Iodine as a donor in CdS

J. Phys. Chem.Solids, 1973,Vol. 34, pp. 1317-1321. PersamonPress. PrintedinGreatBritain

IODINE

AS

A

DONOR

IN

CdS

H. R. VYDYANATH, S. S. CHERN and F. A. KROGER D e p a r t m e n t of Materials Science, University of S o u t h e r n California, U n i v e r s i t y Park, Los Angeles, Ca. 90007, U.S.A. ( R e c e i v e d 2 4 J u l y 1972; in revised f o r m 2 N o v e m b e r 1972) Abstract-- Iodine doped single crystals of C d S were g r o w n from the v a p o r phase. High temperature Hall effect m e a s u r e m e n t s for the crystals equilibrated with Cd and S~ vapors at t e m p e r a t u r e s between 700 a n d 1000~ gave t h e free electron concentration as a function ofpcd o r p,.~ a n d temperature. T h e results c a n be explained on the basis of a model in which the C d S is saturated with iodine at low Pcd

( = highPsi) but unsaturated at high Pcd. The solubility of iodine in CdS is given by --1/8 exp (-- 1.045 e V / k T ) c m -3 a t m -l/s = 4.62 x 1019 p ~ exp (--0.195 e V / k T ) cm -~ cl = 1"73 • 1022 Ps~ atm~/4

T h e formation of pairs (lsVcd)' from I~ a n d Vc'~ is g o v e r n e d by the equilibrium constant K e ~ . w = 4 e x p ( ~< 1.1 e V / k T ) If C d diffusion occurs primarily by free vacancies, the Cd* tracer self diffusion leads to a v a c a n c y mobility of ( 1.2 - 0-5) • 10-5 c m ~ sec -~ at 900~ in a g r e e m e n t with results reported by W o o d b u r y [ 12], but (7 ___3) times larger t h a n reported by K u m a r a n d Kroger [10]. 1.

INTRODUCTION

2.

MUCH work has been done on the effectiveness of trivalent metal donors in CdS, but the knowledge regarding chalcogen donors is limited. Chlorine doped crystals prepared in atmospheres o f Cd and H~, H2S and HCI had electron concentrations varying from 2 x 1017 to 2 • 101Scm-3 with similar chlorine concentrations [ 1 ]. Electron concentrations equal to the chalcogen content at the 101~ cm -3 level have also been observed in electron spin resonance with CdS + CI [2] and CdS + Br or I [3]. Iodine doped crystals prepared in sulfur atmosphere showed low electron concentrations[4,5], a crystal containing 2 . 3 • Is iodine atoms cm -a has only 10 ~ free electrons, the electron concentration decreasing with increasing Ps~[5]. T h e present paper describes results obtained by high-temperature Hall effect measurements on iodine doped crystals in equilibrium with Cd or $2 vapor at various temperatures. In addition the Cd tracer self diffusion coefficient was measured.

Crystals doped with iodine were grown by chemical vapor transport by the following procedure [4, 6]. CdS powder is heated in H.,S at 700~ in a quartz tube. T h e n iodine is added ( ~ 2 5 m g per 10g CdS), the tube evacuated and sealed, and heated for ~ 100 hr at ~ 1000~ with a gradient of 6~ over the 4 in. long tube, the CdS being at the low temperature end. Although marked recrystallization occurs [7], crystals large enough for our measurements were not obtained. Larger crystals were obtained by changing the position of the tube in the furnace, with the coalesced mass now at the high temperature end (1005~ leaving a small crystal as a seed at the low temperature end which is at 980~ Slow transport occurs from the high to the low temperature side, giving one or two pink crystals, ~ 10 • 10 • 5 m m 3, in ~ 100 hr. As we shall see, these crystals contain ~ 1.8 • 1018 1 c m -3. Attempts to grow crystals with higher iodine contents by adding more iodine to the

1317

JPCS VoL 34, No. 8-42

EXPERIMENTAL

Crystal growth

1318

H.R.

VYDYANATH,

S. S. C H E R N and F. A. K R O G E R

growth tube were unsuccessful. F o r the Hall and diffusion m e a s u r e m e n t s , plates of 1 0 § 1 0 - 1 m m 3 were cut f r o m the boule with the aid of a wire saw.

-

900

~o"~_

T(oc)

800

700

= 0 5 otto.

psz

[ '

=

.

