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A defect model for undoped and tellurium doped gallium arsenide
1. Phys. Chem. Solids Vol. 42, No. IO, pp. W-889, Printed in Great Britain.
0022~3697/81/100883-u7#.~ Perp~lnon Press Ltd.
1981
A DEFECT MODEL FOR UNDOPED AND TELLURIUM DOPED GALLIUM ARSENIDE
Department
of Mechanical
P. F. FEWSTER Engineering, The University,
Southampton, Hants, England
(Received 14 January 1981; accepted 4 February 1981) Abstract-The introduction of two new defects, both (100) split-interstitials, can explain obtained from annealing studies on undoped and tellurium doped gallium arsenide. This arsenic and gallium Frenkel reactions only occur at annealing temperatures above - 400 and suggests that gallium diffuses by occupying split-interstitial sites. This model also arsenic-may occupy the hexagonal interstitial sites. INTRODUCTION
the experimental results model concludes that the and - WC respectively suggests that interestitial
Frenkel reactions are likely to be the major reactions since the lattice parameter was found to increase after an anneal and quench and then returned close to its original value [3,4], and therefore likely to have maintained stoichiometry. The above authors concluded that the principle dilating defect was VAs, although they do not rule out other possibilities. As the concentration of Frenkel pairs increases during anneal a possible reaction is:
The large collection of experimental evidence on undoped and tellurium doped gallium arsenide should be sufficient to predict a defect mode1 for this material. The difficulty is for the mode1 to explain all the experimental evidence. Hurle [l] proposed a model which accommodated most of the work on Te-GaAs, but a future experiment [2] put doubt on certain aspects of this model. The basic requirement in any explanation is that it must include a defect capable of dilating the lattice considerably when in concentrations > lo’* cmm3, since large lattice parameters have been observed in undoped [3,4] and Te-doped [2] GaAs. Each dilating defect will have to be equivalent to a substitutional atom with a tetrahedral radius > 1.9 A. The tetrahedral covalent radii for Ga, As and Te are 1.26, 1.18 and 1.32A respectively, Pauling [S]. A defect that may expand the lattice to that observed when in concentrations 10’8cm-3 is a (100) split-interstitial defect, where interstitial atoms straddle a substitutional site, their bond being in a (100) direction and associated bonds sp2 hybridised. Possible split-interstitials in Te-GaAs and GaAs are represented by Te, VoaGair GaiVo.Ga, etc. These proposed split interstitials are the basis of this model. The reactions that are thought to arise on annealing undoped GaAs and Te-doped GaAs are considered and are related to previous work. A reaction (xy) signifies a reaction whose reactant is “x” and product is “y”.
2Gao. + GaiVo.Gai t Voa
(ab)
as well as the As-Frenkel reaction. If this split-interstitial exists in a concentration - lOI crne3 (or 3 X lOI cme3) then this would account for the observed dilation of Driscoll and Willoughby [4] (Potts and Pearson [3]). Annealing in the presence of a high As-pressure would suppress this reaction by the presence of a high concentration of Voa and would immediately annihilate GaiVG.Gai and the dilation of the lattice is suppressed. This highly strained state, which could be stable at high temperatures depending on the equilibrium concentration of VGa would try and relieve itself at room temperature. The strain relaxation can occur by Voa diffusion or Gai diffusion. GaiVo.Gai t Vo. --, 2Gao..
(b’d)
This reaction will be initially fast and then slows since the average distance between a complex and a vacancy varies as the inverse cube-root of their concentrations, therefore the opportunity for reaction (b’d) to occur is reduced, leaving a residual strain which will take a long time to disappear. The lattice parameter is only observed to increase for T > lOOO”C, and a possible explanation for this is that Ga Frenkel defects do not form much below this temperature, Fig. 1. This can still explain the results of Chakraverty and Dreyfus [6], if it is assumed that As, pairs on hexagonal sites (to give the observed (110) symmetry) and not (Vo.Vo.) are the cause of the 140°C internal friction peak in GaAs. Chakraferty and Dreyfus found this peak stable below 400°C (possibly the lower T limit of the As-Frenkel reaction and thus reducing the
IJNDOPED GaAs
Undoped GaAs annealed at T > 1000°C in uacuo for > 12 hr experiences a large lattice strain which anneals out at room temperature, initially fast for - 30 hr and then more slowly leaving a residual strain still detectable after 56 hr [3,4]. To account for this, consider two likely reactions to occur on annealing GaAs: Gas,% Gai t Voa and AsAss Asi + VAT. 883
P. F.
884
FEWSTER
800-
lb) GaGa + A% + VA%
400
____-__
_________-_
600-
~ Cal
200
GaGa +A$,,
-_____--_______-_----____ i
I
-I
ICI
L
GaGa + As; + VA%
id) ~GYLQ
*
01 Fig. 1. The reaction sequence for GaAs for various annealing-temperature domains.
chance of recombination)t, but if GaAs was preheated at 93OT to drive off As the peak disappeared (reducing fAs(Asi)f and returned when preheated at 104o”c in excess As, i.e. Asi + As, + (AsiAsr). TdKWEDGaAs The sequence of reactions in Te-GaAs have to account for complex phenomenon, for example the growth of interstitial loops, changes in free-electron concenmobility, lattice tration, acceptor concentration, parameter and the internal friction spectrum. In as grown Te-GaAs (with n > 2 x 10” cme3) the lattice is observed to be heavily strained where Au/a is linearly related to n, and after a 4 hr anneal (ENY’C)the lattice parameter falls [2], Faulted loops thought to be Te-based, (Laister and Jenkins f7]), have been observed in as-grown Czochralski material and presumably form as the crystal is cooled within the puller. One must expect these faulted defects to start dissolving above the formation temperature of Ga,Te,(GazTes; 827°C; GaTe; 789°C; Panish(81) and Te to go into the GaAs lattice at some temperature higher than this during heat treatment. Dobson et al. [2] accounted for the drop in lattice parameter, free-electron concentration and mobility and the growth of interstitial loops when Te-GaAs was annealed at 890°C in uncuo for 4 hr, with the reaction GaiVo.Tei + As*, + Te,,VG,+
GaiAsi
(A@
tithe Asi defect is assumed to fit well into the lattice and therefore diiusion of VaJAsj is not enhanced by large strains as in the case of ~ai/vG~, and hence only s~n~eous As Frenkel reactions or random VJAsi movement will remove Asi defects.
