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Electrical and optical properties of InAs-In2Te3 alloys
J. Phys. Chem. Solidr
Pergamon Press 1961. Vol. 19, Nos. l/2, pp. 147-154.
ELECTRICAL
AND
OPTICAL
InAs-In,Te,
Printed in Great Britain.
PROPERTIES
OF
ALLOYS
J. C. WOOLLEY, B. It. PAMPLIN and J. A. EVANS Department of Physics, University of Nottingham, England (Received 25 July 1960)
Abstract-The production of suitable InAs-InsTes alloys by annealing and by directional freezing methods is considered and the relevance of the second method to the phase diagram of the system is discussed. The results of measurements of Hall effect, conductivity, thermoelectric power and i&a-red absorption are given for the whole composition range, and values of carrier density tz, mobility p and optical energy gap Ee are obtained. It is seen that the behaviour is similar to that of InSb-InsTes alloys in that the InAs rich alloys are highly degenerate having YZz 5 x 101e/cms and explanations of this behaviour in terms of solubility of tellurium in InAs or of the band structure of InAs are discussed. The variation of p with composition and hence possible scattering mechanisms and types of conduction occurring in the alloys are considered. Assuming certain scattering effects, attempts are made to use the values of thermoelectric power in conjunction with the measured values of Eg to determine the variation of intrinsic energy gap throughout the composition range.
1. INTRODUCTION InsTes has a defect zinc blende structure with one lattice site in three on the A sub lattice vacant, (or alternatively a defect antifluorite AsB structure with two lattice sites in three on the A sub lattice vacant(l)). Thus, when InsTes is alloyed with a normal ArrrBv zinc blende type compound such as InSb or InAs, the resulting alloy will have some A sub lattice sites vacant, the exact fraction being determined by the composition of the alloy. The electrical properties of such alloys may therefore be of interest in that a controlled number of lattice vacancies can be introduced into the alloy. In a recent paper(s) the properties of alloys formed by solid solution of InsTes in InSb have been discussed. In that case the range of composition available to measurement is limited to the available range of solid solution of approximately 15 mol. per cent InsTes* for alloys annealed close to the solidus of the system. As has been shown previously(s) in the case of the InAs-InsTes
system solid solution is obtained throughout the whole range of composition. Thus the limitations of the In%-InsTea system do not apply in this case and hence it is possible to investigate the variation of the various semiconductor parameters over a much wider range of composition and to investigate the gradual transition from the normal type semiconductor InAs to the defect structure InsTea. The present paper reports an investigation of some properties of this alloy system. The alloy system GaAs-Gasses should show similar behaviour(s) and recently NASLEDOV and FELTIN'SW(4) have reported electrical measurements on these alloys. Unfortunately, measurements of conductivity and thermo-electric power only and not of Hall effect were made in this work and so the usefulness of the results is somewhat limited, as separate values of number of carriers and mobility cannot be determined.
* In calculating mol. percentage in systems composed
The InsTes was prepared from indium of 99.999 per cent purity and commercial high purity tellurium which had been purified by repeated distillation. Some of the initial measurements were made
2.PREPA.RATION OF SPECIMENS of one A”‘BV compound and one AsmBsV’ compound, the molecules have been taken as As”‘Bsv and As”‘BsV’, i.e. the percentage is strictly the percentage of BV and Bv’ atoms on the B sub lattice.
147
148
J. C.
WOOLLEY,
B.
R.
PAMPLIN
on specimens using InAs of rather high carrier concentration, but the InAs used in the majority of the work was of good purity having approximately 3 x 10la carriers/cma. Some of the alloys were prepared from the two compounds by melting together the required amounts under vacuum, the resulting ingots then being annealed at a suitable temperature to obtain a good equilibrium condition. The annealing temperatures lay in the range 650°C to SOO”C, the actual value in each case being determined by the composition of the alloy concerned. As has been shown previously(s) there is evidence of a closed miscibility gap in this system, and hence it was necessary to anneal each alloy at a temperature above the miscibility gap limit but below the solidus, neither of these curves having as yet been accurately determined. The majority of the specimens were annealed for some 6 or 7 weeks and X-ray photographs then showed that good single phase ‘conditions had been attained in all alloys except those lying in the range lo-35 mol. per cent InsTes, where a blurring of the lines in the X-ray photograph showed that even after this time of annealing these particular alloys were still partly inhomogeneous. It had already been noted during the initial X-ray work(s) that it was very difficult to attain equilibrium with alloys in this composition range and the results in that case were based on slightly inhomogeneous alloys. The results obtained during the present work tend to indicate that the mean lattice parameter curve shown previously”) is probably too high in this range but is correct beyond 35 mol. per cent InsTes. This will be discussed elsewhere when further c~stallographic work has been carried out. A second method used to produce suitable alloys was to directionally freeze a suitable ingot. This technique has been very useful in alloys of two ArrrBv compounds(s) since, provided the rate of freezing is sufficiently slow to obtain good equilibrium conditions, the alloy composition varies continuously along the ingot giving a useful range of composition in a single ingot. The problem in the case of InAs-InsTea alloys was that the appropriate section of the ternary diagram As-In-Te is not truly pseudobinary as shown by the behaviour in the miscibili~ gap and therefore it was not certain that sections cut from the directionally frozen ingot would be alloys on the InAs-InsTea
