- Email: [email protected]
Tin segregation and donor compensation in melt-grown gallium arsenide
Journal of Crystal Growth 80 (1987) 323—332 North-Holland, Amsterdam
323
TIN SEGREGATION AND DONOR COMPENSATION IN MELT-GROWN GALLIUM ARSENIDE M.R. BROZEL * and E.J. FOULKES
**
Department of Electrical and Electronic Engineering, Trent Polytechnic, Burton Street, Nottingham, UK
I.R. GRANT
***
Cambridge instruments Ltd., Rustat Road, Cambridge CBJ 3QH, UK
and D.T.J. HURLE Royal Signals and Radar Establishment, St. Andrews Road, Great Malvern, Worcs. WRI4 3PS, UK
Received 12 August 1986; manuscript received in final form 7 November 1986
Radio-tin-doped single crystals of GaAs have been grown by the LEC technique from melts of varying composition. Carrier concentration and Sn distribution determined by radio-counting and autoradiography are reported and analysed to show that Sn-related acceptors are incorporated to give a compensation ratio of NA/ND = 0.24 ±0.03 independent of doping level and of melt composition. These concentrations are significantly in excess of a non-Sn-related residual acceptor — believed to be CA, — which is 6 cm3. Modified Sheil plots are used to show that the melt composition shown present in the crystals a level of 1.6x10’ appearstotobemove progressively towardatAs-richness as growth proceeds. The distribution coefficient for tin in crystals growing from a stoichiometric melt is determined to be 4.0><10—~.
1. Introduction The use of n-type GaAs in the fabrication of infrared lasers and other emitters is well established. For these applications highly doped n-type substrates (n 2 x 1018 cm3) grown by the horizontal Bridgman (HB) or liquid encapsulated Czochralski (LEC) method are widely available. It has become clear, however, that the mechanisms by which donor atoms are incorporated into the growing crystal are not well understood (see, for example, Hurle [1] and Mullin et al. [2]). One of the reasons for these uncertainties is the difficulty of accurately measuring the concentrations of *
**
“~‘
Not at Department of Electrical and Electronic Engineering, UMIST, Sackville Street, Manchester, UK. Now at Cambndge Instruments plc, Rustat Road, Cambridge CB1 3QH, UK. Now at ICI Wafer Technology plc, Milton Keynes, Bucks., UK.
donor atoms at various positions in the crystal. Techniques that are available include spark source mass spectrometry (SSMS) and secondary ion mass spectrometry (SIMS), but these cannot provide the accuracy in concentration measurement necessary to allow quantitative assessments of compensation ratios to be made. Thus, there is a paucity of quantitative data relating to one of the most important parameters in GaAs crystal growth the incorporation and compensation of dopant atoms. In this paper we present accurate data on the bulk incorporation of tin atoms in three large (2 inch diameter, 1 kg mass) LEC crystals of GaAs grown from melts of different compositions. We demonstrate that rather complicated segregation behaviour is present and that this can be partially described by a thermodynamic model which takes —
.
into account complexing of dopant atoms with native defects. The compensation ratio derived from the electrical measurements agrees with val-
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
324
M.R. Braze! eta!.
/
Tin segregation and donorcompensation in melt-grown GaAs
ues obtained by less direct means [2]. Mobility data are compared with those of tin doped InP [3] and with the theory of Walukiewicz et al. [4] whilst the overall electrical properties of the crystals are discussed with regard to inadvertent uptake of shallow carbon acceptors by the GaAs melt from the crystal growth ambient.
2. Experimental 2.1. Crystal growth Quantitative estimations of the concentrations of tin atoms, [Sn], in various parts of our crystals have been achieved by employing a radiotracer technique [3,5]. The tin dopant was labelled with a small quantity of 113Sn, a 0.39 MeV gamma-emitter with a half-life of 110 days. Growth was performed in a Cambridge Instruments MSR6/R high-pressure puller under a dry boric oxide encapsulant (water content 300 ppm wt). The —
charges were synthesized “in-situ” from high purity elemental gallium and arsenic [6]. One crystal, A952/R, was pulled from a gallium-rich melt (Ga/As = 1.05). A second crystal, A953/R, was pulled from an “arsenic-rich” melt (Ga/As 0.993). The third crystal, A984/R, was pulled from a “stoichiometric” melt (Ga/As 0.999). The charges for all three crystals were doped with milligram quantities of radioactive tin diluted with larger quantities of natural tin: 500 mg in the case of A952/R and A953/R and 150 mg for A984/R. The tracer component consisted of enriched “2Sn which had been neutron irradiated to yield an activity of 4.0 Ci/g for the isotope “3Sn. Crystal growth resulted in single crystals of 1 kg mass grown along (001) and doped to a carrier concentration of around 2 x 1016 cm3 for A952/R and A953/R at their seed ends. The seed end of A984/R was found to be high resistivity, becoming semiconducting for mass fraction g> 0.15. Details of the crystals and their growth are given in table 1. Each crystal was cut into a series =
=
Table 1 Details of crystal growth parameters, tin concentrations, carrier concentrations and amphotericity ratios of the GaAs boules Crystal No.
Fraction of melt solidified (g)
[Sn]X10~6 (cm3)
n xlO’6
A952/R Ga/As = 1.05 Natural Sn; 500 mg Radiotracer Sn; 2.4 mg
0.040 0.149 0.273 0.396 0.523 0.654 0.790
8.4 8.9 10.1 12.2 15.4 20.0 29.2
2.62 3.15 4.26 4.97 6.01 7.72 15.1
0.27 0.24 0.22 0.26 0.30 0.32 0.25
A953/R Ga/As = 0.993 Natural Sn; 500 mg Radiotracer Sn; 1.6 mg
0.058 0.180 0.313 0.450 0.596 0.774
9.8 10.75 12.24 14.95 19.98 32.8
3.68 4.97 5.46 7.61 10.5 18.2
0.25 0.20 0.23 0.21 0.22 0.23
A984/R Ga/As = 0.999 Natural Sn; 150 mg Radiotracer Sn; 4.2 mg
0.010 0.077 0.190 0.302 0.451 0.569 0.720
3.1 3.2 3.6 4.1 5.2 6.7 10.3
(cm
0.0 0.0 0.33 0.75 1.20 2.00 4.00
3)
Sn acceptor to Sn donor (amphotericity) ratio, f~
— —
0.17 0.16 0.20 0.22 0.24
MR. Broze! eta!.
/
325
Tin segregation and donor compensation in melt-grown GaAs
of (001) slices which were assessed for tin concentration, carbon concentration and electrical properties.
.“,,,
~,,,
~ ~
_•, ..~_4.
2.2. Tin concentration measurements (radiotracer counting)
Tin concentration measurements were per-
• .1
•~ ~ *, ~,
~
‘~# 4.,~g
#
, ~.
~
.~
~
.~
4. ~.
0.979.10~cm~ 17
formed on slices taken from ten sections of each crystal from the seed to near the tail. Each slice, of 1 mm thickness, was cleaved into samples of approximately 3 mm X 3 mm. This resulted in over 100 samples per slice. Each was loaded into an automatic gamma counter for a period of 10 mm.