where TeA,,VG, is thought to be an acceptor, (Hurle [l])
and responsible for the 1.22eV photoluminescence band observed on anneal (Hwang [9]). This reaction probably progresses in stages and the first step probably just involves the dissolution of the dilating complex by the formation of As Frenkel pairs. 400 < T < 950°C GaiV,,Tei
t ASA~+ Te,+,,+ Vd, + Gai + AS. (AB)
This requires Ga to migrate earlier from the complex site than Te to prevent Gao. recombination. Below 400°C the As Frenkel reaction probably does not occur as mentioned previously and also changes in free-electron concentration have been shown not to begin until this temperature is reached, Grinshtein et al. [lo]. Above 950°C we must assume that Ga,Te, precipitates come out into solution, and also that the Frenkel reaction may occur. Hence GaiVo.Tei + ASA% + (1 t N)(TeA, + VO, t Gai t Asi) (AB’)
N(Tei, Gao., Asa,)
I
When Te-GaAs is annealed at 11My”Cfor 15 min and quenched, a large fall in iattice parameter is observed and is accompanied by an increase in the free-electron concentration (Mil’vidskii et al. [ 111). The TeA,Vo, complex must therefore be unstable at 1100°C or the equilibrium ratio of TeAs to TeAsVGato be large at this temperature, since as soon as a low temperature anneal is conducted (7OO’C) the free-electron concentration
A defect modelfor undoped and tellurium doped gallium arsenide
885
_____---_--_I-_--------
( 0’)
As,
I
--
_I l
0'
l
CE ‘1
_I
for n > 2 x 10’8cm-3
Fig. 2. The reaction sequence for Te-GaAs for various annealing-temperature drops dramatically, due to the formation of these acceptor complexes, see appendix. TeA. + VOa+ Gai 4 Asi + TeAsVGP+ Gai + As,. (BC) The intermediate stage, i.e. products B and B’ is very short lived for T 4 llOO°C. Te-GaAs annealed for 2 hr at 1100°C and quenched increases the height of an internal friction peak, which Osvenskii et al. [12] labelled (VG~VCJ, as did Chakraverty and Dreyfus [6] in undoped GaAs, but could equally well be (A% As,) as mentioned previously. This latter observation can be accounted for by the increased As&population on anneal, reaction (AB”), Fig. 2. One assumes from what has been supposed so far that As Frenkels will be continuously forming and recombining providing we are annealing at T > 4QO”C,and that complexes formed in undoped GaAs can still form in doped material. If Ga diffuses by a split-interstitial mec~nism, i.e. GaiV~~Ga~ an intermediate reaction stage would be 4Oi
domains.
N(Teg, Gas., ASA~
and at these elevated temperatures the donor-vacancy complex (TeA.V& would be slow to form giving rise to a momentary increase in the free-electron concentration during anneals in the temperature range (9OO
1100°C anneal
TeASVo.t Gai t Asi + Tea,Vc. t GaiVo,Gai t Asi (CD) f GaG, until Gai have arrived at a dislocation loop site. If the anneal is for T > 950°C then T > 950°C TeAsVGaf Gag+ ASS-+ Te..,,Vo. + GaiVcaGar •t Asi GaCi. f t
-t N(TeA, t VG, + Gar + Asr) (CD’)
i 200
1 400
I 600
I 800
+ T”C
nt actual n at T”C no initial n ns equilibrium n Fig. 3. The patron of Te rem~ning in the substimtio~ solid solution versus temperature.Grinshtein ef ai. [IO].
P. F. FEWSTER
886
{llO} planes and the strain imposed by this complex will be removed. The final reacttons in the low and high temperature cases are therefore:
N,, - N, - lOI cme3, K requires ND - 2 x lOI cm-’ from the dissolution of faulted loops, and NA 10r9cm-“) we must consider the mobility increase with the stage I anneal. If we assume
T<9OO”C n =N,,-N,,
TeA,Vo, t GaiVG*Gai + Asi * TeAsVGa+ Gai Asi (DE) GaCi,.I’ Te,+_Vo.t GaiVGaGai t Asi t Npea,t Voa + Ga, + Asi} 950
K = NAIND r.~= ~(ND
NA)
then ND(l-K)=n
(DE’)
J’
+
which decreases during the low temperature anneal, and since
Both reaction products introduce acceptors (Tet,sVG.) lowering the free electron concentration and mobility, and introduce interstitial loops in agreement with Dobson et al. [2]. The complete reaction sequence is illustrated in Fig, 2, and is now examined to see how it fits to other published literature.
ninitia,= 12 x lo’* cme3 nRnal= 8 x 10” cm-’ Ki
= 0.55
KI =0.2
then NDi = 26.7 x 10” cm-’
PREVIOUS WORK
Grinshtein et al. [lo] observed a two stage fall in free-electron concentration with temperature during an isochronous anneal of Te-GaAs, which has been preheated at 1100°Cand quenched. This was not observed in an as-grown sample, Fig. 3. No changes occur in n until the temperature reached - 350°C. The reaction sequence for the preheated and quenched specimen therefore start at B” and for the as-grown specimen at A, Fig. 2. Grinshtein et al. then subjected a sample exhibiting stage I kinetics to an isothermal anneal (- 3SO’C)and their observations are explained later by the complicating presence of Cu, which could have been introduced with the 1100°Canneal. The stage II isothermal anneal (700°C) shows a fall in n with constant mobility where the dominant reaction could be Te:,+e-tVo.-+Te,+.VG,th’ from reaction B”C, Fig. 2, which accounts for the constant mobility, provided the donor and donor-vacancy acceptor have the same scattering power, see appendix. This would also account for the observed monotonic increase in NJND. Grinshtein et al. also measured the compensation ratio K( = NJND) and found that it was low in as-grown samples (0.1-0.3), increased after quenching from a llOO°C anneal (0.5-0.6) and fell during the fast annealing stage I (0.1-0.3), passed through a minimum and increased monotonically with the slow anneal stage II. To account for this large rise in K with the 1100°C anneal, which increased the free-electron concentration (n = tThe authors stated that stage II was unaffected by this initial anneal, but on close inspection of their published results there is an appreciable difference.
ND, = 10.0x 1018cmA3 NAi = 14.7x 1018cmm3 NA, = 2 x 10” cme3, i.e. 86% of N, and 63% of ND are removed on anneal ( - 3SOQ This suggests that there is a high concentration of acceptors introduced during the 1100°C anneal and removed with a low temperature anneal. Therefore there must be a fast diffusing acceptor which is fairly soluble in GaAs at T - 1100°C but relatively insoluble at low temperatures. Cue. is a possible acceptor to fit these conditions, and therefore must precipitate out or come to the surface during the 350°C anneal. Also since donors are removed, TeL must precipitate out at this temperature. The likely Te precipitate is AsZTeP since this forms at 360°C (Panish [S]). This precipitation only occurs in preheated samples because of the high Asi and Tea. populations created at llOO”C, Fig. 2. The removal of donors and acceptors would then account for the large increase in mobility. As the temperature is raised AszTe3 will dissolve and create Tei, donors, but because of the high concentration of VGa (created at 1lWC) these form Te,,,VG. acceptors and results in a further decrease in n, Fig. 3. If the formation of acceptors is much faster than the dissolution of AszTe3 (the former has previously been considered to be very fast at these temperatures) then the latter will be rate limiting and not seen. Grinshtein also annealed a sample at 1100°Cfor 4 hr, in a large ampoule, and quenched and then carried out similar isothermal annealing experiments with the fast and slow stages. The rate of fall in n for this sample was reduced, presumably because of the removal of Asi (slowing the rate of Te’;, precipitation in stage I) and to a smaller extent the removal of Voa (slowing the acceptor formation (TeA,,Vo.) in stage 1I)t.
