The defect structure of CuInS2. part II: Thermal annealing defects

J. Phys. Chem. Wi& Priati

in Ofcar

Vol. 51. No. 1. pp. 1-10.

0022.3697190

1990

9

Britain.

$3.00 + 0.00

1990Pc?eam0nRarplc

THE DEFECT STRUCTURE OF CuInS,. PART II: THERMAL ANNEALING DEFECTS H. Y. UENG~and H. L. HWANG~ TDepartment of Electrical Engineering, National Sun Yet-sen University, Kaohsiung, Taiwan 80424, Republic of China $Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043. Republic of China (Received 29 November 1988; accepted in revisedform 9 August 1989)

Abstract-Combining the studies of electrical, photoluminescence and stoichiometric analyses, the incorporation of indium and sulfur into CuInS, was studied, and the results were correlated with calculated data based on defect chemistry. The carrier concentration varies as K’Pjf + K”p$. The indium atomic inter-diffusion in CuInS* is dominated by (1) a vacancy mechanism at low indium pressure, and (2) an interstitial mechanism at hi8h indium pressure. The carrier concentration introduced by indium annealing depends on the stoichiometry of each sample and the annealing period, and these two factors may become unimportant in the high indium pressure region. Keywords: CuInS,, indium annealing, sulfur annealing, defect model.

1. INTRODUCTION The Cult& crystals grown in excess indium were n-type [I] and those grown in excess sulfur were p-type [Z]. Both p- and n-type materials could be made by annealing under maximum and minimum sulfur pressure [2]. Native point defects in ternary chalcopyrite semiconductors have been discussed by several authors flO-221, and the electrical properties of CuInS, are controlled by native defects resulting from deviations from the stoichiometric composition of the materials. The p-type conductivity is governed by the cation vacancy or by the anion vacancy and cation interstitial [3], It is convenient to control the conductivity type and carrier concentration by adjusting the stoichiometry and molecularity with respect to sulfur and indium. In previous studies [lO-221, no quantitative investigation was carried out on the carrier type variation and concentration as a function of deviation from stoichiometry. Look and Manthuruthil [4] obtained p-type behavior by annealing at 500°C in a sulfur overpressure, and they obtained n-type characteristics by annealing in indium and excess CuInSr powder in the 725-8OO”C temperature range. Masse et al. [S] reported that the CuInS, crystals were anneaied in: (i) indium (700°C 48 h); (ii) indium (or indium + sulfur), then sulfur (700°C. 40 h); and (iii) indium + sulfur (7OO”C, 48 h), and two types of luminescence spectra were observed. They proposed that n-type conductivity is due to the compensation of the sulfur vacancies by copper vacancies. The results of sulfur annealing reported by several authors [4-l, are given in Table 1. It is noted that a

significant change in electrical conductivity occurs upon sulfur annealing. However, complete descriptions of the dominant defects and their dependence on the annealing conditions are still lacking. In this paper, we report the effects of indium and sulfur annealing in CuInS, under different pressure of indium and sulfur. Following the approach of Kroger et al. [23], models of the defect structures upon indium and sulfur annealing are proposed, which can explain the observed properties and their relationships to the annealing conditions.

2. EXPERIMENTAL TECHNIQUES The CuInS, crystals were grown by the traveling heater method (THM) [9]. N-type single crystals having approximate dimensions of 5 x 5 x 1.5 mm3 were used for the annealing studies. The crystals were heated in an evacuated quartz ampoule in a two-zone furnace, and elemental indium or sulfur of 6N purity was kept at the lower temperature end. The totai pressure in the ampoule depends on the annealing temperature of the indium or sulfur. For indium annealing, the following formula was used to calculate the total pressure [24]: log Pt, = ( - 0.2185 x 55633.4/T) + 7.926809

(1)

with Pr,, in torr, and T in K. Table 2 depicts the annealing conditions and electrical properties of some in&urn-annealed CuInS,. The experimental details of compositional analysis, photoluminescence and electrical measurements, have been reported in our previous papers [8,9].

