Novosibirsk (b)l). The Formation of Partial Misfit Dislocations during Heteroepitaxy. BY. A. K. GUTAKOVSKII (a), S. I. STENIN (b), and B. G. ZAKHAROV (b),.
A. K. GUTAKOVSKII e t al.: The Formation of Partial Misfit Dislocations
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phys. stat. sol. (a) 67, 299 (1981) Subject classification: 1.5 and 10.2; 3; 22.2.1
Novosibirsk State University ( a ) and Institute of Semieondactor Physics, Academy of Sciences of the USSR, Siberian Branch, Novosibirsk ( b ) l )
The Formation of Partial Misfit Dislocations during Heteroepitaxy BY
A . K. GUTAKOVSKII (a), S. I. STENIN(b), and B. G. ZAKHAROV (b), A model for determining the critical mismatch (f*) and mismatch gradient ( k * ) parameters is developed. When f and k are higher than the above parameters the formation of partial misfit dislocations gets energetically preferable. A polar diagram off* on substrate orientation and dependences off* and k* on energy of stacking faults ( y ) for the (100) orientation of interface are worked out. The values f* and k* for the heteroepitaxial system GaAsl-,P,-GaAs (100) are verified experimentally. Doping of GaAsl-,P, films with tellurium up to 10l8 C M - ~ results in lower f* from 7.4 x to 2 x that is due to lower y in doped films compared to films non-doped or doped with Zn. The decrease of y is to be more than 3 x J m-2. P a s p a G o ~ a ~Monenb a n m onpeneneHm KpmTmecmx Benmm napaMeTpa HecooTBeTCTBIlR (f*) H rpanlleHTa IIapaMeTpa HeCOOTBeTCTBHfI ( k * ) , JIpH npeBbIIIIeHE314 IiOTopbIX 3HepTeTkI9eCKM BbIrOnHO 06pa30BaHEIe 9aCTM9HbIX nHCJlOIEaI@ HeCOOTBeTCTBklH. nOCTp0em1 nonHpHaFi EHarpaMMa ~ ~ B H C E I M O C TfH* OT opHeHTaIpm no~lnozmm,a TaKxe ~ ~ B H C E I MOCTEI f * EI k* OT a ~ e p r m neaewa i ynaKoBm ( y ) npm opneHTaqm rpaHwbr paanena no (100). aKCIIepHMeHTaJIbH0 BeJIEI9ElHbI f* II k* IlpOBepeHbI AJIH reTepO3nEITaKCEIaJIbHOfi cmcTeMbi GaAsl -,P,-GaAs (100). n o ~ a 3 a ~ oTO , zer&%poBaHme IIneHoI; GaAsl -%PZ TeJIJIypOM A 0 HoHUeHTpaUEIEI 10'' IIPHBOALIT H CHHmeHEIH) f * OT 7, 4 X m3A0 2 X lo-'. 3 T O T 3@@KT 06bRCHHeTCX IIOHHXeHHeM B JIerHpOBaHHbIX IlJIeHIiaX ll0 CpaBHBHLIH) C HeJIerHpOBaHHbIMH HJIH JIerHpOBaHHbIMH UHHKOM. OueHeHO, 9 T O y AOJIltcHa YMeHbIIIaTCbH 6onee, 9eM Ha 3 X lo-' J m-'.
1. Introduction A theory of stress relaxation with partial misfit dislocations (MD's) has been first developed by the authors [l to 33. By that time partial MD's has been already observed in some metallic heterosystems [2, 4, 51. Later this type of MD's had been discovered for heteroepitaxy of semiconductors [B, '71. The partial MD's form in the film bulk the stacking faults and deformation microtwins which are known to change essentially the properties of both films and heterojunctions. Knowledge of conditions for arising partial MD's is very important. The theoretical analysis [7, 81 has revealed the main heterosystem parameters which determine a dominant type of MD's a t the early stages of stress relaxation. They include the mismatch parameter (f), the mismatch gradient in the buffer layer (k)(if it exists), crystallographic orientation of interface ( a ) , and stacking fault energy ( y ) . I n [7] a polar diagram for the critical thickness of a pseudomorphic film (h,) depending on 01 (Fig. l a ) has been constructed, and also the existence of critical values f * , k*, and a*,a t which M D types are changed, has been deduced. The change of M D type a t 01 =a* was observed in [7] experimentally. The present work has been carried out t o experimentally verify the existence of f * and k* as well as t o investigate the dependence of f * on 01 and the influence of doping on it. l)
Prospekt Nauki 13, 630090 Novosibirsk-90, USSR.
A. K. GUTAPOVSKII,S. I. STENIN,and B. G . ZAKHAROV
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a
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Fig. 1. Polar diagranls of a) h, and b) f* dependences on a. The calculations have been performed with G = 4.7 x lo2 N m-2, v = 0.24, b, = 0.4 nrn, b, = 0.23 nm. a ) (1) f = 0.04, (2) 0.015, and Jm-2; for partial MD, - - - - for perfect (3) 0.007; (1) y = G x ( 2 ) , (3) 5 x MD. For (1) and (2) the distance betmeen circles is 3, for (3) 4.5 nm. b) (1) y = 2.5 X (2) J m-”. The distance between circles corresponds t o f* = 1 x 5 x 10-2, and (3) 6 x ~
2. Theory The condition determining the dominant MD type is written as follows: hc0 5 hcp (1) where hcOand h,, are the critical thicknesses for forming perfect and partial MD’s, respectively. Here and below the index 0 stands for perfect dislocation and p for partial one. With h c O h,, the perfect MD’s form, and with hcO h,, partial ones arise. If MD’s are formed by gliding of half loops from the growth surface, then lice and h,, according t o [7] are Y
>
f * partial ones. I n [7] an approximate expression has been obtained for f * in the case of singular substrate orientation along (111),(110), or (100) when all the active slip systems are equivalent. For arbitrary orientation of the interface the finding of f * is essentially more complicated. Since in diamond or sphalerite lattices (all the calculations have been done for these lattices) there are 12 slip systems for peIfect MD’s characterized by p and 8 angles and the same number for partial ones, then in the most common case for every substrate orientation t o find f * it is necessary t o analyze 144 equations of type (1).As it is shown in [7]MD’s with maximum edge