887
A defect model for undoped and tellurium doped gallium arsenide
Fuller and Wolfstirn [ 141observed changes in electron concentration on annealing nt Te-GaAs in the T range 64ML8oo”C after a 4 min 1100°Cpreheat and quench. The low temperature anneal reduced the concentration of free electrons while maintaining constant mobility. This again suggests the principle reaction is purely: e-+ Te:, t V, + TeAsV& t h’, i.e. stage II anneal of Grinshtein. Fuller and Wolfstirn also found these changes in n reversible with T; this is in agreement with the above acceptor complex being unstable for T - 1100°C. Nishizawa et al. [15] undertook annealing studies on Te-GaAs where they observed p-type conversion. TeGaAs (8 x lOI cmb3 < n < 2.8 x 10” cmm3)was annealed at 1100°C and quenched, and the authors then measured the conductivity at depths into the sample after various annealing times for two As pressures. The low As pressure (PAS- 10Torr) anneal started to turn the sample p-type from the surface fairly quickly (< 16 hr) and eventually throughout the sample. The high As pressure anneal (PAS- 4.8 x lo3 Torr) remained n-type until the annealing time approached 64 hr. Nishizawa et al. then examined the variation in acceptor density and lattice parameter with As pressure for various n and T after a 67 hr T”C anneal (900 and 1IOO’C),to ensure equilibrium within the investigated inner region of each sample. The acceptor density and lattice parameter went through a cuspid minimum at a certain As pressure, PASmin,which was T dependent, Fig. 4. These observations indicate a defect or contaminant acceptor diffusing in from the surface-fast at low As pressure and slow at high As pressure. A possible contaminant is Cu (Hurle [l])t Copper is generally considered to diffuse interstitially through GaAs, which is certainly possible at low As pressures. As the pressure is increased the Cu diffusion rate could decrease because of the increasing [Asi], which are assumed to reside on hexagonal interstitial sites, and therefore inhibit free movement, until the As pressure diminishes [V,,] and increases [Vo,] (from [V,,J[Vo,l - KT) allowing Cu to diffuse predominantly by substitutional means. Since Cu is thought to be an acceptor on a Ga site this could account for the p-type conversion, the minimum in the acceptor density and the slower p-type conversion at higher As-pressures. The number of available Vcs for the in-diffusing Cu also increases with free-electron concentration due to the dissolution of TeArVGa acceptors for T - llOO”C, assuming a constant compensation ratio with n after growth, and therefore the acceptor concentration increases with initial n. The position of the cuspid minimum, with respect to the As pressure (which appears to be only T dependent) is then related to the point defect equilibrium at the annealing temperature. The lattice parameter cuspid minimum tNishizawa et al. have measuredthe Cu content for a sample annealed at 900°C for 65 hr. (As pressure not mentioned) and no Cu was detected above O.Sppm, but [Cu] at this limit is equivalent to -2.2 x lOI crne3 singly ionised (2~0. defects, comparable with the observed acceptor concentration.
lo’5 10-210-l
1
lo
102 103 104 PAa TORR
.s
56532
-I
5.6526 1 10-2
10-l
1
10
102
103
104
PAS TORR
Fig. 4. The variation of acceptor density and lattice constant for various arsenic pressure anneals. Nishizawa et al. [IS]. would vary with the Cu content since Cu has a larger
covalent radius than Ga, 1.35 compared with 1.26& Pauling [5]. The constancy of the lattice parameter minimum is a consequence of the accuracy of measurement. Nishizawa et al. observed three activation energies after their anneal (1100°C); 0.12 eV for P.+,,> 7000 Torr and 0.15 eV for PAN< 1OOTorr when ninitinl < 1.8 x 10” cme3, and 0.18eV for 3OOTorr> PA.> 1000Torr when ninitra- 4.5 X 10” cm-‘. The 0.15 eV acceptor level followed the 1.35eV photoluminescence band and the 0.12 and 0.18 eV followed the 1.30eV band. A 1.20eV emission band (thought to be TeA,VGa, Hwang[9]) is observed in the as-grown specimen but decreases on anneal with the energence of the 1.35 and 1.30eV bands. On reannealing at 300-4OO”Cthe 0.12 eV level disappears with an increase in mobility and decrease in hole density and the 0.18 eV level increases. This could well be the reactions Cui; --f surface and/or precipitates
then C& (or similar complex, e.g. Cuc,As?-) is responsible for the 0.12 eV acceptor level, the mobility and the 1.30eV emission band would then increase if Te,&L, is responsible for the 0.18eV level (since the 0.12 eV level gives rise to only a weak emission band at 1.30eV). A similar effect is observed for the 0.15 eV level which would be due to Cu& (or similar complex, e.g. Ct.t~,Vi;), hence Te:, + Cuo.Vii -+ TeJu&
+ VA.
Blanc and Weisberg [16] have found a one-to-one correlation of the 0.15 eV level with Cu concentration in undoped GaAs annealed in the 6OfJ-1000°Crange. Spe-
P. F. FEWSTER
888
cimens with the 0.18 eV acceptor level are unchanged on anneal (3oo-4oo”C)and therefore the associated defect is much more stable. Although as the temperature of anneal is raised the 1.30eV band, associated with the 0.18eV acceptor level, decreases and could well be the reverse reaction Te.&u&
+Te+As+Cu&.
Similar to the break-up of TeAsVGaat high temperatures. Laister and Jenkins [17] undertook annealing work on Te-GaAs at various temperatures (400-1150°C) and studied the formation of dislocation loops and changes in electrical parameters. They observed three distinct temperature ranges for which significant changes occurred. For T > looo”C the Te-GaAs converted to p-type, which was thought to be from Cu contamination, and then decreases as the annealing time is increased. If this was repeated in a As/KCN atmosphere to remove Cu, type conversion did not occur but an overall increase in n was observed accompanied by a drop in mobility. Samples annealed at T > 1080°Ccontained no stacking faults and remained that way if quenched rapidly, but if they were allowed to cool in the furnace large faults were observed. Samples heated above 1OOOYJ were free from prismatic loops. For 800 < T < 1000°C anneals, all the specimens remained n-type but their mobilities fell and {I lo} prismatic loops grew. Annealing for T < 800°C also maintained n-type conductivity with a reduction in mobility and prismatic loops still grew unless T < 400°C. The p-type conversion of Te-GaAs when annealed at T > 1000°Cis presumably the uptake of Cu to form Cu& acceptors. Much below this temperature we have assumed Ga Frenkel pairs do not form leaving insufficient Vca for p-type conversion. If the annealing time is increased the slower reaction of the dissolution of faulted defects becomes significant and reduces the hole concentration. Annealing in a As/KCN atmosphere prevented type conversion and increased n with a fall in p; this would be caused by the increase in TeA, donors created from faulted loop dissolution, reaction AB’. The absence of prismatic loop growth for samples annealed above 1000°Cprobably results from the removal of small precipitates that punch out dislocation loops for the condensation of point defects, Wagner [18]. In the intermediate temperature range 800< T < 1000°C the specimen remained n-type presumably because of the lack of Vo. since the Ga Frenkel reaction only occurs for T > 950°C. The mobility falls because of the increase in acceptors and the prismatic loops grew for the reasons explained by Wagner [18]. In the low temperature range 400~ T < 800°C much the same occurred but below 400°C no loops could be formed and this is assumed to be the limit for the As-Frenkel reaction and thus reaction AB cannot proceed. A possible mechanism for the formation of the GaiVo.Tei split-interstitial during growth has been proposed by Mullin et al. [19]. During growth there is a high concentration of very mobile arsenic interstitials, Asi, which could displace the donors, Te+ resulting in the TeiVoaGai split-interstitial.