2

H. Y. UENGand H. L. HWANG Table 1. The electrical properties of sulfur-annealed CuInS, reported by several authors Growth method

Annealing condition

Conductivity type

Resistivity (G-em)

Mobility (cm* v-’ s-1)

Melt Melt Melt Melt Melt Melt

450°C SSO”C 650°C 550°C 0.75 atm

n P n P P

1.7 x 10’ 69 78 4.9 x 10’ 4.6 -

22 18
1.6 x IO” 5.2 x 10”

E

Ps, min. Ps, max.

P P

5.0 1.0

200 I5

3.0 1.0 x IO” 10’6

42

E

0.3 14 atm atm

P B

--

16.4 6.3

2.2 1.8 x 1Ou 10’6

18

Table 2. The electrical properties of indium-annealed Growth condition

Annealing condition

Melt-growth cooling rate 2-5°C h-’

In, 700°C 6Oh In, 725°C 6Oh In, 745°C 6Oh In, 755°C 6Oh In, 775°C 6Oh In, 800°C 6Oh

Melt-growth 118O”C, 48 h Melt-growth I lSO”C, 48 h CVT CVT

Carrier con&m-3)

5.4 X1016 7.9 x 10’6 1.0 x toi*

CuInS, reported by several authors Mobility @nrv-’ s-‘f

Refs

4.0 x 10”

0.7

4

n

3.7 x 1ou

160

4

n

1.2 x lOI4

30

4

n

4.4 x 1O’J

60

4

n

2.9 x 10”

150

4

n

3.5 x LO”

75

4

-

In, 700°C In + S 700°C In + Cult& powder 6OO”C,48 h InCl,, 600-700°C

A: TH-3208

-

O.Ol(R-cm)

-

5 25

I (R-cm)

-

6

-.*-

. I#

I 1;

6

I

I

105

1iY

Indium Fig. I. The carrier concentration

4 4 4 4 4

n or p (cm-‘) or resistivity (S2-cm)

Type P

e before annealing

Refs

I 16

pressure

I

I to2

lb

100

(otml

in CuInS, samples annealed under different indium pressures.

Defect structure of CuInS, Table 3. The stoichiometries and mokularitia annealing Sample No.

3

of CuInS, before and after indium

Annealing

Ax

AY

Dominant defects

Before After

-0.0157 -0.0286

-0.0337 -0.0413

vs 1 *V,”

1 CuInS, 32-A

vs V,”

CuInS, 32-B

Before

-0.0121

-0.0208

vs VC”

After

-0.023

-0.0291

vs 9VC”

Before

-0.018

-0.007

In,, qVcu

After

-0.043

-0.032

In,. VP”

1

l

CuInS, 29-A

3. RESULTS AND DISCUSSION

3.1. Electrical properties 3.1.1. Indium annealing. The carrier concentration as a function of indium pressure was determined and is shown in Fig. 1. The curves A, B, and C correspond to different samples at the same indium annealing conditions. From the determined (AX, AY) values (Table 3). we can calculate the dominant defects and their concentrations for the samples before and after the last annealing step. The dominant defects in samples A and B are Vc, and Vs. The dominant defect structures of samples A and B were apparently not influenced by the relevant defects introduced by indium annealing in the low P,, region. But in sample C, since the concentrations of the various defects are comparable, a change in [e’] can therefore be easily brought about during the annealing process. Thus, 16-

I

I

I

I

In- annealed

CulnS2

I

I

the difference in curves A, B and C can be interpreted by the different dominant defect structures. The indium annealing experiments performed by Look and Manthuruthil [4] showed that the carrier concentration was drastically increased from 1.2 x 10’4cm-3 to 3.5 x 1O”cn1-~ (Fig. 1). The carrier concentrations are comparable with our experiments in the high P,, region (75O-NO”C), which means that in the high temperature (high P,.) range the stoichiometry might not be the dominant factor. Typical examples of electrical measurements for the indium-annealed samples with the indium pressure between 1.25 x lo-’ and 1.05 x 10-r atm are shown in Fig. 2. The differential method of Hoffmann [25] was used to analyze the multi-defect levels. The maxima in the -kT dn/dE, vs (EC-E,) curves can be seen from Fig. 2 and can be used to determine the defect levels and concentrations of the relevant

17 10 I

I

I

I

P,,_,~3.80~16~ atm

‘5_

L,

3_

2 EC-Ef

(meV)

Fig. 2. The plots of -kT b/d&,

EC - Ef (mev)

as a function of EC- E, for two indium-annealed

CuInS, crystals.