-3
0.98-1.019.1017cn~3 Cm
‘
I2~
1.02-1.059.l0 1.06-1.099.1017cm~3
,,,
1.00(1.35max).1017cm3 (c)
/‘
*
f4.~ ~
Typical counts were of the order of iO~resulting in accuracies of 1% for each sample. A refer-
C,
—
ence solution made up from a weighed piece of the original 113Sn consignment allowed corrections for the half-life to be made as the measurements
* ~
‘ ~ .‘ .~ ~ ~
,, ~ 4. 4. 4.4. “4.4.
I
4.4.4.
17 -3 1.40-1.49.10 cm
7’
r
F.’
‘
‘
~
,~‘
‘ ,,
~
~ ‘~
I,
\
‘ “
.‘
,,
‘
I
‘‘
,,,,
,jI
‘
‘‘
,,,
‘
~,
f
J 8.40 -8.69.1016cm3 8.70- 9,99.1016cm3 9.00- 9.29 .1016cm~3 9.30 - 9.59 .1O~cm3 9.60(9.7lmax).1O’6cm3 (a)
/ ~
~.
.-
,
,
~
•1
E~J 2.6-2.79.1017cm3 ~J 2.82.99.1017cm3 3.O.3.19.1017cm3 3.2-3.39.1017cm~3 3.4(4.17max)1O17cm~3 (b)
1.50- 1. 59 .1017cm3 1.60- 1.69.1017cm~ 1.70- l.79.1017cm3 (d)
Fig. 1. Mapping of radio-tin distribution across wafers: (a), (b) A952/R: g = 0.13 and and 0.760.43 respectively; (c), (d) A953/R; g = 0.16 respectively.
proceeded. This solution also acted as a reference for the estimation of total tin content as a function of number of registered counts. Errors in making up this solution, together with those in weighing the milligram quantities of “3Sn tracer, constitute the major source of systematic error in the data; we estimate this to be 5% for the present work. After radiotracer measurements on samples from a particular slice were completed, a mapping of [Sn] over the slice was obtained. Two such mappings are presented in fig. 1 for slices taken from near the seeds and tails of A952/R and A953/R. Mappings from A984/R were similar. The mapping of [Sn] in (001) slices as demon-
strated in fig. 1 indicates a nearly radial increase of about 15% from the centre towards the periph-
326
M.R. Broze! et al.
/
Tin segregation and donor compensation in me!t-grown GaAs
ery. However, within the central 80% of each slice, [Sn] is uniform to within 5% of the mean. 2.3. A utoradiography
Whilst gamma counting measurements provide quantitative data for several samples taken from a
single slice, no information on fine scale spatial changes of [Sn] can be derived because of averaging effects. Autoradiography of slices before cutting can give this information, together with evidence of precipitation of second phases. Fig. 2 shows typical results from A953/R. For the majority of each crystal good homogeneity of [Sn]
Fig. 2. Autoradiographs of wafers from A953/R (As-rich): (a) g = 0.6: (b) g
=
0.8; (c) g = 0.9
MR. Brozel et a!.
/
Tin segregation and donor compensation in melt-grown GaAs
is evident, with no evidence of any anomalous segregation due to facet formation. (Indeed, a central facet is not expected for <001) growth). However, a tin-rich second phase is present near the tail sections of each crystal (at g ~ .85 for A952/R and at g ~ 0.9 for A953/R). The onset of two phase growth seen at g 0.9 (A953/R) around the periphery of the slice is consistent with the slightly concave growth interface, =
2.4. Carbon concentration measurements
Because the seed end section of A984/R was of high resistivity (see next section), samples could be assessed for carbon concentration, [C], using localised vibrational mode (LVM) absorption without artificial compensation [7]. Two sections of 5 mm thickness were polished on both sides and the infrared absorption measured between 700 and 500 cm’. An absorption peak due to CAS acceptor centres was observed at 580 cm’. Using the calibration of Brozel et al. [8], the concentration of shallow carbon 3acceptors estimated be in thesewas sections. The tocon5 ±1 x 1016 ofcm centrations the major donor impurities, silicon and sulphur, are estimated to be around 1 x 1015 cm3 typical values for LEC GaAs grown under dry boric oxide while the only other major contaminant is expected to be boron [9] at concentrations of up to 1017 cm3. LVM measurements indicate that these substantial concentrations of boron do not reveal themselves in the form of absorption peaks due to isolated boron atoms, either as isoelectronic BGa centres or as electrically active BAS antisite defects. Because BAS is the only known electrically active centre is as-grown material and this centre is absent in our crystals, we assume that the only significant electrically active impurity species present are Sn and C. —
—
327
crystals is 0.24 (with a standard deviation of 0.03) nearly identical to that for both LPE- and VPEgrown crystals which are both n-type with NA/ND 0.25 [10] (where NA and ND are respectively the acceptor and donor concentrations). This implies that if Sn~ais the dominant donor, Sn~cannot be a significant acceptor since the ratio of these two entities should depend strongly on the arsenic activity in the molten phase and would then be markedly different (typically by a factor of> iO~) in LPE, VPE and LEC growth. Hurle [10] has shown that the matter is resolved if SnGaV~ais assumed to be the dominant acceptor. Adopting this model we can write for the total tin concentration in the crystal [10]: ~ [Sn~a] + [SnuaV~a] —
=
K [1 +
=
~
~t
p~]
[Sn I.] P~(’~2/n81,
(1) where K and K are combinations of some mass action constants and activity coefficients as explained in ref. [10]. ~As2 is the partial pressure of arsenic dimers in equilibrium with the arsenic melt and n81growth is the electron concentration in the crystal at the temperature. For the relatively low doping levels with which we are here concerned: ~ (2) where I~, is a further mass action constant [10]. The concentration of tin in the melt in the present experiments is very small (~ 0.1%), so that we can take the activity coefficients embedded in K and
~
=
—
K to be constant. Further we can express the
dependence of ~As on melt composition as equal to that for a binary melt (i.e. containing no tin). This has been shown by Brozel et al. [14] to be given by: P~
0.75 (1
=
+ 4.9XAS)
(3)
where XAS is the concentration of arsenic in the melt in excess of the congruent concentration. Substituting eqs. (2) and (3) into eq. (1) we obtain:
3. Segregation behaviour [Sn~] In principle, tin can be amphoteric in GaAs occupying a Ga-site as a donor 5I1~a and an arsenic site as an acceptor Sn~. However, the compensation ratio NA/ND in the present LEC
=
0.65KK~’~’2(1 + 4.9XAS)3”2(1 + .k~I~)
X [SnL]. (4) Noting that XAS << 1 we can approximate this: [Sns]
—
k 0(1 +
7.4XAS),
(5)
328
M. R. Broze! et a!.
/
Tin segregation and donorcompensation in melt-grown GaAs -
where 2(1 + k0
=
InC
5 /CL(O) ______________________________________
kA~)
5
,•\
0.65KK~//
is the segregation coefficient for a congruent melt. Hence: k = [SnS]/[SnL]
=
k 0(1 +
~
(6)
7.4XAS).
