Keywords: numbers: 52, 70, Ds, 52, 77, -j

The current of positive ions to a substrate was studied in the pulsed DC hollow cathode plasma jet system for deposition of thin films working at low pressures. Time evolution of electric current to a planar probe with pulsed negative DC bias was measured. The pulsing of the bias of the probe was applied to allow measurements with a dielectric film being deposited on its surface. The frequency of pulsing of the probe bias was higher than the frequency of pulsing of the discharge. Time evolution of the ion current density to the probe j i was determined for the whole period of modulation of the discharge for the discharge repetition frequency 2.5 kHz and different duty cycles D. The mean ion current density j i , averaged over the whole period of the discharge, was rising with the decreasing D although the value of the mean discharge current was kept constant. A simple theoretical model is proposed to explain this effect. It is shown that the observed rise of j i with decreasing D is in major part caused by the rise of the ion current in the afterglow region of the pulsed discharge.

Introduction

Pulsed excitation of discharges has been recently increasingly studied and employed in the plasma-assisted deposition of thin films [1,2]. Originally, pulsed excitation was proposed as a solution to problems connected with the undesired arcing during reactive sputtering. Moreover, it allows to apply much higher instantaneous power to the discharge than continuous excitation [3], leading to different conditions during sputtering and consequently to thin films with properties that might not be obtainable using continuous excitation.

Plasma diagnostic plays a key role in studying new methods and optimizing existing methods of deposition. Monitoring and control of plasma parameters during the deposition ensures namely the reproducibility of deposited films. One of the important parameters to study and observe is the current of positive ions from the plasma to a substrate. The ion bombardment of the substrate can significantly influence the parameters of deposited films, for example their surface morphology or structure [4,5,6]. The substrate is often held on a negative bias potential with respect to the bulk plasma to increase the energy of ions impinging on it and generally to control the ion bombardment.

The aim of the presented work is a study of the ion current to a negatively biased substrate in the pulsed direct current (DC) hollow cathode plasma jet system for deposition of thin films. The hollow cathode plasma jet (HCPJ) [7,8,[START_REF] Hubička | Low Temperature Plasmas. Fundamentals, Technologies, and Techniques[END_REF] is a low-temperature sputtering device working at pressures approximately from 0.1 Pa to 100 Pa. Its deposition rate is comparable to the usual deposition rate of magnetrons. It is favourable for depositions on substrates with complicated shapes or into holes because of the jet-like character of the discharge. It can also be used for sputtering of magnetic materials [START_REF] Kraus | [END_REF]. Pulse modulation of the power applied to the HCPJ allows to increase the power applied to the cathode, and consequently the sputtering of the cathode material, without overheating the cathode since the mean applied power including the space between pulses can be kept low.

The ion current was measured by a negatively biased planar probe immersed into the bulk plasma in the position of the substrate. The configuration of the HCPJ for deposition of TiO x films was used. The titania films are dielectric and therefore the negative bias of the probe was periodically switched down to zero to discharge a positive charge that was accumulating on the surface of the film.

Experimental setup

A schematic representation of the experimental setup is in figure 1. The main part of the HCPJ is a cylindrical nozzle, which is made from the material to be sputtered. The nozzle is placed in a copper block, which is cooled by water. An insulating ceramic cover is placed around the copper block with the nozzle, see figure 1. More details about the HCPJ can be found in [START_REF] Hubička | Low Temperature Plasmas. Fundamentals, Technologies, and Techniques[END_REF] and the works cited therein.

The nozzle is made from pure titanium in the HCPJ system for deposition of TiO x films, which was used in the experiments described in this work. The length of the nozzle was 30 mm and its internal diameter was 5 mm. The outer diameter of the ceramic cover was 30 mm. The HCPJ was placed on the axis of a cylindrical stainless-steel vacuum chamber with the height of 35 cm and the diameter of 30 cm. The outlet of the nozzle was in the distance approximately 10 cm from the flange, on which the whole system was mounted. The chamber was grounded.

Pure argon was fed through the nozzle into the chamber. A part of measurements was performed in pure argon and another part in the mixture of argon and molecular oxygen (Ar/O 2 ). In the latter case the oxygen was fed sideways to the chamber to minimize the poisoning of the nozzle, which is acting as a target for sputtering. The chamber was continuously pumped by a turbomolecular pump backed by a Roots pump and a rotary oil pump. The attained ultimate pressure in the chamber was of the order of 10 -7 Pa. The working pressure was 2.7 Pa for the measurements in argon, with the flow rate set to 0.203 Pa•m -3 •s -1 (120 sccm), and 6.7 Pa for the measurements in Ar/O 2 , with the flow rate of argon set to 0.203 Pa•m -3 •s -1 (120 sccm) and the flow rate of oxygen set to 0.101 Pa•m -3 •s -1 (60 sccm). The working pressure was measured by a capacitive gauge and the flow rates were set using mass flow controllers.

The copper block, which was in close contact with the nozzle, was connected to a negative output of a DC power generator through a resistor and a switch, see figure 1. The resistor was used to stabilize the discharge current. The high-voltage switch was used to pulse-modulate the output of the DC generator. A radio-frequency (RF) power generator was connected through a matching unit to a point between the resistor and the copper block. The RF generator was operated in a continuous mode and provided an auxiliary power to create a background RF discharge to stabilize the ignition of the DC discharge after the DC excitation was switched on. It was not possible to obtain a stable pulsed DC discharge without the auxiliary RF power with the experimental configuration we used. The RF generator was operated at frequency 13.56 MHz and the auxiliary RF power applied to the HCPJ was approximately 3 W.

The DC generator was periodically pulsed with the repetition frequency 2.5 kHz and with the varied duty cycle set from 0.1 to 1. A pulse-modulated DC glow discharge with the hollow cathode effect was ignited between the nozzle and the grounded walls of the vacuum chamber. The mean discharge current was always set to 500 mA. When the duty cycle D = 1 was used, the switch was continuously on and actually a DC HCPJ discharge with the discharge current I d = 500 mA was burning. Even in this case, the small auxiliary RF power was applied to the HCPJ for comparison with measurements at different duty cycles, although it was not necessary since the DC HCPJ discharge burns stably.

Time evolutions of the discharge current I d and the corresponding nozzle voltage V d are depicted in figure 2 for selected duty cycles. The time evolutions for discharge in Ar/O 2 are depicted; the time evolutions for discharge in argon were similar. The time evolutions depicted in figure 2 were obtained from the measured ones using adjacent averaging smoothing so that the RF component of the signals, corresponding to the auxiliary RF discharge, was removed. Consequently, the edges of the pulses in figure 2 were a bit distorted/slowed down; the original speeds of the falling edges of voltage V d , and the rising edges of both voltage V d and current I d were approximately 2 µs.

