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Defect equilibrium in semi-insulating CdTe(Cl)
Nuclear Instruments and Methr, vs in Physics Research A322 (1992) 371-374 North-Holland
e ect equilibrium in semi-i sulatiu P. H®schl, P. Moravec, J. Franc, E. Belas and
e(
l)
. Grill
Institute of Physics, Charles University, Ke Karlovu 5, CS-121 16, Prague 2, Czechoslovakia
The Hall coefficient R H and conductivity o, were measured in the temperature range 250-450 K in semi-insulating CI-doped CdTe crystals . Due to the high electron mobility, a reversal of sign of R H appears at 370 K. A simultaneous analysis of R H(T) and o,(T) was performed with the help of theoretically determined mobilities and Hall factors of both electrons and heavy holes . It yields a position of the deep level connected with the second charge state of a divalent cadmium vacancy Eat = 0.69 eV above the valence band and the position of Fermi level E F = - Eg + Eat +0 .72k o T pinned to Eat . Using these values total concentrations of defects and the energy necessary for the creation of the neutral complex (Vcd C] TE )' = 1 .06 eV were determined on the basis of a detailed point defect model, which describes the association of cadmium vacancies and chlorine atoms. The energy liberated by the compensation of chlorine donors by these complexes ( = 1 .20 eV) is sufficient for the generation of these complexes so that a strong compensation occurs at a growth temperature of 450°C for Te-rich conditions.
1 . introduction Cadmium telluride is a promising material for the use as an epitaxy substrate for (HgCd)Te, infrared windows, electrooptical modulators and gamma-ray detectors . In CdTe crystals both foreign atoms and native point defects determine the electrical properties of the crystals. The concentrations of the dopant atoms and defects are not independent of each other . The introduction of electrically active impurities into a host crystal induces the formation of electrically active defects and complexes which tend to compensate the material closely . Self-compensation has been extensively employed to obtain CdTe samples with a carrier concentration low enough to give a high electrical resistivity ( >_ 108 cm), needed for gamma-ray detectors. Many groups have used the growth of Cl-doped crystals CdTe from Te-rich solution, which yields crystals that are initially Te saturated at the growth temperature, to establish the deviation from stoichiometry needed for self-compensation [1-41 . All the Cl-doped semi-insulating (SI) crystals grown from âe-rich solution are p-type at 300 K, which means, that Fermi level E F is lower than the intrinsic Fermi level EFi = -Eg/2 + 2k O T ln(mhlmé
) 3/2
= -0 .72 eV
for Eg(300 K) = 1 .52 eV . The deep acceptor level EDA < ER plays an essential role in obtaining SI properties. For the material, that contains an excess of shallow donors ND over shallow acceptors NA such that NDA
>- ND - NA in a wide range of deep acceptor concentrations NDA, the Fermi level is pinned to the vicinity of the deep acceptor level E F = EDA . The determination of the carrier mobilities and the identification of deep levels from the temperature dependence of the Hall coefficient R H and conductivity a- are difficult . In the temperature range where the Fermi level lies in the mid-gap near the second energy level of Vcd, R H is determined not only by heavy holes (h) but also by electrons (e) as a resuït of their high mobility (Ic e /A h = 12). The influence of electrons in the range of temperatures T > 300 K is so important that a reversal of the sign of R H appears. In this range the dependence 1 /(eR H ) =f(1 / T) loses its former meaning because the deep acceptor level energies are not directly deductible from it . The product R,,,a does riot represent the Hall mobility of heavy holes too . Our effort was to determine theoretically the mobilities and Hall factors of heavy holes (A h , r h ) and electrons (lie , re ) and to use these parameters to fit the experimental data of R H and a. The obtained data on the deep acceptor level energy and Fermi level enable. ope to establish equilibrium concentrations of defects and complexes.