Asi t TeA, + TeiVoaGai f AsA, Otsuka et al. [20] conducted annealing studies on undoped GaAs (9OO’Cfor 65 hr and quenched), and observed p-type conversion. This is similar to the results of Nishizawa et a/. [El on Te-GaAs discussed earlier and can be interpreted in a similar manner, by assuming Cu to diffuse in from the surface. Above a certain Aspressure ( - 14Torr) the mobility fell and could be interpreted as the point at which the dominant acceptor species changes from, e.g. Cuq.V,, to Cu&. The scattering ability of the latter must therefore be much greater than that of the former, since [C&J -2[Cuo,V,&] to account for the observed hole density. If the samples were re-annealed at a low temperature (23&3OO”C)for 28 hr they recovered to their initial n and CL.This presumably occurs because of the lower solubility of Cu in GaAs at these temperatures, and Cu precipitates out or comes to the surface. Bublik et al. [21] examined the internal friction spectrum, lattice parameter and density of undoped GaAs for various As concentrations in the melt during growth. The 160°C damping decrement from the internal friction experiments, which they assigned to (VGaVoa), was found to increase with As concentration in the melt over the single-phase region. The density was also shown to increase over this region whilst the lattice parameter remained constant, and it was deduced that Asi were predominant for a high As content in the melt and VAs for a low As content in the melt, although both species exist over this region. These results would suggest that an As based defect ((Asi Asi) as mentioned previously) would be more likely to account for the internal friction spectrum than a (Vq,Vq.) defect which would contribute to lowering the density. CONCLUSIONS
This paper has given an explanation of the effects observed on annealing undoped and Te-doped GaAs. The essential difference of this explanation compared with previous explanations is the introduction of two new defects in GaAs, these are (100) split-interstitials GaiVo,Gai and TeiVo.Gai. The formation of these defects is thought to occur by the presence of a Gai or Tei atom which does not have an opportunity of relaxing into a Voe or VA, site (as is the case in n+ Te-GaAs and during conditions of excess Ga). The interstitial Ga or Te atom would then come close to a Gac, site and displace the host atom along a (100) direction, resulting in the intruder and host atoms straddling the now vacant Ga site. This creates a very signiticant strain on the crystal lattice. To account for all the experimental results in the literature surveyed, further conclusions arise. (a) The As-Frenkel reaction only occurs or is significant above - 400°C. (b) The Ga-Frenkel reaction only occurs or is significant above - 900°C. (c) The ratio of the defects [TeA.VG.I : ITeA, decreases with increasing T of anneal or simply that TeA,Vo. + TeA, + Vo.(T > 1looOC) also see appendix.
A defect model for undoped and tellurium doped gallium arsenide
(d) Faulted loops dissolve for T 3 9OWC. (e) Ga diffuses by GaiV~~Gai sites. (f) As can reside on the hexagonal interstitial site and consequently exhibits an insignificant strain on the lattice. It must, however, be noted that no direct independent evidence exists for the presence of split-interstitials in GaAs (but theoretical work 1221on diamond and silicon suggest that the split-interstitial is the favoured interstitial defect) but predictions arising from this model could be tested in detail in order to make a critical comparison of this alongside other models. Acknowledgemwrs-Theauthor is very grateful to Drs. D. T. J. H&e, J. B. Mullin and A. F. W. Willoughby for suggestions and valuable discussions. This work has been carried out with the support of the Procurement Executive (D.C.V.D.), Ministry of Defence.
889
19. Mullin J. B,, Royle A. and Benn S., J. Crystal Growth 50,625 (1980). 20. Otsuka H., Ishida K. and Nishizawa J., Jup. J. Appl. Phys. 8, 632 (1969). 21. Bublik V. T., Karataev V. V., Kufagin R. S., Mil’vidskii M. G., Osvenskii V. B., Stolyarov 0. G. and Kholodnyi L. P., Sou. Phys. Cryst. 18,218 (1973). 22. Corbett J. W., Bourgoin J. C. and Weigel C., Inst. Phys. Con& Ser. No. 16, I (1972). 23. Evans R. C., An lniroductio~ to Crystaf Chemistry 2nd Edn. Cambridge University Press, London (1976). APPENDIX
A difficulty arises in the explanation for the formation of acceptors (if- these are TeA,V&) on annealing Te-GaAs below 1ooo”C.We have assumed that Voa have been created at high temperatures and then form TenrVo, acceptors on re-anneal&g at low temperatures: e- t Tet + Vos + TeA,V& t h+. This assumes that Vanis neutral which is unlikelyin n+ material-it is far more likely to be a double acceptor V&i;;., i.e.
RE~RENCE5 Te’, + V& + TeA,Vo, Hurle D. T. J.. J. Phvs. Chem. Solids 40,627 (1979). VC. would appear to require a sink from which it can rapidly 2. Dobson P. S., Fewster P. F., Hurle D. T. J., Hutchinson P. W.. Mullin J. B.. Straunhan B. W. and Willoughby A. F. W., .diffuse otherwise the free-electron concentration would be unInst. Phys. Cot& Ser. No. 45, 163(1979). changed on anneal and the mobility would decrease (providing 3. Potts H. R. and Pearson G. L., J. Appl. Phys. 37,2098 (1%6). this is the only reaction). 4. Driscoll C. M. H. and Willoughby A. F. W., Inst. Phys. Conf. An alternative explanation is the formation of a complex Ser. No. 16,377 (1972). VaSTeiV&, where Te sits mid-way between the two atomic sites. Te has then exact &fold co-ordin&ion (sp’d2 h brid bonds). The 5. Pauling L., The Nafure of The Chem~cul Bond. Cornell University Press, Ithaca, New York (1960). covalent radius of sp’d* hybridised Te is I.52 2( Evans 1231and 6. Chakraverty B. K. and Dreyfus R. W., J. Appl. Phys. 37,631 hence the Te-Ga(As)lengths are 2.78(2.70) A whereasthe t(GaAs) lengthfor next nearest pairs is 3.08A, so this complex would (1966). lit reasonably well into the lattice. I. Laister D. and Jenkins G. hf., .I. Mat. Sci. 3, 584 (1968). This neutral complex could then be stable at high temperatures 8. Panish M. B., J. Electrochem. Sot. 114, 91 (1967). but at low temperatures on re-annealing would return to the 9. Hwang C. J., .I. Appl. Phys. 40.4584 (1%9). TeAsVoadefect which is likely to be an acceptor in nt material 10. Grinshtein P. M., Ya. Lipkes M., Rytova N. S. and Fistul’ V. I., Sou. Phys. Semicond,.9,725 (1975). V,+TeiV&,-, TeA,V&,t h+. 11. Mil’vidskiiM. G.. Osvenskii V. B.. Novikov A. G., Fomin V. G. and Grishina s. P., Sou. Phys. bryst. 18,519 (1974). The constant mobility observed by Grinshtein[lO] is not 12. Osvenskii V. B., Kholodn~ L. P. and Mil’vidskiiM. G., Soa. explained by this reaction if charge species are the dominant Phys. Solid State 13, 1790(1972). 13. Grishina S. P., Mil’vidskii M. G., Osvenskii V. B. and Fistul’ scattering entities in his experiment. Grinshtein did undertake these measurements at 7OO”i:and therefore phonon scattering V. I., Sou. Phys. Semicond. 4,240 (1970). 14. Fuller C. S. and Wolfstirn K. B., J. Appl. Phys. 34, 2287 may be signi8c~t since their reported mobilit~es were exceptionally low ( - 700cm* V’ s-l). (1963). The same reaction is assumed to have been observed by Fuller IS. Nishizawa J., Otsuka H., Yamakoshi S. and Ishida K., Jap. I. and Wolfstirn [14], where the mobility did fall during anneal Appl. Phys. 13,46 (1974). 16. Blanc J. and Weisberg L. R., J. Phys. Chem. Solids 25, 221 (1380+ 1060cm2V-’ s-r) and these measurements were presumably conducted at room temperature (although not stated (1964). in their paper). It must also be remembered that there are 17. Laister D. and Jenkins G. M., Phil. Mug. 23, 1077(1971). 18. Wagner W. R., Inst. Phys. Coaf. Ser. No. 33b, 65 (1977). uncertainties in mobility theory at high dopant concentrations. 1.