The negative DC value of V d during the space in between pulses corresponds to the DC self-bias of the nozzle due to the auxiliary RF discharge. The mean power applied to the nozzle is depicted in figure 3. The mean power was calculated as

P d = 1 T m Tm 0 I d (t)V d (t)dt, (1)
where T m = 400 µs is the period of the discharge modulation. The ion current was determined using a probe placed on the axis of the nozzle in the distance of 30 mm downstream from the nozzle outlet, i.e. in the usual position of -discharge in argon,

• -discharge in Ar/O 2 .
a substrate. The substrate holder, used for deposition experiments, was removed from the chamber. The probe was a planar copper electrode with the circular cross-section with the diameter 8.1 mm. A ceramic cover was placed from beneath and around the electrode with the space between the electrode and the cover of approximately 1 mm. The electrode was connected by a UHV-suitable coaxial cable to an electrical vacuum feedthrough. On the air side of the chamber a DC generator was connected to the feedthrough through a resistor and a high-voltage switch, see figure 1.

A pulsed negative DC voltage with the repetition frequency of 50 kHz and the duty cycle approximately 0.5 was applied onto the probe. The time evolution of the electric current through the probe I p was measured. Typical time evolution of I p is depicted in figure 4 together with the voltage V g measured between the switch and the resistor on the electrical line to the probe, see figure 1. The generator of the discharge and the generator of the probe pulses were not synchronized. By taking the ion current samples from several consecutive discharge cycles it was possible to acquire the time dependence of the ion current almost continuously over the whole discharge period. The setpoint of voltage V g during the pulses on the probe was held constant, see figure 4. However, the voltage on the probe V p , see figure 1, was varying during the pulses on the probe because the voltage drop on the resistor between the switch and the probe was changing with the current I p , which was different at the different times after the start of the discharge pulse. The voltage V g was set low enough to satisfy V p ≤ -40 V during the pulses on the probe for the whole period of pulse modulation of the discharge. The current I p was approximately constant with V p as was expected from the ion saturation current to a planar probe. Its value for V p = -70 V, which was the lowest voltage used, was only by about 6 % higher than for V p = -40 V. The variaton of I p with V p was therefore neglected.

Depending on the instantaneous probe bias it is possible to follow in figure 4 the time dependence of the negative current (when the probe is grounded) as well as the positive current (when the probe is negatively biased) to the probe. It may seem strange that the negative current component with the probe grounded is comparable to the positive ion current with the probe negatively biased. It is, however, necessary to stress that we cannot separate the positive ion and the electron current to the probe when the probe is grounded. While with the negatively biased probe we measure almost solely the positive ion current with grounded probe we measure the sum of the electron and positive ion current component. That is most probably due to the fact that the plasma potential at the position of the grounded probe lies somewhat above ground, i.e. the probe is sligthly negative with reference to plasma. The grounded probe therefore collects electrons as well as positive ions. The existence of slightly positive plasma potential in a DC driven hollow cathode plasma jet at a certain distance from the nozzle and similar experimental conditions was recently found in [12]. It was also found earlier [8] that the electron temperature in the active phase of the DC driven HCPJ is comparatively low. Hence the electron current to the grounded probe can be reduced down to the level of the ion current by even only small retarding voltage and the positive ion current component to the grounded probe cannot be neglected. Therefore we can see in figure 4 even by a naked eye that the probe positive current averaged over the discharge period exceeds the average value of the negative one. The data illustrated in figure 4 were taken in pure argon so that the only layer on the probe was the (conducting) layer of sputtered Ti. Similar feature, i.e. that the probe positive current averaged over the discharge period exceeds somewhat the average value of the negative one, we observed also in experiments performed in mixture of argon and oxygen. We explain that by the fact that the experiments were made quite quickly and therefore the TiO x layer, which was being deposited on the probe, did not continuously cover the whole surface of the probe and therefore it was still partly conducting.

Results and discussion

The orientation of the probe current I p was chosen as is depicted in figure 1, from the probe to the generator. The current I p is positive during the pulses of negative bias of the probe and equal to the current of positive ions I i from the plasma to the probe since the probe voltage V p is sufficiently negative to repel most electrons there. The composition of positive ions in the plasma under study has not been studied yet, but it can be estimated from the optical emission spectroscopy that the majority of positive ions are Ar + ions, and that some Ti + ions are present. As explained above the negative value of the current I p during the time intervals when the probe bias is off means that electric current of electrons from the plasma to the probe is bigger than the electric current of positive ions there. Only the probe current I p during the pulses of the probe bias, i.e. the total current of positive ions to a negatively biased probe I i , was studied further.

For one period of discharge modulation, the ion current I i was obtained at equidistant time intervals, with spaces between the intervals corresponding to the times when the probe bias was off. Since the frequencies of the discharge and probe pulse generators were not synchronized the phase shift of the equidistant intervals of I i with respect to the discharge modulation was arbitrary for each period of discharge modulation. The temporal dependence of the ion current I i for the whole time interval 0, T m , i.e. without the spaces due to the probe bias being off, was obtained by measuring the probe current I p for several consecutive periods of the discharge modulation. Thanks to the arbitrary phase shift of probe bias modulation with respect the discharge modulation, the intervals of the measured I i covered the whole interval 0, T m typically in less than 10 consecutive discharge cycles.

The time evolution of the ion current density to the probe j i was calculated by dividing the ion current I i by the area of the probe. The measured time evolutions of j i for different duty cycles of discharge modulation D are depicted in figure 5. The time evolution of j i can be divided into the three parts: (i) a transient region after the discharge voltage pulse is turned on, (ii) a stable region during the pulse, and (iii) an afterglow region after the discharge voltage pulse is turned off.

There is a local maximum of j i in the first region. This local maximum and in fact the whole time evolution of j i corresponds to the time evolution of electron density n e at the position of a substrate in the pulsed DC HCPJ, which was studied in [11]. In [11] it was suggested that the local maximum of n e in the transient region can be caused by a short amplification of the auxiliary RF discharge. The hypothesis is following: the auxiliary RF discharge is immediately enhanced by application of high voltage to the nozzle at the start of the discharge pulse, while the hollow cathode discharge does not burn yet. This hypothesis is supported by the fact that the local maximum of j i is bigger for shorter duty cycles, for which the negative voltage applied at the beginning of the discharge pulse to the nozzle has bigger magnitude, see figure 2(b). Then when the hollow cathode discharge starts, matching conditions change and the background RF discharge extinguishes (the RF-formed bias ceases). The main rise of j i starts approximately 50 µs after the discharge voltage pulse is turned on. This delay is most probably caused by a finite velocity of propagation of the dense hollow-cathode plasma from the nozzle to the position of a substrate. From the known distance of the probe from the nozzle this velocity can be estimated to be 600 m•s -1 . The propagation of the plasma from the nozzle can be also observed on the plasma parameters measured in [11] by a Langmuir probe at two different distances downstream from the nozzle, although the propagation was not discussed there. The velocity of the propagation estimated from the mentioned measurements in [11] is 800 m•s -1 , i.e. similar to the velocity estimated form the delay of the rise of j i .

The ion current density j i slightly decreases in the stable region during the pulse of the discharge. This is caused by a slightly decreasing discharge current during the pulse, see figure 2(a).