The measured quantity is the effective distribution coefficient (keff) and this is related to k by the
~\ ‘N \\
When k keff << 1, this latter equation can be approximated Burton, Prim to: and Slichter (BPS) equation [12].
Stoichiometric
3
—
keff = k e5~D,
rich
(7)
As -nc
~
Stope-0.994
h\
3v’~6~’~2
where v = growthboundary velocity, layer 8 = 1.6D’~ is an imaginary thickness, D = melt diffusion coefficient (taken to be iO~cm2 v = kinematic viscosity of the melt (taken to be 5 x iO~ cm2 s’) and w crystal rotation rate. In the present experiments v 9 mm h~ and ~o 2ir/10 rad s~, so that exp(v8/D) 1.6. The rejected excess component will also form a boundary layer obeying the BPS equation written for a solute with k 0. The excess arsenic concentration in the melt at the interface (XAS) at melt fraction g solidified is
2
\ 0
3 1n(i-g)
Fig. 3. Sheil plot for the 3 crystals. The dashed line has a slope of —0.994
=
—
k —1.
=
=
=
=
The intercepts on the ordinate, interpreted as values of In keff show that, as predicted by eq. (6), k is greater for the stoichiometric and —
arsenic-rich crystals than for the gallium-rich one. However, the plots are not linear because of the
X~ 5=exp(v6/D)X~5(1—g),
(8)
-InCs/CL(0)
where XL is the excess arsenic concentration at g = 0. As shown in a companion paper [14], insert-
5
\
~... •~
ing this into the Scheil equation yields: C~ ln~C(0) ____
ji
° (1—koeff )ln(1—g)+A(g), =ln keff~
\\
(9) where k~f=k0 exp(~),
Stoichiom~ 3 ~rich
v8/D, A(g) = 7.4 exp(~)X,~5(1 — k0 exp(~))/(1 — g). =
4
The third term on the right-hand side of eq. (9) represents the correction to the Scheil equation due to the non-congruency of the melt. A Scheil plot with A(g) = 0 for the three crystals is shown in fig. 3.
-
ri (I - g).
A (g)
Fig 4. Modified Scheil plot with the coefficient of 4(g) chosen for each crystal to give a least squares fit to a line of slope 0.994 (see text).
M. R. Broze! et a!.
/
329
Tin segregation and donor compensation in melt-grown GaAs
failure to include the A(g) term from eq. (8). Consequently the data were re-analysed by obtaining for each crystal a least squares fit to a line of slope —(1 0.006) = —0.994 with XAS and ln k0
1fl(Cs/CL(0))
—
as fitting parameters. The results are shown in fig. 4. The initial arsenic concentrations in the melt were determined by measurements of the weight loss assumed to be solely of arsenic. From this and the fitted values of XAS the (initial) arsenic concentration is excess of the congruent composition the deviation of the congruent composition from the stoichiometric composition (12) is obtamed. —
—
—
Ga-rich
12
=
[A5LI
—
0.5
—
X,~5.
(10)
The values of 17 obtained for the three crystals are 0.6%, 0.1% and 0.1% respectively (all on the galhum-rich side). These are unrealistically large values and this is discussed below. (Within experimental limits one would expect 12 0.) The values obtained for k0, the segregation coefficient for a congruent melt, differ somewhat, (The three lines in fig. 4 should have been coincident.) Accordingly we seek to obtain the best single line fit to all the data by taking in k and 12 as fitting parameters. The result is shown in fig. 5 corresponding to 12 = —0.003 (i.e., 0.3% to the Ga-rich side) and —
~
ic’~metnic
2 0
I
I
I
1
2
3
- ln(ig) . A (9) Fig. 5. Modified Scheil plot with single values of Q and In k0 as fitting parameters and with a slope of (k~1~ —1) for all 3 crystals (see text).
that, if we assume a linear relationship between Ga removal and water content, the expected shift in [A5L] would be 0.3%. This is exactly the change in [AsL] required to give 17 0 from an analysis of the data in fig. 5. —
=
keff = 6.4
x iO~
=
exp(1.~)k0,
so that k0 = 4.0 X iO~. We return now to the unrealistically large value of 17. A similar result was obtained by us with Cr-doped GaAs [14]; in these experiments involving nine crystals the average apparent value of 17 was 1.7%. An explanation for this was provided by very recent work by Emori et al. [15], whose results imply that the addition of 2000 ppm of water to the boric oxide encapsulant removes Ga preferentially from the melt by an amount sufficient to change the melt stoichiometry (i.e. to increase [A5L]) by 1.7%. Our Cr-doped crystals were in fact grown under encapsulants containing at least that amount of water and so the anomalously large apparent value of 12 for the Cr-doped crystals is explained, The present Sn-doped crystals were grown under much drier boric oxide (300 ppm water) so
4. Carrier concentration Room temperature Hall-effect measurements were used to obtain both carrier concentration and carrier mobility data. Three small samples of 5 mm x 5 mm were selected from slices taken adjacent to those used for the radiotracer determinations. They were cut into “clover-leaf” pieces and pure tin contacts alloyed to the surface under a reducing atmosphere. The Hall factor was taken to be unity. The data thus obtained for each slice were averaged and are presented in fig. 6 and in table 1. The carrier concentrations increase along the lengths of the boules (except for A984/R which exhibits a substantial region near the seed which is high resistivity) while the electron mobilities decrease. In fig. 6 the carrier concentrations n
330
M. R. Broze! et a!.
/
Tin segregation and donor compensation in melt.grown GaAs
6cm_3)
20 n(slOl
Ga -rich As-rich
/
0.3
/
Stoichiometric
./r
15
~/ =
a
/
/
.
.
1
0.2
.
Ga-rich As-rich Stoichiometnic
‘
//
35. a
3
0
3
0
I
I
I
10
20
30 ( x1016cm3)
[Sn]
0.2
0.4
0.6
0.8
g
1
Fig. 7. Plot of $, the calculated ratio of tin-related acceptors to donors as a function of fraction of melt solidified, g. Dashed line is the mean value.