I

4

H. Y. UENG and H. L. HWANG Table 4. The donor’s ionization energies of CuInS, deterr&ed from the Hall measurements

Ann. P,. bW

As-grown 1.25 x IO-’ 3.80 x lO-4 4.34 x 10-J 3.94 x IO-2 1.05 x IO-’

EC - 4 W

[*I1 (cm-7

0.038 0.037 0.042 0.036 0.032

2.8 x10” 8.0 x 10” 2.0 x 10” 3.5 x IO” 1.4 x 10’6

U&l

e “;kE2

b=-‘)

0.074 0.074 0.070 0.070 0.067 0.063

defects (Table 4). The results show variations of the energy levels from EC- 0.042eV to E,-O.O32eV, EC - 0.074 eV to EC - 0.063 eV and EC - 0.152 eV to EC - 0.145 eV with increasing indium pressure. It is noted that all these defect levels are distributed separately below the conduction band, and so the interactions among the defects would be small. Hence, the results may be used to interpret the various defect levels related to the inter-diffusion of the indium atoms. The Hall mobility for samples annealed at different indium pressures is plotted in Fig. 3. For the lower indium pressure the mobility drastically increases with P,, because (i) the number of inter-diffusion indium atoms is still small. and (ii) in view of the formation energy of the defects [26], In, and V,, may associate to form a complex defect or In,-” during the annealing process, which would reduce the number of scattering centers. The mobility decrease as a function of increasing indium pressure is the result of increased scattering by impurities and native defects such as point defects, associates and precipitates. Therefore, the mobility decreases with increasing indium pressure, but should level off as the concentration of the incorporated species approaches the saturation solubility. For the as-grown CuInS, single crystals, the temperature dependence of the mobility was analyzed by taking into account the scattering of the charge

1.0 x 7.2 x 1.5 x 7.1 x 1.65 x 1.0 x

IO” 10” lOI IO’J lOI IO”

EC - 4

[*It (cm-?

~41

(eV)

(~-‘I

0.152 0.148 0.145 -

3.0 x 10” 8.0 x IO” 1.2 x 10” 1 -

4.0 x 9.0 x 1.43 x 9.0 x 2.0 x 1.14 x

10” IO” IO” IO” 10’6 10”

carrier by ionized impurities, by acoustic polar, and non-polar optical modes and by pair scatterings. For indium-annealed samples, indium inter-diffusion would decrease the compensation ratio by increasing the donor concentrations such as In,, Incu and decreasing the acceptor concentration of Vc,. Therefore, the contribution from pair scattering can be neglected here. In addition, piezoelectric scattering and neutral impurity scattering are also neglected since their contributions to the total mobility are insignificant. In the present case, contributions from scattering by ionized impurities, acoustic phonons, and polar optical modes were examined following the considerations described in our first paper. The total mobility was calculated by using Mathiessen’s approximation [41 as WY’= II,‘+

U,‘+

UiL

(2)

and the results of calculations for the as-grown and indium-annealed crystals are shown in Figs 4 and 5. The results indicate that the compensation between donors and acceptors was removed by the sequential annealing steps, and the increase of the donor concentration by incorporating the indium atoms plays a key role in the ionized impurity scattering, and it is the dominant factor in the determination of the electron mobility in the low temperature region.

60--

Indium Pressure

(otm 1

Fig. 3. The Hall mobilities for samples annealed in different indium pressures.

Defect structure of CuInS,

III,

’ ’ ’ ’ ’ \\\.

b-grown

CuIr62

I

IllIll

I

\,;,

.