In the afterglow region, after the discharge pulse is turned off, j i decreases approximately exponentially. This corresponds to the exponential decrease of n e measured in [11], which means the plasma decays by diffusion to the grounded walls of the vacuum chamber. It has to be noted that a fourth region was observed on the time evolution of plasma parameters in the pulsed DC HCPJ in [11]: a region of stable plasma parameters in the space in between pulses, with the plasma parameters corresponding to the auxiliary RF discharge. In this work, no similar region of stable j i was observed in the space, due to the shorter space and lower auxiliary RF power applied here. The new pulse of discharge starts earlier than the plasma decays to a possible equilibrium state with the stable j i corresponding to the auxiliary continuous RF discharge.

The presence of oxygen in the chamber did not significantly change the time evolution of j i , most probably due to the fact that oxygen was added sideways and did not influence the processes in the hollow cathode too much.

The mean ion current density j i was determined by integration of the time evolution of j i over the whole period of discharge modulation. The dependence of j i on the duty cycle of discharge modulation is depicted in figure 6. The mean ion current to a substrate rises with the decreasing D although the average discharge current is kept constant. Although the mean power applied to the discharge P d was rising with decreasing D, the relative rise of P d was much lower than the relative rise of j i , especially for D < 0.4, compare figure 3 and figure 6. Therefore, the rise of j i cannot be explained by the rise of P d only.

We believe that the rise of j i with the decreasing D can be qualitatively explained by a following theoretical model. In the model, j i is divided into the sum of two terms: one corresponding to the time interval of the pulse of the discharge and the second corresponding to the afterglow region in the space in between the pulses. The contribution of the auxiliary continuous RF discharge is neglected in the model. The division of j i into the two parts can be described as:

j i = 1 T m Tm 0 j i (t)dt = 1 T m TmD 0 j i,p (t)dt + 1 T m Tm TmD j i,a (t)dt, (2)
where j i,p is the ion current density during the pulse and j i,a is the ion current density in the afterglow region.

The first term on the right-hand side of ( 2) is assumed to be proportional to the mean discharge current during the pulse. This assumption is based on the fact that j i is directly proportional to the density of the charged particles that is in turn proportional to the discharge current in the HCPJ under the studied conditions [8]. The discharge current is further assumed to be zero in the afterglow region, which is well satisfied, see figure 2(a). Following these two assumptions, the first term on the right-hand side of ( 2) is proportional to the mean discharge current during the whole cycle, which was kept constant. Therefore, the mentioned term is constant as well, and will be marked j i,DC because it corresponds to the ion current density for a DC discharge with the same discharge current as is the mean discharge current in the pulsed DC discharge. It must be stressed that the assumption concerns only the mean ion current density during the pulse [the first term on the right-hand side of (2)] and no assumption about the actual time evolution of j i,p was made.

The time evolution of the ion current density in the afterglow region will be assumed in the form:

j i,a (t) = j i,a0 • exp - t -T m D τ r , (3)
which is the exponential decay from the value j i,a0 at the end of the discharge pulse, with τ r as the time constant of the decay. The ion current density at the end of the discharge pulse is assumed to be:

j i,a0 = j i,DC D . (4)
At the equation ( 4) we arrived by considering the ideal case of a constant ion current density j i,p during the pulse. In such case, the current density j i,p equal to the righthand side of (4) satisfies the condition that the first term on the right-hand side of (2) is equal to j i,DC .

In fact, the ion current density is not constant during the pulse, see figure 5, but it can be expected that it satisfies (4) at the end of the pulse where j i is stabilized, at least for higher D. Again, it has to be noted that no assumption is made regarding the actual time evolution of j i,p , i.e. of the ion current density in the discharge pulse. Only the assumption (4) about the value of the ion current density at the end of discharge pulse is made. The ideal case of constant j i,p serves only to illustrate (4), and to explain how we arrived to that equation.

The proof that (4) is a good approximation is the figure 7, in which the dependence of the experimentally determined product j i,a0 D on D is depicted. The alignment of the data points in the figure 7 around the horizontal dash-dot lines that are defined by the values j i,DC determined for D = 1 means that (4) can be in our case used to reasonably Table 1. The parameters to determine j i according to the model equation ( 5) for the pulsed DC HCPJ with the repetition frequency of the discharge 2.5 kHz and the mean discharge current 500 mA. determine j i,a0 from a single parameter j i,DC for different D, with a good agreement with experiment for D ≥ 0.3, for which duty cycles the ion current density is already stabilized at the end of the discharge pulse.

j i,DC [mA•cm -1 ] τ r [µs] T m [µs]
The mean ion current density can be determined from ( 2)-( 4) together with the assumptions given above as:

j i = j i,DC + j i,DC D τ r T m 1 -exp - T m -T m D τ r . ( 5
)
This equation is the theoretical model of j i , in which D is the independent variable and j i,DC , τ r , and T m are the parameters. The values of the parameters are listed in table 1. The period of pulse modulation of the discharge T m was fixed. The ion current density j i,DC was determined experimentally for a DC discharge with the discharge current 500 mA under the same conditions, including the auxiliary RF power applied. The time constant τ r was for a particular working gas determined as the average value of the time constants determined for each D from the decrease of j i in the afterglow region. This decrease is not exactly exponential in the whole afterglow region and for all D, but it can be fitted well linearly in the semilogarithmic scale, i.e. according to (3), between 50 µs and 100 µs after the pulse is turned off for all cases. The time constants τ r in table 1 were determined from the fits in this time interval.

The comparison of the model with the experimentally determined dependence of j i on D is in figure 8. It can be seen that the model is qualitatively in a very good agreement with the experimentally determined data -the model curve has a very similar shape to the experimentally determined dependence, including the steep rise of j i for D < 0.4. A very good quantitative agreement between the model and the experiment for the discharge in argon, see figure 8(a), is more likely just a coincidence in view of the rough assumptions of the model. From the agreement of the model with the data it can be concluded that the model equation ( 5) describes well the behaviour of j i with the changing duty cycle D under the presented discharge conditions. According to the model, the rise of j i with the decreasing D is caused by the rising contribution of the second term on the right-hand side of (2), i.e. by the rising contribution of the ion current in the afterglow region. That can be qualitatively explained, since for lower D the decay of the ion current in the afterglow region starts from a higher value, see (4), and lasts longer (due to a longer idle time in between pulses while τ r does not differ significantly with D) than for higher D, thus contributing more to the mean ion current. The contribution of the ion current in the afterglow part of the discharge cycle to the mean ion current is then more significant for lower duty cycles.

Conclusion

The current of positive ions to a substrate was studied in the pulsed DC HCPJ system for depositions of thin films. The time evolution of the density of the ion current j i was measured for the discharge repetition frequency of 2.5 kHz and different duty cycles D. Measurements in argon and in the mixture of argon with molecular oxygen, used for actual deposition experiments of TiO x , were performed. The time evolution of j i corresponds to the time evolution of electron density n e at the position of a substrate in the pulsed DC HCPJ. A local maximum of j i is present in the transition region after the pulse of the discharge is turned on, which can possibly be caused by a short amplification of the auxiliary RF discharge by the appearance of the high negative voltage on the nozzle. The main rise of j i is delayed by approximately 50 µs after the pulse is turned on, which is most probably caused by a finite velocity of propagation of the dense plasma from the nozzle to the position of a substrate.