and
J. A.
EVANS
section of the ternary diagram. Nevertheless an ingot of length 17 cm and mean composition 66 mol. per cent InsTes was directionally frozen so that there was a temperature gradient of approximately SC/cm. along the ingot and the freezing surface travelled along the ingot at about 1.5 cm/day. Sections were taken from positions at l-7, 5 -0, 14.0 cm along the ingot and chemicafly analysed, and these were found to have compositions of the form seIn&s (1 -x)InsTes within a limit of 1 per cent. Also sections from various points along the ingot were X-rayed and found to show the zinc blende structure associated with InAs-InsTea alloys.(s) It was therefore assumed that the solidus-liquidus area of the InAs-InsTes system shows pseudo-binary behaviour and that all cross sections cut from the ingot represented stoichiometric InAs-InaTes alloys. Such sections were used for measurements, the composition of the section being found by determining the lattice parameter and comparing this with the previous results for this system@) and with the chemically analysed specimens mentioned above. In some of these sections the high angle X-ray lines were found to be just split into two lines indicating that some sections of the ingot had cooled into the top of the closed miscibility gap. This effect appeared to be quite small, however, and the results from all specimens were found to be in good agreement with those obtained from the lump annealed ingots. 3. METHODS
OF MEASUREMENTS RESULTS
AND
Conductivity and Hall coefficient were investigated for alloys of various compositions. For alloys cont~ing less than 50 mol. per cent InsTea measurements were made over a range of temperature from liquid air to room temperature, while for alloys with more than 50 moi. per cent InsTea the conductivity became so low at low temperatures that only room temperature measurements were made. The methods used for the measurements were the same as those described previously for the InSb-InaTea alloys.(s) Optical measurements were also made on all alloys to determine the value of optical energy gap Eg at room temperature and again the method was the same as described previously.(s) For alloys of less than 70 mol. per cent InsTea measurements were made of thermoelectric power
ELECTRICAL
AND
OPTICAL
PROPERTIES
over the temperature range from liquid air to room temperature. A conventional apparatus was used for these measurements, the temperature gradient being produced by means of a heat source consisting of a heating coil wound on a solid copper cylinder and coated with alumina and a heat sink in the form of a copper block. On either side of the specimen and insulated from both source and sink by thin sheets of mica two copper electrodes were placed. Set into these were two calibrated chrome1 alumel thermocouples used to obtain the temperature difference AT across the specimen, and a lead was taken from each electrode to the potentiometer to determine the potential
OF
InAs-InaTe
ALLOYS
149
P N$ 0
<
20
40 Mole
60 %
60
100
I #2TQ
InpTe3
FIG. 2. Variation of room temperature electron mobility
~1with composition.
0 Annealed specimens. + Directionally frozen specimens.
p were practically independent of temperature. In all such cases the carrier concentration n as determined from the Hall coefficient was greater that lOls/cma indicating the material to be highly degenerate. In order to compare the values of
40 Mole
60 %
too I n,Te,
In,Te3
FIG. 1. Variation of room temperature carrier concentration ft with composition. 0 Annealed specimens. + Directionally frozen specimens.
AV across the specimen. The whole apparatus was enclosed in either a tubular furnace or in a vacuum flask to provide the required ambient temperature. AVfAT was taken as the thermoelectric power at the ambient temperature, AT being usually of the order 5°C. This was the thermoelectric power relative to copper, but in all cases the correction for this was assumed to be negligible. For the alloys for which electrical measurements were made over a range of temperature (i.e. those with less than 50 mol. per cent InaTes) it was found that the values of conductivity cr and Hall coefficient RR and hence the derived Hall mobility
c 0
Ill,AS,
20
40
60
Mole %
60
100 _ 1 n,Tej
In,Te3
Variation of room temperature conductivity o with composition. 0 Annealed specimens. + Directional frozen specimens,
FIG.
3.
150
J.
WOOLLEY,
C.
B. R. PAMPLIN
and
J.
A.
EVANS
0 100
150
200 Absolute
250 temperature,
0
300 T,
OK
4. Variation of thermoelectric power Q with temperature for typical specimens. (a) 15 mol. per cent InsTea (c) 49 mol. per cent InsTes (b) 37.5 mol. per cent IngTea (d) 69 mol. per cent InsTea FIG.
it, p and o for the various compositions, it was therefore necessary to consider only the room temperature values and the variations of room temperature values of n, p and o with composition are shown in Figs. l-3. The two points shown on each graph for InsTes itself represent the values for orde;ed and disordered stateof the compound.
The variation of thermoelectric power Q with temperature for a number of typical specimens is shown in Fig. 4. It was found that for all alloys investigated, Q was directly proportional to the absolute temperature T. This is as expected in degenerate material and the value of Q/T can be directly related to the height of the Fermi
1000
0 0 /
Mole % InzTe3 FIG. 5. Variation
of room temperature thermoelectric power Qseo with composition.
0 Annealed specimens.
+ Directionally
frozen specimens.
ELECTRICAL
AND
OPTICAL
PROPERTIES
level in the conduction band. The variation of the room temperature value of Q(Qs@@) with composition is shown in Fig. 5 where the value of Qs@@ is given for alloys ranging from pure InAs to 90 mol. per cent InsTes. The form of this curve is very similar to that for the GaAs-Gasses allays(4) over the range O-70 mol. per cent Gasses. In the latter case beyond 70 mol. per cent the value of Q falls and becomes negative because of the p-type behaviour of Gasses.
OF
InAs-InaTes
ALLOYS
151
upon the value of n in each case. Secondly, with the large carrier concentration in this range, the resulting free carrier absorption will be large and hence the accuracy in determination of Er will be less here than elsewhere. Finally, as already indicated the alloys in this range were inhomogeneous to some extent and this factor can affect the shape of the absorption vs. wavelength curve and hence the determination of EB. Thus the values of Eg in this range are only approximate. 4. DISCUSSION
In,As,
Mole % InpTe3
FIG. 6. Variation with composition of room temperature optical energy gap Ep and values of intrinsic energy gap I&O calculated for different values of scattering coefficient S. (a) s = +t ‘J Annealed specimens.
In Fig.
(b) s = -&
+ Directionally
frozen specimens.
6 the variation
of optical energy gap It is seen that in the range from 0-6Omol. per cent InsTes where the material is highly degenerate, the results show a very considerable filling of the conduction band and the optical measurements do not give the intrinsic energy gap. In the range from 5 to 35 mol. per cent InsTes there is some spread in the experimental points. Three factors contribute to this effect. Firstly, as the level to which the conduction band is filled depends upon the carrier concentration there will be a real variation from one specimen to another depending
E, is shown as a function of composition.