2 . Theory
First we collect the results oî measurements on our SI CdTe(CI) samples, which we have already published [3-51 and which are the basis for a vcôification of the pojni defect model on the cxplanadon of experimental Hall and conductivity data,
016$9002/92/$05 .00 © 1992 - Elsevier Science Publishers B .V . All rights reserved
1 . CdTe
372
P. Hôschl et al. / Defect equilibritan of CdTe(CI)
a) The very high degree of compensation between shallow donors and shallow acceptors is not possible to obtain by residual impurities, which is supported by the fact that SI CdTe(Cl) of the same properties was prepa-d in various laboratories from source elernnents Cd and Te of various origin . b) SI CdTe(Cl) is prepared at Te-rich conditions, which are equivalent io annealing under a very low pressure of Cd vapours ; e.g. pod = S x 10-" atm at 450°C. Besides the dopant CI can therefore also play a role of defects and complexes containing Vcd and Te i . The influence of Vod appears to be dominating (for Te i the similar holds well). c) Witn ttie help of the time of flight technique [5] the activation energies of the shallow donor CI Te Ed = 0.025 eV and that of the acceptor 0.145 eV were determined . The energy of the acceptor is correlated with the concentration of [CITe ] = 5 x 10" em -3 in such a way, 'hat for each donor CI Te one acceptor is created. It means that the acceptor must be singly ionized . Therefore Véd and (Vcd Cl- re )' come into question. The second one is much more probable because the ionization energy of the first charge state of the divalent acceptor Vod was determined from luminiscence measurements considerably lower, Eal = 0.069 eV [6,7]. Also, as will be shown further, the energy necessary for the creation of the neutral complex (t d CI T,, )_r is about three times lower than the energy necessary for the creation of the neutral vacancy Vcd . e creation of the complex is therefore more probable. In this case previous experimental results on our Si C Te(Cl) can be summarized : [(VCdC'T,)] = [CITe] = 5 x 10 1 cm` 3 and Eac = 0.145 eV [5]. d) in agreement with a number of compensation models [5-12] the deep level in the position E a , = 0.60.9 eV above the valence band is often connected with the second charge state of the divalent acceptor formed bv metal vacancy Vcd . The concentration of the deep level is 2-3 orders of magnitude lower than the concentration of the compensating shallow donors and acceptors . As will be shown further, the analysis of RH and o- data yields the value Eat = 0.69 eV. A very similar value for E a , = 0.65 eV was determined on our Si CdTc(Cl) samples by do measurements of SCLC 13] . A scheme of energy levels in ST CdTe(Cl) is shown in fig . 1 .
c
2.1 . Low temperature equilibrium (250-450 K)
E
c %=0025eV1
1 ~ I
I
I
i I
I IEF
IE F , = -072eV
Fig . 1. Scheme of energy levels in SI CdTe(Cl). The value for level Ea, was obtained by the analysis of experimental data of R I- 1 plotted in fig. 2. when [ VCd1 = Nd1 +
Md1 + [VCd ]+
(2)
[(VCdClTe)] = [(VCdC1 Te)' ] + [(VcdCÎT,)x],
(
fi(' - f2) [V~d] - 1 [Vcd] =Fl[Vcd, _f, +fif2
(4)
[Vëd] -
ft f2
1 _f,+ .fif2
[VCd1 = F, [Vod]-
(5)
[(VCdClTe), ] -f3t(VCdC'Te)J , [C'Te] - (1 _M[CITe],
(6a)
fi = { 1 +gi exp[(Ei - EF )/koT ]) -1 ,
(6c)
(6b)
where gl 2, 93 = 4, g .4 =2! and E 1 = -E g + Eal , E, = -Eg + Eat , E 3 = -E g + E a3 , E4 = -Ed . The total concentrations of Cl and Vod are [ c1 Te]tot = [C1 Te] + [( VCdClTe)] ,
( 7a)
[ VCdI + [( VCdCl Te)I*
(Tb)
According to the values of activation energies introduced above, eq. (1) becomes simpler for the case when the Fermi level E F is pinned in the vicinity of the deep level in the mid-gap : ( 1 + f2)LvCd] = [C 1 Te] - [(VCdC'Te)], f2 = [VëdI/[VCd1 ,
ô
(9a)
1 - f2 = [Véd l/[YCA (9b) Fitting R H (T) we can determine the values E F and E at , which unambiguously determine f,. 2.2. High temperature equilibrium (723 K)
In the temperature range 250-450 I{, where the measurements of R H and o" were performed, the electric neutrality condition (ENO is [14,15] :
The neutral and the ionized complexes (VCd C' Te ) are created as follows
p + [C'Te] = n + [Védl + 2 [Vëd ] + [(VCdC 1 Te) ' ]
Ved + C'Te ;'~' (VCdC'Te) , - 2He .
