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Preparation and electrical properties of InSb thin films heavily doped with tellurium, selenium and sulphur
Thin Solid Films, 111(1984)~351-366
351
PREPARATION AND CHARACTERIZATION
PREPARATION AND ELECTRICAL PROPERTIES OF InSb THIN FILMS HEAVILY DOPED WITH TELLURIUM, SELENIUM AND SULPHUR T. BERUS, J. GOC, M. NOWAK, M. OSZWALDOWSKI
AND M. ZIMPEL
Instiiute of Physics, Technical University of Poznari, 60-965 Poznati, Piotrowo 3 (Poland) (Received April 19, 1983; accepted October 21, 1983)
A method of controlled donor doping of flash-evaporated InSb thin films in the concentration range 10’7-10’g cmm3 is described. When such films are regrown from the melt the electron concentration increases several times and the room temperature electron mobility increases by about an order of magnitude. The room temperature mobility of the regrown films is close to that observed in bulk InSb. The temperature dependence of the mobility between 80 and 700 K shows that barrier scattering plays an important role in all flash-evaporated and melt-regrown films with effective donor concentrations Nd of 1018 cmm3 or less. In the flashevaporated films the barrier height increases from a value of 65 meV for N, = IO” cme3 to 150 meV for N, = 9 x 10’s cme3. No such increase is observed in regrown films. This suggests that the barriers in the two types of films are different. The increase in electron concentration in regrown films is discussed and the most consistent explanation of the effect is that a large number of conduction electrons are trapped at grain boundaries in the flash-evaporated films. The application of the heavily doped melt-regrown InSb films as Hall generators is also discussed.
1. INTRODUCTION
The group VI elements are incorporated into the InSb crystal lattice substitutionally, replacing the antimony atoms. In these positions they are shallow donors forming an impurity band that overlaps the conduction band at concentrations above lOi cmm3. Many papers published in the last decade have been devoted to the transport properties of heavily doped n-InSb crystak. Earlier results were summarized in a review article by Filipchenko and Nasledov’. In contrast with the case for crystals, little is known about the properties of heavily doped InSb thin films. Wieder and Clawson’ investigated the room temperature electron mobility in vacuumevaporated sulphur-doped InSb thin films which had been regrown from the melt, They found that in the donor concentration range from 5 x 1016 to 7 x 10” crn3 the mobility was about two-thirds of that in tellurium-doped InSb crystals. Wieder and Collins3 investigated the thermal dependence of the Hall coefficient in films heavily doped with sulphur and tellurium. In the work reported in refs. 2 and 3 the 0040~6090/84/$3.00
0 Elsevier Sequoia/Printed in The Netherlands
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dopants were introduced into the InSb films by adding sulphur or tellurium to the indium used as the starting material for the film preparation. In the present paper we describe an alternative method of preparing heavily doped InSb thin films. The method offers controlled doping and high electron mobility and therefore can be used for practical applications such as the preparation of Hall generators for precision measurements of magnetic field strength. In this case the virtual magnetic field independence of the Hall coefficient of heavily doped InSb and its greatly reduced dependence on temperature can be exploited. These important properties can be fully achieved only in a high mobility thin film material. Investigations of InSb crystals heavily doped with tellurium, selenium and sulphur suggest that the transport properties depend on the nature of the dopant1*4. It therefore appeared interesting to examine whether a similar dependence exists in InSb thin films. Investigations of InSb films doped with various donors over a wide concentration range should also lead to a better understanding of their electrical properties, in particular the anomalous temperature dependence of the electron mobility. The electrical properties of InSb thin films are strongly affected by structural defects. However, it is known that impurities in heavily doped semiconductors can interact with structural defects’. For this reason our investigations were carried out on InSb films with various structural properties. 2.
FILM PREPARATION
The experimental arrangement used for the film preparation is shown in Fig. 1. It was set up in a standard vacuum apparatus in which the working pressure was below 10e3 Pa. Doped InSb films were obtained by flash evaporation with simultaneous dopant sublimation from an independent dopant source. The starting materials were a zone-refined InSb crystal with a net donor concentration of about 10” cme3 powdered to grains of size 100-150 urn and a Specpure dopant material. A tungsten strip heated to 1600 K was used as the InSb evaporation source. The mean film deposition rate was 2-3 urn h- ‘. The films were deposited through a mask which was part of the substrate holder onto a substrate of dimensions 12 mm x 8 mm heated to 700 K. B-Si glass and Sital ST-50-l (a sintered polycrystalline material composed of MgO, CaO, Al,O, and SiOZ which is made in the U.S.S.R.) were utilized as substrate materials. The substrates were carefully cleaned prior to the deposition process. The final stages of the cleaning were surface purification in an isopropyl alcohol vapour stream and vacuum annealing at 750 K for 30-60 min which was performed immediately before the film deposition. Graphite Knudsen cells heated by a tungsten wire were used as dopant sublimation sources. Sublimation of the dopant and evaporation of InSb were started simultaneously, and when thermal equilibrium was achieved a rotary shutter located above the sources was displaced to allow film deposition. The Knudsen cell heater current was increased in successive evaporation runs, resulting in the preparation of InSb films with increasing impurity concentration until the limiting concentration for a given dopant was reached. Before starting this doping procedure with another dopant, the Knudsen cell was removed and the inside of the vacuum chamber was cleaned to remove the residual dopant contamination. The substrate holder allowed up to 22 InSb films to
InSb THIN FILMS DOPED WITHT~,S~
1 -1 -_ 3 -. 4 -.
AND S
353
I- 2 ,_ 1 2
6, 7
.- 1 6
-- 1
Fig. 1. The arrangement used for the flash evaporation of doped InSb thin films: 1, thermal screens; 2, substrate furnace; 3, substrate holder; 4, thermocouple; 5, powdered InSb feeding mechanism; 6, shutter; 7, InSb evaporation source; 8, dopant evaporation source.
be obtained in a single evaporation run. The electrical properties of the films appeared to be slightly dependent on the substrate material used. In general, higher electron mobilities were obtained for films evaporated on the Sital substrates. All the films were covered with a protective layer of SiO, (1 < x < 2) 0.1 urn thick obtained by sublimation of high purity SiO in a separate vacuum apparatus at a pressure of about 10m2 Pa. About 500 InSb films doped with tellurium, selenium and sulphur were prepared in this way. Half of these films were regrown from the melt in ambient air. Both natural crystallization6 and microzone crystallization’ were used for this purpose. Since the electrical properties of the films prepared using the two methods were the same, most of those investigated were prepared by the
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simpler natural crystallization method. Most of the films were deposited on Sital substrates and were 2-3 urn thick. The film thickness was measured using an interference microscope. It should be pointed out, however, that the InSb films which were regrown from the melt had slightly warped surfaces and therefore their thickness was taken as the average value along the film. All the electrical measurements were carried out on InSb films protected by an SiO, layer. Chromium electrodes were vacuum evaporated onto the films for the measurements. An InSb film equipped with electrodes is displayed in Fig. 2. Chromium was used because of its small diffusion coefficient and low solubility in InSb *. Thus the possibility of diffusion of the electrode material into the InSb films during high temperature measurements was reduced and in fact was not detected. Good electrical contact was formed between the chromium electrodes and the edges of the protected InSb films.
Fig. 2. InSb thin film equipped with chromium electrodes for Hall and conductivity measurements. The substrate dimensions are 12 mm x 8 mm.
3. STRUCTURAL ANALYSIS Flash evaporation is a well-known method for the preparation of stoichiometric InSb thin films9. The electrical properties of flash-evaporated InSb films are strongly affected by their structural defects. The most important defects limiting the electron mobility are grain boundaries. The mobility increases with increasing grain size, and the mean grain size depends on preparation conditions such as the substrate temperature during deposition and post-deposition annealing and the film thickness’-“. We have found that doping has little effect on the structural properties of flashevaporated InSb films. The surface of such a film treated with a selective etchant to reveal the crystal defects in InSb is shown in Fig. 3(a). It is seen that the film consists of randomly oriented crystallites of dimensions about 1 pm. Twinning along (111) planes can be seen in some of these crystallites. The random orientation of the crystallites is confirmed by X-ray analysis. The analysis shows that crystallites with (11 l), (lOO), (1 lo), (112), (113) and (133) planes parallel to the substrate appear in roughly equal numbers. When a film such as that shown in Fig. 3(a) is not etched, its top surface is
InSb
THIN FILMS DOPED
WITH
Te, Se
AND
S
355
(W
500 brn Fig. 3. Surfaces of InSb thin films etched in a 1:3 solution of HNOe-400/, C2H402 (COOH), in water: (a) replica electron micrograph of a flash-evaporated film;(b) optical micrograph of a film regrown from the melt.
decorated with partly oxidized indium droplets of diameter about 0.1 pm. The mean distance between the droplets is of the order of 1 pm. Comparison of the electrical properties of the etched and unetched films showed that the indium exclusions did not seriously affect the electrical properties of the films. Because the exclusions were absent in Sims evaporated at lower substrate temperatures, we concluded that they were due to the partial re-evaporation of antimony at a substrate temperature of 700 K. However, we observed that the amount of agglomerated indium increased in films doped with selenium and sulphur to the solubility limit. This phenomenon was not observed in the tellurium-doped films. We cannot offer any explanation for the behaviour of the films which were heavily doped with selenium and sulphur.