Fig. 6. Plot of room temperature carrier concentration n versus
the arsenic site substituent Sn~
total tin concentration in the 3 crystals.
of the three crystals are plotted as a function of tin content. Values of n are proportional to [Sn], indicating that a constant proportion of [Sn] produces free electrons. The negative intercept on the carrier concentration axis suggests that there is a background 3. acceptor of fig. [A—] The slopeconcentration of the line in 6 =is 1.6 lessx 10i6 than cm unity implying additional compensation due to tin-related acceptors. If we assume that: 5MG a J ~SnGVG LA j, t~ll) a aI1 + 1 r F _1 —
n
=
—
—
1
then, from eqs. (1) and (11), we obtain the amphotericity ratio $: F~
$=
v
L nGa Gal
[Sn~a]
5is not present in significant concentration. It does not depend either on position down the crystal (i.e. on the time for which crystal was exposed to high temperatures) and hence is not likely to be a result of post-grown annealing. From the slope of fig. 6 a “carrier concentration effective segregation coefficient” for a congruent melt is: k~ is 1 k 0 F5 1 = ~ X L n LI I n5 which compares with the value obtained by Mullin stoichiometry. et al. [2] of 5.2>< i0~ for a crystal of unknown Values of 77 K carrier mobility ~i as a function of carrier concentration are presented in fig. 8 for =
=
F 5 =
~SJ
1
[Sn~1
—
—
I
A~11
[A
—
~
,
(12)
I~
This is plotted against fraction of crystal solidified, g, for each of the three crystals in fig. 7 from which it can be seen that the ratio of tin-related acceptors to donors is about 0.24 ±0.03. This ratio does not appear to depend significantly on the stoichiometry of the crystal in agreement with Hurle’s model [10] supporting the postulate that
crystals A952/R Also plotted fig. 8 (dashed line)andareA953/R. the theoretical curves on of Walukiewicz et al. [4,13] for a compensation ratio of NA/ND = 0.24. It can be simply shown that NA
/3n + [A] =
,~
+
[A]
3
1
Taking $ = 0.24 and [A ~] = 1.6 X 1016, and using the table of Walukiewicz et al. [13], we can plot a theoretical curve p. = p.(n) where for each value of
M. R. Broze! et a!.
/
Tin segregation and donor compensation in me!t-grown GaAs
3 ).Lx10 (cm2V~s~)
I
331
I
\ \
a
6
\
1
• Stoichiometric Ga-rich • As—rich
‘
°io15
io17
io16
n (cm3)
io18
Fig. 8. Mobility versus carrier concentration at 77 K. Data for the three crystals. The dashed liuie is the value predicted by Walukiewicz et al. [4,13] for fixed NA/ND = 0.24. The full line is for values of NA/ND given by eq. (13) with /~ = 0.24 and
[A] =1.6X10’6cm3.
n, NA/ND is given by eq. (13). This is shown in
fig. 8 (solid line) from which it can be seen that fair agreement is obtained. In particular the the-
We observe this up to a total [Sn] 3 x 3 10i6 cmof corresponding to a net tin donor concentration 2 X 10i6 cm This fixes the3carbon acceptor conin marked contrast centration at 1.6 x 1016ofcm to our measured [CAS] 5>< 1016 cm3 using the LVM calibration of Brozel et al. [8]. There are two possible explanations for this discrepancy; either there exist extra donors in the GaAs which act to compensate the carbon acceptors, or the LVM calibration is inaccurate at the relatively high carbon concentration. Concentrations of acceptors other than carbon would lead to the discrepancy being worse. The presence of donors at a level of 2 x 1016 cm is unlikely for two reasons. Firstly, this concentration is rarely encountered in undoped GaAs analysed by SSMS or SIMS and, secondly, the presence of this concentration of donors would render undoped GaAs with low [C] n-type and of low resistivity; this is not the case. We conclude, therefore, that the presence of other donor species is improbable and that the LVM calibration predicts too high values of [C]. This is discussed in detail elsewhere [11]. —
~.
ory predictsThe theresults observed maximum as n is decreased. shown in fig. 8inarep. broadly in agreement with the data on melt grown Sndoped GaAs obtained by Mulhin et al. [2]. These authors similarly observe a mobility maximum but their results suggest slightly larger values for both $ and [A—]. We have shown recently [13] that Sn-doped InP is incompensated and that the predictions of mobility theory are seriously in error for this material. In contrast, Sn-doped GaAs is compensated by Sn-related acceptors ($ — 0.24) and the predictions of mobility theory [4,13]are broadly compatible when the effect of residual carbon acceptors are also taken into account. The dominant background acceptor in undoped LEC GaAs is known to be carbon [16]. Such material is semi-insulating due to the presence of the native deep donor defect, EL2. Thus in our material the Fermi level will be pinned near the centre of the band gap and the material will be high resistivity if [EL2]> [CAS]~ [Sn~a]
—
[SflGa~’~5aL
5. Conclusions There are two conclusions of importance in this work: firstly, as was observed with the
332
MR. Brozel eta!.
/
Tin segregation and donor compensation in meh.grown GaAs
chromium-doped gallium arsenide [14], the modified Sheil plots indicate that almost all melts appear to get more arsenic-rich as growth proceeds. Recent work by Ernori et al. [15] strongly suggests that this is due to uptake of Ga from the melt by the residual water in the encapsulant. Radiotracer measurements are shown to provide a valuable method for inferring melt stoichiometry. Secondly, unlike tin in indium phosphide [3] tin-doped gallium arsenide is markedly cornpensated. Significantly, the compensation ratio NA/ND = 0.24 ±0.03 is identical to that found in LPE and VPE material [10], which strongly mdicates that the compensation is due to the presence of tin—acceptor complexes.
Acknowledgements The authors are grateful to J.N. Crookes for the provision of the radiocounting facilities, to R.M. Ware for valuable discussions, to G. Davis for growth of the crystals and to B. Waldock for making the electrical measurements.
References [1] D.T.J. Hurle, J. Phys. Chem. Solids 40 (1979) 627. [2] lB. Mullin, (1980) 625. A. Royle and S. Benn, J. Crystal Growth 50 [3] MR. Brozel, El. Foulkes, I.R. Grant, L. Li, D.T.J. Hurle and R.M. Ware, J. Crystal Growth 70 (1984) 191. [4] W. Walukiewicz, L. Lagowski, L. Jastrzebski, M. Lichtensteiger and H.C. Gatos, J. Appl. Phys. 50 (1979) 899. [5] MR. Brozel, B. Tuck, D. Rumsby and R.M. Ware, J. Crystal Growth 60 (1982) 113. [6] D. Rumsby and R.M. Ware, in: Proc. 9th Intern. Symp. on GaAs and Related Compounds, Oiso, 1981, Inst. Phys. Conf. Ser. 63, Ed. T. Sugano (Inst. Phys., London—Bristol, 1982) p. 573. [7] R.C. Newman, Infra-Red Studies of Crystal Defects (Taylor and Francis, London, 1973). [8] MR. Brozel, lB. Clegg and R.C. Newman, J. Phys. Dli (1978) 1331. [9] C.G. Hopkins, yR. Devine, C.J. Blattner, CA. Evans, Jr. and TI. Magee, AppI. Phys. Letters 36 (1980) 989. [10] D.T.J. Hurle, J. Phys. Chem. Solids 40 (1979) 639. [11] MR. Brozel, E.J. Foulkes, R.W. Series and D.T.J. Hurle, Appi. Phys. Letters 49 (1986) 337. [12] J.A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys. 20 (1953), 1987. [13] W. Walukiewicz, J. Lagowski and H.C. Gatos, J. Appl. Phys. 53 (1982) 769. [14] MR. Brozel, I.R. Grant and D.T.J. Hurle, J. Crystal Growth 80 (1987) 315. [15] H. Emori, T. Kikuta, T. Inada, T. Obokata and T. Fukuda, Japan. I. AppI. Phys. 24 (1985) L291. [16] LB. Ta, H.M. Hobgood, A. Rehatgi and RN. Thomas, J. AppI. Phys. 53 (1982) 5771.