-

exp( I,.05 e V i k r ' -

High temperature Hall effect measurements High t e m p e r a t u r e Hall effect m e a s u r e m e n t s on the crystals in contact with c a d m i u m or sulfur v a p o r at t e m p e r a t u r e s varying from 700 to 1000~ were carried out in an a p p a r a t u s described in Refs. [8] and [9]. T h e electron concentrations calculated from the Hall I I I0 constant Rn by the relation Ce = (3r 0.8 0-9 1.0 IO00/T(~ ( R , q ) -1, are shown in Figs. 1 and 2. A t high Pcd the electron concentration--~ 1 . 8 • 1018 Fig. 2. Temperature dependence of the electron concentration in C d S - 1 . 7 • 10 TM I cm -3 atps, = 0.33 atm. c m -a, independent of Pea and T, and virtually the same for samples cut f r o m crystals grown 1/4 exp ( - - 0 . 1 9 5 eV/kT) cm -3 in two different runs. T h e electron concentra- c~ = 4"62 X 10 19Pco tions found at 750~ at Ps, ~ 0 - 3 3 a t m (la) (Pod ~ 1 0 - r a t m ) initially were ~ 3 " 6 x 1017 cm-a; later determinations gave values 2-3 • Cd tracer self diffusion T w o Cd* tracer self diffusion experiments, l o w e r and showed a c a d m i u m and sulfur pressure d e p e n d e n c e oonu~ or ps~ t8 F o r the carried out by the method described in Ref. loCd latter data, the t e m p e r a t u r e d e p e n d e n c e at [11 ] at 900~ and Ps~ = 2.5 atm (corresponding constant Ps, -- 0,33 atm s h o w n in Fig. 2, is to Pea = 2 • 10 -5 atm) gave the values D~d = 4.27 x 10 - n and 1.06 x 10 -~~ cm 2 sec -1. represented by

C e = l ' 7 3 X 10 2s p -1/8 s2 exp ( - - 1.045 eV/kT) cm -3

3.

(1)

T h r e e models m a y be considered to explain the Hall effect results shown in Figs. 2 and 3. (I) A t high Pea, [ e ' ] = [ I s ] = [l]totai. A t low Pea, [ I s ] ~ 2[ Vcd ] or [I~] ~ [ (lsVcd)']. This

or, using Pod ol/2 ~S~ = Kcds = 2 • 101~exp ( -- 3.4 eV/kT)

[l 1],

l(a) 5 x I0~e

I

DISCUSSION

Hal~ data

i

I

[

/

l0 le v

r

Sample ~1

T

/

/

id 7 5X Id 6 los

Sample ~ 2

9 900~ 9 800~ 850~ 9 750~

0 850 ~ 9 975~

700 ~ I

10-5

I

I0 -4

f

I0- 3 9 PCd(otto.)

[

I

lo-Z

lO-I

Fig. I. Electron concentrations for t w o samples of CdS containing ~ 1-7 • 1@s iodine cm -~ as determined by high temperature Hall effect measurement at 700~ < T < 975~ under various cadmium and sulfur pressures.

10~

IODINE

AS A DONOR

model gives [ e' ] ~ n~/z r C d - A w e a k e r dependence may occur close to the range boundary, which is the case when [ e ' ] is close to [Is]. This might apply to the high temperature results but not to the 700~ data. T h e r e f o r e , this model has to be rejected. (II) [l]total ~ 2 [ (IsVcdls) • (lsVcdls) • + Cd(g) --* C d c d

constant; 21~ + 2e'; Kr.

=

+

(2) F o r l / s ] ~ [ e ' ] < [/]total, this gives the Pea dependence observed at low p c a : [ e ' ] = (KT,Pcd[l]total]2) xt4, but it cannot explain the behavior at high Pcd. (III) At highpca, [Is] = [e'] = [/]total H e r e the sample is unsaturated with respect to iodine as witnessed by the o b s e r v e d independence o f [ e ' ] of Pea and T. At low Pea the sample is saturated, with CdIz as a second phase, and the iodine content and the electron concentration are determined by the reaction and corresponding mass action relation: CdI2 (s) + Cd(g) ~ 2Cdca + 21~.+ 2e'; Ksa t

[1~] ~ [e'] = {a(CdI2)PcdKsat} TM.