I

I’

1

lIttIll

I

1

sxrd 102 Temproture

,

,I‘U

I

I

i

,llif

I

i

( K)

Temperoture

rlltltl_

5x10* 1

5x101 w2

/

5x102

( K)

Fig. 4. The results of calculated and measured mobilities for as-grown CuInS, crystals.

Fig. 5. The results of calculated and measured mobilities for indium-anneakd crystals.

3.1.2. Wfur annealing. Figure 6 shows the changes in resistivity for CuInS, samples annealed in sulfur vapor. The initial resistivity of the sampIes was about 3 x lO’R-cm. It was found that samples with lower resistivity could be obtained by prolonged annealing at elevated temperatures. Since the predominant defect pairs for as-grown samples are sulfur and copper vacancies, and the concentration of sulfur vacancies is greater than that of the copper vacancies in n-type C&S, crystals, and during the sulfur annealing the con~ntration of copper vacancies increases and the sulfur vacancy decreases, the n-type conductivity

would then decrease and the crystals would become more heavily compensated. After further sulfur annealing the donor defects such as In,,, In, and V, are almost removed, and the copper vacancies are then responsible for the carrier concentration and conductivity. The carrier concentration and conductivity type at different sulfur annealing conditions are summarized in Table 5. The carrier concentrations and mob&ties of our samples are basically consistent with other reports as shown in Table 1. The differen~s among the results are possibly due to the variation of the AX

Anneoling

period

(hrs)

Fig. 6. The changes in the resistivity of CuInS, samples by annealing in sulfur vapor.

H. Y. UENG and H. L.

HWANG

Table 5. The electrical properties of sulfur-annealed CuInS, Substrate temp.(T)

Sulfur temp.(T)

550 550

250 350

750

450

750 750

700 750

Conductivity type n n

Carrier Conc.(cm-‘)

P

4.1 x lOI

48.6 8.6

P P

8.6 x 10” 1.68 x 10” 3.4 x IO”

9.7 11.3 10.7

trations. As shown in Table 5, the sulfur-annealed samples were p-type and could have an effective carrier concentration as high as 3.4 x lOi cm-‘. The p-type conductivity is produced by cation vacancy and the anion interstitial such as V,, and Si. Referring to the formation energies of V,, (2.6 eV) and Sei (22.4 eV) in CuInSe, [26,27], and since the formation energy of Si should be larger than that of Se, due to their ionic nature, we conclude that the copper vacancy is the dominant defect responsible for the p-type conductivity. The concentration of holes is related to the concentration of ionized species according to the simple formula P = WN,IN,-

IO” - IO” 3.0 x 10’5

P

and AY values, which will drastically change the defect pairs in CuInS, and the corresponding concen-

(3)

I)exp( - E,lkT),

where E,, is the ionization energy above the valence band edge and N, is the effective density of states in the valence band equal to 2(2rrm*kT/h2)“2. The plot of log PT-‘.” vs 1000/T for P-type sulfur-annealed

Mobility (cm? V-l s-l) 39.1

samples is shown in Fig. 7. The linear dependence indicates the non-degeneracy and low degree of compensation in our sulfur-annealed CuInS, crystals [4, 191. Under prolonged sulfur annealing, we can determine the ionization energy of the acceptor (Fig. 7) to be 0.11 eV, which is in agreement with the result reported for the copper vacancy by Binsma [19].

3.2. Photoluminescence 3.2.1. Indium annealing. Figure 8 shows the 14 K photoluminescence spectra for samples grown by the THM and annealed in indium vapor for a period of 148 h. A comparison of the curves shows that the predominant emissions are changed after the annealing, and the change in the emission intensities of the donor-acceptor pairs would be indicative of the fact that a change has been made in the defect structure by the indium annealing process. The enhancement of the emission intensity at 1.41 and 1.36 eV, indicates that In, and Incu are the most probable defects, and, after prolonged indium annealing, it is expected that the concentration of the copper vacancy decreases and those of Incu and In, increase. 3.2.2. Sulfur annealing. Figure 9 shows the 14 K photoluminescence spectra for samples grown by the THM and annealed in sulfur vapor. The photoluminescence spectrum of the CuIn$ sample PHOTON 1.6 I 1 TH-2905 As grown

ENERGY

(eV)

1.5 I

1.L I

-

In annealing----

I

2

I

L

I

6

I

6

I

10

I

12

I

14

1000/T (K-l 1

Fig. 7. The plot of In PT-“? vs l/T for p-type sulfur-annealed samples.