The mean ion current density (ion density averaged over the discharge modulation period) j i was determined. The mean ion current density is rising with the decreasing D although the mean discharge current is kept constant. The rise of the mean ion current density cannot be wholly explained by a relatively smaller rise of the mean power applied to the discharge that was observed for decreasing D. To qualitatively explain the increase of j i a simple theoretical model was presented. In the model, j i is divided into the sum of two terms: (i) one accounting for the contribution of j i during the discharge pulse and (ii) the other accounting for the contribution of j i during the afterglow part of the period, i.e. in the space in between discharge pulses.

The model corresponds well with the experimentally determined dependence of j i on D. According to the model, the rise of j i with the decreasing D is caused by the significantly rising contribution of the ion current in the afterglow region with the decreasing D. We can then conclude that the use of a pulsed mode of the discharge increases the mean ion current to a substrate, especially at low duty cycles, in the deposition experiments of TiO x with the DC HCPJ system with mean discharge current kept constant.

Figure 1 .

 1 Figure 1. A schematic representation of the experimental setup. DC -DC generator, HS -high-voltage switch, MU -matching unit, RF -RF generator.

Figure 2 .

 2 Figure 2. Time evolutions of the discharge current I d and the voltage of the nozzle V d for selected duty cycles D and repetition frequency 2.5 kHz of the pulsed DC HCPJ discharge in Ar/O 2 . The mean discharge current was always 500 mA. D = 1 corresponds to the DC HCPJ with I d = 500 mA.

Figure 3 .

 3 Figure 3. The mean power applied to the nozzle for different duty cycles.

Figure 4 .

 4 Figure 4. The time evolutions of the electric current through the probe I p and the voltage V g measured between the switch and the resistor on the electrical line to the probe. Pulsed DC HCPJ discharge in pure argon with D = 0.3. The pulsing of the discharge is schematically indicated in the lower part of the graph.

Figure 5 .

 5 Figure 5. The time evolutions of the density of ion current to a substrate with the voltage V p ≤ -40 V. The pulsed DC HCPJ discharge in argon and in Ar/O 2 with the mean discharge current 500 mA, repetition frequency 2.5 kHz, and different duty cycle: (a) D = 0.1, (b) D = 0.2, (c) D = 0.4, (d) D = 0.7. The start of the pulse of discharge is at t = 0 s and the end of the pulse is indicated by a vertical dash-dot line in each graph. Note the different scale of the y-axis in different graphs.

Figure 6 .

 6 Figure 6. The dependence of the mean ion current density on the duty cycle of discharge modulation. -discharge in argon, • -discharge in Ar/O 2 .

Figure 7 .

 7 Figure 7. The product of the ion current density measured at the end of the pulse and the duty cycle for different duty cycles of pulsed DC excitation of the HCPJ discharge. -discharge in argon, • -discharge in Ar/O 2 . The horizontal dashdot lines indicate the values of j i,DC determined for the DC discharge (rightmost points, D = 1).

Figure 8 .

 8 Figure 8. The comparison of the model with the experimentally determined dependence of the mean ion current density to a substrate on the duty cycle of the discharge modulation: line -model, symbols -experiment. (a) Discharge in Ar, (b) discharge in Ar/O 2 .

Acknowledgments

This work was supported by projects KAN301370701 and M100100915 of the Academy of Sciences of the Czech Republic, by projects 202/09/0800 and 202/09/P159 of the Grant Agency of the Czech Republic, and by project MSM0021620834 of the Ministry of Education, Youth, and Sports of the Czech Republic.


Amitesh Paul
email: amitesh.paul@helmholtz-berlin.de

Stefan Mattauch

Chemical and Magnetic profile of magnetic semiconductors as probed by Polarized Neutron Reflectivity

Keywords: numbers: 61.05.fj, 75.70.Cn, 75.70.-i, 75.50.Pp

We investigate the depth dependency of magnetic species in co-doped dilute magnetic semiconductor (DMS) specimens. We also compare the reliability in nuclear and magnetization depth profile of these specimens at different polarized neutron reflectivity (PNR) instruments. These reflectometers were not only angle dispersive but also wavelength dispersive instrument. Measurements, indicate a segregation of DMS species on to the top into the cap-layer for lower Fe-doping.

However, for higher Fe-doping, as we alter the doping concentrations of magnetic species, it indicates no segregation and lower clustering tendencies. Thus sensitive depth-profiling, for specimens with such low magnetic-ion concentrations, may not be a challenge for brighter sources and careful measurements. Our results shows that the homogeneity can be achieved with Fe co-doping within the Ge matrix which can make it a potential candidate for spintronic applications.

I. INTRODUCTION A. Ge based Magnetic semiconductors

In recent years one of the remarkable achievements in spintronics was the observation of hole-mediated ferromagnetism in III-V compounds. 1 However, the growth of group-IV ferromagnetic (FM) semiconductors such as Mn x Ge 1-x has also triggered strong interest in searching for higher ordering temperatures T C in Ge-based compounds. 2 Trivalent state of the Mn ion, Mn 3+ (d4, S = 2) is usually coexistent with divalent Mn 2+ (d5, S = 5/2). However, Mn 2+ is necessary for high-temperature ferromagnetism and can be enhanced by appropriate co-doping which are substituted for Ge. These ions, acting as acceptors, generate holes (ptype carriers) that mediate the ferromagnetic exchange interaction. Introducing additional electrons (n-type carriers), on the other hand, can fill the empty Mn d states in the gap, destroying the ferromagnetism.

An ideal magnetic substitution would have increased the magnetization and hence the T C . Low temperature post-growth annealing has been shown to significantly affect the T C as diffusion of Mn into the layer may redistribute the as-grown Mn site occupation, initialized during molecular beam epitaxial (MBE) growth. However, Mn atoms are often susceptible to surface segregation or form segregated phases 3 during annealing. Such phases make the interpretation of ferromagnetic behavior ambiguous as isolated domains may be formed.

Recently, it was reported 4,5 on the synthesis of another candidate for a DMS compound: an alloy of Ge, Fe, and Mn. The addition of Fe to MnGe enables us to conserve the epitaxial growth for higher total concentrations of magnetic species, which results in an increase of T C . The alloy films are prepared by growing repeatedly Ge/Mn/Fe trilayers with various thicknesses of the Ge base layers. When the Ge thickness becomes comparable with the diffusion length of Mn and Fe in Ge, a homogeneous material without interfaces is formed as confirmed by X-ray reflectivity (XRR).