The results for alloys of low InsTes content are very similar to those for the InSb-InsTes system,(s) where solid solution is limited to 15 mol. per cent InsTes, and to the conductivity measurements in the GaAs-Gasses system.(4) Thus as InsTes is added to InAs the value of tt rises rapidly and reaches a maximum of 5 x lOl@/cms at 2mol. per cent InsTes. It then drops slowly reaching a value of 8 x lOls/cms at 50 mol. per cent InsTes. As indicated previously, (2) it would appear that initially when InsTes is added to InAs (or InSb) the In and Te atoms enter the lattice without leaving lattice vacancies and the Te atoms in the As lattice act as donors. As the concentration of Te is increased some lattice vacancies appear and beyond 2 mol. per cent InsTes each InsTes molecule added causes the associated vacancy on the In lattice. On this basis the maximum carrier concentration of 5 x lOl@/cms would be determined by the limit of solid solution of Te in InAs. A second possible explanation can be put forward however if it is suggested that the maximum observed value of n of 5 x lOl@/cms is determined by the band structure of InAs. On this basis it would be postulated that solid solution of Te continues beyond the value corresponding to 5 x 1019 carriers/cm3 but that the resulting electrons enter the conduction band in a region where they have considerably larger effective mass than the electrons at the normal band minimum and hence would contribute very little to the Hall coefficient and would not be effectively observed. Two factors which possibly favour this second explanation can be cited. Firstly, the results of adding InsSes to InAs and to InSb(s) give maximum values of n of 6 x lOl@/cms and 9 x lOls/cms respectively which are very similar to the values when InsTes is added to the compounds. Secondly, for every
152
J. C. WOOLLEY,
B. R. PAMPLIN
three Te atoms giving electrons in the conduction band there will be one lattice vacancy less than the number expected from the stoichiometric formula and this should cause a small increase in density. Unfortunately specimens with less than 37 mol. per Cent were found to contain numerous blowholds which render density measurements inaccurate. At higher percentage and particularly for the directionally frozen ingot the specimens were more uniform and hence density measurements were made on various samples. The values obtained appeared to be nearly 1 per cent higher than those expected from the values of lattice parameter and stoichiometric formulae. It was considered, however, that this difference probably lay within the limits of experimental error, Until further evidence is available it is difficult to decide which of the postulated explanations is more correct. The variation in the n vs. composition curve for alloys with more than 50 mol. per cent InsTes is very large and as seen from Fig. 1 the room temperature value of a falls from 4 x 1OlsJcma at 50 mol. per cent InsTes to approximately 5 x 1011,’ cm3 for InsTes itself. While the return to a stoichiometric condition could explain a fall of two or three orders of magnitude inn, corresponding to the rise in it from the value at InAs to that at 5 mol. per cent InsTes, the much larger change in 91of seven orders of magnitude needs further explanation. Various factors have to be considered in discussing this large change. Firstly, bearing in mind the suggestions of &iFFEf7f, Z~ER(~~, and others it is possible that the normal ideas of conduction cannot be applied to InsTes and that “hopping” conduction must be considered. If this is so, it is not certain that the value of 91obtained here from Hall data can be correlated with the values obtained for the more normal substance such as InAs and the high percentage InAs alloys. If it is assumed that the value of n has its normal significance, it is necessary to explain this very large fall in carrier concentration. In this range of composition the energy gap has such a value that we are dealing with impurity carriers at room temperature. An obvious suggestion is that the donor levels are depressed as InsTes is added and the impurity activation energy is therefore increased. A factor of 107 in carrier concentration could be explained by a change in position of donor levels from approximately 0.01 eV below the conduction
and J. A. EVANS
band, a value typical of normal ArI’Bv compounds, to the centre of the forbidden gap in InsTes itself. Such an effect could explain the very low carrier concentration observed in InsTea. (9) Because of the nature of InsTes however, other explanations are possible for the very low carrier concentration observed in this compound. With the preparation described above, it would be expected from experience with other intermetallic compounds that the InsTea would contain impurities of the order 1017/ems or more, and that some reasonable proportion of these would act as donors or acceptors. But as has been shown, InsTes will take into solid solution both AIIIBv compounds such as InAs and AIIBvr compounds such aa CdTe(10) and for low percentages of these substances the ideal stoichiometry may be lost. Thus it is possible that small amounts of elements from the 2nd, 3rd, 4th, 5th or 6th columns of the periodic table can be accommodated in the lattice, and by suitable loss or gain of lattice vacancies the electron concentration can remain at a value of 4 electrons per site. With such an electron distribution, no donors or acceptors would be present in the lattice and no impurity levels, in the usual semiconductor sense, would occur. An important factor in this case is the possibility, as yet unconfirmed,(l) that InsTes has a defect antifluorite rather than a defect zinc blende structure. It this were the case, the presence of the enantiomorphous fluorite sites would give even more flexibility in the lattice to accommodate impurity atoms. If the behaviour of InzTes is as described above, the very rapid fall in n over the range of alloys from 50 mol. per cent InsTea to InsTes itself can be looked upon as a gradual transition from the normal impurity behaviour of the InAs rich alloys to the effectively intrinsic behaviour of InsTea. The variation of mobility p with composition (Fig. 2) shows that p falls very rapidly from 30,000 for InAs to 2000 at 2 mol. per cent InsTes and then falls more slowly to a value between 10 and 50 for InsTea. Various scattering mechanisms can be postulated to explain this reduction in p, but such a discussion must be linked with the considerations of the alloying effects given above. Over the first few per cent of InsTes the predominant scattering effect could be due to ionized tellurium atoms or to neutral tellurium atoms and
ELECTRICAL
AND
OPTICAL
PROPERTIES
lattice vacancies in the lattice. It is of interest to note that up to 15 mol. per cent InsTes a logarithmic plot (Fig. 7) shows that TVvaries approximately as N-l/a where N represents the concentration of InsTes. The same type of result was obtained with the In!%--InsTes alloys. At higher concentrations of InsTes the scattering is almost certainly due to the presence of lattice impurities and at such high densities that alloy scattering is relevant. In this range the possibilities of antifluorite structure and “hopping” conduction become important. Some further evidence on scattering mechanisms may be obtained from a consideration of the thermoelectric effects. 10,000
iY
,r
I FGi
I
I
1000
E
0
i
too
K)~
I
C
I.0
Mole % In2Te3
+ 4
IO N
FIG. 7. Variation of loglo p with loglo N where iV is InaTes concentration. 0 Annealed specimens. f Directionally frozen specimen.