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Regrowth of the vapour-grown (VG) InSb films results in a complete reconstruction of the crystal. As can be seen in Fig. 3 the melt-regrown (MR) InSb films consist of large irregular crystallites. The crystallite shape is the result of partial dendritic growth due to the rapid crystallization of the melt. Structural defects typical of dendritic growth” are therefore expected to appear in the MR InSb films. Defects associated with the plastic deformation occurring in crystals constrained during the freezing process are also expected. No preferential crystallographic orientation is found in the MR films. The result of the X-ray analysis is essentially the same as that obtained for the VG films. The structural properties of the present MR films are substantially the same as those reported for undoped MR films6. 4.
HALL COEFFICIENT AND ELECTRON MOBILITY
The Hall coefficient in InSb films was determined using the conventional d.c. technique with a magnetic field of 0.4T. The driving current in the film and the voltages on the Hall and conductivity contacts were measured using sensitive digital meters. The electron concentration n and the Hall electron mobility pn in the films were determined from the experimental values of the Hall coefficient RH and the conductivity 0 using the relations
RHden
A conventional cryostat equipped with a temperature controller was used for the Hall measurements in the temperature range 77-300 K. The measurements in the temperature range 300-700 K were performed in a specially designed small furnace placed between the magnet poles. The furnace temperature was programmed using the temperature controller. Owing to the good protective properties of the SiO, overlayer the measurements were carried out in ambient air. The first task was to determine the limiting concentrations of the dopants in the MR InSb films. The limiting concentration of tellurium was obtained directly from the Hall coefficient measurements as 1.5 x 10” cm- 3. However, only approximate values of the limiting concentrations of selenium and sulphur could be obtained because the indium exclusions (see Section 3) decreased the measured Hall coefficient as a result of shortcircuit effects. The approximate values obtained were 8 x 10” cm- 3 for selenium and 6 x 10” cm- 3 for sulphur. These limiting concentrations are in good agreement with those determined for InSb monocrystals’. The dependence of the room temperature electron mobility on electron concentration in InSb films doped with tellurium, selenium and sulphur is shown in Fig. 4. The electron mobilities of the MR films are the maximum values found in our experiments. The figure shows that the electron mobilities in the tellurium- and selenium-doped MR films can be as high as those obtained in bulk InSb. In contrast, the electron mobilities in the sulphur-doped MR films are generally lower than those in the tellurium- and selenium-doped MR films. Thus the dependence of the electron mobility on the nature of the dopant, which was reported for bulk InSb 13, is only
InSb
THIN FILMS DOPED
Te, Se
WITH
AND
S
357
partially manifested in the MR films as no difference between the electron mobilities of tellurium- and selenium-doped films was detected. However, it should be noted that the occurrence of high electron mobilities is statistically more frequent in tellurium-doped films. The electron mobility in the VG InSb films is about an order of magnitude less than that in the MR InSb films for the same doping level. It is interesting that, despite the difference in magnitude, the electron mobilities in the two types of InSb film show very similar concentration dependences. Another puzzling feature is the increase in the effective donor concentration in the MR films: the concentration increases by a factor of 2-3 in the tellurium- and selenium-doped films and by as much as an order of magnitude in the sulphur-doped films.
lo2
1016
1
I
t
II 10"
I
I
I
II
1
lo'8
I
III
I
lP n Icmsl
Fig. 4. The dependence of the room temperature electron mobility on electron concentration in VG (0, A, I) and MR (0, A, 0) InSb films doped with tellurium (0, 0) selenium (A, A) and sulphur (I, 0): ---, lines linking parameters of the same films before and after regrowth from the melt; -, theoretical dependence for InSb monocrystaW3; shaded area, the experimental dependence for InSb monocrystalsr3.
The temperature dependence of the electron mobility in the doped InSb films is shown in Fig. 5. It can be seen that the dependence in the VG films differs from that in the MR films. In the VG films the electron mobility decreases with temperature, in contrast with the behaviour of bulk InSb. This anomalous behaviour also occurs in undoped VG and MR InSb films 2*g-11. At high temperatures phonon scattering comes into operation and produces a maximum in the curve of mobility uersus temperature. The position of the maximum depends on the magnitude of the mobility: the lower the mobility the higher is the temperature at which the maximum appears. For this reason the mobility maximum in Fig. 5(a) is observed only for the films with low dopant concentrations. A similar anomaly in the temperature
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loJl-uL-J loll 102
64
TCKI
103
(W
102
T [Kl
Id
Fig. 5. Temperature dependence of the electron mobility in (a) the VG InSb films and (b) the MR InSb films: ---, barrier-limited mobilities calculated from eqn. (10). The symbols are as defined in Fig. 4 and the numbers on the curves denote the effective donor concentration in the films.
dependence of the electron mobility is observed for MR films with donor concentrations below about lo’* cme3. At higher dopant concentrations the mobility increases with decreasing temperature in a similar manner to the behaviour of bulk InSb. The temperature dependence of the Hall coefficient of the InSb films is shown in Fig. 6. As expected it does not depend on either the film structure or the nature of the dopant. R, decreases at high temperatures in all the films with donor concentrations below 4 x lo’* cme3 as a result of the transition from extrinsic to intrinsic conductivity. However, RH increases at high temperatures in films with donor
-‘H
I0 1
2
3
4
5
6 7 8 9 lo'?/, [K-'I
10 11 12 13 14 15
Fig. 6. Temperature dependence of the Hall coefficient in doped InSb thin films. The symbols are as defined in Fig. 4 and the numbers on the curves denote the effective donor concentration in the tilms.
InSb
THIN FILMS DOPED WITH
Te, Se AND S
359
concentrations above 4 x 10’s cm- j. This 1 and InSb thin films3, is interpreted in terms of electron transfer from the minimum of the I conduction band to the subsidiary L minima at the edges of the Brillouin zone. In the transition range, i.e. at donor concentrations between 2 x 10’s cm - 3 and 4 x lOi* cme3, the Hall coefficient is virtually temperature independent in the vicinity of room temperature. The electron mobility in the MR films at such donor concentrations is about 1 m2 V-’ s-r, and hence these films are suitable for applications in Hall generators. In view of these applications and the known drastic reduction of the electron mobility in undoped InSb films of thickness below 2 urn l4 it appeared desirable to investigate the thickness dependence of the electron mobility in the heavily doped MR InSb films. The results of the investigation for tellurium-doped films with a dopant concentration of (l-2) x lo’* cmm3 are shown in Fig. 7 where it can be seen that there is no drastic reduction in the mobility down to a film thickness of about 0.3 urn. In fact the observed small drop in the mobility is due to the non-uniformity in film thickness rather than to any additional scattering mechanism, e.g. surface scattering. The surface tension which exists during melting has a more marked effect on the thinner films, and therefore we were unable to obtain films with thicknesses less than 0.3 urn as they were torn during the regrowth procedure.
5 t
Fig. 7. Thickness dependence of the room temperature electron mobility in tellurium-doped InSb films with a donor concentration of (l-2) x 10’s cmJ. 5. DISCUSSION
Our investigations have shown that regrowth from the melt increases not only the electron mobility but also the electron concentration in doped InSb films. The following mechanisms may be responsible for this concentration increase. (1) Some of the doping atoms in the VG films may be incorporated into the crystal matrix in an electrically inactive form, e.g. they may occupy interstitial sites. During the regrowth they will enter substitutional sites and thus become donors. (2) Some of the doping atoms in the VG films may precipitate at defect sites such as grain boundaries, twin planes and dislocations. During the regrowth they will dissolve in the film and become donors. (3) Donors in the VG films may be partially compensated by defect acceptor centres. The regrowth will substantially reduce the number of acceptors created during vapour film growth.