323
TIN SEGREGATION AND DONOR COMPENSATION IN MELT-GROWN GALLIUM ARSENIDE M.R. BROZEL * and E.J. FOULKES
**
Department of Electrical and Electronic Engineering, Trent Polytechnic, Burton Street, Nottingham, UK
I.R. GRANT
***
Cambridge instruments Ltd., Rustat Road, Cambridge CBJ 3QH, UK
and D.T.J. HURLE Royal Signals and Radar Establishment, St. Andrews Road, Great Malvern, Worcs. WRI4 3PS, UK
Received 12 August 1986; manuscript received in final form 7 November 1986
Radio-tin-doped single crystals of GaAs have been grown by the LEC technique from melts of varying composition. Carrier concentration and Sn distribution determined by radio-counting and autoradiography are reported and analysed to show that Sn-related acceptors are incorporated to give a compensation ratio of NA/ND = 0.24 ±0.03 independent of doping level and of melt composition. These concentrations are significantly in excess of a non-Sn-related residual acceptor — believed to be CA, — which is 6 cm3. Modified Sheil plots are used to show that the melt composition shown present in the crystals a level of 1.6x10’ appearstotobemove progressively towardatAs-richness as growth proceeds. The distribution coefficient for tin in crystals growing from a stoichiometric melt is determined to be 4.0><10—~.
1. Introduction The use of n-type GaAs in the fabrication of infrared lasers and other emitters is well established. For these applications highly doped n-type substrates (n 2 x 1018 cm3) grown by the horizontal Bridgman (HB) or liquid encapsulated Czochralski (LEC) method are widely available. It has become clear, however, that the mechanisms by which donor atoms are incorporated into the growing crystal are not well understood (see, for example, Hurle [1] and Mullin et al. [2]). One of the reasons for these uncertainties is the difficulty of accurately measuring the concentrations of *
**
“~‘
Not at Department of Electrical and Electronic Engineering, UMIST, Sackville Street, Manchester, UK. Now at Cambndge Instruments plc, Rustat Road, Cambridge CB1 3QH, UK. Now at ICI Wafer Technology plc, Milton Keynes, Bucks., UK.
donor atoms at various positions in the crystal. Techniques that are available include spark source mass spectrometry (SSMS) and secondary ion mass spectrometry (SIMS), but these cannot provide the accuracy in concentration measurement necessary to allow quantitative assessments of compensation ratios to be made. Thus, there is a paucity of quantitative data relating to one of the most important parameters in GaAs crystal growth the incorporation and compensation of dopant atoms. In this paper we present accurate data on the bulk incorporation of tin atoms in three large (2 inch diameter, 1 kg mass) LEC crystals of GaAs grown from melts of different compositions. We demonstrate that rather complicated segregation behaviour is present and that this can be partially described by a thermodynamic model which takes —
.
into account complexing of dopant atoms with native defects. The compensation ratio derived from the electrical measurements agrees with val-
0022-0248/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
324
M.R. Braze! eta!.
/
Tin segregation and donorcompensation in melt-grown GaAs
ues obtained by less direct means [2]. Mobility data are compared with those of tin doped InP [3] and with the theory of Walukiewicz et al. [4] whilst the overall electrical properties of the crystals are discussed with regard to inadvertent uptake of shallow carbon acceptors by the GaAs melt from the crystal growth ambient.
2. Experimental 2.1. Crystal growth Quantitative estimations of the concentrations of tin atoms, [Sn], in various parts of our crystals have been achieved by employing a radiotracer technique [3,5]. The tin dopant was labelled with a small quantity of 113Sn, a 0.39 MeV gamma-emitter with a half-life of 110 days. Growth was performed in a Cambridge Instruments MSR6/R high-pressure puller under a dry boric oxide encapsulant (water content 300 ppm wt). The —
charges were synthesized “in-situ” from high purity elemental gallium and arsenic [6]. One crystal, A952/R, was pulled from a gallium-rich melt (Ga/As = 1.05). A second crystal, A953/R, was pulled from an “arsenic-rich” melt (Ga/As 0.993). The third crystal, A984/R, was pulled from a “stoichiometric” melt (Ga/As 0.999). The charges for all three crystals were doped with milligram quantities of radioactive tin diluted with larger quantities of natural tin: 500 mg in the case of A952/R and A953/R and 150 mg for A984/R. The tracer component consisted of enriched “2Sn which had been neutron irradiated to yield an activity of 4.0 Ci/g for the isotope “3Sn. Crystal growth resulted in single crystals of 1 kg mass grown along (001) and doped to a carrier concentration of around 2 x 1016 cm3 for A952/R and A953/R at their seed ends. The seed end of A984/R was found to be high resistivity, becoming semiconducting for mass fraction g> 0.15. Details of the crystals and their growth are given in table 1. Each crystal was cut into a series =
=
Table 1 Details of crystal growth parameters, tin concentrations, carrier concentrations and amphotericity ratios of the GaAs boules Crystal No.
Fraction of melt solidified (g)
[Sn]X10~6 (cm3)
n xlO’6
A952/R Ga/As = 1.05 Natural Sn; 500 mg Radiotracer Sn; 2.4 mg
0.040 0.149 0.273 0.396 0.523 0.654 0.790
8.4 8.9 10.1 12.2 15.4 20.0 29.2
2.62 3.15 4.26 4.97 6.01 7.72 15.1
0.27 0.24 0.22 0.26 0.30 0.32 0.25
A953/R Ga/As = 0.993 Natural Sn; 500 mg Radiotracer Sn; 1.6 mg
0.058 0.180 0.313 0.450 0.596 0.774
9.8 10.75 12.24 14.95 19.98 32.8
3.68 4.97 5.46 7.61 10.5 18.2
0.25 0.20 0.23 0.21 0.22 0.23
A984/R Ga/As = 0.999 Natural Sn; 150 mg Radiotracer Sn; 4.2 mg
0.010 0.077 0.190 0.302 0.451 0.569 0.720
3.1 3.2 3.6 4.1 5.2 6.7 10.3
(cm
0.0 0.0 0.33 0.75 1.20 2.00 4.00
3)
Sn acceptor to Sn donor (amphotericity) ratio, f~
— —
0.17 0.16 0.20 0.22 0.24
MR. Broze! eta!.
/
325
Tin segregation and donor compensation in melt-grown GaAs
of (001) slices which were assessed for tin concentration, carbon concentration and electrical properties.
.“,,,
~,,,
~ ~
_•, ..~_4.
2.2. Tin concentration measurements (radiotracer counting)
Tin concentration measurements were per-
• .1
•~ ~ *, ~,
~
‘~# 4.,~g
#
, ~.
~
.~
~
.~
4. ~.
0.979.10~cm~ 17
formed on slices taken from ten sections of each crystal from the seed to near the tail. Each slice, of 1 mm thickness, was cleaved into samples of approximately 3 mm X 3 mm. This resulted in over 100 samples per slice. Each was loaded into an automatic gamma counter for a period of 10 mm.