As indicated above for degenerate material the thermoelectric power Q is found to be directly proportional to the absolute temperature T, and the value of Q/T can be used to determine the height of the Fermi level (5) above the conduction band minimum. The appropriate equational) is
kp2 p[1+ ;(&g-),,l Q=-zand if it is assumed that
then
L? = -t-a5
OF
InAs-InaTes
ALLOYS
153
A determination of (5) from Q thus requires a knowledge of s which depends upon the particular scattering mechanism concerned. The two mechanisms expected to predominate are ionized impurity scattering at low InsTes content and alloy scattering at higher InaTes content. Thus values of 5 have been calculated from the mean Q vs. composition curve assuming that s = -4 for alloy scattering(ls1 and s = +$ for ionized impurity scat~ring,(ls) and these values of 1 subtracted from the optical values of l$. The resultant values should approximate to the intrinsic energy gap Effo>and these are plotted in Fig. 6. In the range 40-70 mol. per cent InaTes the values of Ego obtained by assuming s = -4 are consistent with the values of E,, from 70-100 mol. per cent InsTes, in which range the carrier concentration is so small that the optical value is the intrinsic gap. Also, using s = +a, the values of Ego at low In2Te3 concentrations are in good agreement with the intrinsic gap for InAs itself. Thus it would appear correct to assume that alloy scattering is predominant in the range 40-70 mol. per cent InsTes and ionized impurity scattering for compositions from InAs to approximately 5 mol. per cent InsTes. It cannot be seen from these results what values of .&J apply in the range 5-40 mol. per cent InsTes, but it seems unlikely that in this range either of the plotted Ego curves are applicable. Probably no single scattering mechanism predominates, but that alloy scattering increasingly dominates over ionized impurity scattering. With highly degenerate material the value of 4 can be used to determine an effective mass (m,) of the conduction electrons, the equation ?Z=
&rz(2m43’2
_
~
3
p/2
h3
giving a “density of states” effective mass. If the values of 1 for alloys containing up to 3 mol. per cent InsTes are used in this way values for mR lying between 0.08 m and 0.09 mo are obtained, (ms being the free electron mass). For alloys of InsTes content rather higher than this the values of 5 are not known but from Fig. 6 a rough estimate can be made, shown by the dotted line, and this indicates values of m,, similar to those for the lower percentage alloys. As the values are almost three times the accepted value for non-degenerate I& it
154
J.
C. WOOLLEY,
3.
R. PAMPLIN
appears that the InAs band shows considerable deviation from parabolic form at these values of electron concenkion. The values obtained here are consistent with the values calculated by STERN using a KANBtypeus) model for InAs. In alloy systems of this type the possibility of ordering at various special compositions should be considered. An investigation of the possible types of ordering in this caseffs) indicates that the most probable percentages at which ordering may occur are 75 mol. per cent InsTes, 50 mol. per cent InsTes and 375 mol. per cent InsTes where the formulae of the alloys would be Ins [7 AsTes, Ins [7 AssTes and In7 •JAsaTes respectively (where q indicates a lattice vacancy). No direct X-ray evidence has been obtained at any of these compositions but some evidence in the case of the 75 mol. per cent InsTes alloy may be obtained from the optical data, for Fig. 6 shows the values of EB at this percentage sig~~~tly above the mean curve for Eg values in this range. It is of interest to note that in an analogous system IuAs-InsSes ordering at the 75 mol. per cent InsSes composition has been reported.u7) ~~~~~~The authors are indebted to Professor L. F. BATIZ~ for the facilities of hia Laboratory.
and J. A. EVANS
The work described forma part of an investigation
carriedOutfor the Admiraltv+
1. WOOLLSV J. C., &MPLIN B, R. and How P. J. J. Less Conunmt Metals 1, 362 (1959). 2. WOOLLSY J. C., GILLBTTC. M. and EVANSJ. A., J. PFzys. Chem. Solids 16,138 (1960). 3. WOOLLEY J. C. and SMITW B. A., Proc. P&s. Sot. Lo&. 72, 867 (1958). 4. NASLEDOVD. N. and F~LTIN’SH I. A., So&t Piiys. Solid State 1, 510 (1959). 5. WOOLLEY f. C., EVANS J. A. and GILLKI-T C. M., Proc. Phys. sot. Lad- 74, 244 (1959). 6. WOOLLEY T. C. and Kwrx~d P. N.. to be published. 7. JOPPE A. F., J. Phys. Chw. Solidr.8,6 (1959). 8. ZENER C., J. Phys. Chem. So&a%8,26 (1959). 9. WOOLLEY J. C. and PAMPLIN B. R., to be published. 10. WOOLLEY J. C. and RAY B., J. Phys. Chem. Solids 15, 27 (1960). Il. BARRIER. and EDMONDJ. T., _J. EIect~onics 1, 161 (1955).
12. NORDHEIML., Ann. Phys., Lps. 9,607 (1931). 13. SCLARN., Phys. Reu. 104,1548 (1956). 14. STERNF., Bull. Amer. Plays. Sot. (ser. 2) 4, 28 (1959). 15. KANEE. O., J. Phys. Chem. Solids 1, 249 (1957). 16. PAMPLIN B. R., Nawq Land. 188,136 (1960). S. I., Sowiet 17, GORYLTNOVAN. A. and RADATJXXXAN Phys. Tech. Phys. 3, 1762 (1958).