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(4) Some of the electrons in the VG films may be captured in traps localized at the grain boundaries. The number of grain boundaries is substantially reduced on regrowth and consequently most of the captured electrons will be released. Mechanism (1) can be ruled out for the following reasons. The number of atoms occupying interstitial sites should be negligibly small at low doping levels and should rapidly increase as the solubility limit is approacheds. This is not the case, as can be seen in Fig. 4. In addition the neutral impurity scattering associated with the interstitials should cause a much larger decrease in the electron mobility, particularly in the sulphur-doped VG filmsis. Mechanism (2) can also be ruled out because the precipitation of dopant atoms on structural defects would form barriers at the interfaces or would affect any barriers already present. This in turn would result in a substantial difference between the electrical properties of sulphur-doped films and those of selenium- or telluriumdoped films. Thus, if it is assumed that the number of sulphur atoms precipitated at the defects in VG films is much higher than the number of selenium or tellurium atoms precipitated, the barrier height in the sulphur-doped films would also be expected to be higher. Any substantial difference in barrier height should result in a difference in the magnitude of the electron mobility and its temperature dependence. In practice, the electron mobility in sulphur-doped VG films is lower than that in selenium- and tellurium-doped films with the same electron concentration, but the temperature dependences are the same. However, the electron concentration in the VG films is always lower by a constant factor than that in the MR films, regardless of the doping dose. This is confirmed by the results of doping experiments with tellurium where it was found that, even for tellurium doses substantially exceeding the minimum dose necessary to reach the limiting concentration in the MR films, the corresponding effective donor concentration in the VG films was always lower than that in the MR films by a factor of about 2. In terms of mechanism (2) this implies that the number ofdopant atoms precipitated at defects is closely correlated with the number of atoms at the substitutional sites and that this correlation is completely independent of the doping dose. This is unlikely. In addition it is not clear why the limiting concentration of donors in the VG films is lower than that in the MR films. At this point mechanisms (3) and (4) offer a more plausible explanation of the behaviour of the films as they do not assume that there is any difference in the solubility of the donor atoms in the two types of doped film. Mechanism (3) assumes that the number of defect acceptor centres created is proportional to the number of dopant atoms incorporated. The acceptor centres could be antimony vacancies which arise in the evaporation process owing to the large difference between the vapour pressures of indium and antimony and to the annealing effect’ 6 which is unavoidable in the film preparation. Doping may also lead to an increase in the vacancy concentration. It has been shown” that when the acceptor vacancies are fully ionized and the temperature is such that the concentration N, of ionized donors is much higher than the concentration n, of intrinsic electrons the following relation holds: N N -Lx-!! N,i ni where Nvi and N, are the acceptor vacancy concentrations
(3) in a pure and a donor-
InSb
THIN FILMS DOPED
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Te, Se
AND
S
361
doped semiconducting crystal respectively. Therefore the interaction of ionized acceptor vacancies with ionized donors will lead to an increase in the vacancy concentration which is proportional to the donor concentration. It can be assumed that the concentration pi of intrinsic holes in heavily doped InSb is zero even at high temperatures. In this case we have, from the neutrality condition, n = N,--N
”
(4)
and the total concentration N, = N,+N,
of ionized centres is
= n+2N,
(5)
However, because of the high electron mobility in the MR films it can be assumed that they are virtually uncompensated, i.e. Nd is much greater than N, in the MR films. Therefore the ratio k of the electron concentration n2 after regrowth to the electron concentration ItI before regrowth is given by
k=n,=_ Nd nl
(6)
N,-N,
This ratio is almost constant for the tellurium- and selenium-doped InSb films over the whole range of electron concentration and has a value of approximately 2. The electron gas is degenerate in heavily doped InSb (Nd > 10” cmW3)even at high temperatures, and the electron mobility is limited by ionized impurity scattering. In this case the electron mobility is described well by the relation’* 3n: --E2h2
’ = 2
e3
1
n
B(n)m*2 N,
(7)
where E is the dielectric constant, m* is the effective electron mass and B(n) is a slowly varying function. The ratio of the electron mobility pi associated with the compensation effect in the VG films to the electron mobility pLbin uncompensated bulk InSb (n = NJ is obtained from eqns. (6) and (7) as p1 nl -_=-=pb
NI,
1 2k-1
(8)
Thus pL1x $pb for the tellurium- and selenium-doped films for which k x 2. In practice, as can be seen in Fig. 4, ,ul x O.lp,.‘Therefore compensation cannot be the most important factor acting to decrease the mobility in the tellurium- and selenium-doped films. In the case of the sulphur-doped films the values of k can approach 10, which results in ~1~= O.O$b. Such a low mobility is observed in practice, but it cannot be assumed that compensation accounts for the whole mobility decrease, because firstly the other scattering mechanisms operating in the tellurium- and seleniumdoped films should play a role and secondly, according to eqn. (7), the mobility should be almost independent of temperature which is not the case. Therefore the large increase in electron concentration on regrowth cannot be due to the removal of compensation, and we can conclude that mechanism (3) does not explain the behaviour of the VG films.
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A grain boundary model is required for the discussion of mechanism (4), and the well-known model of a potential barrier associated with carrier trapping at the interfacei is generally assumed in cases of this type. For example, Ling et aLzOused a modified form of this model to interpret the properties of lightly doped flashevaporated InSb thin films: the potential barrier was assumed to have a notch-like shape and the trap levels formed a quasi-continuous distribution. This model is valid for uniformly doped samples; if the doping is non-uniform, the dopant distribution is of major importance in determining the shape of the potential barrier”. The following well-known expression for potential-barrier-limited conductivity in a polycrystalline material was derived from this model: 0=
e2n(v)D kT
(9
where D is the grain diameter, (u) is the mean thermal velocity of the electrons and e4 is the barrier height measured from the bottom of the conduction band. The barrier-limited electron mobility can now be determined from eqns. (l), (2) and (9). Unfortunately eqn. (9) is only applicable to a non-degenerate electron gas. However, Ling et al. suggested that eqn. (9) could be applied to weakly degenerate InSb samples if the barrier height were replaced by some value proportional to it. In the present case of strongly degenerate samples further limitations are imposed on the validity of the model. In InSb samples with electron concentrations greater than 2 x 1Or8 cmd3 the Fermi level is located more than 0.20 eV above the conduction band and its position is virtually independent of temperature in the temperature range of interest 22. Therefore in films with electron concentrations of 2 x 1018 cmw3 or more any potential barriers, if they exist, must be higher than 0.20 eV, i.e. they must be higher than the band gap in InSb (EB x 0.20 eV), and the model is no longer applicable 21. In view of this difficulty and the fact that an expression such as eqn. (9) does not describe the low temperature conductivity dependence of the VG films, it is clear that this model cannot be used to interpret the electrical properties of the films. However, we can use a similar model in which it is assumed that potential barriers are formed at grain boundaries and that numerous trap states of various energies are distributed within the barriers. In this model the barrier shape is unknown and it is assumed that the barrier height can exceed the band gap. This model can be used to give an approximate explanation of the behaviour of the selenium- and tellurium-doped samples. The increase in electron concentration after regrowth is assumed to be due to the recovery of electrons trapped at grain boundaries. The number of trapped electrons will be proportional to the number of conduction electrons because the Fermi level will be higher in more strongly doped samples and consequently more traps will be filled. We also expect that the conductivity of the film should have a thermally activated character over at least some part of the temperature range in the presence of barriers which are higher than the Fermi level. Therefore the exponential term should play an important role in any expression for the conductivity. In fact, we have found that the electron mobility of the VG films determined using eqn. (2) is described by the expression
(10)
InSb
THIN FILMS DOPED WITH
Te, Se
AND
363
s
where pt, is the mobility in bulk InSb for a given donor concentration, C and y are dimensionless constants and W is a parameter with the dimensions of energy. Since eqn. (10) is not supported by any strict theoretical reasoning, the meaning of W is not obvious. Nevertheless it is reasonable to assume that it is the height of the barrier above the Fermi level. The fit of the mobility calculated from eqn. (10) to the experimental results is shown in Fig. 5(a). The parameters used in the calculations, which were obtained from the best fit of the curves to the experimental data, are given in Table I. In the calculations we neglected a weak temperature dependence of p,, and used the room temperature mobility in bulk InSb with the appropriate donor concentration’3. TABLE I PARAMETERS EXPERIMENTAL
FITTING THE TEMPERATURE
DEPENDENCE
n (sample)
Dopant
~d3~
(cm - 3, 1.2 x 5.2 x 5.4 x 6.7 x 1.6 x 2.2 x 8.5 x
OF THE ELECTRON
MOBILITY
GIVEN BY EQN. (lo)
TU THE
DATA (SEE FIG. 5)
10” 10” 10” 10” 10’s 10’8 10”
Te s Te Se S Se Se
K)
(cm2 V -‘s-Y
(&)
5.0 x 3.0 x 2.9 x 2.7 x 1.8 x 1.6 x 0.7 x
0.060 0.070 0.075 0.070 0.100 0.120 0.150
lo4 lo4 104 lo4 lo4 lo4 lo4
C
Y
0.62 0.23 0.35 0.32 0.30 0.74 0.71
0.050 0.057 0.043 0.048 0.047 0.052 0.067
The tabulated dependence of the barrier height on the effective donor concentration is displayed in graphical form in Fig. 8. It can be seen that the barrier height increases rapidly for donor concentrations above 1018 cm- 3. However, for Nd c 10’s cane3 the barrier height approaches the value of about 0.05 eV reported for undoped flash-evaporated InSb films”.