IPCSVol.42.No. IQ-B
0022~3697/81/100883-u7#.~ Perp~lnon Press Ltd.
1981
A DEFECT MODEL FOR UNDOPED AND TELLURIUM DOPED GALLIUM ARSENIDE
Department
of Mechanical
P. F. FEWSTER Engineering, The University,
Southampton, Hants, England
(Received 14 January 1981; accepted 4 February 1981) Abstract-The introduction of two new defects, both (100) split-interstitials, can explain obtained from annealing studies on undoped and tellurium doped gallium arsenide. This arsenic and gallium Frenkel reactions only occur at annealing temperatures above - 400 and suggests that gallium diffuses by occupying split-interstitial sites. This model also arsenic-may occupy the hexagonal interstitial sites. INTRODUCTION
the experimental results model concludes that the and - WC respectively suggests that interestitial
Frenkel reactions are likely to be the major reactions since the lattice parameter was found to increase after an anneal and quench and then returned close to its original value [3,4], and therefore likely to have maintained stoichiometry. The above authors concluded that the principle dilating defect was VAs, although they do not rule out other possibilities. As the concentration of Frenkel pairs increases during anneal a possible reaction is:
The large collection of experimental evidence on undoped and tellurium doped gallium arsenide should be sufficient to predict a defect mode1 for this material. The difficulty is for the mode1 to explain all the experimental evidence. Hurle [l] proposed a model which accommodated most of the work on Te-GaAs, but a future experiment [2] put doubt on certain aspects of this model. The basic requirement in any explanation is that it must include a defect capable of dilating the lattice considerably when in concentrations > lo’* cmm3, since large lattice parameters have been observed in undoped [3,4] and Te-doped [2] GaAs. Each dilating defect will have to be equivalent to a substitutional atom with a tetrahedral radius > 1.9 A. The tetrahedral covalent radii for Ga, As and Te are 1.26, 1.18 and 1.32A respectively, Pauling [S]. A defect that may expand the lattice to that observed when in concentrations 10’8cm-3 is a (100) split-interstitial defect, where interstitial atoms straddle a substitutional site, their bond being in a (100) direction and associated bonds sp2 hybridised. Possible split-interstitials in Te-GaAs and GaAs are represented by Te, VoaGair GaiVo.Ga, etc. These proposed split interstitials are the basis of this model. The reactions that are thought to arise on annealing undoped GaAs and Te-doped GaAs are considered and are related to previous work. A reaction (xy) signifies a reaction whose reactant is “x” and product is “y”.
2Gao. + GaiVo.Gai t Voa
(ab)
as well as the As-Frenkel reaction. If this split-interstitial exists in a concentration - lOI crne3 (or 3 X lOI cme3) then this would account for the observed dilation of Driscoll and Willoughby [4] (Potts and Pearson [3]). Annealing in the presence of a high As-pressure would suppress this reaction by the presence of a high concentration of Voa and would immediately annihilate GaiVG.Gai and the dilation of the lattice is suppressed. This highly strained state, which could be stable at high temperatures depending on the equilibrium concentration of VGa would try and relieve itself at room temperature. The strain relaxation can occur by Voa diffusion or Gai diffusion. GaiVo.Gai t Vo. --, 2Gao..
(b’d)
This reaction will be initially fast and then slows since the average distance between a complex and a vacancy varies as the inverse cube-root of their concentrations, therefore the opportunity for reaction (b’d) to occur is reduced, leaving a residual strain which will take a long time to disappear. The lattice parameter is only observed to increase for T > lOOO”C, and a possible explanation for this is that Ga Frenkel defects do not form much below this temperature, Fig. 1. This can still explain the results of Chakraverty and Dreyfus [6], if it is assumed that As, pairs on hexagonal sites (to give the observed (110) symmetry) and not (Vo.Vo.) are the cause of the 140°C internal friction peak in GaAs. Chakraferty and Dreyfus found this peak stable below 400°C (possibly the lower T limit of the As-Frenkel reaction and thus reducing the
IJNDOPED GaAs
Undoped GaAs annealed at T > 1000°C in uacuo for > 12 hr experiences a large lattice strain which anneals out at room temperature, initially fast for - 30 hr and then more slowly leaving a residual strain still detectable after 56 hr [3,4]. To account for this, consider two likely reactions to occur on annealing GaAs: Gas,% Gai t Voa and AsAss Asi + VAT. 883
P. F.
884
FEWSTER
800-
lb) GaGa + A% + VA%
400
____-__
_________-_
600-
~ Cal
200
GaGa +A$,,
-_____--_______-_----____ i
I
-I
ICI
L
GaGa + As; + VA%
id) ~GYLQ
*
01 Fig. 1. The reaction sequence for GaAs for various annealing-temperature domains.
chance of recombination)t, but if GaAs was preheated at 93OT to drive off As the peak disappeared (reducing fAs(Asi)f and returned when preheated at 104o”c in excess As, i.e. Asi + As, + (AsiAsr). TdKWEDGaAs The sequence of reactions in Te-GaAs have to account for complex phenomenon, for example the growth of interstitial loops, changes in free-electron concenmobility, lattice tration, acceptor concentration, parameter and the internal friction spectrum. In as grown Te-GaAs (with n > 2 x 10” cme3) the lattice is observed to be heavily strained where Au/a is linearly related to n, and after a 4 hr anneal (ENY’C)the lattice parameter falls [2], Faulted loops thought to be Te-based, (Laister and Jenkins f7]), have been observed in as-grown Czochralski material and presumably form as the crystal is cooled within the puller. One must expect these faulted defects to start dissolving above the formation temperature of Ga,Te,(GazTes; 827°C; GaTe; 789°C; Panish(81) and Te to go into the GaAs lattice at some temperature higher than this during heat treatment. Dobson et al. [2] accounted for the drop in lattice parameter, free-electron concentration and mobility and the growth of interstitial loops when Te-GaAs was annealed at 890°C in uncuo for 4 hr, with the reaction GaiVo.Tei + As*, + Te,,VG,+
GaiAsi
(A@
tithe Asi defect is assumed to fit well into the lattice and therefore diiusion of VaJAsj is not enhanced by large strains as in the case of ~ai/vG~, and hence only s~n~eous As Frenkel reactions or random VJAsi movement will remove Asi defects.