(1)
VCd + CITe ;~:' (VCdC'T,)x - Hc,
(l0a) (10b)
P. Misch! et al. / Defect equilibrium of CdTe(CI)
373
The ionization of Ad and that of the complex (VcdCl-,.,,) are as follows : Vd ;'~ Wd + e' - Eg +
(Ila)
Ea2l
M " Q + e'- Q - Eo ,.
(I lb)
(Ado"), " (vCWOK) + e'- Q X
- + &c .
(12)
With the help of relations ( l0a), (1 la) and (12) we obtain H. = El,, - Ea2 = -0.54 eV for the binding energy of the complex (Vc,CIT,:)' . This value is in good agreement with the Coulomb binding energy for the first nearest neighbours: H(')= -e 2/( e,,r,) = -0.54 eV (for E,) = 9.7, r, = 2.8 X 10" cm). For the equilibrium constant of reaction (10b) we obtain Kac =
1(AdC 1 Te) ' 1 . I
L"JI.""i 4
1 .48
KL%Jll TO 2k
(13)
exp X 1022 (_ kOT)_
We introduce, as in ref. [12], the description a for : a = [(VCdCITe )]/[CITe ],.t ,
10 JAWL = 1 - a ,
IvCdl/[ClTeltot = (I - 2a)/(I
(14a) +f2)-
3 -
2
+f
1 2 -
I
2f2 Ka,[C'T,:],.,
I 2
+- =1
3. Experimental
(14c)
The vertical Bridgman method was used to grow CdTe single crystals by normal freezing from Te-rich solution of the composition 30 at_% Cd and M at% A [4]. The total concentration of chlorine in the form of anhydrous CdCl-, in the starting charge was 3-5 X 103 ppm. Due to the very small value of the segregation coefficient of Cl (= 0.005) a significant reduction of CI occurred during the growth ; CdTe single crystals contain Cl amounting to = 1017 CM-3 . This value was checked by mass spectrographic analysis . After the end of a growth run at 450"C, CdTe crystal was equilibrated at this temperature for several days (Te-rich conditions).
(15)
It is possible to determine the degree of compensation either with the help of d or the complexes (AdClTe) by comparison of the energy liberated by compensation and that necessary for the creation of the neutral vacancy Vid - Hf(Ad) or the neutral complex (vCdC'Te)x - Hf(vCdC'Te)* Che-ri et al. [16] determined the quasichernical reaction :
A
Cd'Cd ;
è=>-
Cd(g) + VËd - 2e'- 0.88 eV
(16)
from which we obtain with the help of relations (10a) and (10b) (17) Cd'Cd :é-:t Cd(g) + V& - 0.88 - 2E9 + Ea2 + E~, 1 . For Eg = 136 eV at 450'C we obtain Hf (Ad) = 2.84 eV. The energy obtained by compensation is: Eg - E,, I - Ed = 1.24 eV, which is not sufficient for the creation of neutral vacancy Vjd. With the help of relations (17), (10a), (12) and the ionization reaction Cl'Te -Cl T* e -Ed we obtain Cd'Cd + CIT'e z:--- Cd(g) + (VCdC'Te) Hf (Ad) + Eg - Eal - Ed - Hc*
(AdC1Te)x. The degree of compensation should be strong .