Pergamon Press 1961. Vol. 19, Nos. l/2, pp. 147-154.
ELECTRICAL
AND
OPTICAL
InAs-In,Te,
Printed in Great Britain.
PROPERTIES
OF
ALLOYS
J. C. WOOLLEY, B. It. PAMPLIN and J. A. EVANS Department of Physics, University of Nottingham, England (Received 25 July 1960)
Abstract-The production of suitable InAs-InsTes alloys by annealing and by directional freezing methods is considered and the relevance of the second method to the phase diagram of the system is discussed. The results of measurements of Hall effect, conductivity, thermoelectric power and i&a-red absorption are given for the whole composition range, and values of carrier density tz, mobility p and optical energy gap Ee are obtained. It is seen that the behaviour is similar to that of InSb-InsTes alloys in that the InAs rich alloys are highly degenerate having YZz 5 x 101e/cms and explanations of this behaviour in terms of solubility of tellurium in InAs or of the band structure of InAs are discussed. The variation of p with composition and hence possible scattering mechanisms and types of conduction occurring in the alloys are considered. Assuming certain scattering effects, attempts are made to use the values of thermoelectric power in conjunction with the measured values of Eg to determine the variation of intrinsic energy gap throughout the composition range.
1. INTRODUCTION InsTes has a defect zinc blende structure with one lattice site in three on the A sub lattice vacant, (or alternatively a defect antifluorite AsB structure with two lattice sites in three on the A sub lattice vacant(l)). Thus, when InsTes is alloyed with a normal ArrrBv zinc blende type compound such as InSb or InAs, the resulting alloy will have some A sub lattice sites vacant, the exact fraction being determined by the composition of the alloy. The electrical properties of such alloys may therefore be of interest in that a controlled number of lattice vacancies can be introduced into the alloy. In a recent paper(s) the properties of alloys formed by solid solution of InsTes in InSb have been discussed. In that case the range of composition available to measurement is limited to the available range of solid solution of approximately 15 mol. per cent InsTes* for alloys annealed close to the solidus of the system. As has been shown previously(s) in the case of the InAs-InsTes
system solid solution is obtained throughout the whole range of composition. Thus the limitations of the In%-InsTea system do not apply in this case and hence it is possible to investigate the variation of the various semiconductor parameters over a much wider range of composition and to investigate the gradual transition from the normal type semiconductor InAs to the defect structure InsTea. The present paper reports an investigation of some properties of this alloy system. The alloy system GaAs-Gasses should show similar behaviour(s) and recently NASLEDOV and FELTIN'SW(4) have reported electrical measurements on these alloys. Unfortunately, measurements of conductivity and thermo-electric power only and not of Hall effect were made in this work and so the usefulness of the results is somewhat limited, as separate values of number of carriers and mobility cannot be determined.
* In calculating mol. percentage in systems composed
The InsTes was prepared from indium of 99.999 per cent purity and commercial high purity tellurium which had been purified by repeated distillation. Some of the initial measurements were made
2.PREPA.RATION OF SPECIMENS of one A”‘BV compound and one AsmBsV’ compound, the molecules have been taken as As”‘Bsv and As”‘BsV’, i.e. the percentage is strictly the percentage of BV and Bv’ atoms on the B sub lattice.
147
148
J. C.
WOOLLEY,
B.
R.
PAMPLIN
on specimens using InAs of rather high carrier concentration, but the InAs used in the majority of the work was of good purity having approximately 3 x 10la carriers/cma. Some of the alloys were prepared from the two compounds by melting together the required amounts under vacuum, the resulting ingots then being annealed at a suitable temperature to obtain a good equilibrium condition. The annealing temperatures lay in the range 650°C to SOO”C, the actual value in each case being determined by the composition of the alloy concerned. As has been shown previously(s) there is evidence of a closed miscibility gap in this system, and hence it was necessary to anneal each alloy at a temperature above the miscibility gap limit but below the solidus, neither of these curves having as yet been accurately determined. The majority of the specimens were annealed for some 6 or 7 weeks and X-ray photographs then showed that good single phase ‘conditions had been attained in all alloys except those lying in the range lo-35 mol. per cent InsTes, where a blurring of the lines in the X-ray photograph showed that even after this time of annealing these particular alloys were still partly inhomogeneous. It had already been noted during the initial X-ray work(s) that it was very difficult to attain equilibrium with alloys in this composition range and the results in that case were based on slightly inhomogeneous alloys. The results obtained during the present work tend to indicate that the mean lattice parameter curve shown previously”) is probably too high in this range but is correct beyond 35 mol. per cent InsTes. This will be discussed elsewhere when further c~stallographic work has been carried out. A second method used to produce suitable alloys was to directionally freeze a suitable ingot. This technique has been very useful in alloys of two ArrrBv compounds(s) since, provided the rate of freezing is sufficiently slow to obtain good equilibrium conditions, the alloy composition varies continuously along the ingot giving a useful range of composition in a single ingot. The problem in the case of InAs-InsTea alloys was that the appropriate section of the ternary diagram As-In-Te is not truly pseudobinary as shown by the behaviour in the miscibili~ gap and therefore it was not certain that sections cut from the directionally frozen ingot would be alloys on the InAs-InsTea
