Semiconductor Physics, Quantum Electronics & Optoelectronics. 2001. V. 4, N 1. P. 5-8.

PACS 72.20.M, 73.40

Crystallochemistry of defects in films

D.M. Freik, M.A. Ruvinskii, B.M. Ruvinskii, M.A. Galushchak Physico-chemical institute at Precarpathian university named by V.Stefanyk, Shevchenko Str., 57, Ivano-Frankivsk, 76000, Ukraine. Abstract. The crystallochemical model of vapor-phase epitaxy of the lead telluride films has been proposed with the supposition about the simultaneous formation of singly charged, doubly charged and electroneutral Frenkel defects in the cationic sublattice. It has been shown that in spite of the large concentration of partly compensated doubly charged defects the singly charged Frenkel pairs + and − also play an essential role in change carrier concen- Pbi VPb tration in PbTe films. The results of numerical calculation agree with the available experimen- tal data of the dependence of charge carrier’s concentration in films upon the partial pressure of vapor and the deposition’s temperature in the hot-wall method. Keywords: crystallochemistry, defects, films, lead telluride. Paper received 14.09.00; revised manuscript received 10.01.01; accepted for publication 16.02.01.

stitial lead atoms + , 2+, 0 and lead vacancies 1. It is known that it is possible to control the electric Pbi Pbi Pbi − , 2− , 0 . properties (i.e. conduction type and charge carrier con- VPb VPb VPb centration) of lead chalcogenides by varying their com- The equilibrium of «bulk weight – vapour» and «va- position within the homogeneity region. However, there pour – condensate» systems in the process of film growth is no agreement in the literature concerning the predomi- from the vapour phase by the hot-wall method can be nant type of intrinsic defects in AIVBVI and their charge described by the following system of quasi-chemical re- state. For instance, based on analysis of the state dia- actions [10]: grams and processes of annealing of lead telluride, the PbTe S ↔ PbV + 1 TeV , K (T ) = P ⋅ P1/ 2 ; (1) authors of [3] assumed the existence of singly charged 2 2 PbTe e Pb Te − 2 acceptors V . Conclusions about the predominance of Pb V ↔ + + − ' = + ⋅ ⋅ −1 (2) disordering in metal sublattice with formation of singly Pb Pbi e , KPb,V (Ts ) [Pbi ] n PPb ; charge defects + and − , regardless of enrichment Pbi VPb by lead or chalcogenide, are drawn in [4]. There are also 1 V ↔ − + 0 + + Te2 VPb TeTe h , various opinions concerning the charge state of intersti- 2 (3) − − tial lead [5]. While in [6] it is assumed to be the doubly K ' (T ) = [V ]⋅ p ⋅ P 1/ 2 ; Te2,V s Pb Te ionized donor ( 2+ ), in [3] it is considered as singly 2 Pbi ionized + . There have been attempts to explain the + − + − Pbi PbV ↔ Pb2 + 2e , K " (T ) = [Pb2 ]⋅ n2 ⋅ P 1; (4) experimental dependence of electrical parameters of i Pb,V s i Pb PbTe thin films on growth conditions by formation of 1 V ↔ 2− + 0 + + singly charged interstitial atoms + and doubly charged Te2 VPb TeTe 2h , Pbi 2 (5) 2− vacancies V . In calculations of energy spectrum of " = 2− ⋅ 2 ⋅ −1/ 2 Pb KTe ,V (Ts ) [VPb ] p P . atomic defects, their electrical activity is explained within 2 Te2 2− the model assuming doubly charged metal V and Here equation (1) determines the equilibrium of «bulk 2+ vacancies [5]. In [8] it has beenPb shown VTe weight – vapour» system in the process of PbTe decom- that at low temperatures and high chalcogen vapour pres- position in the evaporator at temperature Te. Reactions sure, PbTe crystals have significant number of neutral (2)–(5) determine the equilibrium in the system «vapour – intrinsic point defects along with singly ionized defects. condensate» that is responsible for the intrinsic atomic 2. For the first time we introduce the model of metal defects at precipitation (substrate) temperature Ts. sublattice disordering in PbTe thin films according to The intrinsic conductivity and ionization of Frenkel Frenkel mechanism with simultaneous formation of sin- defects are described by equations (6) and (7)–(12), re- gly and doubly charged, as well as neutral defects: inter- spectively: © 2001, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 5 D.M. Freik et al.: Crystallochemistry of defects in lead telluride films