(14b)
From relation (13) we obtain the equation for a: a 2-
Fig . 2. The Hall coefficient RH and the electric conductivity as a function of reciprocal temperature for St CdTe(Cl) in the range 250-450 K. Solid lines indicate the fit .
0'
- [(VCdC'Te) ] .
X
-
(18)
This yields Hf(Ado) = 1.06 eV. The energy obtained by compensation is: Eg - E,,c - Ed = 1.19 eV, which is enough for the creation of the neutral complex
4. Results and discussion The R H M and a(T) dependences at temperatures of 250-450 K are depicted in fig. 2. A sign reversal occurs at = 370 K as a result of the high mobility of electrons . The R H M and or(T) dependences were analyzed for two types of carriers (heavy holes and electrons) in the way described in our papers [14,15,17] . For the calculation of the carriers mobilities and of the fall factors r H the scattering on polar optical phonons is substantial . The fit has resulted in the determination of the Fermi level EF = -Eg + Ear + 0.72k OT and of the deep acceptor level Ea2 = 0.69 cV, which fix the value of the distribution function f2. It was calculated that f2 0.422 in the whole temperature range . 1. CdTe
374
P. 116schl et A / Defect equilibrium of CtITe(CI) introduced in fig. 3 . It is evident that trie compensating complexes dominate at 4500C, but at higher temperatures (= 800'C) they are damaged. References
Fig. 3. Temperature dependences of concentrations of defects and complexes for the sample with a total concentration of chlorine [Cl-r°],,,, = 10'' cm - '. At 300 K Sl CdTe(CI) is characterized by the Fermi ievel in the position EF = - E~ + 0.67 eV and by the concentrations of holes and defects: p = 8.8 X 107 cm - 3 . [(VCjClTe )] = 4.983 x 10 "0 cm - ', [Cl T, ] = 5.017 X 10'6 cm - ': and ["I = 2.347 x 10 " cm - '. Relation [C1Tj,,, = 2[(Vc-dCI Tz )] = 2[Vcd ],,,, confirms the assumption of the strong compensation of CI T. by complexes MOM . Ming to the fact that only a redistribution of carriers occurs by cooling down iroir. the growth temperature = 450'C to room temperature, the total concentrations of defects at 300 K characterize the sample at temperature T = 450"C. too. Using the found value of f2 from the (ENC) condition glen by eqj 1) we can also determine the concentrations [VCd] , [(VCdC')] and 10 .1 at higher temperatures (T> 450'C). The results obtained from eq. (15) are for [Cl TA .1 = 1() i ' cm -3
[1] F.V . Wald and R.O . Bell, Nature Phys. Sci . 237 (1972) 13. [21 R. Triboulet, Y. Marfaing, A. Cornet and P. Siffert, J. Appl. Phys . 45 (1974) 2759 . [3] P. Höschl, P. Polivka, V. Prosser and A. Sakalas, Czech. J. Phys . B25 (1975) 585. [4] P. Höschl, P. Polivka. V. Prosser, M. Van66ek and M. Skfiv5nkov5, Rev. Phys . Appl. 12 (11977) 229. [5] P. Hbschl . P. Polivka, F. Nava and R. Minder . Czech. J. Phys. B26 (1978) 812. [6] N.V. Agrinskaya, O.A. Matveev, A.V. Nikitin and V.A . Sladkova, Fiz. Tekh. Poluprov . 21 (1987) 666. [7] E. Molva, J.P . C hamonal, G. Michlberg, K. Samindayar and G. Neu, Solid State Comm . 44 (1982) 351 . [8] Y. Marfaing, Rev. Phys . Appl . 12 (1977) 211 . ["'] F.A . Kriiger, Rev . Phys . Appl . 12 (1977) 205. [10] N.V . Agrinskaya and E.N. Arkadeva, Nucl . Insu . and Meth . A2283 (1989) 260. [11] N.V . Agrinskaya and O.A . Matveev, Nucl. Insu. and Meth . A283 (1989) 263. [12] C. Canali, G. Ottaviani. R.O . Bell and F.V . Wald . J. Phys . Chem. Solids 35 (1974) 1405 . [13] A. Zoul and E. Klier, Czech. J. Phys . B27 (1977) 789. [14] P. Höschl, P. Moravec, V. Prosser, V. Sz6cz and R. Grill, Phys . Status Solidi B145 (1988) 637. [15] P. Höschl, P. Moravec, V. Prosser, R. KOO, R. Grill, J. Franc, E. Betas and Yu .M . lvanov, J. Cryst. Growth 101 (1990) 822. [16] S.S. Chers, H.R . Vydyanath and F.A . Kr6ger, J. Solid State Chem . 14 (1975) 33 . [17] P. Höschl, P. Moravec, J. Franc, R. Grill and E. Betas, J. Appl . Phys. 70 (1991) 313.
e ect equilibrium in semi-i sulatiu P. H®schl, P. Moravec, J. Franc, E. Belas and