where TeA,,VG, is thought to be an acceptor, (Hurle [l])
and responsible for the 1.22eV photoluminescence band observed on anneal (Hwang [9]). This reaction probably progresses in stages and the first step probably just involves the dissolution of the dilating complex by the formation of As Frenkel pairs. 400 < T < 950°C GaiV,,Tei
t ASA~+ Te,+,,+ Vd, + Gai + AS. (AB)
This requires Ga to migrate earlier from the complex site than Te to prevent Gao. recombination. Below 400°C the As Frenkel reaction probably does not occur as mentioned previously and also changes in free-electron concentration have been shown not to begin until this temperature is reached, Grinshtein et al. [lo]. Above 950°C we must assume that Ga,Te, precipitates come out into solution, and also that the Frenkel reaction may occur. Hence GaiVo.Tei + ASA% + (1 t N)(TeA, + VO, t Gai t Asi) (AB’)
N(Tei, Gao., Asa,)
I
When Te-GaAs is annealed at 11My”Cfor 15 min and quenched, a large fall in iattice parameter is observed and is accompanied by an increase in the free-electron concentration (Mil’vidskii et al. [ 111). The TeA,Vo, complex must therefore be unstable at 1100°C or the equilibrium ratio of TeAs to TeAsVGato be large at this temperature, since as soon as a low temperature anneal is conducted (7OO’C) the free-electron concentration
A defect modelfor undoped and tellurium doped gallium arsenide
885
_____---_--_I-_--------
( 0’)
As,
I
--
_I l
0'
l
CE ‘1
_I
for n > 2 x 10’8cm-3
Fig. 2. The reaction sequence for Te-GaAs for various annealing-temperature drops dramatically, due to the formation of these acceptor complexes, see appendix. TeA. + VOa+ Gai 4 Asi + TeAsVGP+ Gai + As,. (BC) The intermediate stage, i.e. products B and B’ is very short lived for T 4 llOO°C. Te-GaAs annealed for 2 hr at 1100°C and quenched increases the height of an internal friction peak, which Osvenskii et al. [12] labelled (VG~VCJ, as did Chakraverty and Dreyfus [6] in undoped GaAs, but could equally well be (A% As,) as mentioned previously. This latter observation can be accounted for by the increased As&population on anneal, reaction (AB”), Fig. 2. One assumes from what has been supposed so far that As Frenkels will be continuously forming and recombining providing we are annealing at T > 4QO”C,and that complexes formed in undoped GaAs can still form in doped material. If Ga diffuses by a split-interstitial mec~nism, i.e. GaiV~~Ga~ an intermediate reaction stage would be 4Oi
domains.
N(Teg, Gas., ASA~
and at these elevated temperatures the donor-vacancy complex (TeA.V& would be slow to form giving rise to a momentary increase in the free-electron concentration during anneals in the temperature range (9OO
1100°C anneal
TeASVo.t Gai t Asi + Tea,Vc. t GaiVo,Gai t Asi (CD) f GaG, until Gai have arrived at a dislocation loop site. If the anneal is for T > 950°C then T > 950°C TeAsVGaf Gag+ ASS-+ Te..,,Vo. + GaiVcaGar •t Asi GaCi. f t
-t N(TeA, t VG, + Gar + Asr) (CD’)
i 200
1 400
I 600
I 800
+ T”C
nt actual n at T”C no initial n ns equilibrium n Fig. 3. The patron of Te rem~ning in the substimtio~ solid solution versus temperature.Grinshtein ef ai. [IO].
P. F. FEWSTER
886
{llO} planes and the strain imposed by this complex will be removed. The final reacttons in the low and high temperature cases are therefore:
N,, - N, - lOI cme3, K requires ND - 2 x lOI cm-’ from the dissolution of faulted loops, and NA 10r9cm-“) we must consider the mobility increase with the stage I anneal. If we assume
T<9OO”C n =N,,-N,,
TeA,Vo, t GaiVG*Gai + Asi * TeAsVGa+ Gai Asi (DE) GaCi,.I’ Te,+_Vo.t GaiVGaGai t Asi t Npea,t Voa + Ga, + Asi} 950
K = NAIND r.~= ~(ND
NA)
then ND(l-K)=n
(DE’)
J’
+
which decreases during the low temperature anneal, and since
Both reaction products introduce acceptors (Tet,sVG.) lowering the free electron concentration and mobility, and introduce interstitial loops in agreement with Dobson et al. [2]. The complete reaction sequence is illustrated in Fig, 2, and is now examined to see how it fits to other published literature.
ninitia,= 12 x lo’* cme3 nRnal= 8 x 10” cm-’ Ki
= 0.55
KI =0.2
then NDi = 26.7 x 10” cm-’
PREVIOUS WORK
Grinshtein et al. [lo] observed a two stage fall in free-electron concentration with temperature during an isochronous anneal of Te-GaAs, which has been preheated at 1100°Cand quenched. This was not observed in an as-grown sample, Fig. 3. No changes occur in n until the temperature reached - 350°C. The reaction sequence for the preheated and quenched specimen therefore start at B” and for the as-grown specimen at A, Fig. 2. Grinshtein et al. then subjected a sample exhibiting stage I kinetics to an isothermal anneal (- 3SO’C)and their observations are explained later by the complicating presence of Cu, which could have been introduced with the 1100°Canneal. The stage II isothermal anneal (700°C) shows a fall in n with constant mobility where the dominant reaction could be Te:,+e-tVo.-+Te,+.VG,th’ from reaction B”C, Fig. 2, which accounts for the constant mobility, provided the donor and donor-vacancy acceptor have the same scattering power, see appendix. This would also account for the observed monotonic increase in NJND. Grinshtein et al. also measured the compensation ratio K( = NJND) and found that it was low in as-grown samples (0.1-0.3), increased after quenching from a llOO°C anneal (0.5-0.6) and fell during the fast annealing stage I (0.1-0.3), passed through a minimum and increased monotonically with the slow anneal stage II. To account for this large rise in K with the 1100°C anneal, which increased the free-electron concentration (n = tThe authors stated that stage II was unaffected by this initial anneal, but on close inspection of their published results there is an appreciable difference.
ND, = 10.0x 1018cmA3 NAi = 14.7x 1018cmm3 NA, = 2 x 10” cme3, i.e. 86% of N, and 63% of ND are removed on anneal ( - 3SOQ This suggests that there is a high concentration of acceptors introduced during the 1100°C anneal and removed with a low temperature anneal. Therefore there must be a fast diffusing acceptor which is fairly soluble in GaAs at T - 1100°C but relatively insoluble at low temperatures. Cue. is a possible acceptor to fit these conditions, and therefore must precipitate out or come to the surface during the 350°C anneal. Also since donors are removed, TeL must precipitate out at this temperature. The likely Te precipitate is AsZTeP since this forms at 360°C (Panish [S]). This precipitation only occurs in preheated samples because of the high Asi and Tea. populations created at llOO”C, Fig. 2. The removal of donors and acceptors would then account for the large increase in mobility. As the temperature is raised AszTe3 will dissolve and create Tei, donors, but because of the high concentration of VGa (created at 1lWC) these form Te,,,VG. acceptors and results in a further decrease in n, Fig. 3. If the formation of acceptors is much faster than the dissolution of AszTe3 (the former has previously been considered to be very fast at these temperatures) then the latter will be rate limiting and not seen. Grinshtein also annealed a sample at 1100°Cfor 4 hr, in a large ampoule, and quenched and then carried out similar isothermal annealing experiments with the fast and slow stages. The rate of fall in n for this sample was reduced, presumably because of the removal of Asi (slowing the rate of Te’;, precipitation in stage I) and to a smaller extent the removal of Voa (slowing the acceptor formation (TeA,,Vo.) in stage 1I)t.