IN

CdS

1319

Combining equation (1 a) with

Kcd = [ Vcd]Ped/[ e ' ]

2 = 3"6 • 109 exp ( -- 2-34 e V / k T ) atm atom fr.-'

(6) as given in Ref.[10], remembering that ce = 2 • 1022 let] cm -3, and using (4) we find [ V c j = 1"92 • 104pc~/2 exp (--2-73 e V / k T ) atom fr. atm -1/2 (7) F o r T----900~ Pcd----10-4atm, this gives [ Vcd] = 3,66 • 10 -6 : 7-32 • 1016cm -3, < [ 1~.]. T h e concentration o f pairs is subject to the pairing equilibrium relation

Kp(1 Vl = [ ( lsVcd) ' ] , [1~][ Fed] = 4 f e x p (-- Hp(,.v,/kT) with f = exp Sp(t,v)/k. T h e requirement [ (lsVcd)'] < [Is] now sets an upper limit to Kp(t,v) a n d / o r - Hv(t,v): Kp(~9v) < [ v" vz exnr (2"73 " Cd J1-1 = 5.2 • 10-5t'Cd e V / k T ) atom ft. -1 atm l/2

(3)

Assuming f - = 1,

(4)

- H p u , v ) < 2.73--0.965 • 10-3 T + 9.92 • 10 -5 T log Pcd

H e r e a(CdI.,) is the activity of CdI2 in the second phase, equation (4) gives the Pea dependence observed at low Pea. T h e transition between the two ranges occurs at the point where the CdI2 second phase dissappears with increasing Pea due to the fact that the solubility o f iodine in CdS as given by (4), increasing ~ or e TM reaches the d, amount of iodine that is present. Only this last model fits all the data. In this model (1) and (la) give the iodine solubility in CdS. Comparison with (4), with (CdI2) = 1 gives • 1078exp ( - 0.78 e V / k T ) cm -12 atm -1. (5)

g s a t ~--- 4.6

We still have to check whether the model is consistent, in particular whether [V'cd] and [ (lsVcd)'] < [Is] = [ e ' ] .

F o r T = 700~ = 973~ and P c d = 10 -7 atm -- Hv(1,v)

< 1.11 eV.

This value is somewhat smaller than the one expected on the basis of coulomb attraction:

-- Hp(l,V) ~ 2q2/E*rca-s = 1"27 ~ eV for

rCd-S

= 2.5/~. e is the average dielectric constant ( -- 9), and e* is the effective dielectric constant; for nearest neighbors e* may be < ~ but not > E. T h e fact that our limit lies below the coulomb value may be due to the fact that the actual defect distance is somewhat larger than rcd-s. N o t e that owing to the fact that in the pair 1~ and Vea o c c u p y neighboring sites whereas in the pair (IncaVca)', In& and Ved

1320

H.R.

V Y D Y A N A T H , S, S. C H E R N and F. A. K R O G E R

occupy next neighbor sites with a larger rCd-Cd= 4-14 ,~, the pairing enthalpy - - H.,.~l.V) is probably larger than-Hetm.v~ which was found to be 0 - 4 7 - 0-3 eV [9], The precipitation model III can also explain our inability to achieve higher doping concentrations. Preparation by sublimation must have taken place close to the point of minimum total pressure; for T = 980~ this is at Pcd = 2Ps2 = 2113 K 2/3 = 7 X 10-3 atm. The ~ maximum amount of iodine that can be dissolved under these conditions as calculated from (la) is 1.36• 101Sere-a-close to the iodine content of our crystals as indicated by the concentration of electrons found at high PCd( 1 "6 -- 2 • 10 TM c m -a) The precipitation model also explains the initially observed higher electron concentration. The crystal as prepared at high t e m p e r a ture is just saturated at that temperature but does not contain nuclei of CdIz. W h e n the crystal is cooled, it becomes supersaturated but fails to form precipitates owing to nucleation problems. As soon as nucleation occurs, however, precipitation occurs, and the equilibrium values of all defects including the electrons are reached. The value of the electron concentration observed at 750~ in the supersaturated sample represents a lower limit: we are not certain that precipitation is not already taking place. It can be used to determine another upper limit to the iodine.cadmium vacancy pairing constant Kin,v). Using expression (6) for Kca v, we find [V'cd] /> 3.5• 10-*=7.1 • 1015 cm -3. Since both [ e ' ] and [ Vcd] ~ [1], the neutrality condition must have been governed by [16] ~ [(lsVcd)']. Therefore at 750~ Kptl, v) [ (IsVcd)' " " ~ [ V" ]-1 2.8 x 10~ =

Assuming K~t,v)~ 4, this leads t o - - H ~ , n ~< 1.19eV, close to the limit set by the consistency check carded out earlier a n d - a s e x p e c t e d - c o n s i d e r a b l y larger than the pairing energy for vacancies with metal donors. The

best estimate of Kt,~Lv~is presently

Km,n = 4 exp ( ~< 1.1 eV/kT)

(8)