e(
l)
. Grill
Institute of Physics, Charles University, Ke Karlovu 5, CS-121 16, Prague 2, Czechoslovakia
The Hall coefficient R H and conductivity o, were measured in the temperature range 250-450 K in semi-insulating CI-doped CdTe crystals . Due to the high electron mobility, a reversal of sign of R H appears at 370 K. A simultaneous analysis of R H(T) and o,(T) was performed with the help of theoretically determined mobilities and Hall factors of both electrons and heavy holes . It yields a position of the deep level connected with the second charge state of a divalent cadmium vacancy Eat = 0.69 eV above the valence band and the position of Fermi level E F = - Eg + Eat +0 .72k o T pinned to Eat . Using these values total concentrations of defects and the energy necessary for the creation of the neutral complex (Vcd C] TE )' = 1 .06 eV were determined on the basis of a detailed point defect model, which describes the association of cadmium vacancies and chlorine atoms. The energy liberated by the compensation of chlorine donors by these complexes ( = 1 .20 eV) is sufficient for the generation of these complexes so that a strong compensation occurs at a growth temperature of 450°C for Te-rich conditions.
1 . introduction Cadmium telluride is a promising material for the use as an epitaxy substrate for (HgCd)Te, infrared windows, electrooptical modulators and gamma-ray detectors . In CdTe crystals both foreign atoms and native point defects determine the electrical properties of the crystals. The concentrations of the dopant atoms and defects are not independent of each other . The introduction of electrically active impurities into a host crystal induces the formation of electrically active defects and complexes which tend to compensate the material closely . Self-compensation has been extensively employed to obtain CdTe samples with a carrier concentration low enough to give a high electrical resistivity ( >_ 108 cm), needed for gamma-ray detectors. Many groups have used the growth of Cl-doped crystals CdTe from Te-rich solution, which yields crystals that are initially Te saturated at the growth temperature, to establish the deviation from stoichiometry needed for self-compensation [1-41 . All the Cl-doped semi-insulating (SI) crystals grown from âe-rich solution are p-type at 300 K, which means, that Fermi level E F is lower than the intrinsic Fermi level EFi = -Eg/2 + 2k O T ln(mhlmé
) 3/2
= -0 .72 eV
for Eg(300 K) = 1 .52 eV . The deep acceptor level EDA < ER plays an essential role in obtaining SI properties. For the material, that contains an excess of shallow donors ND over shallow acceptors NA such that NDA
>- ND - NA in a wide range of deep acceptor concentrations NDA, the Fermi level is pinned to the vicinity of the deep acceptor level E F = EDA . The determination of the carrier mobilities and the identification of deep levels from the temperature dependence of the Hall coefficient R H and conductivity a- are difficult . In the temperature range where the Fermi level lies in the mid-gap near the second energy level of Vcd, R H is determined not only by heavy holes (h) but also by electrons (e) as a resuït of their high mobility (Ic e /A h = 12). The influence of electrons in the range of temperatures T > 300 K is so important that a reversal of the sign of R H appears. In this range the dependence 1 /(eR H ) =f(1 / T) loses its former meaning because the deep acceptor level energies are not directly deductible from it . The product R,,,a does riot represent the Hall mobility of heavy holes too . Our effort was to determine theoretically the mobilities and Hall factors of heavy holes (A h , r h ) and electrons (lie , re ) and to use these parameters to fit the experimental data of R H and a. The obtained data on the deep acceptor level energy and Fermi level enable. ope to establish equilibrium concentrations of defects and complexes.