887
A defect model for undoped and tellurium doped gallium arsenide
Fuller and Wolfstirn [ 141observed changes in electron concentration on annealing nt Te-GaAs in the T range 64ML8oo”C after a 4 min 1100°Cpreheat and quench. The low temperature anneal reduced the concentration of free electrons while maintaining constant mobility. This again suggests the principle reaction is purely: e-+ Te:, t V, + TeAsV& t h’, i.e. stage II anneal of Grinshtein. Fuller and Wolfstirn also found these changes in n reversible with T; this is in agreement with the above acceptor complex being unstable for T - 1100°C. Nishizawa et al. [15] undertook annealing studies on Te-GaAs where they observed p-type conversion. TeGaAs (8 x lOI cmb3 < n < 2.8 x 10” cmm3)was annealed at 1100°C and quenched, and the authors then measured the conductivity at depths into the sample after various annealing times for two As pressures. The low As pressure (PAS- 10Torr) anneal started to turn the sample p-type from the surface fairly quickly (< 16 hr) and eventually throughout the sample. The high As pressure anneal (PAS- 4.8 x lo3 Torr) remained n-type until the annealing time approached 64 hr. Nishizawa et al. then examined the variation in acceptor density and lattice parameter with As pressure for various n and T after a 67 hr T”C anneal (900 and 1IOO’C),to ensure equilibrium within the investigated inner region of each sample. The acceptor density and lattice parameter went through a cuspid minimum at a certain As pressure, PASmin,which was T dependent, Fig. 4. These observations indicate a defect or contaminant acceptor diffusing in from the surface-fast at low As pressure and slow at high As pressure. A possible contaminant is Cu (Hurle [l])t Copper is generally considered to diffuse interstitially through GaAs, which is certainly possible at low As pressures. As the pressure is increased the Cu diffusion rate could decrease because of the increasing [Asi], which are assumed to reside on hexagonal interstitial sites, and therefore inhibit free movement, until the As pressure diminishes [V,,] and increases [Vo,] (from [V,,J[Vo,l - KT) allowing Cu to diffuse predominantly by substitutional means. Since Cu is thought to be an acceptor on a Ga site this could account for the p-type conversion, the minimum in the acceptor density and the slower p-type conversion at higher As-pressures. The number of available Vcs for the in-diffusing Cu also increases with free-electron concentration due to the dissolution of TeArVGa acceptors for T - llOO”C, assuming a constant compensation ratio with n after growth, and therefore the acceptor concentration increases with initial n. The position of the cuspid minimum, with respect to the As pressure (which appears to be only T dependent) is then related to the point defect equilibrium at the annealing temperature. The lattice parameter cuspid minimum tNishizawa et al. have measuredthe Cu content for a sample annealed at 900°C for 65 hr. (As pressure not mentioned) and no Cu was detected above O.Sppm, but [Cu] at this limit is equivalent to -2.2 x lOI crne3 singly ionised (2~0. defects, comparable with the observed acceptor concentration.
lo’5 10-210-l
1
lo
102 103 104 PAa TORR
.s
56532
-I
5.6526 1 10-2
10-l
1
10
102
103
104
PAS TORR
Fig. 4. The variation of acceptor density and lattice constant for various arsenic pressure anneals. Nishizawa et al. [IS]. would vary with the Cu content since Cu has a larger
covalent radius than Ga, 1.35 compared with 1.26& Pauling [5]. The constancy of the lattice parameter minimum is a consequence of the accuracy of measurement. Nishizawa et al. observed three activation energies after their anneal (1100°C); 0.12 eV for P.+,,> 7000 Torr and 0.15 eV for PAN< 1OOTorr when ninitinl < 1.8 x 10” cme3, and 0.18eV for 3OOTorr> PA.> 1000Torr when ninitra- 4.5 X 10” cm-‘. The 0.15 eV acceptor level followed the 1.35eV photoluminescence band and the 0.12 and 0.18 eV followed the 1.30eV band. A 1.20eV emission band (thought to be TeA,VGa, Hwang[9]) is observed in the as-grown specimen but decreases on anneal with the energence of the 1.35 and 1.30eV bands. On reannealing at 300-4OO”Cthe 0.12 eV level disappears with an increase in mobility and decrease in hole density and the 0.18 eV level increases. This could well be the reactions Cui; --f surface and/or precipitates
then C& (or similar complex, e.g. Cuc,As?-) is responsible for the 0.12 eV acceptor level, the mobility and the 1.30eV emission band would then increase if Te,&L, is responsible for the 0.18eV level (since the 0.12 eV level gives rise to only a weak emission band at 1.30eV). A similar effect is observed for the 0.15 eV level which would be due to Cu& (or similar complex, e.g. Ct.t~,Vi;), hence Te:, + Cuo.Vii -+ TeJu&
+ VA.
Blanc and Weisberg [16] have found a one-to-one correlation of the 0.15 eV level with Cu concentration in undoped GaAs annealed in the 6OfJ-1000°Crange. Spe-
P. F. FEWSTER
888
cimens with the 0.18 eV acceptor level are unchanged on anneal (3oo-4oo”C)and therefore the associated defect is much more stable. Although as the temperature of anneal is raised the 1.30eV band, associated with the 0.18eV acceptor level, decreases and could well be the reverse reaction Te.&u&
+Te+As+Cu&.
Similar to the break-up of TeAsVGaat high temperatures. Laister and Jenkins [17] undertook annealing work on Te-GaAs at various temperatures (400-1150°C) and studied the formation of dislocation loops and changes in electrical parameters. They observed three distinct temperature ranges for which significant changes occurred. For T > looo”C the Te-GaAs converted to p-type, which was thought to be from Cu contamination, and then decreases as the annealing time is increased. If this was repeated in a As/KCN atmosphere to remove Cu, type conversion did not occur but an overall increase in n was observed accompanied by a drop in mobility. Samples annealed at T > 1080°Ccontained no stacking faults and remained that way if quenched rapidly, but if they were allowed to cool in the furnace large faults were observed. Samples heated above 1OOOYJ were free from prismatic loops. For 800 < T < 1000°C anneals, all the specimens remained n-type but their mobilities fell and {I lo} prismatic loops grew. Annealing for T < 800°C also maintained n-type conductivity with a reduction in mobility and prismatic loops still grew unless T < 400°C. The p-type conversion of Te-GaAs when annealed at T > 1000°Cis presumably the uptake of Cu to form Cu& acceptors. Much below this temperature we have assumed Ga Frenkel pairs do not form leaving insufficient Vca for p-type conversion. If the annealing time is increased the slower reaction of the dissolution of faulted defects becomes significant and reduces the hole concentration. Annealing in a As/KCN atmosphere prevented type conversion and increased n with a fall in p; this would be caused by the increase in TeA, donors created from faulted loop dissolution, reaction AB’. The absence of prismatic loop growth for samples annealed above 1000°Cprobably results from the removal of small precipitates that punch out dislocation loops for the condensation of point defects, Wagner [18]. In the intermediate temperature range 800< T < 1000°C the specimen remained n-type presumably because of the lack of Vo. since the Ga Frenkel reaction only occurs for T > 950°C. The mobility falls because of the increase in acceptors and the prismatic loops grew for the reasons explained by Wagner [18]. In the low temperature range 400~ T < 800°C much the same occurred but below 400°C no loops could be formed and this is assumed to be the limit for the As-Frenkel reaction and thus reaction AB cannot proceed. A possible mechanism for the formation of the GaiVo.Tei split-interstitial during growth has been proposed by Mullin et al. [19]. During growth there is a high concentration of very mobile arsenic interstitials, Asi, which could displace the donors, Te+ resulting in the TeiVoaGai split-interstitial.