l5/’
, ,4
/’
A,,/
2
et 3
,/’
lo-
8 ye_--=-
, ,m #.--
/”
5-
t 01 10"
1
I
1018 Ndbri3]
I
lo
Fig. 8. The dependence of the barrier height Won the effective donor concentration in VG InSb films. The symbols are as defined in Fig. 4.
364
T. BERUS
et ai.
Unfortunately, this mechanism does not satisfactorily explain the behaviour of the sulphur-doped films. As can be seen in Fig. 8 the barrier heights of the sulphurdoped films are similar to those of the selenium- and tellurium-doped films. Thus the number of electrons trapped by a unit area of grain boundary should be independent of the nature of the dopant. However, the value of k (eqn. (6)) for the sulphur-doped films is about three times the values obtained for the other films. This suggests that the grain boundary density in the sulphur-doped films is also three times that found in the other films. If this were the case barrier scattering in the sulphur-doped films should be more pronounced and the values of C (eqn. (10)) for the sulphur-doped films should be a factor of about 3 less than those for the other films. This is not observed experimentally (Table I). Ionized impurity scattering should also play a more important role in the sulphur-doped films. A simple re-examination of the mechanism shows that, instead of eqn. (8), we have crll~b = ilk
(11)
where ,ui is now the ionized-impurity-limited mobility inside the grains. For k < 10, p1 is comparable with the room temperature barrier-limited mobility. When the effect of both scattering mechanisms is taken into account the room temperature mobility in the sulphur-doped films is expected to be several times lower than that in the selenium- and tellurium-doped films. As is seen in Fig. 4, this is not the case. Therefore the behaviour of the sulphur-doped films can only be explained qualitatively using mechanism (4). Regrowth from the melt reduces the number of barriers in the InSb thin films with a consequent increase in the mobility. The temperature dependence of the mobility in the MR films varies with the level of doping. In films with donor concentrations below lo’* cme3 the mobility decreases with temperature owing to barrier scattering. In more strongly doped films the mobility increases with temperature, as in doped bulk InSb, although the increase is rather smaller than that observed in the bulk material. Therefore the behaviour of the MR films differs from the behaviour of the VG films as no increase in the barrier height with doping level is observed. This suggests that the barriers existing in the two types of film may be different. 6.
SUMMARIZING
REMARKS
AND CONCLUSIONS
The aim of this paper was to describe a method of preparing InSb thin films with a high electron mobility and a controlled donor doping level and to report investigations of the dependence of the electrical properties of the films on the doping level, temperature and film thickness. The technology previously developed for the deposition of undoped InSb films with a high electron mobility6g7 was adopted for the preparation of doped films. The method comprised two stages: the flash evaporation of InSb films (the VG films) and the subsequent regrowth from the melt of InSb films covered with a protective SiOs layer (the MR films). The doping was performed during the first stage by the coevaporation of InSb and the dopants (sulphur, selenium and tellurium) from independent evaporation sources (Fig. 1). Using this method we were able to obtain InSb films with donor concentrations in the range from 10” to 2 x 10” crn3. The
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lower limit approaches the natural donor concentration in undoped InSb films and the upper limit is the tellurium solubility limit in InSb. The room temperature electron mobility in the MR films is about an order of magnitude higher than that in VG films with the same electron concentration and can be as high as that in doped bulk InSb (Fig. 4). The increase in mobility on regrowing the films is a result of improvements to the film structure. Regrowth increases not only the mobility but also the electron concentration in InSb films. The electron concentration is increased by a factor of about 2 in the selenium- and tellurium-doped films and by a factor of up to 10 in the sulphur-doped films. A qualitative explanation of this increase is that the conduction electrons which are trapped at the grain boundaries in the VG films are released in the MR films owing to the reduction in the grain boundary density. The trapped electrons form potential barriers within the InSb films. Barrier scattering is the predominant mechanism limiting the mobility near room temperature. However, the mobility is virtually temperature independent at low temperatures. We have not been able to explain this behaviour. An interesting feature of the VG films is the increase in the barrier height with increasing doping level (Fig. 8) which is not observed in the MR films. This suggests that the barriers in the two types of InSb film may be different. The barriers in the VG films are unexpectedly high. For example, in the VG films with donor concentrations of 8 x 10” cm- 3 the barrier height is about 150 meV and the Fermi level is about 400 meV above the conduction band 22. Thus the overall barrier height is about 550meV, i.e. about three times the band gap of InSb. The nature of the barriers is unknown and needs further investigations. The MR films are suitable for use as Hall generators for precision magnetic field measurements. Films with donor concentrations between 2 x lo’* and 4 x 10” cme3 are preferred for this application because their Hall coefficients are virtually temperature independent near room temperature (Fig. 6). The electron mobility in such films is about 1 m2 V-i s- ’ , which is a large value for such a thin film. We have found that the decrease in the mobility with decreasing thickness is less in the doped films than in the undoped films (Fig. 7). However, the reproducibility of the parameters of films of thickness less than 1 urn is poor. RJZERENCES 1 A. S. Filipchenko and D. N. Nasledov, Phys. StatusS+idi A, 27 (1975) 11. H. H. Wieder and A. R. Clawson, Solid-State Electron., I1 (1968) 887. H. H. Wieder and D. A. Collins, Thin SolidFilms, 20 (1974) 201. E. Litwin-Staszewska, S. Porowski and A. A. Filipchenko, Phys. Status Solidi B, 48 (1971) 519. V. J, Fistul, Heavily Doped Semiconductors, Nauka, Moscow, 1967, p. 239 (in Russian). 6 M. Oszwaidowski and W. Harms, Proc. Int. ConJ on the Physics and Chemistry of Heterojunction andL.uyer Structures, Budapest. 1971, Akademiai Kiado, Budapest, 1971, Vol. 3, p. 219. 7 M. Oszwaldowski, H. Szweycer, T. Bents, J. Got and M. Zimpel, Thin SolidFilms, 85 (1981) 319. 8 V. V. Popov and V. V. Kasarev, Phys. Status Solidi A, 58 (1980) 23 1. 9 H. H. Wieder, J. Vat. Sci. Technol., 8 (1971) 210. 10 M. Oszwaidowski, Acta Phys. Pal. A, 37(1970) 617. 11 M. Le Contellec and J. Richard, Thin Solid Films, 36 (1976) 151. 12 M. Oszwaldowski, Acta Phys. Pal., 26 (1969) 21. 13 E. Litwin-Staszewska, W. Szymatiska and R. Piotrzkowski, Phys. Status Solidi B, 106 (198 1) 551. 2 3 4 5
366 14 H. H. Wieder, J. Vuc. Sci. Technol., 9 (1972) 1193. 15 K. Seeger, Semiconductor Physics, Springer, Vienna, 1973, Chapter 6. 16 W. Hanus and M. Oszwatdowski, Thin SolidFilms, 61(1979) 235. 17 R. L. Longini and R. F. Greene, Phys. Rev., 102 (1956) 992. 18 J. Kotodziejczak, Acta Phys. Pal., 20 (1961) 289. 19 W. E. Taylor, N. H. Ode11and H. Y. Fan, Phys. Rev., 88 (1952) 867. 20 C. H. Ling, J. H. Fisher and J. C. Anderson, Thin Solid Films, 14 (1972) 267. 21 A. Broniatowski, J. Phys. (Paris), Coffoq. Cl, 43 (Suppl.) (1982) 63. 22 P. Pfeffer and W. Zawadzki, Phys. Status Solidi B,88 (1978) 247.