− + «0» = e + h , K (T ) = n ⋅ p; (6) = ⋅ ⋅ −Eg / kT , (19) i s Ki (Ts ) Nc NV e − + − + «0» = V + Pb , K ' (T ) = [V ][Pb ]; (7) Pb i F s Pb i = = πh2 3/ 2 Nc NV 2(mkT / 2 ) , − + − + «0» = V 2 + Pb2 , K " (T ) = [V 2 ][Pb2 ]; (8) Pb i F s Pb i m(T ) = g 2/3K1/3 ⋅ 0,048⋅ m T / 300,  c 0 − + − − + = + 2 + (e) = 2 (9) g = 4, K = m / m⊥ = 9 (T ≥ 300K), (20) «0» VPb Pbi e , K F (Ts ) [VPb ][Pbi ]n;  c || = + ⋅ −4 − ý = 2− + + + + (h) = 2− + (10) Eg (T ) 0,217 4.5 10 (T 77)( ), «0» VPb Pbi h , K F (Ts ) [VPb ][Pbi ]p; (T ≥ 77K). 0 ↔ + + − = + 0 (11) Pbi Pbi e , Ka (Ts ) [Pbi ]n /[Pbi ]; Here, m0 is the free electron mass, and K is the anisotropy 0 ↔ − + + = − 0 (12) VPb VPb h , Kb (Ts ) [VPb ]p /[VPb ]; constant of effective mass of electrons in conduction band and light holes in valence band. + − + Pb0 ↔ Pb2 + 2e , K ' (T ) = [Pb2 ]n2 /[Pb0 ]; (13) ' was determined from equilibrium condition: i i a s i i K F − + − 0 ↔ 2 + ' = 2 2 0 (14) − VPb VPb 2h , Kb (Ts ) [VPb ]p /[VPb ]. K ' = K (T )K ' (T )K ' (T )K 1(T ). (21) F PbTe s Pb,V s Te2,V s i s The general electroneutrality condition is: Assuming that in the studied pressure range vapour can + + + 2+ = + − + 2− (15) be treated as ideal gas, for the quasi-equilibrium state of p [Pbi ] 2[Pbi ] n [VPb ] 2[VPb ]. «vapour–condensate» system we get: From (1)–(15) we obtain the equation determining the charge carriers concentration (n) in terms of quasi-chemi- 3/ 2  T  cal reaction constants K and P : K (T ) = K (T ) ⋅ s  . Te2 PbTe s PbTe e    Te  An4 + Bn3 − Cn − D = 0. (16) Other reaction constants used in this paper are listed in Here the Table; they were taken from previous results for PbTe − A = 2K " K ' ⋅ P1/ 2 ⋅ (K K ' K ' K ) 1; crystals [2, 3]. Te2,V F Te2 PbTe Pb,V Te2,V i − 4. Experimental and theoretical results of dependency of B = 1+ K ' ⋅ P1/ 2 ⋅ (K K ' ) 1; F Te2 PbTe Pb,V charge carrier and defect concentration in PbTe films on technological factors (i.e. partial Te vapour pressure = + ' ⋅ −1/ 2 2 C Ki KPbTe KPb,V P ; Te2 P and substrate temperature Ts) in the hot-wall method Te2 − are presented in Fig. 1, 2. It is clear (Fig. 1) that the in- D = 2K K " ⋅ P 1/ 2. PbTe Pb,V Te2 crease in Te vapour pressure in precipitation region and The charge carrier concentration is determined experi- increase in substrate temperature lead to the initial de- crease in electron concentration. At some values * and mentally by Hall effect: Ts P* , the inversion of conductivity type from n to p oc- = − = − ⋅ −1 (17) Te2 nH n p n Ki n . Within the suggested model, it is also possible to deter- mine the concentrations of charged and electroneutral Table. Equilibrium constants = −Ä of the K K0exp( H/kT) defects: quasi-chemical reactions. + − − [Pb ] = K K' n 1P 1/2; i PbTe Pb,V Te2 + − − Constants K ∆H,eV [Pb2 ] = K K" n 2P 1/ 2; 0 i PbTe Pb,V Te2 3/ 2 18 − − K , Pa 1.4⋅10 3.51 [V ] = K' ⋅n⋅ P1/2(K K' ) 1; (18) PbTe Pb F Te2 PbTe Pb,V ' −6 −1 30 − − K , cm Pa 5.5⋅10 −1.01 [V 2 ] = K" K' ⋅n2 ⋅ P1/ 2(K K' K' K ) 1; Pb,V Pb Te2,V F Te2 PbTe Pb,V Te2,V i ' −6 −1/ 2 38 −1 − K ,cm Pa 1.2⋅10 0.25 [Pb0] = K K' K P 1/2; Te2 ,V i PbTe Pb,V a Te2 − " −9 −1 ⋅ 51 − [V 0 ] = K' K P1/ 2(K K' K ) 1. KPb,V ,cm Pa 1.2 10 0.87 Pb F i Te2 PbTe Pb,V b " −9 −1/ 2 ⋅ 59 KTe ,V ,cm Pa 1.5 10 0.39 3. The intrinsic conductivity constant Ki in equation (6) 2 was determined from the temperature dependencies of the Ê Ê -3 ⋅ 20 à , b, cm 6.5 10 0.14 band-gap Eg(T) and effective mass m(T) [11]:

6 SQO, 4(1), 2001 D.M. Freik et al.: Crystallochemistry of defects in lead telluride films

n H , cm nH , cm 1018

1018

17 10 1017

n p a) b) 1016 n p

1016

10 −3 10 −2 10 −1 500 600 700 p , Pa T s , K Te 2

Fig. 1. Dependence of carrier concentration in PbTe films on:

(a) – the partial pressure of tellurim vapour (Ts = 653K, Te = 833K) [12]; −2 (b) – the substrate temperature (P =1.65⋅10 Pa , Te=720K); the substrates are splinters of (111) BaF2; the solid lines are calcu- Te2 lated curves according to (16), (17).

+ −3 [Pb ], [V ], [Pb00 ], [V ], cm 2+ 20 −3 + 2+ 0 0 −3 iPb i Pb [PbiPb ], [V ], 10 , cm [PbiPb ], [V ], [PbiPb ], [V ] [Pbi ], [VPb ], cm 2.44 1021

4 20 10 2.43 1 1019 4 1 2 2. 3 10 18 2 1017 2.41 5 3 5 1015 6 10 16 2.4

6 a) 2.39 b) 1013 10 14 – – –1 0 10 3 10 2 10 10 500 600 700 P , Pa Te 2 Ts , K

Fig. 2. Dependence of calculated concentration of defects according to (18) in PbTe films on:

(a) – the partial pressure of tellurim vapour (Ts = 653K, Te = 833K); −2 (b) – the substrate temperature ( P = 1.65 ⋅10 Pa , Te=720K). Te 2 The solid lines are singly charged defects + (1) and − (2), the dotted lines are doubly charged defects 2+ (3) and [Pbi ] [VPb ] [Pbi ] 2− (4), the stroke-dotted lines are the electroneutral defects 0 (5) and 0 (6). [VPb ] [Pbi ] [VPb ]