Transition metals are susceptible to form heterogeneous regions within Ge matrix due to their low solubility which may not be completely avoidable even with the help of co-doping process. Thus it is important to know the depth dependent segregation of magnetic species also within such co-doped DMS specimens. Such a study can be extremely sensitive to the quality of the data measured and its subsequent analysis. Thus we present here a detailed investigation that identifies and distinguish such magnetic segregation or non-segregation within the same semiconductor matrix. This paper is organized as follows: Firstly, we describe the interest in our DMS specimens in particular as they are co-doped with Fe and Mn in alternate concentrations. Secondly, we describe the main experimental technique which is polarized neutron reflectivity. Thirdly, it is followed by comparing the instruments at which the measurements are performed. Fourthly, we discuss upon two different models that we employ in analysing the data. Finally we present a comparative study of the polarized neutron reflectivity data obtained from various instruments on different neutron sources, with the purpose to understand the depth dependent segregation of magnetic species in co-doped DMS specimens. The samples are grown by MBE, the details of which have been given elsewhere. 5 For an annealing temperature T A = 300 C a homogeneous alloy is observed by XRR measurements. 6 Magnetization measurements by a superconducting quantum interference device (SQUID) and magnetotransport measurements reveal ferromagnetic ordering, but show two different T C s at 205 K and above 300 K for "DMS2Fe4Mn", which we relate to two magnetic phases.

B. Co-doping with alternating composition of magnetic species

Here

Interestingly, "DMS4Fe2Mn" does not show the high-T C phase and appears in the transmission electron microscope (TEM) picture to be fairly homogeneous compared to the other samples. 5,6 TEM indeed showed the formation of precipitates depending upon the content of magnetic species 5 for the two compositions. A 50 nm of cap-layer (ZnS) on top imposes a serious limitation in extracting the changes in non-magnetic SLD profiles by x-ray after the samples are annealed 6 .

The role of chemical composition, magnetic composition and its diffusion in DMS com-pounds can be explored by a depth sensitive technique such as polarized neutron reflectivity (PNR). 7,8 Such information would be a help in growing uniform films with higher T C . However, from the earlier measurements of the specimens on the HADAS reflectometer at FRJ-2, 6

depth-dependent profile of buried magnetic species was found to be largely restricted by the low signal-to-background ratio. Here, we report on the PNR investigation of any variation in the Mn-Fe distribution with depth after annealing for the homogeneous (DMS4Fe2Mn)

and inhomogeneous (DMS2Fe4Mn) specimens.

For the identification of magnetization in various spintronic materials such as interlayercoupled systems or exchange bias systems 9 or in magnetic semiconducting systems 7 , depth sensitive neutron scattering under grazing incidence 10 with polarization analysis has been proven decisive. Due to the interaction between polarized neutrons and magnetic moments in the specimen, polarized neutron reflectivity (PNR) is sensitive to the in-plane magnetization for a homogeneous film on a microscopic scale and helps in vector-magnetometery of buried interfaces.

II. EXPERIMENT

Over the years, there has been a constant urge to develop new reflectometers on brighter sources. Different reflectometers often use different polarization technique and different options for neutron optical components such as flippers and polrizer/analyzer. In fact it is often felt that it would be quite useful to present the data from different PNR instruments (measuring the same specimens), including angle dispersive and wavelength dispersive instrument, with respect to their reliability of obtaining a proper nuclear and magnetization depth profile. This has not been done yet.

We take this opportunity to use our specimens in measuring at different reflectometers with the aim of digging out the magnetic and compositional depth profile while exploiting the various extrinsic parameters involved with a reflectometer. Our specimens serve an unique example of magnetic-multilayered structure with low magnetic concentration as we show the respective quantitative data analysis in deducing comparative magnetization profiles.

Depth profiling of magnetic semiconductors are particularly challenging as they have very small concentration of magnetic species doped in, as compared to any other. This paper, however, does not intend to state the superiority or inferiority of one reflectometer over the others, but simply tries to convey the practical factors that are to be taken care of or to be incorporated, while measuring such specimens.

A. Reflectometers

Reflectometers have been constructed at both steady state and pulsed neutron sources.

The reflectivity is solely a function of the momentum transfer along the z direction, Q z : a range of Q z can be spanned either by changing the wavelength, and keeping fixed the angle of incidence, or by changing the angle of incidence at fixed wavelength. In the former mode the wavelength is selected by Bragg-reflecting the beam from the moderator with a crystal monochromator. In the second mode the neutron beam is chopped in short pulses:

the neutron wavelength is sorted out by the time-of-flight (TOF) from chopper to detector.

Reflectometers built at steady-state sources are of both kind, while at pulsed sources only TOF reflectometers are feasible. Both types of instruments have distinct advantages. In a TOF instrument a substantial region of Q z is covered simultaneously, without changing the footprint on the sample, by the entire neutron spectrum. On the other hand, with a monochromator instrument one can use all available neutrons to measure the intensities at a selected value of Q z .

We performed measurements of the specimens on various neutron reflectometers, pulsed (TOF) and steady-state sources. The instruments are TREFF(HADAS) at FMR-2(FRJ-2). 6,[START_REF]TREFF at FRM-2 is the recomissioned instrument HADAS from FRJ-2[END_REF] (Forshungreactor Juelich, Germany) 6 , D17 at the ILL (Institut Laue-Langevin, France) [START_REF] Cubitt | [END_REF] and CRISP at ISIS (United Kingdom) 13 . Each of these instruments has some unique features distinctly different from the other (discussed later). This makes the data obtained from each of them interesting to look into with respect to the effect of such changes.

On HADAS, and D17, polarization channels of the specular reflectivities are measured by 2-dimensional position sensitive detector, whereas on CRISP 3 He single detector was used. The measurements are done at different external fields H a , in monochromatic mode for wavelength λ=5.5 Å on D17 (λ=4.5 Å on HADAS and λ=4.73 Å on TREFF) and TOF mode for two different incident angles (0.25 and 0.5 ) on CRISP covering the normal wave

vector transfer (Q ⊥ = 2π λ [sin(α i )+sin(α f )]
) ranging from 0.005 to 0.1 Å-1 . The measurements from CRISP are done without polarization analysis. In specular geometry the angle of incidence α i equals the final angle α f , and λ from a band is selected by the monochromator (HADAS/TREFF and D17) or by set of chopper selecting the wavelength band for the pulsed source (CRISP). All measurements are done after the sample was cooled to 50 K and 250 K from RT by a cryomagnet on D17 and a continuous flow cryostat (inserted between an electromagnet) on HADAS, TREFF and CRISP.

B. Polarized neutron scattering

PNR is sensitive to the nuclear and in-plane magnetic composition throughout the depth of the sample (the neutron absorption cross-sections for the atomic species in the sample are negligible). The scattering-length densities of the magnetic specimen is given by either the sum or difference of the nuclear (ρ n ) and magnetic (ρ m ) components. The neutron interaction potential is given by:

V = 2πh 2 m N b n + µ N σ • B (1) V ∝ (ρ n ± ρ m ),
where N is the atomic density, b n the coherent nuclear scattering length, m the neutron mass, B the internal magnetic field of the specimen, and σ represents the operator associated with the Pauli spin matrices while µ N being the nuclear magneton. The scattering-length densities (SLD) of a magnetic specimen are given by either the sum or difference of the nuclear (ρ n )

and magnetic (ρ m ) components. The ± signs refers to the spin-up and spin-down states of the incident neutron with respect to the polarization of the specimen.