and
J. A.
EVANS
section of the ternary diagram. Nevertheless an ingot of length 17 cm and mean composition 66 mol. per cent InsTes was directionally frozen so that there was a temperature gradient of approximately SC/cm. along the ingot and the freezing surface travelled along the ingot at about 1.5 cm/day. Sections were taken from positions at l-7, 5 -0, 14.0 cm along the ingot and chemicafly analysed, and these were found to have compositions of the form seIn&s (1 -x)InsTes within a limit of 1 per cent. Also sections from various points along the ingot were X-rayed and found to show the zinc blende structure associated with InAs-InsTea alloys.(s) It was therefore assumed that the solidus-liquidus area of the InAs-InsTes system shows pseudo-binary behaviour and that all cross sections cut from the ingot represented stoichiometric InAs-InaTes alloys. Such sections were used for measurements, the composition of the section being found by determining the lattice parameter and comparing this with the previous results for this system@) and with the chemically analysed specimens mentioned above. In some of these sections the high angle X-ray lines were found to be just split into two lines indicating that some sections of the ingot had cooled into the top of the closed miscibility gap. This effect appeared to be quite small, however, and the results from all specimens were found to be in good agreement with those obtained from the lump annealed ingots. 3. METHODS
OF MEASUREMENTS RESULTS
AND
Conductivity and Hall coefficient were investigated for alloys of various compositions. For alloys cont~ing less than 50 mol. per cent InsTea measurements were made over a range of temperature from liquid air to room temperature, while for alloys with more than 50 moi. per cent InsTea the conductivity became so low at low temperatures that only room temperature measurements were made. The methods used for the measurements were the same as those described previously for the InSb-InaTea alloys.(s) Optical measurements were also made on all alloys to determine the value of optical energy gap Eg at room temperature and again the method was the same as described previously.(s) For alloys of less than 70 mol. per cent InsTea measurements were made of thermoelectric power
ELECTRICAL
AND
OPTICAL
PROPERTIES
over the temperature range from liquid air to room temperature. A conventional apparatus was used for these measurements, the temperature gradient being produced by means of a heat source consisting of a heating coil wound on a solid copper cylinder and coated with alumina and a heat sink in the form of a copper block. On either side of the specimen and insulated from both source and sink by thin sheets of mica two copper electrodes were placed. Set into these were two calibrated chrome1 alumel thermocouples used to obtain the temperature difference AT across the specimen, and a lead was taken from each electrode to the potentiometer to determine the potential
OF
InAs-InaTe
ALLOYS
149
P N$ 0
<
20
40 Mole
60 %
60
100
I #2TQ
InpTe3
FIG. 2. Variation of room temperature electron mobility
~1with composition.
0 Annealed specimens. + Directionally frozen specimens.
p were practically independent of temperature. In all such cases the carrier concentration n as determined from the Hall coefficient was greater that lOls/cma indicating the material to be highly degenerate. In order to compare the values of
40 Mole
60 %
too I n,Te,
In,Te3
FIG. 1. Variation of room temperature carrier concentration ft with composition. 0 Annealed specimens. + Directionally frozen specimens.
AV across the specimen. The whole apparatus was enclosed in either a tubular furnace or in a vacuum flask to provide the required ambient temperature. AVfAT was taken as the thermoelectric power at the ambient temperature, AT being usually of the order 5°C. This was the thermoelectric power relative to copper, but in all cases the correction for this was assumed to be negligible. For the alloys for which electrical measurements were made over a range of temperature (i.e. those with less than 50 mol. per cent InaTes) it was found that the values of conductivity cr and Hall coefficient RR and hence the derived Hall mobility
c 0
Ill,AS,
20
40
60
Mole %
60
100 _ 1 n,Tej
In,Te3
Variation of room temperature conductivity o with composition. 0 Annealed specimens. + Directional frozen specimens,
FIG.
3.
150
J.
WOOLLEY,
C.
B. R. PAMPLIN
and
J.
A.
EVANS
0 100
150
200 Absolute
250 temperature,
0
300 T,
OK
4. Variation of thermoelectric power Q with temperature for typical specimens. (a) 15 mol. per cent InsTea (c) 49 mol. per cent InsTes (b) 37.5 mol. per cent IngTea (d) 69 mol. per cent InsTea FIG.
it, p and o for the various compositions, it was therefore necessary to consider only the room temperature values and the variations of room temperature values of n, p and o with composition are shown in Figs. l-3. The two points shown on each graph for InsTes itself represent the values for orde;ed and disordered stateof the compound.
The variation of thermoelectric power Q with temperature for a number of typical specimens is shown in Fig. 4. It was found that for all alloys investigated, Q was directly proportional to the absolute temperature T. This is as expected in degenerate material and the value of Q/T can be directly related to the height of the Fermi
1000
0 0 /
Mole % InzTe3 FIG. 5. Variation
of room temperature thermoelectric power Qseo with composition.
0 Annealed specimens.
+ Directionally
frozen specimens.
ELECTRICAL
AND
OPTICAL
PROPERTIES
level in the conduction band. The variation of the room temperature value of Q(Qs@@) with composition is shown in Fig. 5 where the value of Qs@@ is given for alloys ranging from pure InAs to 90 mol. per cent InsTes. The form of this curve is very similar to that for the GaAs-Gasses allays(4) over the range O-70 mol. per cent Gasses. In the latter case beyond 70 mol. per cent the value of Q falls and becomes negative because of the p-type behaviour of Gasses.
OF
InAs-InaTes
ALLOYS
151
upon the value of n in each case. Secondly, with the large carrier concentration in this range, the resulting free carrier absorption will be large and hence the accuracy in determination of Er will be less here than elsewhere. Finally, as already indicated the alloys in this range were inhomogeneous to some extent and this factor can affect the shape of the absorption vs. wavelength curve and hence the determination of EB. Thus the values of Eg in this range are only approximate. 4. DISCUSSION
In,As,
Mole % InpTe3
FIG. 6. Variation with composition of room temperature optical energy gap Ep and values of intrinsic energy gap I&O calculated for different values of scattering coefficient S. (a) s = +t ‘J Annealed specimens.
In Fig.
(b) s = -&
+ Directionally
frozen specimens.
6 the variation
of optical energy gap It is seen that in the range from 0-6Omol. per cent InsTes where the material is highly degenerate, the results show a very considerable filling of the conduction band and the optical measurements do not give the intrinsic energy gap. In the range from 5 to 35 mol. per cent InsTes there is some spread in the experimental points. Three factors contribute to this effect. Firstly, as the level to which the conduction band is filled depends upon the carrier concentration there will be a real variation from one specimen to another depending
E, is shown as a function of composition.