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PREPARATION AND CHARACTERIZATION
PREPARATION AND ELECTRICAL PROPERTIES OF InSb THIN FILMS HEAVILY DOPED WITH TELLURIUM, SELENIUM AND SULPHUR T. BERUS, J. GOC, M. NOWAK, M. OSZWALDOWSKI
AND M. ZIMPEL
Instiiute of Physics, Technical University of Poznari, 60-965 Poznati, Piotrowo 3 (Poland) (Received April 19, 1983; accepted October 21, 1983)
A method of controlled donor doping of flash-evaporated InSb thin films in the concentration range 10’7-10’g cmm3 is described. When such films are regrown from the melt the electron concentration increases several times and the room temperature electron mobility increases by about an order of magnitude. The room temperature mobility of the regrown films is close to that observed in bulk InSb. The temperature dependence of the mobility between 80 and 700 K shows that barrier scattering plays an important role in all flash-evaporated and melt-regrown films with effective donor concentrations Nd of 1018 cmm3 or less. In the flashevaporated films the barrier height increases from a value of 65 meV for N, = IO” cme3 to 150 meV for N, = 9 x 10’s cme3. No such increase is observed in regrown films. This suggests that the barriers in the two types of films are different. The increase in electron concentration in regrown films is discussed and the most consistent explanation of the effect is that a large number of conduction electrons are trapped at grain boundaries in the flash-evaporated films. The application of the heavily doped melt-regrown InSb films as Hall generators is also discussed.
1. INTRODUCTION
The group VI elements are incorporated into the InSb crystal lattice substitutionally, replacing the antimony atoms. In these positions they are shallow donors forming an impurity band that overlaps the conduction band at concentrations above lOi cmm3. Many papers published in the last decade have been devoted to the transport properties of heavily doped n-InSb crystak. Earlier results were summarized in a review article by Filipchenko and Nasledov’. In contrast with the case for crystals, little is known about the properties of heavily doped InSb thin films. Wieder and Clawson’ investigated the room temperature electron mobility in vacuumevaporated sulphur-doped InSb thin films which had been regrown from the melt, They found that in the donor concentration range from 5 x 1016 to 7 x 10” crn3 the mobility was about two-thirds of that in tellurium-doped InSb crystals. Wieder and Collins3 investigated the thermal dependence of the Hall coefficient in films heavily doped with sulphur and tellurium. In the work reported in refs. 2 and 3 the 0040~6090/84/$3.00
0 Elsevier Sequoia/Printed in The Netherlands
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dopants were introduced into the InSb films by adding sulphur or tellurium to the indium used as the starting material for the film preparation. In the present paper we describe an alternative method of preparing heavily doped InSb thin films. The method offers controlled doping and high electron mobility and therefore can be used for practical applications such as the preparation of Hall generators for precision measurements of magnetic field strength. In this case the virtual magnetic field independence of the Hall coefficient of heavily doped InSb and its greatly reduced dependence on temperature can be exploited. These important properties can be fully achieved only in a high mobility thin film material. Investigations of InSb crystals heavily doped with tellurium, selenium and sulphur suggest that the transport properties depend on the nature of the dopant1*4. It therefore appeared interesting to examine whether a similar dependence exists in InSb thin films. Investigations of InSb films doped with various donors over a wide concentration range should also lead to a better understanding of their electrical properties, in particular the anomalous temperature dependence of the electron mobility. The electrical properties of InSb thin films are strongly affected by structural defects. However, it is known that impurities in heavily doped semiconductors can interact with structural defects’. For this reason our investigations were carried out on InSb films with various structural properties. 2.
FILM PREPARATION
The experimental arrangement used for the film preparation is shown in Fig. 1. It was set up in a standard vacuum apparatus in which the working pressure was below 10e3 Pa. Doped InSb films were obtained by flash evaporation with simultaneous dopant sublimation from an independent dopant source. The starting materials were a zone-refined InSb crystal with a net donor concentration of about 10” cme3 powdered to grains of size 100-150 urn and a Specpure dopant material. A tungsten strip heated to 1600 K was used as the InSb evaporation source. The mean film deposition rate was 2-3 urn h- ‘. The films were deposited through a mask which was part of the substrate holder onto a substrate of dimensions 12 mm x 8 mm heated to 700 K. B-Si glass and Sital ST-50-l (a sintered polycrystalline material composed of MgO, CaO, Al,O, and SiOZ which is made in the U.S.S.R.) were utilized as substrate materials. The substrates were carefully cleaned prior to the deposition process. The final stages of the cleaning were surface purification in an isopropyl alcohol vapour stream and vacuum annealing at 750 K for 30-60 min which was performed immediately before the film deposition. Graphite Knudsen cells heated by a tungsten wire were used as dopant sublimation sources. Sublimation of the dopant and evaporation of InSb were started simultaneously, and when thermal equilibrium was achieved a rotary shutter located above the sources was displaced to allow film deposition. The Knudsen cell heater current was increased in successive evaporation runs, resulting in the preparation of InSb films with increasing impurity concentration until the limiting concentration for a given dopant was reached. Before starting this doping procedure with another dopant, the Knudsen cell was removed and the inside of the vacuum chamber was cleaned to remove the residual dopant contamination. The substrate holder allowed up to 22 InSb films to
InSb THIN FILMS DOPED WITHT~,S~
1 -1 -_ 3 -. 4 -.
AND S
353
I- 2 ,_ 1 2
6, 7
.- 1 6
-- 1
Fig. 1. The arrangement used for the flash evaporation of doped InSb thin films: 1, thermal screens; 2, substrate furnace; 3, substrate holder; 4, thermocouple; 5, powdered InSb feeding mechanism; 6, shutter; 7, InSb evaporation source; 8, dopant evaporation source.
be obtained in a single evaporation run. The electrical properties of the films appeared to be slightly dependent on the substrate material used. In general, higher electron mobilities were obtained for films evaporated on the Sital substrates. All the films were covered with a protective layer of SiO, (1 < x < 2) 0.1 urn thick obtained by sublimation of high purity SiO in a separate vacuum apparatus at a pressure of about 10m2 Pa. About 500 InSb films doped with tellurium, selenium and sulphur were prepared in this way. Half of these films were regrown from the melt in ambient air. Both natural crystallization6 and microzone crystallization’ were used for this purpose. Since the electrical properties of the films prepared using the two methods were the same, most of those investigated were prepared by the
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simpler natural crystallization method. Most of the films were deposited on Sital substrates and were 2-3 urn thick. The film thickness was measured using an interference microscope. It should be pointed out, however, that the InSb films which were regrown from the melt had slightly warped surfaces and therefore their thickness was taken as the average value along the film. All the electrical measurements were carried out on InSb films protected by an SiO, layer. Chromium electrodes were vacuum evaporated onto the films for the measurements. An InSb film equipped with electrodes is displayed in Fig. 2. Chromium was used because of its small diffusion coefficient and low solubility in InSb *. Thus the possibility of diffusion of the electrode material into the InSb films during high temperature measurements was reduced and in fact was not detected. Good electrical contact was formed between the chromium electrodes and the edges of the protected InSb films.
Fig. 2. InSb thin film equipped with chromium electrodes for Hall and conductivity measurements. The substrate dimensions are 12 mm x 8 mm.
3. STRUCTURAL ANALYSIS Flash evaporation is a well-known method for the preparation of stoichiometric InSb thin films9. The electrical properties of flash-evaporated InSb films are strongly affected by their structural defects. The most important defects limiting the electron mobility are grain boundaries. The mobility increases with increasing grain size, and the mean grain size depends on preparation conditions such as the substrate temperature during deposition and post-deposition annealing and the film thickness’-“. We have found that doping has little effect on the structural properties of flashevaporated InSb films. The surface of such a film treated with a selective etchant to reveal the crystal defects in InSb is shown in Fig. 3(a). It is seen that the film consists of randomly oriented crystallites of dimensions about 1 pm. Twinning along (111) planes can be seen in some of these crystallites. The random orientation of the crystallites is confirmed by X-ray analysis. The analysis shows that crystallites with (11 l), (lOO), (1 lo), (112), (113) and (133) planes parallel to the substrate appear in roughly equal numbers. When a film such as that shown in Fig. 3(a) is not etched, its top surface is
InSb
THIN FILMS DOPED
WITH
Te, Se
AND
S
355
(W
500 brn Fig. 3. Surfaces of InSb thin films etched in a 1:3 solution of HNOe-400/, C2H402 (COOH), in water: (a) replica electron micrograph of a flash-evaporated film;(b) optical micrograph of a film regrown from the melt.
decorated with partly oxidized indium droplets of diameter about 0.1 pm. The mean distance between the droplets is of the order of 1 pm. Comparison of the electrical properties of the etched and unetched films showed that the indium exclusions did not seriously affect the electrical properties of the films. Because the exclusions were absent in Sims evaporated at lower substrate temperatures, we concluded that they were due to the partial re-evaporation of antimony at a substrate temperature of 700 K. However, we observed that the amount of agglomerated indium increased in films doped with selenium and sulphur to the solubility limit. This phenomenon was not observed in the tellurium-doped films. We cannot offer any explanation for the behaviour of the films which were heavily doped with selenium and sulphur.