The reflectivity is calculated by applying the time-independent Schrödinger equation for the neutron wavefunction inside and outside the specimen. One can solve the equation by taking into account the spin dependencies of the scattering potential and the neutron wave function. In this way we get the expressions for non spin-flip (NSF) and spin-flip (SF)

scattering. The NSF scattering amplitude provides information about ρ n ± ρ m cosφ A , i.e.

the magnetization component M parallel or anti-parallel to the applied field, where φ A is the angle between the magnetization direction M and the applied field H a . The SF channels measure ρ 2 m sin 2 φ A , i.e. the magnetization component M ⊥ perpendicular to the applied field. In this approach, the magnetic scattering length b m (ρ m = Nb m ) includes the magnetization M and the neutron magnetic moment µ N . specimens. Exact reflection coefficients can be retrieved by the dynamical approach (low Q) within the Parratt formalism. 10 Here a model density profile is considered (prior knowledge of the scattering density) which should be sufficiently close to the correct one. We fit our data within the dynamical approach.

The quality of the fits are found to be similar to that of Kirby et al. 7 which also rely on a similar dynamical range as that of ours. Regarding the sensitivity of our measurements as compared to that of Kirby et al., 7 one may recall that our total thickness of DMS is lower. But this may have been largely compensated by a much higher concentration of magnetic species per unit thickness. On the other hand, similar thicknesses of the cap-layer and that of the DMS (≈ 500 Å) may have reduced the effective sensitivity.

III. RESULTS

Figure 1 shows the measurements for both specimens, at 50 K and at saturating applied fields. The specular reflectivities in the non-spin-flip (NSF) channels (R ++ and R --) are shown for the HADAS measurements. Here + and -sign refers to the intensity R represent the polarization parallel and antiparallel to the guiding field. The SF reflectivities (R +- and R -+ ) are always found to remain below the background intensities (comparing them with that in saturation) and are due to the inefficiencies of the polarizer or analyzer components. As we do not observe any significant SF scattering in HADAS 6 , we do not opt to measure/show the SF scattering in CRISP/D17/TREFF data. The background level was included in all fits as well as the polarization efficiencies were taken care of in the fitting routine. The TREFF data show a comparatively similar background as that of CRISP.

A splitting of the NSF reflectivity channels can been observed for both the specimens at an applied field corresponding to the saturation field (e.g. at H a = 2000 Oe). The splitting is due to the difference in the index of refraction of spin up and spin down neutrons travelling in a magnetic medium. The splitting at low Q (∼ 0.015 Å-1 ) indicates the presence of a ferromagnetic moment pointing along H a . It is visible only at 50K for both specimens. Similar contrast is seen for "DMS2Fe4Mn" even at somewhat lower fields at 50 K, and this net magnetization was seen pronounced at higher fields even at 250 K.

Figure 2 compares the spin-asymmetry (SA) (difference in R ++ and R --divided by the sum of the two) at 50 K and at saturation. The spin asymmetry determines the averaged magnetic moment of the film and the peak amplitudes are largely determined by the magnitude of the net magnetization within the film. Oscillations in SA (recast of the measured data) are observed in the CRISP data, however, they suffer form large error bars specially at higher Q-range. On the other hand, even if the error bars are comparatively lower, the signal is seen to smear out in the background for the HADAS as well as for the D17 data at higher Q-range. The data from TREFF also retains the oscillations for similar Q-range.

IV. DISCUSSION

A. Comparison of the data from various reflectometers

As the measurements are from the same two samples under similar conditions but on three (four) reflectometers, we compare the respective measurement parameters to account for their differences in the spectrum.

One may recall that

∆Q/Q = cot 2 α i (∆α i ) 2 + ( ∆λ λ ) 2 , (2)
which can be expressed as (for small α i , cosα i ∼ 1 and sinα i ∼ α i )

∆Q/Q = ( ∆α i α i ) 2 + ( ∆λ λ ) 2 (3)
The wavelength resolution and the angular resolution are determined by ∆λ λ and ∆α i α i respectively, as the wavelength

λ = 4π sin α i Q (4)
(Q=momentum transfer vector). Here ∆λ and ∆α i are the uncertainties in wavelength and angle respectively. The wavelength resolution was fixed (by the neutron monochromator)

for D17 (optionally chosen in the present case), TREFF and HADAS. For CRISP this can be made variable with choppers. The angular resolution, on the other hand, can be adjusted by using a pair of slits in front of the sample (and also on the binning of the data on the detector).

HADAS/TREFF measurements were done with a wavelength resolution (∆λ/λ) of 1.5% while at D17 and CRISP it was around 4% and 3% respectively. The difference between TREFF and HADAS being primarily the neutron flux from the high-flux reactor FRM-2 in This gives a direct example on the effect of flux on the data. A further comparison can be made following the HADAS and TREFF data as the angular resolution was restricted for TREFF (with same wavelength resolution) as compared to that for HADAS. The relaxed angular resolution (which in turn relaxes the overall Q resolution) and low neutron flux with with formidable background was found not to be suitable for very sensitive data analysis.

D17 being based on a high-flux reactor, the measurements were done with relaxed resolution. A similar relaxed resolution (as that of D17) was employed while measuring on the TOF reflectometer CRISP. This gives an example of measuring on reactor based instrument and that on TOF mode. The difference in the data with D17 and CRISP is basically due to their respective angular and wavelength resolutions in obtaining a relaxed Q-resolution for both that was chosen to increase the intensity.

For CRISP, though the drop in intensity is below 1 × 10 -5 (five orders of magnitude), it suffers from large error bars (owing to the relaxed binning in TOF mode). On the other hand, the measured dynamical range remain small (as the intensity drops by 1 × 10 -3 ) for HADAS and for D17 (drops by 7 × 10 -2 ) which limits the information that can be retrieved from them (due to limited Q range).

We present the data from different reflectometers (for the first time) to show that the extraction of the data from various detectors by different means can bring some minor changes in the interpretation of the data. The respective differences in SLD profiles are nominal and do not affect the overall interpretation. The fits to the data are done with the same program, which indicates to the fact that the interpretations are not dependent upon data treatment. For practical purpose, data extraction from a 2d-detector (done in case of the HADAS data) or from a linear detector (as done in case of the ISIS data) can suffer from little discrepancies as well. This presents therefore a realistic scenario which cannot be ignored. If they were not measured at different sources and/or instruments this discrepancies would have been unnoticed.

B. Segregation and non-segregation model treatments

The data has been fitted considering a mixed layer of Ge, Fe, and Mn capped with another layer of ZnS. We employ here two different models for our fits. Model-1 (M 1 ) considers no segregation of species (magnetic) on to the top cap layer while model-2 (M 2 ) considers a segregation of co-dopants in the DMS layer. Segregation of the DMS layer is identified by the movement of the magnetic species along the thickness of the sample. Such a segregation, on annealing, may lead to an inhomogeneous distribution of the species within the layer.