The results for alloys of low InsTes content are very similar to those for the InSb-InsTes system,(s) where solid solution is limited to 15 mol. per cent InsTes, and to the conductivity measurements in the GaAs-Gasses system.(4) Thus as InsTes is added to InAs the value of tt rises rapidly and reaches a maximum of 5 x lOl@/cms at 2mol. per cent InsTes. It then drops slowly reaching a value of 8 x lOls/cms at 50 mol. per cent InsTes. As indicated previously, (2) it would appear that initially when InsTes is added to InAs (or InSb) the In and Te atoms enter the lattice without leaving lattice vacancies and the Te atoms in the As lattice act as donors. As the concentration of Te is increased some lattice vacancies appear and beyond 2 mol. per cent InsTes each InsTes molecule added causes the associated vacancy on the In lattice. On this basis the maximum carrier concentration of 5 x lOl@/cms would be determined by the limit of solid solution of Te in InAs. A second possible explanation can be put forward however if it is suggested that the maximum observed value of n of 5 x lOl@/cms is determined by the band structure of InAs. On this basis it would be postulated that solid solution of Te continues beyond the value corresponding to 5 x 1019 carriers/cm3 but that the resulting electrons enter the conduction band in a region where they have considerably larger effective mass than the electrons at the normal band minimum and hence would contribute very little to the Hall coefficient and would not be effectively observed. Two factors which possibly favour this second explanation can be cited. Firstly, the results of adding InsSes to InAs and to InSb(s) give maximum values of n of 6 x lOl@/cms and 9 x lOls/cms respectively which are very similar to the values when InsTes is added to the compounds. Secondly, for every
152
J. C. WOOLLEY,
B. R. PAMPLIN
three Te atoms giving electrons in the conduction band there will be one lattice vacancy less than the number expected from the stoichiometric formula and this should cause a small increase in density. Unfortunately specimens with less than 37 mol. per Cent were found to contain numerous blowholds which render density measurements inaccurate. At higher percentage and particularly for the directionally frozen ingot the specimens were more uniform and hence density measurements were made on various samples. The values obtained appeared to be nearly 1 per cent higher than those expected from the values of lattice parameter and stoichiometric formulae. It was considered, however, that this difference probably lay within the limits of experimental error, Until further evidence is available it is difficult to decide which of the postulated explanations is more correct. The variation in the n vs. composition curve for alloys with more than 50 mol. per cent InsTes is very large and as seen from Fig. 1 the room temperature value of a falls from 4 x 1OlsJcma at 50 mol. per cent InsTes to approximately 5 x 1011,’ cm3 for InsTes itself. While the return to a stoichiometric condition could explain a fall of two or three orders of magnitude inn, corresponding to the rise in it from the value at InAs to that at 5 mol. per cent InsTes, the much larger change in 91of seven orders of magnitude needs further explanation. Various factors have to be considered in discussing this large change. Firstly, bearing in mind the suggestions of &iFFEf7f, Z~ER(~~, and others it is possible that the normal ideas of conduction cannot be applied to InsTes and that “hopping” conduction must be considered. If this is so, it is not certain that the value of 91obtained here from Hall data can be correlated with the values obtained for the more normal substance such as InAs and the high percentage InAs alloys. If it is assumed that the value of n has its normal significance, it is necessary to explain this very large fall in carrier concentration. In this range of composition the energy gap has such a value that we are dealing with impurity carriers at room temperature. An obvious suggestion is that the donor levels are depressed as InsTes is added and the impurity activation energy is therefore increased. A factor of 107 in carrier concentration could be explained by a change in position of donor levels from approximately 0.01 eV below the conduction
and J. A. EVANS
band, a value typical of normal ArI’Bv compounds, to the centre of the forbidden gap in InsTes itself. Such an effect could explain the very low carrier concentration observed in InsTea. (9) Because of the nature of InsTes however, other explanations are possible for the very low carrier concentration observed in this compound. With the preparation described above, it would be expected from experience with other intermetallic compounds that the InsTea would contain impurities of the order 1017/ems or more, and that some reasonable proportion of these would act as donors or acceptors. But as has been shown, InsTes will take into solid solution both AIIIBv compounds such as InAs and AIIBvr compounds such aa CdTe(10) and for low percentages of these substances the ideal stoichiometry may be lost. Thus it is possible that small amounts of elements from the 2nd, 3rd, 4th, 5th or 6th columns of the periodic table can be accommodated in the lattice, and by suitable loss or gain of lattice vacancies the electron concentration can remain at a value of 4 electrons per site. With such an electron distribution, no donors or acceptors would be present in the lattice and no impurity levels, in the usual semiconductor sense, would occur. An important factor in this case is the possibility, as yet unconfirmed,(l) that InsTes has a defect antifluorite rather than a defect zinc blende structure. It this were the case, the presence of the enantiomorphous fluorite sites would give even more flexibility in the lattice to accommodate impurity atoms. If the behaviour of InzTes is as described above, the very rapid fall in n over the range of alloys from 50 mol. per cent InsTea to InsTes itself can be looked upon as a gradual transition from the normal impurity behaviour of the InAs rich alloys to the effectively intrinsic behaviour of InsTea. The variation of mobility p with composition (Fig. 2) shows that p falls very rapidly from 30,000 for InAs to 2000 at 2 mol. per cent InsTes and then falls more slowly to a value between 10 and 50 for InsTea. Various scattering mechanisms can be postulated to explain this reduction in p, but such a discussion must be linked with the considerations of the alloying effects given above. Over the first few per cent of InsTes the predominant scattering effect could be due to ionized tellurium atoms or to neutral tellurium atoms and
ELECTRICAL
AND
OPTICAL
PROPERTIES
lattice vacancies in the lattice. It is of interest to note that up to 15 mol. per cent InsTes a logarithmic plot (Fig. 7) shows that TVvaries approximately as N-l/a where N represents the concentration of InsTes. The same type of result was obtained with the In!%--InsTes alloys. At higher concentrations of InsTes the scattering is almost certainly due to the presence of lattice impurities and at such high densities that alloy scattering is relevant. In this range the possibilities of antifluorite structure and “hopping” conduction become important. Some further evidence on scattering mechanisms may be obtained from a consideration of the thermoelectric effects. 10,000
iY
,r
I FGi
I
I
1000
E
0
i
too
K)~
I
C
I.0
Mole % In2Te3
+ 4
IO N
FIG. 7. Variation of loglo p with loglo N where iV is InaTes concentration. 0 Annealed specimens. f Directionally frozen specimen.