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Regrowth of the vapour-grown (VG) InSb films results in a complete reconstruction of the crystal. As can be seen in Fig. 3 the melt-regrown (MR) InSb films consist of large irregular crystallites. The crystallite shape is the result of partial dendritic growth due to the rapid crystallization of the melt. Structural defects typical of dendritic growth” are therefore expected to appear in the MR InSb films. Defects associated with the plastic deformation occurring in crystals constrained during the freezing process are also expected. No preferential crystallographic orientation is found in the MR films. The result of the X-ray analysis is essentially the same as that obtained for the VG films. The structural properties of the present MR films are substantially the same as those reported for undoped MR films6. 4.
HALL COEFFICIENT AND ELECTRON MOBILITY
The Hall coefficient in InSb films was determined using the conventional d.c. technique with a magnetic field of 0.4T. The driving current in the film and the voltages on the Hall and conductivity contacts were measured using sensitive digital meters. The electron concentration n and the Hall electron mobility pn in the films were determined from the experimental values of the Hall coefficient RH and the conductivity 0 using the relations
RHden
A conventional cryostat equipped with a temperature controller was used for the Hall measurements in the temperature range 77-300 K. The measurements in the temperature range 300-700 K were performed in a specially designed small furnace placed between the magnet poles. The furnace temperature was programmed using the temperature controller. Owing to the good protective properties of the SiO, overlayer the measurements were carried out in ambient air. The first task was to determine the limiting concentrations of the dopants in the MR InSb films. The limiting concentration of tellurium was obtained directly from the Hall coefficient measurements as 1.5 x 10” cm- 3. However, only approximate values of the limiting concentrations of selenium and sulphur could be obtained because the indium exclusions (see Section 3) decreased the measured Hall coefficient as a result of shortcircuit effects. The approximate values obtained were 8 x 10” cm- 3 for selenium and 6 x 10” cm- 3 for sulphur. These limiting concentrations are in good agreement with those determined for InSb monocrystals’. The dependence of the room temperature electron mobility on electron concentration in InSb films doped with tellurium, selenium and sulphur is shown in Fig. 4. The electron mobilities of the MR films are the maximum values found in our experiments. The figure shows that the electron mobilities in the tellurium- and selenium-doped MR films can be as high as those obtained in bulk InSb. In contrast, the electron mobilities in the sulphur-doped MR films are generally lower than those in the tellurium- and selenium-doped MR films. Thus the dependence of the electron mobility on the nature of the dopant, which was reported for bulk InSb 13, is only
InSb
THIN FILMS DOPED
Te, Se
WITH
AND
S
357
partially manifested in the MR films as no difference between the electron mobilities of tellurium- and selenium-doped films was detected. However, it should be noted that the occurrence of high electron mobilities is statistically more frequent in tellurium-doped films. The electron mobility in the VG InSb films is about an order of magnitude less than that in the MR InSb films for the same doping level. It is interesting that, despite the difference in magnitude, the electron mobilities in the two types of InSb film show very similar concentration dependences. Another puzzling feature is the increase in the effective donor concentration in the MR films: the concentration increases by a factor of 2-3 in the tellurium- and selenium-doped films and by as much as an order of magnitude in the sulphur-doped films.
lo2
1016
1
I
t
II 10"
I
I
I
II
1
lo'8
I
III
I
lP n Icmsl
Fig. 4. The dependence of the room temperature electron mobility on electron concentration in VG (0, A, I) and MR (0, A, 0) InSb films doped with tellurium (0, 0) selenium (A, A) and sulphur (I, 0): ---, lines linking parameters of the same films before and after regrowth from the melt; -, theoretical dependence for InSb monocrystaW3; shaded area, the experimental dependence for InSb monocrystalsr3.
The temperature dependence of the electron mobility in the doped InSb films is shown in Fig. 5. It can be seen that the dependence in the VG films differs from that in the MR films. In the VG films the electron mobility decreases with temperature, in contrast with the behaviour of bulk InSb. This anomalous behaviour also occurs in undoped VG and MR InSb films 2*g-11. At high temperatures phonon scattering comes into operation and produces a maximum in the curve of mobility uersus temperature. The position of the maximum depends on the magnitude of the mobility: the lower the mobility the higher is the temperature at which the maximum appears. For this reason the mobility maximum in Fig. 5(a) is observed only for the films with low dopant concentrations. A similar anomaly in the temperature
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loJl-uL-J loll 102
64
TCKI
103
(W
102
T [Kl
Id
Fig. 5. Temperature dependence of the electron mobility in (a) the VG InSb films and (b) the MR InSb films: ---, barrier-limited mobilities calculated from eqn. (10). The symbols are as defined in Fig. 4 and the numbers on the curves denote the effective donor concentration in the films.
dependence of the electron mobility is observed for MR films with donor concentrations below about lo’* cme3. At higher dopant concentrations the mobility increases with decreasing temperature in a similar manner to the behaviour of bulk InSb. The temperature dependence of the Hall coefficient of the InSb films is shown in Fig. 6. As expected it does not depend on either the film structure or the nature of the dopant. R, decreases at high temperatures in all the films with donor concentrations below 4 x lo’* cme3 as a result of the transition from extrinsic to intrinsic conductivity. However, RH increases at high temperatures in films with donor
-‘H
I0 1
2
3
4
5
6 7 8 9 lo'?/, [K-'I
10 11 12 13 14 15
Fig. 6. Temperature dependence of the Hall coefficient in doped InSb thin films. The symbols are as defined in Fig. 4 and the numbers on the curves denote the effective donor concentration in the tilms.
InSb
THIN FILMS DOPED WITH
Te, Se AND S
359
concentrations above 4 x 10’s cm- j. This 1 and InSb thin films3, is interpreted in terms of electron transfer from the minimum of the I conduction band to the subsidiary L minima at the edges of the Brillouin zone. In the transition range, i.e. at donor concentrations between 2 x 10’s cm - 3 and 4 x lOi* cme3, the Hall coefficient is virtually temperature independent in the vicinity of room temperature. The electron mobility in the MR films at such donor concentrations is about 1 m2 V-’ s-r, and hence these films are suitable for applications in Hall generators. In view of these applications and the known drastic reduction of the electron mobility in undoped InSb films of thickness below 2 urn l4 it appeared desirable to investigate the thickness dependence of the electron mobility in the heavily doped MR InSb films. The results of the investigation for tellurium-doped films with a dopant concentration of (l-2) x lo’* cmm3 are shown in Fig. 7 where it can be seen that there is no drastic reduction in the mobility down to a film thickness of about 0.3 urn. In fact the observed small drop in the mobility is due to the non-uniformity in film thickness rather than to any additional scattering mechanism, e.g. surface scattering. The surface tension which exists during melting has a more marked effect on the thinner films, and therefore we were unable to obtain films with thicknesses less than 0.3 urn as they were torn during the regrowth procedure.
5 t
Fig. 7. Thickness dependence of the room temperature electron mobility in tellurium-doped InSb films with a donor concentration of (l-2) x 10’s cmJ. 5. DISCUSSION
Our investigations have shown that regrowth from the melt increases not only the electron mobility but also the electron concentration in doped InSb films. The following mechanisms may be responsible for this concentration increase. (1) Some of the doping atoms in the VG films may be incorporated into the crystal matrix in an electrically inactive form, e.g. they may occupy interstitial sites. During the regrowth they will enter substitutional sites and thus become donors. (2) Some of the doping atoms in the VG films may precipitate at defect sites such as grain boundaries, twin planes and dislocations. During the regrowth they will dissolve in the film and become donors. (3) Donors in the VG films may be partially compensated by defect acceptor centres. The regrowth will substantially reduce the number of acceptors created during vapour film growth.