7500

7900

6300

6700

WAVELENGTH

9100

9603

(A,

Fig. 8. The photoluminescence spectra for as-grown and indium-annealed CuInS,.

Defect structure of CuInS, PHOTON ENERGY (eV 1 1.6 I

1.L I

l.5 I

1

7

yield an expression for [e’] and Ph, and [e ‘] could then be given as a function of P,,. The concentration of charged imperfections may be derived according to the scheme proposed by Kroger et al. [23] and Verheijen [I81 [v,] = [e’]-“P~~‘Kv, [In?]

= [e’]-“P,,K,,,

[In&r] = [e’]-‘P$‘KIwV [if;;‘] = [el+jPi!,’ KvCU

WAVELENGTH

(A,

Fig. 9. The photoluminescence spectra for as-grown and sulfur-annealed CuInS,.

annealed at a minimum sulfur pressure is basically similar to that of the as-grown samples. Tell et al. [2] proposed that the most probable acceptors in the sulfur-annealed CuInS, samples are the copper vacancies. The photoluminescence spectrum of the annealed samples (Fig. 9) shows the peak energy shifted to lower energy with reduced intensity. It is possible that the defect concentrations are reduced as a function of Psr during the annealing process, the average donor-acceptor separation, R, is then increased and leads to a shift of the emission peak and a decrease of the peak intensity according to the following relations [28]: hv = E, -(E,

+ Ed) + e’/cR

(4)

and IccR’exp(

-4xN,R’/3)exp(

-2Rla).

n=o,

1.2

(6)

m=O, l,2,3

(7)

m = 0, I, 2

(8)

j=O, I.

(9)

The indium inter-diffusion in CuInS, is determined by the dominant diffusion mechanism. Copper vacancies, sulfur vacancies and indium interstitials and associates of these species are important for the indium inter-diffusion mechanism. If we concentrate on single defects, we would have copper vacancies (VcU), indium interstitials (In) and indium at the copper sites (In-,) participating in the indium exchanges. At equilibrium the defect concentrations in CuIn& are determined by the interaction of the crystal surface with the vapor phase, indium diffusion in the bulk, and interaction of the bulk defects. The defects are related to each other by the following reaction mechanisms. Case I ZIn(g) + Cu,S * 2CuInSr + 3ne’ f 3Vl”

(10)

Case II ZIn(g) * CuIn& + V& + 2V;” + (2n - j)e’

(11)

Case III In(g) + Vi =J InTm + me’

(12)

In:” + V& * In:: -j

(13)

Case IV In(g) + Vi * In+ + me’

(14)

(In: +,) + In;: * (In:: ‘) + In:m

(15)

(5)

The samples which were under prolonged annealing at high sulfur pressure showed a shift of the peak position to higher energy (from curve B to curve C in Fig. 9). The shift of the emission peak indicates that the sample might have a defect structure of a different form, and the peak located at 1.437 eV might correspond to the transition from the conduction band to an acceptor level, which was assigned to the copper vacancy (191. 3.3.Model of the defect structure 3.3.1. Indium annealing. From electrical, photoluminescence and compositional analyses, the dominant defects in CuInS, crystals (n-type, indium excess) could be identified as V,, V,-. , In, and In,-,, . In general, for a well-defined system, the charged imperfection concentration may be expressed in terms of two variables such as [e] and P,,,, and substitution of them into the electroneutrality condition would

Case V In(g) + Vi” * In;’ + (g - n)e’

(16)

Case VI In, S3= 3/2S2(g) + 3V,+” + 2In,, + 3ne’.