As indicated above for degenerate material the thermoelectric power Q is found to be directly proportional to the absolute temperature T, and the value of Q/T can be used to determine the height of the Fermi level (5) above the conduction band minimum. The appropriate equational) is
kp2 p[1+ ;(&g-),,l Q=-zand if it is assumed that
then
L? = -t-a5
OF
InAs-InaTes
ALLOYS
153
A determination of (5) from Q thus requires a knowledge of s which depends upon the particular scattering mechanism concerned. The two mechanisms expected to predominate are ionized impurity scattering at low InsTes content and alloy scattering at higher InaTes content. Thus values of 5 have been calculated from the mean Q vs. composition curve assuming that s = -4 for alloy scattering(ls1 and s = +$ for ionized impurity scat~ring,(ls) and these values of 1 subtracted from the optical values of l$. The resultant values should approximate to the intrinsic energy gap Effo>and these are plotted in Fig. 6. In the range 40-70 mol. per cent InaTes the values of Ego obtained by assuming s = -4 are consistent with the values of E,, from 70-100 mol. per cent InsTes, in which range the carrier concentration is so small that the optical value is the intrinsic gap. Also, using s = +a, the values of Ego at low In2Te3 concentrations are in good agreement with the intrinsic gap for InAs itself. Thus it would appear correct to assume that alloy scattering is predominant in the range 40-70 mol. per cent InsTes and ionized impurity scattering for compositions from InAs to approximately 5 mol. per cent InsTes. It cannot be seen from these results what values of .&J apply in the range 5-40 mol. per cent InsTes, but it seems unlikely that in this range either of the plotted Ego curves are applicable. Probably no single scattering mechanism predominates, but that alloy scattering increasingly dominates over ionized impurity scattering. With highly degenerate material the value of 4 can be used to determine an effective mass (m,) of the conduction electrons, the equation ?Z=
&rz(2m43’2
_
~
3
p/2
h3
giving a “density of states” effective mass. If the values of 1 for alloys containing up to 3 mol. per cent InsTes are used in this way values for mR lying between 0.08 m and 0.09 mo are obtained, (ms being the free electron mass). For alloys of InsTes content rather higher than this the values of 5 are not known but from Fig. 6 a rough estimate can be made, shown by the dotted line, and this indicates values of m,, similar to those for the lower percentage alloys. As the values are almost three times the accepted value for non-degenerate I& it
154
J.
C. WOOLLEY,
3.
R. PAMPLIN
appears that the InAs band shows considerable deviation from parabolic form at these values of electron concenkion. The values obtained here are consistent with the values calculated by STERN using a KANBtypeus) model for InAs. In alloy systems of this type the possibility of ordering at various special compositions should be considered. An investigation of the possible types of ordering in this caseffs) indicates that the most probable percentages at which ordering may occur are 75 mol. per cent InsTes, 50 mol. per cent InsTes and 375 mol. per cent InsTes where the formulae of the alloys would be Ins [7 AsTes, Ins [7 AssTes and In7 •JAsaTes respectively (where q indicates a lattice vacancy). No direct X-ray evidence has been obtained at any of these compositions but some evidence in the case of the 75 mol. per cent InsTes alloy may be obtained from the optical data, for Fig. 6 shows the values of EB at this percentage sig~~~tly above the mean curve for Eg values in this range. It is of interest to note that in an analogous system IuAs-InsSes ordering at the 75 mol. per cent InsSes composition has been reported.u7) ~~~~~~The authors are indebted to Professor L. F. BATIZ~ for the facilities of hia Laboratory.
and J. A. EVANS
The work described forma part of an investigation
carriedOutfor the Admiraltv+
1. WOOLLSV J. C., &MPLIN B, R. and How P. J. J. Less Conunmt Metals 1, 362 (1959). 2. WOOLLSY J. C., GILLBTTC. M. and EVANSJ. A., J. PFzys. Chem. Solids 16,138 (1960). 3. WOOLLEY J. C. and SMITW B. A., Proc. P&s. Sot. Lo&. 72, 867 (1958). 4. NASLEDOVD. N. and F~LTIN’SH I. A., So&t Piiys. Solid State 1, 510 (1959). 5. WOOLLEY f. C., EVANS J. A. and GILLKI-T C. M., Proc. Phys. sot. Lad- 74, 244 (1959). 6. WOOLLEY T. C. and Kwrx~d P. N.. to be published. 7. JOPPE A. F., J. Phys. Chw. Solidr.8,6 (1959). 8. ZENER C., J. Phys. Chem. So&a%8,26 (1959). 9. WOOLLEY J. C. and PAMPLIN B. R., to be published. 10. WOOLLEY J. C. and RAY B., J. Phys. Chem. Solids 15, 27 (1960). Il. BARRIER. and EDMONDJ. T., _J. EIect~onics 1, 161 (1955).
12. NORDHEIML., Ann. Phys., Lps. 9,607 (1931). 13. SCLARN., Phys. Reu. 104,1548 (1956). 14. STERNF., Bull. Amer. Plays. Sot. (ser. 2) 4, 28 (1959). 15. KANEE. O., J. Phys. Chem. Solids 1, 249 (1957). 16. PAMPLIN B. R., Nawq Land. 188,136 (1960). S. I., Sowiet 17, GORYLTNOVAN. A. and RADATJXXXAN Phys. Tech. Phys. 3, 1762 (1958).