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(4) Some of the electrons in the VG films may be captured in traps localized at the grain boundaries. The number of grain boundaries is substantially reduced on regrowth and consequently most of the captured electrons will be released. Mechanism (1) can be ruled out for the following reasons. The number of atoms occupying interstitial sites should be negligibly small at low doping levels and should rapidly increase as the solubility limit is approacheds. This is not the case, as can be seen in Fig. 4. In addition the neutral impurity scattering associated with the interstitials should cause a much larger decrease in the electron mobility, particularly in the sulphur-doped VG filmsis. Mechanism (2) can also be ruled out because the precipitation of dopant atoms on structural defects would form barriers at the interfaces or would affect any barriers already present. This in turn would result in a substantial difference between the electrical properties of sulphur-doped films and those of selenium- or telluriumdoped films. Thus, if it is assumed that the number of sulphur atoms precipitated at the defects in VG films is much higher than the number of selenium or tellurium atoms precipitated, the barrier height in the sulphur-doped films would also be expected to be higher. Any substantial difference in barrier height should result in a difference in the magnitude of the electron mobility and its temperature dependence. In practice, the electron mobility in sulphur-doped VG films is lower than that in selenium- and tellurium-doped films with the same electron concentration, but the temperature dependences are the same. However, the electron concentration in the VG films is always lower by a constant factor than that in the MR films, regardless of the doping dose. This is confirmed by the results of doping experiments with tellurium where it was found that, even for tellurium doses substantially exceeding the minimum dose necessary to reach the limiting concentration in the MR films, the corresponding effective donor concentration in the VG films was always lower than that in the MR films by a factor of about 2. In terms of mechanism (2) this implies that the number ofdopant atoms precipitated at defects is closely correlated with the number of atoms at the substitutional sites and that this correlation is completely independent of the doping dose. This is unlikely. In addition it is not clear why the limiting concentration of donors in the VG films is lower than that in the MR films. At this point mechanisms (3) and (4) offer a more plausible explanation of the behaviour of the films as they do not assume that there is any difference in the solubility of the donor atoms in the two types of doped film. Mechanism (3) assumes that the number of defect acceptor centres created is proportional to the number of dopant atoms incorporated. The acceptor centres could be antimony vacancies which arise in the evaporation process owing to the large difference between the vapour pressures of indium and antimony and to the annealing effect’ 6 which is unavoidable in the film preparation. Doping may also lead to an increase in the vacancy concentration. It has been shown” that when the acceptor vacancies are fully ionized and the temperature is such that the concentration N, of ionized donors is much higher than the concentration n, of intrinsic electrons the following relation holds: N N -Lx-!! N,i ni where Nvi and N, are the acceptor vacancy concentrations
(3) in a pure and a donor-
InSb
THIN FILMS DOPED
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Te, Se
AND
S
361
doped semiconducting crystal respectively. Therefore the interaction of ionized acceptor vacancies with ionized donors will lead to an increase in the vacancy concentration which is proportional to the donor concentration. It can be assumed that the concentration pi of intrinsic holes in heavily doped InSb is zero even at high temperatures. In this case we have, from the neutrality condition, n = N,--N
”
(4)
and the total concentration N, = N,+N,
of ionized centres is
= n+2N,
(5)
However, because of the high electron mobility in the MR films it can be assumed that they are virtually uncompensated, i.e. Nd is much greater than N, in the MR films. Therefore the ratio k of the electron concentration n2 after regrowth to the electron concentration ItI before regrowth is given by
k=n,=_ Nd nl
(6)
N,-N,
This ratio is almost constant for the tellurium- and selenium-doped InSb films over the whole range of electron concentration and has a value of approximately 2. The electron gas is degenerate in heavily doped InSb (Nd > 10” cmW3)even at high temperatures, and the electron mobility is limited by ionized impurity scattering. In this case the electron mobility is described well by the relation’* 3n: --E2h2
’ = 2
e3
1
n
B(n)m*2 N,
(7)
where E is the dielectric constant, m* is the effective electron mass and B(n) is a slowly varying function. The ratio of the electron mobility pi associated with the compensation effect in the VG films to the electron mobility pLbin uncompensated bulk InSb (n = NJ is obtained from eqns. (6) and (7) as p1 nl -_=-=pb
NI,
1 2k-1
(8)
Thus pL1x $pb for the tellurium- and selenium-doped films for which k x 2. In practice, as can be seen in Fig. 4, ,ul x O.lp,.‘Therefore compensation cannot be the most important factor acting to decrease the mobility in the tellurium- and selenium-doped films. In the case of the sulphur-doped films the values of k can approach 10, which results in ~1~= O.O$b. Such a low mobility is observed in practice, but it cannot be assumed that compensation accounts for the whole mobility decrease, because firstly the other scattering mechanisms operating in the tellurium- and seleniumdoped films should play a role and secondly, according to eqn. (7), the mobility should be almost independent of temperature which is not the case. Therefore the large increase in electron concentration on regrowth cannot be due to the removal of compensation, and we can conclude that mechanism (3) does not explain the behaviour of the VG films.
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A grain boundary model is required for the discussion of mechanism (4), and the well-known model of a potential barrier associated with carrier trapping at the interfacei is generally assumed in cases of this type. For example, Ling et aLzOused a modified form of this model to interpret the properties of lightly doped flashevaporated InSb thin films: the potential barrier was assumed to have a notch-like shape and the trap levels formed a quasi-continuous distribution. This model is valid for uniformly doped samples; if the doping is non-uniform, the dopant distribution is of major importance in determining the shape of the potential barrier”. The following well-known expression for potential-barrier-limited conductivity in a polycrystalline material was derived from this model: 0=
e2n(v)D kT
(9
where D is the grain diameter, (u) is the mean thermal velocity of the electrons and e4 is the barrier height measured from the bottom of the conduction band. The barrier-limited electron mobility can now be determined from eqns. (l), (2) and (9). Unfortunately eqn. (9) is only applicable to a non-degenerate electron gas. However, Ling et al. suggested that eqn. (9) could be applied to weakly degenerate InSb samples if the barrier height were replaced by some value proportional to it. In the present case of strongly degenerate samples further limitations are imposed on the validity of the model. In InSb samples with electron concentrations greater than 2 x 1Or8 cmd3 the Fermi level is located more than 0.20 eV above the conduction band and its position is virtually independent of temperature in the temperature range of interest 22. Therefore in films with electron concentrations of 2 x 1018 cmw3 or more any potential barriers, if they exist, must be higher than 0.20 eV, i.e. they must be higher than the band gap in InSb (EB x 0.20 eV), and the model is no longer applicable 21. In view of this difficulty and the fact that an expression such as eqn. (9) does not describe the low temperature conductivity dependence of the VG films, it is clear that this model cannot be used to interpret the electrical properties of the films. However, we can use a similar model in which it is assumed that potential barriers are formed at grain boundaries and that numerous trap states of various energies are distributed within the barriers. In this model the barrier shape is unknown and it is assumed that the barrier height can exceed the band gap. This model can be used to give an approximate explanation of the behaviour of the selenium- and tellurium-doped samples. The increase in electron concentration after regrowth is assumed to be due to the recovery of electrons trapped at grain boundaries. The number of trapped electrons will be proportional to the number of conduction electrons because the Fermi level will be higher in more strongly doped samples and consequently more traps will be filled. We also expect that the conductivity of the film should have a thermally activated character over at least some part of the temperature range in the presence of barriers which are higher than the Fermi level. Therefore the exponential term should play an important role in any expression for the conductivity. In fact, we have found that the electron mobility of the VG films determined using eqn. (2) is described by the expression
(10)
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THIN FILMS DOPED WITH
Te, Se
AND
363
s
where pt, is the mobility in bulk InSb for a given donor concentration, C and y are dimensionless constants and W is a parameter with the dimensions of energy. Since eqn. (10) is not supported by any strict theoretical reasoning, the meaning of W is not obvious. Nevertheless it is reasonable to assume that it is the height of the barrier above the Fermi level. The fit of the mobility calculated from eqn. (10) to the experimental results is shown in Fig. 5(a). The parameters used in the calculations, which were obtained from the best fit of the curves to the experimental data, are given in Table I. In the calculations we neglected a weak temperature dependence of p,, and used the room temperature mobility in bulk InSb with the appropriate donor concentration’3. TABLE I PARAMETERS EXPERIMENTAL
FITTING THE TEMPERATURE
DEPENDENCE
n (sample)
Dopant
~d3~
(cm - 3, 1.2 x 5.2 x 5.4 x 6.7 x 1.6 x 2.2 x 8.5 x
OF THE ELECTRON
MOBILITY
GIVEN BY EQN. (lo)
TU THE
DATA (SEE FIG. 5)
10” 10” 10” 10” 10’s 10’8 10”
Te s Te Se S Se Se
K)
(cm2 V -‘s-Y
(&)
5.0 x 3.0 x 2.9 x 2.7 x 1.8 x 1.6 x 0.7 x
0.060 0.070 0.075 0.070 0.100 0.120 0.150
lo4 lo4 104 lo4 lo4 lo4 lo4
C
Y
0.62 0.23 0.35 0.32 0.30 0.74 0.71
0.050 0.057 0.043 0.048 0.047 0.052 0.067
The tabulated dependence of the barrier height on the effective donor concentration is displayed in graphical form in Fig. 8. It can be seen that the barrier height increases rapidly for donor concentrations above 1018 cm- 3. However, for Nd c 10’s cane3 the barrier height approaches the value of about 0.05 eV reported for undoped flash-evaporated InSb films”.