(17)

Based on the defect formation energies reported by Neumann [26,271 and the formation energy of CuIn&, 6.54 eV, reported by Wiedemier and Santandrea [29], we can predict that: (i) cases I and I1 are less probable than cases III, V and VI in the indium annealing process because of the larger formation energy required for the diffusion reactions; (ii) because of its formation energy, case III is more probable than the other processes, and occupation of the interstitial sites is favored for the THM crystal

H. Y. UENG and H. L. HWANG Table 6. The relationship between [e’] and Pr, at different indium pressures Indium pressure:

Low pressure

Medium pressure

High pressure

KP p

K’P&’ f K”P?’ Ill

K”Pfi

Case IV

KP;R

K’p;;‘+

C&A

KP;:

K’P;;3 -k K”Pf*’

CaKS

Case III VI

K”P12

I”

K”P

I,z

KmP;i3

VI Where K = K&, K’ = K;,,

K” = K&.

(using indium solvent) and the non-stoichiometric compounds in the chemical diffusion reaction (at high In pressure); and (iii) case V is less important for two reasons, namely that a larger formation energy is required than for cases III and VI, and also the formation energy of In, is higher than that of In, because of the increasing ionic nature of CuInSr. Finally, if we assume that singly-ionized defects are dominant, then the carrier concentrations will he deduced from the electroneutrality equation and Brouwer’s approximation [30], and can he expressed in terms of P,, as follows. Case III [e’] + K&,Pfa + K;,nPfi3

+ K;,,P~f w

Case VI [e’] + K’vs Pr’3 In + Ki,,cu Pf6 + K;,.P$’ I . 0-N

fH-,?905(ofter indiumcnneo~ing) AX a-o.053 a=i :-0.018

tS$l

’

By solving the electroneutrality equation with Brouwer’s approximation [30], we obtain the reiationships between [e’] and PI, as listed in Table 6. By fitting the theoretical and experimental data (Fig. l), WC obtain two limiting cases, namely that case III is the dominant mechanism in the low Pi, region ([e’] _ Pia), and case IV is the dominant mechanism in the high P,, region ([e’] _ Pi:). These investigations represent two diffusion mechanisms in CuInS,, namely (i) a vacancy mechanism, a substitution reaction between indium atoms and copper vacancies (case III) [31], which is a the~odynamitally-controlled reaction, with a reaction rate that depends on the concentration of indium species and (ii) an interstitial or inte~titialcy m~hanism (case IV), which is a reaction-controlled case depending on the concentration of indium occupying the copper vacancy [3 I]. In addition, if the defects we considered are not almost all singly-ionized defects then the calculated results would deviate far from the experimental data; we can, therefore, conclude that the singfy-ionized states of the defects are the main species in CuInS: during the indium annealing process. We could then calculate the defect concentrations by our model derived in this work as shown in Fig. 10. 3.3.2. Surfur annealing. From electrical, photoluminescence and compositional analyses, the dominant defects in CuInSr crystals (n-type, indium excess) were identified as V,, VcU, Inj and In,,. For a we&defined system, the concentration of charged imperfections can be expressed in terms of two variables such as [h’] and P,,, and substitution of them into the electroneutrality condition would yield an expression for [/I’] and Ps2 and [h’] could then be given as a function of Ps2. The concentration of the charged im~rfections can be derived again according to the scheme proposed by Kroger ef al. [23] and Verheijen [18]. Iv:“] = [e’]-“P<“’ Kvs [In:“] = fe’]+“PS;3i4Kt, [In&‘] = [e’]-‘P<21’z K k” yV;i] = [e’]+jP~K&

Fig. 10. The calculated defect concentrations by our model as a function of Pi,.

n=o,

1.2

n = 0, 1,2,3

(21) (22)

l=O,

1.2

(23)

j=o,

1,2.