2 . Theory
First we collect the results oî measurements on our SI CdTe(CI) samples, which we have already published [3-51 and which are the basis for a vcôification of the pojni defect model on the cxplanadon of experimental Hall and conductivity data,
016$9002/92/$05 .00 © 1992 - Elsevier Science Publishers B .V . All rights reserved
1 . CdTe
372
P. Hôschl et al. / Defect equilibritan of CdTe(CI)
a) The very high degree of compensation between shallow donors and shallow acceptors is not possible to obtain by residual impurities, which is supported by the fact that SI CdTe(Cl) of the same properties was prepa-d in various laboratories from source elernnents Cd and Te of various origin . b) SI CdTe(Cl) is prepared at Te-rich conditions, which are equivalent io annealing under a very low pressure of Cd vapours ; e.g. pod = S x 10-" atm at 450°C. Besides the dopant CI can therefore also play a role of defects and complexes containing Vcd and Te i . The influence of Vod appears to be dominating (for Te i the similar holds well). c) Witn ttie help of the time of flight technique [5] the activation energies of the shallow donor CI Te Ed = 0.025 eV and that of the acceptor 0.145 eV were determined . The energy of the acceptor is correlated with the concentration of [CITe ] = 5 x 10" em -3 in such a way, 'hat for each donor CI Te one acceptor is created. It means that the acceptor must be singly ionized . Therefore Véd and (Vcd Cl- re )' come into question. The second one is much more probable because the ionization energy of the first charge state of the divalent acceptor Vod was determined from luminiscence measurements considerably lower, Eal = 0.069 eV [6,7]. Also, as will be shown further, the energy necessary for the creation of the neutral complex (t d CI T,, )_r is about three times lower than the energy necessary for the creation of the neutral vacancy Vcd . e creation of the complex is therefore more probable. In this case previous experimental results on our Si C Te(Cl) can be summarized : [(VCdC'T,)] = [CITe] = 5 x 10 1 cm` 3 and Eac = 0.145 eV [5]. d) in agreement with a number of compensation models [5-12] the deep level in the position E a , = 0.60.9 eV above the valence band is often connected with the second charge state of the divalent acceptor formed bv metal vacancy Vcd . The concentration of the deep level is 2-3 orders of magnitude lower than the concentration of the compensating shallow donors and acceptors . As will be shown further, the analysis of RH and o- data yields the value Eat = 0.69 eV. A very similar value for E a , = 0.65 eV was determined on our Si CdTc(Cl) samples by do measurements of SCLC 13] . A scheme of energy levels in ST CdTe(Cl) is shown in fig . 1 .