Asi t TeA, + TeiVoaGai f AsA, Otsuka et al. [20] conducted annealing studies on undoped GaAs (9OO’Cfor 65 hr and quenched), and observed p-type conversion. This is similar to the results of Nishizawa et a/. [El on Te-GaAs discussed earlier and can be interpreted in a similar manner, by assuming Cu to diffuse in from the surface. Above a certain Aspressure ( - 14Torr) the mobility fell and could be interpreted as the point at which the dominant acceptor species changes from, e.g. Cuq.V,, to Cu&. The scattering ability of the latter must therefore be much greater than that of the former, since [C&J -2[Cuo,V,&] to account for the observed hole density. If the samples were re-annealed at a low temperature (23&3OO”C)for 28 hr they recovered to their initial n and CL.This presumably occurs because of the lower solubility of Cu in GaAs at these temperatures, and Cu precipitates out or comes to the surface. Bublik et al. [21] examined the internal friction spectrum, lattice parameter and density of undoped GaAs for various As concentrations in the melt during growth. The 160°C damping decrement from the internal friction experiments, which they assigned to (VGaVoa), was found to increase with As concentration in the melt over the single-phase region. The density was also shown to increase over this region whilst the lattice parameter remained constant, and it was deduced that Asi were predominant for a high As content in the melt and VAs for a low As content in the melt, although both species exist over this region. These results would suggest that an As based defect ((Asi Asi) as mentioned previously) would be more likely to account for the internal friction spectrum than a (Vq,Vq.) defect which would contribute to lowering the density. CONCLUSIONS
This paper has given an explanation of the effects observed on annealing undoped and Te-doped GaAs. The essential difference of this explanation compared with previous explanations is the introduction of two new defects in GaAs, these are (100) split-interstitials GaiVo,Gai and TeiVo.Gai. The formation of these defects is thought to occur by the presence of a Gai or Tei atom which does not have an opportunity of relaxing into a Voe or VA, site (as is the case in n+ Te-GaAs and during conditions of excess Ga). The interstitial Ga or Te atom would then come close to a Gac, site and displace the host atom along a (100) direction, resulting in the intruder and host atoms straddling the now vacant Ga site. This creates a very signiticant strain on the crystal lattice. To account for all the experimental results in the literature surveyed, further conclusions arise. (a) The As-Frenkel reaction only occurs or is significant above - 400°C. (b) The Ga-Frenkel reaction only occurs or is significant above - 900°C. (c) The ratio of the defects [TeA.VG.I : ITeA, decreases with increasing T of anneal or simply that TeA,Vo. + TeA, + Vo.(T > 1looOC) also see appendix.
A defect model for undoped and tellurium doped gallium arsenide
(d) Faulted loops dissolve for T 3 9OWC. (e) Ga diffuses by GaiV~~Gai sites. (f) As can reside on the hexagonal interstitial site and consequently exhibits an insignificant strain on the lattice. It must, however, be noted that no direct independent evidence exists for the presence of split-interstitials in GaAs (but theoretical work 1221on diamond and silicon suggest that the split-interstitial is the favoured interstitial defect) but predictions arising from this model could be tested in detail in order to make a critical comparison of this alongside other models. Acknowledgemwrs-Theauthor is very grateful to Drs. D. T. J. H&e, J. B. Mullin and A. F. W. Willoughby for suggestions and valuable discussions. This work has been carried out with the support of the Procurement Executive (D.C.V.D.), Ministry of Defence.
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19. Mullin J. B,, Royle A. and Benn S., J. Crystal Growth 50,625 (1980). 20. Otsuka H., Ishida K. and Nishizawa J., Jup. J. Appl. Phys. 8, 632 (1969). 21. Bublik V. T., Karataev V. V., Kufagin R. S., Mil’vidskii M. G., Osvenskii V. B., Stolyarov 0. G. and Kholodnyi L. P., Sou. Phys. Cryst. 18,218 (1973). 22. Corbett J. W., Bourgoin J. C. and Weigel C., Inst. Phys. Con& Ser. No. 16, I (1972). 23. Evans R. C., An lniroductio~ to Crystaf Chemistry 2nd Edn. Cambridge University Press, London (1976). APPENDIX
A difficulty arises in the explanation for the formation of acceptors (if- these are TeA,V&) on annealing Te-GaAs below 1ooo”C.We have assumed that Voa have been created at high temperatures and then form TenrVo, acceptors on re-anneal&g at low temperatures: e- t Tet + Vos + TeA,V& t h+. This assumes that Vanis neutral which is unlikelyin n+ material-it is far more likely to be a double acceptor V&i;;., i.e.
RE~RENCE5 Te’, + V& + TeA,Vo, Hurle D. T. J.. J. Phvs. Chem. Solids 40,627 (1979). VC. would appear to require a sink from which it can rapidly 2. Dobson P. S., Fewster P. F., Hurle D. T. J., Hutchinson P. W.. Mullin J. B.. Straunhan B. W. and Willoughby A. F. W., .diffuse otherwise the free-electron concentration would be unInst. Phys. Cot& Ser. No. 45, 163(1979). changed on anneal and the mobility would decrease (providing 3. Potts H. R. and Pearson G. L., J. Appl. Phys. 37,2098 (1%6). this is the only reaction). 4. Driscoll C. M. H. and Willoughby A. F. W., Inst. Phys. Conf. An alternative explanation is the formation of a complex Ser. No. 16,377 (1972). VaSTeiV&, where Te sits mid-way between the two atomic sites. Te has then exact &fold co-ordin&ion (sp’d2 h brid bonds). The 5. Pauling L., The Nafure of The Chem~cul Bond. Cornell University Press, Ithaca, New York (1960). covalent radius of sp’d* hybridised Te is I.52 2( Evans 1231and 6. Chakraverty B. K. and Dreyfus R. W., J. Appl. Phys. 37,631 hence the Te-Ga(As)lengths are 2.78(2.70) A whereasthe t(GaAs) lengthfor next nearest pairs is 3.08A, so this complex would (1966). lit reasonably well into the lattice. I. Laister D. and Jenkins G. hf., .I. Mat. Sci. 3, 584 (1968). This neutral complex could then be stable at high temperatures 8. Panish M. B., J. Electrochem. Sot. 114, 91 (1967). but at low temperatures on re-annealing would return to the 9. Hwang C. J., .I. Appl. Phys. 40.4584 (1%9). TeAsVoadefect which is likely to be an acceptor in nt material 10. Grinshtein P. M., Ya. Lipkes M., Rytova N. S. and Fistul’ V. I., Sou. Phys. Semicond,.9,725 (1975). V,+TeiV&,-, TeA,V&,t h+. 11. Mil’vidskiiM. G.. Osvenskii V. B.. Novikov A. G., Fomin V. G. and Grishina s. P., Sou. Phys. bryst. 18,519 (1974). The constant mobility observed by Grinshtein[lO] is not 12. Osvenskii V. B., Kholodn~ L. P. and Mil’vidskiiM. G., Soa. explained by this reaction if charge species are the dominant Phys. Solid State 13, 1790(1972). 13. Grishina S. P., Mil’vidskii M. G., Osvenskii V. B. and Fistul’ scattering entities in his experiment. Grinshtein did undertake these measurements at 7OO”i:and therefore phonon scattering V. I., Sou. Phys. Semicond. 4,240 (1970). 14. Fuller C. S. and Wolfstirn K. B., J. Appl. Phys. 34, 2287 may be signi8c~t since their reported mobilit~es were exceptionally low ( - 700cm* V’ s-l). (1963). The same reaction is assumed to have been observed by Fuller IS. Nishizawa J., Otsuka H., Yamakoshi S. and Ishida K., Jap. I. and Wolfstirn [14], where the mobility did fall during anneal Appl. Phys. 13,46 (1974). 16. Blanc J. and Weisberg L. R., J. Phys. Chem. Solids 25, 221 (1380+ 1060cm2V-’ s-r) and these measurements were presumably conducted at room temperature (although not stated (1964). in their paper). It must also be remembered that there are 17. Laister D. and Jenkins G. M., Phil. Mug. 23, 1077(1971). 18. Wagner W. R., Inst. Phys. Coaf. Ser. No. 33b, 65 (1977). uncertainties in mobility theory at high dopant concentrations. 1.
IPCSVol.42.No. IQ-B