(24)

The sulfur atomic diffusion in CuInS, is determined

9

Defect structure of CuInS,

by the dominant diffusion mechanisms, and sulfur vacancies and sulfur interstitials and associates of these species are important for the sulfur atomic transport. If the native defects are responsible for the annealing, we have sulfur vacancies (V,), indium interstitials (In,) and indium at the copper sites (In,,) participating in the sulfur exchanges, and the equilibrium defect concentrations of CuInS2 are determined by the interaction of the crystal surface with the vapor phase, sulfur diffusion in the bulk, and interaction of the bulk defects. The defects are related to each other by the following reaction mechanisms: Case I 1/2S2(g)+V:“+ne’*Ss

(25)

measurements, we can conclude that the copper vacancy is the dominant defect and is responsible for the P-type conductivity in the sulfur-annealed reaction. The carrier concentrations deduced from the neutrality equation and Brouwer’s approximation can be expressed in terms of Psr as follows. Case I [e’] = K,Ps, 1;2(n+1) + K2P(S2m-#n+lWo+l) f +

Case

IV

K,p$-(n+I))/?(fl+I)

_

[h’] = K, PC-W+

(or Case III)

Case II 3/2&(g) + 2In:” + 2me’ 2 In,&

(26)

Case III 3/2!!+(g) + 2In,$ + 2(1 -j)e’ e In,& + 2V&

(27)

Gz In, S, + 2V& + 2( 1 - j)h’

(28)

Case IV 3/2S2 (g) i- 2In;J

Case V 1/2&(g) + Vi $G S;’ + kh’

K*pg-3v+I~)~Yi+Il

+

K

(30)

Case VII 3/2&(g) + 2In,, G In* Sj + 2VGm+ 2mh’.

_

pcl-Z(j+lW4j+ s2

I)

K&~+“.

(33)

Although theoretical investigations have laid down the foundations for the sulfur annealing studies, our experiments were hampered mainly because the dependence of the carrier concentration on the sulfur pressure was difficult to obtain.

4. CONCLUSIONS (2%

Case VI l/Z!&(g) + 2Cu,, * Cu, S + 2V& + 2jh’

11114(i+ II

+

3

(32)

&pf;+l)-2,WYfi+I)

(3 I)

Based on thermodynamic considerations, reactions I, II, III are likely to occur in the sulfur annealing process because the formation energies are smaller than those of the reaction between sulfur atoms with lattice atoms to create copper and/or indium vacancies. A comparison of the formation energies among cases I, II and III, suggests that case I would be the most probable reaction to occur in the sulfurannealed samples. However, the defect concentrations present in reactions I and II are reduced more than those of case III after a period of the sulfur inter-diffusion reaction. Finally, reactions IV, V, VI and VII are likely to occur and show p-type conductivity after prolonged sulfur inter-diffusion reactions, and case IV could then become the dominant reaction. Furthermore, the case V reaction could still be one of the dominant reactions, and the most probable defects existing in the crystals would probably be sulfur interstitials and copper vacancies, which is consistent with the p-type conductivity. By comparing their formation energies (22.3 eV for Si and 3.67eV for Vc-), we would predict that the most probable defect present in the sulfurannealed samples is the copper vacancy. By correlating the results of photoluminescence and electrical

Our study of the isothermal annealing of CuInS* yielded the following conclusions: (1) The defects considered are all singly ionized species. (2) At low P,,, the vacancy mechanism is dominant in the diffusion process, and is a thermodynamically controlled case. The carrier concentrations were calculated to have the relation [e’] w Pi;‘. (3) At high Pr”, the interstitial or interstitial mechanism becomes dominant in the diffusion process, and it is a reaction controlled case. The relation is [e’] _ PiA2. (4) The increase in the carrier concentration by indium annealing depends on the initial stoichiometry of each sample; however, this factor may become unimportant in the high temperature region. (5) We may conclude that the copper vacancy acts as the main acceptor at the maximum sulfur pressure (or saturation in sulfur pressure) annealing, and the sulfur vacancy and the copper vacancy are responsible for the minimum sulfur pressure annealing. Acknowledgement-The financial support of the National Science Council of the Republic of China is acknowledged.

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