Self diffusion For K~,v) as given by (8), at T = 900~ and Pcd = 2 • 10 -5 atm, the conditions under which the self diffusion experiments were done, the neutrality condition is no longer governed by [1~] ~ [ e ' ] but by the more general expression [I~] = [ (IsVcd)'] + [e'] + 2[V'~d ] with [l],otal = fl~] + [(IsVcd)'] ~4"3• 1017cm -3, independent of Pea. Using equation (20) o f Ref.[9] we find [e'] = 1"3 • 1017cm -3, [Ved] = 1"23• 101~cm:-3=6-17• 10 -6, [(IsVcd)'] = 3 • 101ncm-L and [1~] = 4 • 101~ cm -3. If we neglect contributions tO D~a by the pairs, the observed D~a---- (7-5--3"2) • 10 -11 cm ~ see -1 with D~a =fvDv[Ved] gives for the product of the tracer-vacancy correlation coefficient fv and the vacancy diffusion coefficient Dv the value ( f v D v ) ~ e = (1-2--+0-5) • 10-5 cm ~ sec -1. This value is (7_+3) • larger than the value (fvDv)9oo,e = 1"7 • 10-6 cm ~ sec -a calculated from the twoparameter expression for this quantity[11] given in Ref.[10]. There are three possible reasons for this discrepancy: (1) it may be due to the neglect of the pair contribution. F o r the concentrations of single vacancies and pairs as given above, a ratio fcaxa,Dp/fvDv ~-28--+12 is needed to remove the discrepancy, which .is unacceptable. (2) [ V~d] as calculated may be somewhat in error due to a possible error in Kedv. We do not think, however, that the correction in /(ca v that is necessary to remove the discrepancy is acceptable. (3) fvDv as given in Ref.[10] may be in error. This finds support in the fact that there is reasonable agreement with fvDv obtained from Woodbury's data[12]. This author reports on Cd self diffusion in donor doped CdS at 800~ from which, with [donor] 2[Vcd ], one deduces (fvDv)a0~c = 4 x 10-6 cm 2 sec -1. Assuming a temperature depend-

I O D I N E AS A D O N O R IN CdS

ence identical to that reported in Ref. [10], fvD v = 35-7 exp ( -- 1-48 eV/kT)cm 2 sec -1,

gives 0 e v D v ) 90ooc =

1 "56

x

1 0 -5 c m 2

sec -1,

close to our present value. 4.

SUMMARY

Iodine acts as a shallow donor in CdS. Its solubility is much smaller than that of metal donors such as indium, gallium or aluminum. The neutrality condition is governed by [Is] [ e'] at almost all Cd and Sz pressures, and leads to a solubility proportional to p ~ . Pairing of iodine and Cd vacancies is governed by getl,V) = 4 exp ( ~< 1.1 eV/kT). Cd self diffusion measurements at 900~ and Ps~ = 2.5 atm lead to ( f v D v ) 9 o o o c = (1.2_+0-5) X I 0 -5 c m 2 s e c -1.

1321 REFERENCES

1. K R O G E R F. A., V I N K H. J. and VAN D E N B O O M G A A R D J., Z. Phys. Chem. 203, 1 (1954). 2. L A M B E J. and K I K U C H I C.,J. Phys. Chem. Solids 9, 492 (1958). 3. S L A G S V O L D B. J. and S C H W E R D T F E G E R C. F., Canad.J. Phys. 43, 2092 (1965). 4. B E U N J. A. N I T S C H E R. and BOLSTERLI H. U., Physica 28, 184 (1962). 5. B U B E R. H.,J. chem. Phys. 30, 288 (1959). 6. N I T S C H E R.,J. Phys. Chem. Solids 1% 163 (1960); B E U N J. A., N I T S C H E R. and L I C H T E N S T E I G E R M., Physica 26, 647 (1960); N I T S C H E R. and R I C H M A N D., Z. elektrochem. 66, 709 (1962). 7. M I K U L Y A K R. M., J. Cryst. Growth 8, 149 (1971). 8. H E R S H M A N G. H. and K R O G E R F. A., J. Solid St. Chem. 2, 483 (1970). 9. H E R S H M E N G. H., Z L O M A N O V V. P. and K R O G E R F. A.,J. SolidSt. Chem. 3, 401 (1971). 10. K U M A R V. and K R O G E R F. A., J. Solid St. Chem. 3, 387 (1971). 11. Actually Ref.[10], erroneously assuming D~a = Dv[ I/ca], gives an expression for Dv which has to be interpreted as fDv.

12. W O O D B U R Y H. H., Phys. Rev. 134, A 492, (1964).