c
2.1 . Low temperature equilibrium (250-450 K)
E
c %=0025eV1
1 ~ I
I
I
i I
I IEF
IE F , = -072eV
Fig . 1. Scheme of energy levels in SI CdTe(Cl). The value for level Ea, was obtained by the analysis of experimental data of R I- 1 plotted in fig. 2. when [ VCd1 = Nd1 +
Md1 + [VCd ]+
(2)
[(VCdClTe)] = [(VCdC1 Te)' ] + [(VcdCÎT,)x],
(
fi(' - f2) [V~d] - 1 [Vcd] =Fl[Vcd, _f, +fif2
(4)
[Vëd] -
ft f2
1 _f,+ .fif2
[VCd1 = F, [Vod]-
(5)
[(VCdClTe), ] -f3t(VCdC'Te)J , [C'Te] - (1 _M[CITe],
(6a)
fi = { 1 +gi exp[(Ei - EF )/koT ]) -1 ,
(6c)
(6b)
where gl 2, 93 = 4, g .4 =2! and E 1 = -E g + Eal , E, = -Eg + Eat , E 3 = -E g + E a3 , E4 = -Ed . The total concentrations of Cl and Vod are [ c1 Te]tot = [C1 Te] + [( VCdClTe)] ,
( 7a)
[ VCdI + [( VCdCl Te)I*
(Tb)
According to the values of activation energies introduced above, eq. (1) becomes simpler for the case when the Fermi level E F is pinned in the vicinity of the deep level in the mid-gap : ( 1 + f2)LvCd] = [C 1 Te] - [(VCdC'Te)], f2 = [VëdI/[VCd1 ,
ô
(9a)
1 - f2 = [Véd l/[YCA (9b) Fitting R H (T) we can determine the values E F and E at , which unambiguously determine f,. 2.2. High temperature equilibrium (723 K)
In the temperature range 250-450 I{, where the measurements of R H and o" were performed, the electric neutrality condition (ENO is [14,15] :
The neutral and the ionized complexes (VCd C' Te ) are created as follows
p + [C'Te] = n + [Védl + 2 [Vëd ] + [(VCdC 1 Te) ' ]
Ved + C'Te ;'~' (VCdC'Te) , - 2He .
(1)
VCd + CITe ;~:' (VCdC'T,)x - Hc,
(l0a) (10b)
P. Misch! et al. / Defect equilibrium of CdTe(CI)
373
The ionization of Ad and that of the complex (VcdCl-,.,,) are as follows : Vd ;'~ Wd + e' - Eg +
(Ila)
Ea2l
M " Q + e'- Q - Eo ,.
(I lb)
(Ado"), " (vCWOK) + e'- Q X
- + &c .
(12)
With the help of relations ( l0a), (1 la) and (12) we obtain H. = El,, - Ea2 = -0.54 eV for the binding energy of the complex (Vc,CIT,:)' . This value is in good agreement with the Coulomb binding energy for the first nearest neighbours: H(')= -e 2/( e,,r,) = -0.54 eV (for E,) = 9.7, r, = 2.8 X 10" cm). For the equilibrium constant of reaction (10b) we obtain Kac =
1(AdC 1 Te) ' 1 . I
L"JI.""i 4
1 .48
KL%Jll TO 2k
(13)
exp X 1022 (_ kOT)_
We introduce, as in ref. [12], the description a for : a = [(VCdCITe )]/[CITe ],.t ,
10 JAWL = 1 - a ,
IvCdl/[ClTeltot = (I - 2a)/(I
(14a) +f2)-
3 -
2
+f
1 2 -
I
2f2 Ka,[C'T,:],.,
I 2
+- =1
3. Experimental
(14c)
The vertical Bridgman method was used to grow CdTe single crystals by normal freezing from Te-rich solution of the composition 30 at_% Cd and M at% A [4]. The total concentration of chlorine in the form of anhydrous CdCl-, in the starting charge was 3-5 X 103 ppm. Due to the very small value of the segregation coefficient of Cl (= 0.005) a significant reduction of CI occurred during the growth ; CdTe single crystals contain Cl amounting to = 1017 CM-3 . This value was checked by mass spectrographic analysis . After the end of a growth run at 450"C, CdTe crystal was equilibrated at this temperature for several days (Te-rich conditions).