-3
0.98-1.019.1017cn~3 Cm
‘
I2~
1.02-1.059.l0 1.06-1.099.1017cm~3
,,,
1.00(1.35max).1017cm3 (c)
/‘
*
f4.~ ~
Typical counts were of the order of iO~resulting in accuracies of 1% for each sample. A refer-
C,
—
ence solution made up from a weighed piece of the original 113Sn consignment allowed corrections for the half-life to be made as the measurements
* ~
‘ ~ .‘ .~ ~ ~
,, ~ 4. 4. 4.4. “4.4.
I
4.4.4.
17 -3 1.40-1.49.10 cm
7’
r
F.’
‘
‘
~
,~‘
‘ ,,
~
~ ‘~
I,
\
‘ “
.‘
,,
‘
I
‘‘
,,,,
,jI
‘
‘‘
,,,
‘
~,
f
J 8.40 -8.69.1016cm3 8.70- 9,99.1016cm3 9.00- 9.29 .1016cm~3 9.30 - 9.59 .1O~cm3 9.60(9.7lmax).1O’6cm3 (a)
/ ~
~.
.-
,
,
~
•1
E~J 2.6-2.79.1017cm3 ~J 2.82.99.1017cm3 3.O.3.19.1017cm3 3.2-3.39.1017cm~3 3.4(4.17max)1O17cm~3 (b)
1.50- 1. 59 .1017cm3 1.60- 1.69.1017cm~ 1.70- l.79.1017cm3 (d)
Fig. 1. Mapping of radio-tin distribution across wafers: (a), (b) A952/R: g = 0.13 and and 0.760.43 respectively; (c), (d) A953/R; g = 0.16 respectively.
proceeded. This solution also acted as a reference for the estimation of total tin content as a function of number of registered counts. Errors in making up this solution, together with those in weighing the milligram quantities of “3Sn tracer, constitute the major source of systematic error in the data; we estimate this to be 5% for the present work. After radiotracer measurements on samples from a particular slice were completed, a mapping of [Sn] over the slice was obtained. Two such mappings are presented in fig. 1 for slices taken from near the seeds and tails of A952/R and A953/R. Mappings from A984/R were similar. The mapping of [Sn] in (001) slices as demon-
strated in fig. 1 indicates a nearly radial increase of about 15% from the centre towards the periph-
326
M.R. Broze! et al.
/
Tin segregation and donor compensation in me!t-grown GaAs
ery. However, within the central 80% of each slice, [Sn] is uniform to within 5% of the mean. 2.3. A utoradiography
Whilst gamma counting measurements provide quantitative data for several samples taken from a
single slice, no information on fine scale spatial changes of [Sn] can be derived because of averaging effects. Autoradiography of slices before cutting can give this information, together with evidence of precipitation of second phases. Fig. 2 shows typical results from A953/R. For the majority of each crystal good homogeneity of [Sn]
Fig. 2. Autoradiographs of wafers from A953/R (As-rich): (a) g = 0.6: (b) g
=
0.8; (c) g = 0.9
MR. Brozel et a!.
/
Tin segregation and donor compensation in melt-grown GaAs
is evident, with no evidence of any anomalous segregation due to facet formation. (Indeed, a central facet is not expected for <001) growth). However, a tin-rich second phase is present near the tail sections of each crystal (at g ~ .85 for A952/R and at g ~ 0.9 for A953/R). The onset of two phase growth seen at g 0.9 (A953/R) around the periphery of the slice is consistent with the slightly concave growth interface, =
2.4. Carbon concentration measurements
Because the seed end section of A984/R was of high resistivity (see next section), samples could be assessed for carbon concentration, [C], using localised vibrational mode (LVM) absorption without artificial compensation [7]. Two sections of 5 mm thickness were polished on both sides and the infrared absorption measured between 700 and 500 cm’. An absorption peak due to CAS acceptor centres was observed at 580 cm’. Using the calibration of Brozel et al. [8], the concentration of shallow carbon 3acceptors estimated be in thesewas sections. The tocon5 ±1 x 1016 ofcm centrations the major donor impurities, silicon and sulphur, are estimated to be around 1 x 1015 cm3 typical values for LEC GaAs grown under dry boric oxide while the only other major contaminant is expected to be boron [9] at concentrations of up to 1017 cm3. LVM measurements indicate that these substantial concentrations of boron do not reveal themselves in the form of absorption peaks due to isolated boron atoms, either as isoelectronic BGa centres or as electrically active BAS antisite defects. Because BAS is the only known electrically active centre is as-grown material and this centre is absent in our crystals, we assume that the only significant electrically active impurity species present are Sn and C. —
—
327
crystals is 0.24 (with a standard deviation of 0.03) nearly identical to that for both LPE- and VPEgrown crystals which are both n-type with NA/ND 0.25 [10] (where NA and ND are respectively the acceptor and donor concentrations). This implies that if Sn~ais the dominant donor, Sn~cannot be a significant acceptor since the ratio of these two entities should depend strongly on the arsenic activity in the molten phase and would then be markedly different (typically by a factor of> iO~) in LPE, VPE and LEC growth. Hurle [10] has shown that the matter is resolved if SnGaV~ais assumed to be the dominant acceptor. Adopting this model we can write for the total tin concentration in the crystal [10]: ~ [Sn~a] + [SnuaV~a] —
=
K [1 +
=
~
~t
p~]
[Sn I.] P~(’~2/n81,
(1) where K and K are combinations of some mass action constants and activity coefficients as explained in ref. [10]. ~As2 is the partial pressure of arsenic dimers in equilibrium with the arsenic melt and n81growth is the electron concentration in the crystal at the temperature. For the relatively low doping levels with which we are here concerned: ~ (2) where I~, is a further mass action constant [10]. The concentration of tin in the melt in the present experiments is very small (~ 0.1%), so that we can take the activity coefficients embedded in K and
~
=
—
K to be constant. Further we can express the
dependence of ~As on melt composition as equal to that for a binary melt (i.e. containing no tin). This has been shown by Brozel et al. [14] to be given by: P~
0.75 (1
=
+ 4.9XAS)
(3)
where XAS is the concentration of arsenic in the melt in excess of the congruent concentration. Substituting eqs. (2) and (3) into eq. (1) we obtain:
3. Segregation behaviour [Sn~] In principle, tin can be amphoteric in GaAs occupying a Ga-site as a donor 5I1~a and an arsenic site as an acceptor Sn~. However, the compensation ratio NA/ND in the present LEC
=
0.65KK~’~’2(1 + 4.9XAS)3”2(1 + .k~I~)
X [SnL]. (4) Noting that XAS << 1 we can approximate this: [Sns]
—
k 0(1 +
7.4XAS),
(5)
328
M. R. Broze! et a!.
/
Tin segregation and donorcompensation in melt-grown GaAs -
where 2(1 + k0
=
InC
5 /CL(O) ______________________________________
kA~)
5
,•\
0.65KK~//
is the segregation coefficient for a congruent melt. Hence: k = [SnS]/[SnL]
=
k 0(1 +
~
(6)
7.4XAS).