l5/’
, ,4
/’
A,,/
2
et 3
,/’
lo-
8 ye_--=-
, ,m #.--
/”
5-
t 01 10"
1
I
1018 Ndbri3]
I
lo
Fig. 8. The dependence of the barrier height Won the effective donor concentration in VG InSb films. The symbols are as defined in Fig. 4.
364
T. BERUS
et ai.
Unfortunately, this mechanism does not satisfactorily explain the behaviour of the sulphur-doped films. As can be seen in Fig. 8 the barrier heights of the sulphurdoped films are similar to those of the selenium- and tellurium-doped films. Thus the number of electrons trapped by a unit area of grain boundary should be independent of the nature of the dopant. However, the value of k (eqn. (6)) for the sulphur-doped films is about three times the values obtained for the other films. This suggests that the grain boundary density in the sulphur-doped films is also three times that found in the other films. If this were the case barrier scattering in the sulphur-doped films should be more pronounced and the values of C (eqn. (10)) for the sulphur-doped films should be a factor of about 3 less than those for the other films. This is not observed experimentally (Table I). Ionized impurity scattering should also play a more important role in the sulphur-doped films. A simple re-examination of the mechanism shows that, instead of eqn. (8), we have crll~b = ilk
(11)
where ,ui is now the ionized-impurity-limited mobility inside the grains. For k < 10, p1 is comparable with the room temperature barrier-limited mobility. When the effect of both scattering mechanisms is taken into account the room temperature mobility in the sulphur-doped films is expected to be several times lower than that in the selenium- and tellurium-doped films. As is seen in Fig. 4, this is not the case. Therefore the behaviour of the sulphur-doped films can only be explained qualitatively using mechanism (4). Regrowth from the melt reduces the number of barriers in the InSb thin films with a consequent increase in the mobility. The temperature dependence of the mobility in the MR films varies with the level of doping. In films with donor concentrations below lo’* cme3 the mobility decreases with temperature owing to barrier scattering. In more strongly doped films the mobility increases with temperature, as in doped bulk InSb, although the increase is rather smaller than that observed in the bulk material. Therefore the behaviour of the MR films differs from the behaviour of the VG films as no increase in the barrier height with doping level is observed. This suggests that the barriers existing in the two types of film may be different. 6.
SUMMARIZING
REMARKS
AND CONCLUSIONS
The aim of this paper was to describe a method of preparing InSb thin films with a high electron mobility and a controlled donor doping level and to report investigations of the dependence of the electrical properties of the films on the doping level, temperature and film thickness. The technology previously developed for the deposition of undoped InSb films with a high electron mobility6g7 was adopted for the preparation of doped films. The method comprised two stages: the flash evaporation of InSb films (the VG films) and the subsequent regrowth from the melt of InSb films covered with a protective SiOs layer (the MR films). The doping was performed during the first stage by the coevaporation of InSb and the dopants (sulphur, selenium and tellurium) from independent evaporation sources (Fig. 1). Using this method we were able to obtain InSb films with donor concentrations in the range from 10” to 2 x 10” crn3. The
InSb THIN FILMS DOPED WITH Te, Se AND S
365
lower limit approaches the natural donor concentration in undoped InSb films and the upper limit is the tellurium solubility limit in InSb. The room temperature electron mobility in the MR films is about an order of magnitude higher than that in VG films with the same electron concentration and can be as high as that in doped bulk InSb (Fig. 4). The increase in mobility on regrowing the films is a result of improvements to the film structure. Regrowth increases not only the mobility but also the electron concentration in InSb films. The electron concentration is increased by a factor of about 2 in the selenium- and tellurium-doped films and by a factor of up to 10 in the sulphur-doped films. A qualitative explanation of this increase is that the conduction electrons which are trapped at the grain boundaries in the VG films are released in the MR films owing to the reduction in the grain boundary density. The trapped electrons form potential barriers within the InSb films. Barrier scattering is the predominant mechanism limiting the mobility near room temperature. However, the mobility is virtually temperature independent at low temperatures. We have not been able to explain this behaviour. An interesting feature of the VG films is the increase in the barrier height with increasing doping level (Fig. 8) which is not observed in the MR films. This suggests that the barriers in the two types of InSb film may be different. The barriers in the VG films are unexpectedly high. For example, in the VG films with donor concentrations of 8 x 10” cm- 3 the barrier height is about 150 meV and the Fermi level is about 400 meV above the conduction band 22. Thus the overall barrier height is about 550meV, i.e. about three times the band gap of InSb. The nature of the barriers is unknown and needs further investigations. The MR films are suitable for use as Hall generators for precision magnetic field measurements. Films with donor concentrations between 2 x lo’* and 4 x 10” cme3 are preferred for this application because their Hall coefficients are virtually temperature independent near room temperature (Fig. 6). The electron mobility in such films is about 1 m2 V-i s- ’ , which is a large value for such a thin film. We have found that the decrease in the mobility with decreasing thickness is less in the doped films than in the undoped films (Fig. 7). However, the reproducibility of the parameters of films of thickness less than 1 urn is poor. RJZERENCES 1 A. S. Filipchenko and D. N. Nasledov, Phys. StatusS+idi A, 27 (1975) 11. H. H. Wieder and A. R. Clawson, Solid-State Electron., I1 (1968) 887. H. H. Wieder and D. A. Collins, Thin SolidFilms, 20 (1974) 201. E. Litwin-Staszewska, S. Porowski and A. A. Filipchenko, Phys. Status Solidi B, 48 (1971) 519. V. J, Fistul, Heavily Doped Semiconductors, Nauka, Moscow, 1967, p. 239 (in Russian). 6 M. Oszwaidowski and W. Harms, Proc. Int. ConJ on the Physics and Chemistry of Heterojunction andL.uyer Structures, Budapest. 1971, Akademiai Kiado, Budapest, 1971, Vol. 3, p. 219. 7 M. Oszwaldowski, H. Szweycer, T. Bents, J. Got and M. Zimpel, Thin SolidFilms, 85 (1981) 319. 8 V. V. Popov and V. V. Kasarev, Phys. Status Solidi A, 58 (1980) 23 1. 9 H. H. Wieder, J. Vat. Sci. Technol., 8 (1971) 210. 10 M. Oszwaidowski, Acta Phys. Pal. A, 37(1970) 617. 11 M. Le Contellec and J. Richard, Thin Solid Films, 36 (1976) 151. 12 M. Oszwaldowski, Acta Phys. Pal., 26 (1969) 21. 13 E. Litwin-Staszewska, W. Szymatiska and R. Piotrzkowski, Phys. Status Solidi B, 106 (198 1) 551. 2 3 4 5
366 14 H. H. Wieder, J. Vuc. Sci. Technol., 9 (1972) 1193. 15 K. Seeger, Semiconductor Physics, Springer, Vienna, 1973, Chapter 6. 16 W. Hanus and M. Oszwatdowski, Thin SolidFilms, 61(1979) 235. 17 R. L. Longini and R. F. Greene, Phys. Rev., 102 (1956) 992. 18 J. Kotodziejczak, Acta Phys. Pal., 20 (1961) 289. 19 W. E. Taylor, N. H. Ode11and H. Y. Fan, Phys. Rev., 88 (1952) 867. 20 C. H. Ling, J. H. Fisher and J. C. Anderson, Thin Solid Films, 14 (1972) 267. 21 A. Broniatowski, J. Phys. (Paris), Coffoq. Cl, 43 (Suppl.) (1982) 63. 22 P. Pfeffer and W. Zawadzki, Phys. Status Solidi B,88 (1978) 247.
T. BERUS et al.