SQO, 4(1), 2001 7 D.M. Freik et al.: Crystallochemistry of defects in lead telluride films curs, followed by the further increase in hole concentra- References tion. It is worth mentioning that this change in charge carrier concentration (Fig. 1) is accompanied by the chan- 1. N.Ch. Abrikosov, L.E. Shelimova, Semiconductor materials ge of concentration of vacancies and interstitial lead atoms based on AIVBVI compounds. Nauka, Moscow (1975) (in Rus- (Fig. 2). With the increase in T and , concentration sian). s PTe of singly charged lead vacancies increases2 (Fig. 2, cur- 2. V.P. Zlomanov, P-T-X – diagrams of two-component sys- tems. MGU, Moscow (1980) (in Russian). ve 1), and the concentration of singly ionized interstitial 3. A.M. Gas’kov, V.P. Zlomanov, A.V. Novoselova, Homoge- lead atoms decreases (Fig. 2, curve 2). neity region of lead telluride // Izv. AN SSSR, Neorgan. Doubly charged defects appear to be strongly com- mater. 15 (8), pp. 1476-1478 (1979) (in Russian). pensated. According to our calculation (Fig. 2, curves 3, 4. M. Schenk, H. Berger, A. Klinakov, Non-stoichiometry and 4), their concentration is rather high and amounts to point defects in PbTe // Cryst. Res. And Technol. 23 (1), pp. 20 –3 77-84 (1988). ~10 cm at Ts = 653 K. This is two orders of magni- 5. D.M. Zayachuk, V.A. Shenderovskii, Intrinsic defects and tude higher than the concentration of singly ionized de- electronic processes in AIVBVI // Ukr. Fiz. Zh. 36 (11), pp. fects (~1018 cm–3, Fig. 2), which is in turn exceeds the 1692-1713 (1991) (in Ukrainian). concentration of neutral defects (Fig. 2, curves 5, 6). This 6. H. Heinrich, Defects in IV-VI compounds // Lect. Notes. 133, is in full agreement with our assumption about the pre- pp. 407-426 (1980). 7. D.M. Freik, Ya.P. Saliy, I.M. Lishchinsky, The properties of dominance of the multiply charged vacancies and inter- PbTe thin films and quasi-chemical modelling of vapor-phase stitial atoms that can be in different charge states in the epitaxy // Zh. Fiz. Chim. 71 (12), pp. 2135-2137 (1997) (in presence of sufficiently shallow acceptor and donor lev- Russian). els [13]. Due to strong but incomplete compensation of 8. Ya.L. Charif, I.Ch. Avetisov, T.V. Zaychuk, P.V. Kovtunenko, Ionized and electroneutral intrinsic point defects in PbTe the doubly charged defects (Fig. 2, curves 3,4), singly and PbSe // Izv. AN SSSR, Neorgan. mater. 25 (4), pp. 567- charged defects play comparably important role in chan- 570 (1989) (in Russian). ging charge carrier concentration in PbTe films. 9. D.M. Freik, M.A. Galushchak and L.I. Mezhylovskaya, Thus, the crystal-chemical calculation of equilibrium Physics and technology of semiconductor films. Vyshcha of intrinsic atomic defects in cation sublattice of PbTe shkola, Lvov (1988) (in Russian). 10. F.A. Kröger. The chemistry of imperfect crystals. Mir, Mos- films shows that the assumption of simultaneous exist- cow (1969) (in Russian). ence of singly and doubly charged defects is most reason- 11. T.S. Moss, G.J. Burrel, B. Ellis, Semiconductor optoelecronics. able and is in agreement with the experimental data. Mir, Moscow (1976) (in Russian). 12. A. Lopez-Otero. The use of a phase diagram as a guide for the growth of PbTe films // Appl. Phys. Lett. 26 (8). pp. 470- 472 (1975). 13. V.L.Vinetskii, G.A.Cholodar. Statistical interaction of elec- trons and defects in semiconductors. Naukova dumka, Kiev (1969).

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