The measured quantity is the effective distribution coefficient (keff) and this is related to k by the
~\ ‘N \\
When k keff << 1, this latter equation can be approximated Burton, Prim to: and Slichter (BPS) equation [12].
Stoichiometric
3
—
keff = k e5~D,
rich
(7)
As -nc
~
Stope-0.994
h\
3v’~6~’~2
where v = growthboundary velocity, layer 8 = 1.6D’~ is an imaginary thickness, D = melt diffusion coefficient (taken to be iO~cm2 v = kinematic viscosity of the melt (taken to be 5 x iO~ cm2 s’) and w crystal rotation rate. In the present experiments v 9 mm h~ and ~o 2ir/10 rad s~, so that exp(v8/D) 1.6. The rejected excess component will also form a boundary layer obeying the BPS equation written for a solute with k 0. The excess arsenic concentration in the melt at the interface (XAS) at melt fraction g solidified is
2
\ 0
3 1n(i-g)
Fig. 3. Sheil plot for the 3 crystals. The dashed line has a slope of —0.994
=
—
k —1.
=
=
=
=
The intercepts on the ordinate, interpreted as values of In keff show that, as predicted by eq. (6), k is greater for the stoichiometric and —
arsenic-rich crystals than for the gallium-rich one. However, the plots are not linear because of the
X~ 5=exp(v6/D)X~5(1—g),
(8)
-InCs/CL(0)
where XL is the excess arsenic concentration at g = 0. As shown in a companion paper [14], insert-
5
\
~... •~
ing this into the Scheil equation yields: C~ ln~C(0) ____
ji
° (1—koeff )ln(1—g)+A(g), =ln keff~
\\
(9) where k~f=k0 exp(~),
Stoichiom~ 3 ~rich
v8/D, A(g) = 7.4 exp(~)X,~5(1 — k0 exp(~))/(1 — g). =
4
The third term on the right-hand side of eq. (9) represents the correction to the Scheil equation due to the non-congruency of the melt. A Scheil plot with A(g) = 0 for the three crystals is shown in fig. 3.
-
ri (I - g).
A (g)
Fig 4. Modified Scheil plot with the coefficient of 4(g) chosen for each crystal to give a least squares fit to a line of slope 0.994 (see text).
M. R. Broze! et a!.
/
329
Tin segregation and donor compensation in melt-grown GaAs
failure to include the A(g) term from eq. (8). Consequently the data were re-analysed by obtaining for each crystal a least squares fit to a line of slope —(1 0.006) = —0.994 with XAS and ln k0
1fl(Cs/CL(0))
—
as fitting parameters. The results are shown in fig. 4. The initial arsenic concentrations in the melt were determined by measurements of the weight loss assumed to be solely of arsenic. From this and the fitted values of XAS the (initial) arsenic concentration is excess of the congruent composition the deviation of the congruent composition from the stoichiometric composition (12) is obtamed. —
—
—
Ga-rich
12
=
[A5LI
—
0.5
—
X,~5.
(10)
The values of 17 obtained for the three crystals are 0.6%, 0.1% and 0.1% respectively (all on the galhum-rich side). These are unrealistically large values and this is discussed below. (Within experimental limits one would expect 12 0.) The values obtained for k0, the segregation coefficient for a congruent melt, differ somewhat, (The three lines in fig. 4 should have been coincident.) Accordingly we seek to obtain the best single line fit to all the data by taking in k and 12 as fitting parameters. The result is shown in fig. 5 corresponding to 12 = —0.003 (i.e., 0.3% to the Ga-rich side) and —
~
ic’~metnic
2 0
I
I
I
1
2
3
- ln(ig) . A (9) Fig. 5. Modified Scheil plot with single values of Q and In k0 as fitting parameters and with a slope of (k~1~ —1) for all 3 crystals (see text).
that, if we assume a linear relationship between Ga removal and water content, the expected shift in [A5L] would be 0.3%. This is exactly the change in [AsL] required to give 17 0 from an analysis of the data in fig. 5. —
=
keff = 6.4
x iO~
=
exp(1.~)k0,
so that k0 = 4.0 X iO~. We return now to the unrealistically large value of 17. A similar result was obtained by us with Cr-doped GaAs [14]; in these experiments involving nine crystals the average apparent value of 17 was 1.7%. An explanation for this was provided by very recent work by Emori et al. [15], whose results imply that the addition of 2000 ppm of water to the boric oxide encapsulant removes Ga preferentially from the melt by an amount sufficient to change the melt stoichiometry (i.e. to increase [A5L]) by 1.7%. Our Cr-doped crystals were in fact grown under encapsulants containing at least that amount of water and so the anomalously large apparent value of 12 for the Cr-doped crystals is explained, The present Sn-doped crystals were grown under much drier boric oxide (300 ppm water) so
4. Carrier concentration Room temperature Hall-effect measurements were used to obtain both carrier concentration and carrier mobility data. Three small samples of 5 mm x 5 mm were selected from slices taken adjacent to those used for the radiotracer determinations. They were cut into “clover-leaf” pieces and pure tin contacts alloyed to the surface under a reducing atmosphere. The Hall factor was taken to be unity. The data thus obtained for each slice were averaged and are presented in fig. 6 and in table 1. The carrier concentrations increase along the lengths of the boules (except for A984/R which exhibits a substantial region near the seed which is high resistivity) while the electron mobilities decrease. In fig. 6 the carrier concentrations n
330
M. R. Broze! et a!.
/
Tin segregation and donor compensation in melt.grown GaAs
6cm_3)
20 n(slOl
Ga -rich As-rich
/
0.3
/
Stoichiometric
./r
15
~/ =
a
/
/
.
.
1
0.2
.
Ga-rich As-rich Stoichiometnic
‘
//
35. a
3
0
3
0
I
I
I
10
20
30 ( x1016cm3)
[Sn]
0.2
0.4
0.6
0.8
g
1
Fig. 7. Plot of $, the calculated ratio of tin-related acceptors to donors as a function of fraction of melt solidified, g. Dashed line is the mean value.