However, it has been often observed that such a segregation which occurs particularly for the magnetic species, results in their movement to the top of the layer surface. Such segregated magnetic species are susceptible to form small clusters and act as independent magnetic regions. Thus they behave as isolated domains within the semiconductor matrix and cannot therefore be considered as a true DMS layer any more.

A homogeneous layer is characterized by a single magnetic phase (magnetization curve showing single transition temperature as in the case of DMS4Fe2Mn) while clustered species can lead to a second transition temperature (as in the case of DMS2Fe4Mn). Now as our specimens are covered with a cap-layer, it is likely that the magnetic species may even move into the cap-layer of ZnS. This is why we consider two different models for our simulations or fits where the ZnS layer is considered as non-magnetic in model-1 and as magnetic in model-2. In this way, by comparing the two situations for a single specimen, we would be able to identify any segregation in the sample.

The nuclear part (ρ n ) as well as the magnetic part (ρ m ) of SLD is considered as fitting parameters for model-2, as a segregation magnetic species would also alter the nuclear part of the SLD for both (cap and DMS) layers. This is done by keeping in mind of the typically observed 'phase problem' in neutron scattering which arises due to implicit phase information in the scattering terms from individual layers. As we rely on analyzing the data from a Fourier transform of the nuclear and magnetization profile, treating the data in such a way, would not only identify any segregation but also crosscheck our inference on the magnetization profile. The goodness of any fit is certainly dependents upon the quality of the data. Thus if any modification of the layer characteristics (comparing the fits from M 1 and M 2 ) i) fails to improve the quality of the fit, then we may infer it as a case of no segregation into the cap-layer. ii) if the quality of the fit remains similar, then any inference drawn from the data would obviously be ambiguous. iii) On the other hand, if the quality of the fit is significantly improved, then the data (even within the limited range) can be considered as sensitive enough to identify such segregation.

Now we compare the fits to the data involving the two models M 1 and M 2 (note that fits to the data in Figure 1 are shown for treatment with M 1 only). The fits in black and red lines, in Figure 2, corresponds to the treatment of the data without considering any chemical or magnetic variation with depth for the DMS layer (M 1 ). This is the case we start our least square fits by restricting the parameters to the situation where we consider the DMS layer to be homogeneous. The fitting parameters that are let free are the individual layer thicknesses, the nuclear part and magnetic part of the DMS layer SLD and the nuclear part of the cap-layer SLD. Note that the magnetic part of the cap layer (ρ m ) is restricted to zero in this model. The abruptness or smoothness of SLD profiles are dependent upon the number of slices one undertakes in the density profile during the fitting. The case presented here are to show that even with an abrupt profile the fits are reasonably good enough for our interpretation.

On the other hand, the fits in gray and cyan lines, consider DMS layer to segregate on to the top (M 2 ). In this case, we consider that the DMS layer is inhomogeneous and the magnetization observed, is due to the formation of isolated domains that may have crept into the ZnS layer. The restriction on the magnetic part of the cap-layer is now lifted and has been used as a fitting parameter, free to converge. The corresponding SLD variation in depth has been shown alongside of Figure 2. The SLD variation incorporates a variation in the nuclear as well as the magnetic part simultaneously.

C. Sample: DMS4Fe2Mn

We now look into the fits following M 1 . In this case, the ρ n (black line) and ρ m (red line) remains fairly similar for the data from the three reflectometers. Note the goodness of fit factor (χ 2 ≈ 0.01(HADAS), 0.08(D17) and 0.28(CRISP)) for the respective data. Larger error bars in the CRISP data has lead to an increased χ 2 . However, similar SLD values have been obtained from the fits to the data from all the instruments (variation is around 5%). This is probably the first representation of similar data measured at different instruments.

On the other hand, if we look into the fits to the data following M 2 , the χ 2 remain very similar to that obtained with M 1 for the HADAS data with no real change in the fit parameters. Thus the HADAS data is considered as insensitive to any segregation of magnetic species. The D17 data on the other hand do show a considerable increase in the magnetic part of SLD but without any drastic change in the other free parameters and even manages to attain a similar χ 2 . This is therefore a typical example of the fact that any depth-information from such data can lead to ambiguous results.

The fits to the CRISP data, do not allow much changes for the nuclear parts of the respective layers as they remain close to the fitted value as that has been obtained using M 1 . Even though the magnetic part of the ZnS layer shows some increase with respect to that in M 1 , the bad quality of the data at higher Q values (large error bars) does not permit any convincing interpretation and the χ 2 remains almost similar.

No improvement in χ 2 (rather worsen by ∼0.07) is obtained for DMS4Fe2Mn when treated by M 1 and M 2 for the data set from TREFF. This implies that a segregation model (M 2 ) fails to improve the fit over non-segregation model (M 1 ) for DMS4Fe2Mn. Instead of a similar χ 2 (as in case of HADAS or CRISP data when treated with the two models), we found an increase in χ 2 while fitting within M 2 as compared to M 1 . This already strongly indicates the non-segregation in this specimen.

D. Sample: DMS2Fe4Mn

Within the M 1 model, the goodness of fit factors (χ 2 ≈ 0.01(HADAS), 0.07(D17) and 0.33(CRISP)) for the respective data are given alongside the figures. The fits to the data from HADAS, D17 as well as from CRISP hardly show any significant difference with respect to DMS4Fe2Mn, expect for the relative changes in the nuclear and magnetic part of the SLD (here the variation of the fitted values on different instruments is around 7-10%). Even the respective χ 2 remains similar to the case of DMS4Fe2Mn.

Interestingly, when they are fitted with M 2 , the χ 2 (≈ 0.01(HADAS), 0.05(D17) and 0.20(CRISP)) is found to be somewhat lower (for D17 and CRISP). This in way indicates a validity for the segregated model. The HADAS data, however, remain similarly insensitive.

The fits to the D17 data, which does not allow any drastic change of the nuclear part,

shows some magnetic contribution throughout the depth of the layer thicknesses as the χ 2 is slightly reduced by (∼0.02) as compared to the fits by M 1 . Now let us focus onto the fits to the CRISP data. Here, similar to the case of DMS4Fe2Mn, the nuclear part remains almost similar to that obtained using M 1 . However, the corresponding magnetic part has attained a uniform distribution. This tendency, was also obtained from from D17 and in a way indicates to the fact that DMS2Fe4Mn is more susceptible to segregate than DMS4Fe2Mn. The magnetization that was observed for DMS4Fe2Mn from SQUID, is therefore cannot be intrinsic to the DMS layer but, can be owed to the presence of segregated clusters. Our present results for DMS2Fe4Mn corroborate with previous measurements by TEM or SQUID on similar specimens 5,6 . This is further confirmed with the TREFF data as we find that for DMS2Fe4Mn, a clear improvement (improved by ∼0.05) is achieved when M 2 is employed as compared to M 1 .

Therefore, it can be concluded, that a sufficient level of segregation of magnetic species into the cap layer has taken place in DMS2Fe4Mn (inhomogeneities for higher Mn-doped specimens). While in DMS4Fe2Mn, no such segregation has been indicated by PNR, at least from the TREFF data (the data from HADAS, D17 and CRISP remain ambiguous).