(15)
It is possible to determine the degree of compensation either with the help of d or the complexes (AdClTe) by comparison of the energy liberated by compensation and that necessary for the creation of the neutral vacancy Vid - Hf(Ad) or the neutral complex (vCdC'Te)x - Hf(vCdC'Te)* Che-ri et al. [16] determined the quasichernical reaction :
A
Cd'Cd ;
è=>-
Cd(g) + VËd - 2e'- 0.88 eV
(16)
from which we obtain with the help of relations (10a) and (10b) (17) Cd'Cd :é-:t Cd(g) + V& - 0.88 - 2E9 + Ea2 + E~, 1 . For Eg = 136 eV at 450'C we obtain Hf (Ad) = 2.84 eV. The energy obtained by compensation is: Eg - E,, I - Ed = 1.24 eV, which is not sufficient for the creation of neutral vacancy Vjd. With the help of relations (17), (10a), (12) and the ionization reaction Cl'Te -Cl T* e -Ed we obtain Cd'Cd + CIT'e z:--- Cd(g) + (VCdC'Te) Hf (Ad) + Eg - Eal - Ed - Hc*
(AdC1Te)x. The degree of compensation should be strong .
(14b)
From relation (13) we obtain the equation for a: a 2-
Fig . 2. The Hall coefficient RH and the electric conductivity as a function of reciprocal temperature for St CdTe(Cl) in the range 250-450 K. Solid lines indicate the fit .
0'
- [(VCdC'Te) ] .
X
-
(18)
This yields Hf(Ado) = 1.06 eV. The energy obtained by compensation is: Eg - E,,c - Ed = 1.19 eV, which is enough for the creation of the neutral complex
4. Results and discussion The R H M and a(T) dependences at temperatures of 250-450 K are depicted in fig. 2. A sign reversal occurs at = 370 K as a result of the high mobility of electrons . The R H M and or(T) dependences were analyzed for two types of carriers (heavy holes and electrons) in the way described in our papers [14,15,17] . For the calculation of the carriers mobilities and of the fall factors r H the scattering on polar optical phonons is substantial . The fit has resulted in the determination of the Fermi level EF = -Eg + Ear + 0.72k OT and of the deep acceptor level Ea2 = 0.69 cV, which fix the value of the distribution function f2. It was calculated that f2 0.422 in the whole temperature range . 1. CdTe
374
P. 116schl et A / Defect equilibrium of CtITe(CI) introduced in fig. 3 . It is evident that trie compensating complexes dominate at 4500C, but at higher temperatures (= 800'C) they are damaged. References
Fig. 3. Temperature dependences of concentrations of defects and complexes for the sample with a total concentration of chlorine [Cl-r°],,,, = 10'' cm - '. At 300 K Sl CdTe(CI) is characterized by the Fermi ievel in the position EF = - E~ + 0.67 eV and by the concentrations of holes and defects: p = 8.8 X 107 cm - 3 . [(VCjClTe )] = 4.983 x 10 "0 cm - ', [Cl T, ] = 5.017 X 10'6 cm - ': and ["I = 2.347 x 10 " cm - '. Relation [C1Tj,,, = 2[(Vc-dCI Tz )] = 2[Vcd ],,,, confirms the assumption of the strong compensation of CI T. by complexes MOM . Ming to the fact that only a redistribution of carriers occurs by cooling down iroir. the growth temperature = 450'C to room temperature, the total concentrations of defects at 300 K characterize the sample at temperature T = 450"C. too. Using the found value of f2 from the (ENC) condition glen by eqj 1) we can also determine the concentrations [VCd] , [(VCdC')] and 10 .1 at higher temperatures (T> 450'C). The results obtained from eq. (15) are for [Cl TA .1 = 1() i ' cm -3
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