Fig. 6. Plot of room temperature carrier concentration n versus
the arsenic site substituent Sn~
total tin concentration in the 3 crystals.
of the three crystals are plotted as a function of tin content. Values of n are proportional to [Sn], indicating that a constant proportion of [Sn] produces free electrons. The negative intercept on the carrier concentration axis suggests that there is a background 3. acceptor of fig. [A—] The slopeconcentration of the line in 6 =is 1.6 lessx 10i6 than cm unity implying additional compensation due to tin-related acceptors. If we assume that: 5MG a J ~SnGVG LA j, t~ll) a aI1 + 1 r F _1 —
n
=
—
—
1
then, from eqs. (1) and (11), we obtain the amphotericity ratio $: F~
$=
v
L nGa Gal
[Sn~a]
5is not present in significant concentration. It does not depend either on position down the crystal (i.e. on the time for which crystal was exposed to high temperatures) and hence is not likely to be a result of post-grown annealing. From the slope of fig. 6 a “carrier concentration effective segregation coefficient” for a congruent melt is: k~ is 1 k 0 F5 1 = ~ X L n LI I n5 which compares with the value obtained by Mullin stoichiometry. et al. [2] of 5.2>< i0~ for a crystal of unknown Values of 77 K carrier mobility ~i as a function of carrier concentration are presented in fig. 8 for =
=
F 5 =
~SJ
1
[Sn~1
—
—
I
A~11
[A
—
~
,
(12)
I~
This is plotted against fraction of crystal solidified, g, for each of the three crystals in fig. 7 from which it can be seen that the ratio of tin-related acceptors to donors is about 0.24 ±0.03. This ratio does not appear to depend significantly on the stoichiometry of the crystal in agreement with Hurle’s model [10] supporting the postulate that
crystals A952/R Also plotted fig. 8 (dashed line)andareA953/R. the theoretical curves on of Walukiewicz et al. [4,13] for a compensation ratio of NA/ND = 0.24. It can be simply shown that NA
/3n + [A] =
,~
+
[A]
3
1
Taking $ = 0.24 and [A ~] = 1.6 X 1016, and using the table of Walukiewicz et al. [13], we can plot a theoretical curve p. = p.(n) where for each value of
M. R. Broze! et a!.
/
Tin segregation and donor compensation in me!t-grown GaAs
3 ).Lx10 (cm2V~s~)
I
331
I
\ \
a
6
\
1
• Stoichiometric Ga-rich • As—rich
‘
°io15
io17
io16
n (cm3)
io18
Fig. 8. Mobility versus carrier concentration at 77 K. Data for the three crystals. The dashed liuie is the value predicted by Walukiewicz et al. [4,13] for fixed NA/ND = 0.24. The full line is for values of NA/ND given by eq. (13) with /~ = 0.24 and
[A] =1.6X10’6cm3.
n, NA/ND is given by eq. (13). This is shown in
fig. 8 (solid line) from which it can be seen that fair agreement is obtained. In particular the the-
We observe this up to a total [Sn] 3 x 3 10i6 cmof corresponding to a net tin donor concentration 2 X 10i6 cm This fixes the3carbon acceptor conin marked contrast centration at 1.6 x 1016ofcm to our measured [CAS] 5>< 1016 cm3 using the LVM calibration of Brozel et al. [8]. There are two possible explanations for this discrepancy; either there exist extra donors in the GaAs which act to compensate the carbon acceptors, or the LVM calibration is inaccurate at the relatively high carbon concentration. Concentrations of acceptors other than carbon would lead to the discrepancy being worse. The presence of donors at a level of 2 x 1016 cm is unlikely for two reasons. Firstly, this concentration is rarely encountered in undoped GaAs analysed by SSMS or SIMS and, secondly, the presence of this concentration of donors would render undoped GaAs with low [C] n-type and of low resistivity; this is not the case. We conclude, therefore, that the presence of other donor species is improbable and that the LVM calibration predicts too high values of [C]. This is discussed in detail elsewhere [11]. —
~.
ory predictsThe theresults observed maximum as n is decreased. shown in fig. 8inarep. broadly in agreement with the data on melt grown Sndoped GaAs obtained by Mulhin et al. [2]. These authors similarly observe a mobility maximum but their results suggest slightly larger values for both $ and [A—]. We have shown recently [13] that Sn-doped InP is incompensated and that the predictions of mobility theory are seriously in error for this material. In contrast, Sn-doped GaAs is compensated by Sn-related acceptors ($ — 0.24) and the predictions of mobility theory [4,13]are broadly compatible when the effect of residual carbon acceptors are also taken into account. The dominant background acceptor in undoped LEC GaAs is known to be carbon [16]. Such material is semi-insulating due to the presence of the native deep donor defect, EL2. Thus in our material the Fermi level will be pinned near the centre of the band gap and the material will be high resistivity if [EL2]> [CAS]~ [Sn~a]
—
[SflGa~’~5aL
5. Conclusions There are two conclusions of importance in this work: firstly, as was observed with the
332
MR. Brozel eta!.
/
Tin segregation and donor compensation in meh.grown GaAs
chromium-doped gallium arsenide [14], the modified Sheil plots indicate that almost all melts appear to get more arsenic-rich as growth proceeds. Recent work by Ernori et al. [15] strongly suggests that this is due to uptake of Ga from the melt by the residual water in the encapsulant. Radiotracer measurements are shown to provide a valuable method for inferring melt stoichiometry. Secondly, unlike tin in indium phosphide [3] tin-doped gallium arsenide is markedly cornpensated. Significantly, the compensation ratio NA/ND = 0.24 ±0.03 is identical to that found in LPE and VPE material [10], which strongly mdicates that the compensation is due to the presence of tin—acceptor complexes.
Acknowledgements The authors are grateful to J.N. Crookes for the provision of the radiocounting facilities, to R.M. Ware for valuable discussions, to G. Davis for growth of the crystals and to B. Waldock for making the electrical measurements.
References [1] D.T.J. Hurle, J. Phys. Chem. Solids 40 (1979) 627. [2] lB. Mullin, (1980) 625. A. Royle and S. Benn, J. Crystal Growth 50 [3] MR. Brozel, El. Foulkes, I.R. Grant, L. Li, D.T.J. Hurle and R.M. Ware, J. Crystal Growth 70 (1984) 191. [4] W. Walukiewicz, L. Lagowski, L. Jastrzebski, M. Lichtensteiger and H.C. Gatos, J. Appl. Phys. 50 (1979) 899. [5] MR. Brozel, B. Tuck, D. Rumsby and R.M. Ware, J. Crystal Growth 60 (1982) 113. [6] D. Rumsby and R.M. Ware, in: Proc. 9th Intern. Symp. on GaAs and Related Compounds, Oiso, 1981, Inst. Phys. Conf. Ser. 63, Ed. T. Sugano (Inst. Phys., London—Bristol, 1982) p. 573. [7] R.C. Newman, Infra-Red Studies of Crystal Defects (Taylor and Francis, London, 1973). [8] MR. Brozel, lB. Clegg and R.C. Newman, J. Phys. Dli (1978) 1331. [9] C.G. Hopkins, yR. Devine, C.J. Blattner, CA. Evans, Jr. and TI. Magee, AppI. Phys. Letters 36 (1980) 989. [10] D.T.J. Hurle, J. Phys. Chem. Solids 40 (1979) 639. [11] MR. Brozel, E.J. Foulkes, R.W. Series and D.T.J. Hurle, Appi. Phys. Letters 49 (1986) 337. [12] J.A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys. 20 (1953), 1987. [13] W. Walukiewicz, J. Lagowski and H.C. Gatos, J. Appl. Phys. 53 (1982) 769. [14] MR. Brozel, I.R. Grant and D.T.J. Hurle, J. Crystal Growth 80 (1987) 315. [15] H. Emori, T. Kikuta, T. Inada, T. Obokata and T. Fukuda, Japan. I. AppI. Phys. 24 (1985) L291. [16] LB. Ta, H.M. Hobgood, A. Rehatgi and RN. Thomas, J. AppI. Phys. 53 (1982) 5771.