From the measurements at various instruments, we realized that sensitive measurements are significantly determined by the angular resolution and the wavelength resolution that has been employed during the measurements in addition to the neutron flux at the sample position and the background level at the instrument. The HADAS data was measured with a relaxed angular resolution ( 3.5%) but with a restrained wavelength resolution ( 1.5%) and most importantly was also limited in its neutron flux. The D17 data, on the other hand, was rich in its neutron flux and was measured with a stricter ( 1.5%) angular resolution.

However, the wavelength resolution was relaxed to ∼4%. Thus the overall Q resolution was relaxed to ∆Q Q ≈4% for both measurements. Apparently such a resolution would have been sufficient in observing the differences in spin-asymmetry. However, such is not the case here, as the background level at the instruments was found unsatisfactory for such sensitive measurements. The CRISP data, on the other hand, had the advantage of high neutron flux and also lower background. However, the wavelength resolution was again relaxed to be around 3% which might have affected the overall Q resolution. The error bars in the CRISP data also contributed to its inconclusiveness. Comparing the CRISP data with that of others one may notice that the CRISP data has many more data points. A more aggressive rebinning would have reduced the magnitude of the error bars (reducing the number of data points at the same time), particularly at high Q.

It is quite evident from the fact that the fits to the data (HADAS, CRISP and D17) remain largely insensitive to the two different models (M 1 and M 2 ) employed for the two specimens. Although segregation model (M 2 ) apparently implied magnetic contribution within the cap-layer (see SLD variation from the D17 and CRISP data) for DMS2Fe4Mn (lowering of χ 2 ), nothing conclusively can be inferred about segregation or non-segregation in these specimens. Thus, in addition to a high neutron flux, it was felt that a stricter Q resolution and a cleaner background are required for such challenging experiments. The spin-asymmetry signal is seen to die down at around 0.03 Å-1 . One may note that we have made no corrections to the raw data and have incorporated the resolution functions and the background level into the fitting routine. In Figure 3 Here the neutron flux was high, the wavelength resolution was restricted (similar to that at HADAS), the angular resolution was restricted (similar to that at D17) and the background level was also kept as low (close to that at CRISP) as possible. The overall Q resolution was restricted to ∆Q Q ≈2%. Even though this cannot be a strong reason for the observed differences in SLD values, we would like to draw the attention over the spin-asymmetry signal with Q. The spin asymmetry signal can be seen even around 0.06 Å-1 for TREFF as compared to 0.03 Å-1 for the other two angle-resolved instruments. We believe that all of these factors -in combination -have certainly assisted in a better estimation of the parameters particularly being able to observe a spin-asymmetry signal at a higher Q.

Without the experience from the different reflectometers it would not have been possible to perform such a sensitive and challenging measurement. Variation of different instrumental parameters and conditions are certainly not expected within a single reflectometer. This also justifies our effort in measuring at different reflectometers in digging out a comparative depth sensitive magnetic segregation from our DMS specimens. One must also remember here that retrieving the SLD profile from a measured data is restricted primarily by the phase problem as conventional reflectivity measures only | r(Q) | 2 of the complex reflection amplitude r(Q) and suffers from general nonlinear dependence of measurements on the SLD. 10 Thus even two different SLD's can simulate similar patterns or vice-versa. This is more significant in the low-Q regime where the Born approximation typically breaks down. With polarized beam, retrieving the profile becomes even more difficult due the additional magnetic parameters get involved along with halving the available intensity. However, methods that can be used, in principle, for determining the phase of reflection is beyond the scope of this paper.

We compare the fitted parameters from the two specimens as obtained from the PNR data. The average magnetic moment per magnetic atom (µ m ), estimated from the fitted values of ρ m , are are slightly different from different fit values. However, considering the average values from TREFF (and other instruments), assuming atomic density of magnetic species to be 0.19N Ge and using the equation ρ m =N µm µ B 2.695×10 -6 nm we arrive at the respective values of 0.07µ B (DMS4Fe2Mn) and 0.09µ B (DMS2Fe4Mn) per magnetic impurity atom respectively (here µ B is the Bohr magneton). Here, the respective scattering length densities (Nb m ) are 1.35 µm -2 and 1.75 µm -2 . The atomic density of the DMS layer can be approximated as the density of Ge (=38 nm -3 ) from where one can determine N (= 0.19 × 38 = 7.22 nm -3 ). Our calculations are in agreement with our magnetization data reported earlier 6 . For DMS4Fe2Mn, larger error bars in the data (CRISP) along with a lower effective magnetic moment, could not indicate of the inhomogeneities throughout the depth of the film. Recent theoretical calculations on similar systems have shown that the physics of magnetic interaction between the two different dopant magnetic species in Ge based systems, are in complete agreement with the findings of this paper 14 .

V. CONCLUSION

In conclusion, we present a comparison of the PNR data obtained from various instruments on different neutron sources in an effort to investigate the depth dependent segregation of magnetic species in co-doped DMS specimens. We find that PNR could effectively indicate of such segregation when the effective magnetization within the DMS layer (due to co-doped magnetic-ion concentration) is significant enough. Depth profiling for specimens with even lower magnetization (due to alternate co-doping of magnetic-ion concentrations), is a challenge that can be overcome with the brightest sources available and with proper care of the overall Q resolution and a lower background level at the instrument. The samples investigated indicate no segregation and lower clustering tendencies for higher Fe co-doping.

  40 Å)/Fe(4 Å)/Mn(2 Å)] ×11 /ZnS(500 Å) named DMS4Fe2Mn and [Ge(40 Å)/Fe(2 Å)/Mn(4 Å)] ×11 /ZnS(500 Å) named DMS2Fe4Mn. These samples are particularly interesting as they are covered with thick cap-layers and therefore become a challenge in the extraction for the depth profile, not possible by other techniques. More particularly when they lack in periodic layer structures and thus evaluating the Fourier transformed spectra is even more susceptible to complication.

  Figure 4 the unpolarized data (measured with the same angular and wavelength resolutions as that for the polarized one) from the two specimens that clearly indicate of their high quality -needed for our measurements. The difference in their respective critical angles of total reflection does indicate different chemical compositions of the cap-layer and the shift of the Kiessig fringes indicates slightly different total thicknesses for the two specimens.

FIG. 1 :FIG. 4 :

 14 FIG. 1: (Color online) Measured (solid symbols) and fitted (open circle) NSF [R --(black square) and R ++ (red circle)] reflectivity patterns of "DMS4Fe2Mn" and "DMS2Fe4Mn" measured at saturating applied fields H a and at 50 K. The earlier measurements from HADAS are also shown for comparison. The fits to the data are treated within the dynamical approach considering no segregation (model M 1 ) and uniform scattering length density of individual layers with thickness.No background substraction or correction for polarizing efficiencies are done to the data as they are considered within the fitting routine.

We thank H. Braak for providing the samples. A. Paul acknowledges the support from Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany during a part of the work. The cooperation of A. Wildes and T. Charlton are also appreciated during the measurements at the respective beamlines.