Kinetics and Morphological Instabilities of Stressed Solid-Solid Phase Transformations

Abstract

An atomistic model of the growth kinetics of stressed solid-solid phase transformations is presented. Solid phase epitaxial growth of (001) Si was used for comparison of new and prior models with experiments. The results indicate that the migration of crystal island ledges in the growth interface may involve coordinated atomic motion. The model accounts for morphological instabilities during stressed solid-solid phase transformations. DOI: 10.1103/PhysRevLett.100.165501 PACS numbers: 61.72.uf, 61.43.Dq, 68.55.Aÿ The study of stressed solid-solid phase transformations has been a topic of fundamental and technological importance for several years [1][2][3]. However, there are inconsistencies between understanding the atomistic nature of solid-solid phase transformations and the current model of stress-dependent growth. Current atomistic theory suggests growth occurs via nucleation of two-dimensional crystal islands of the growing phase with subsequent migration of island ledges in the interface between the two phases [4,5]. However, the current stress-dependent growth model does not address this and assumes growth occurs via a single, unspecified atomistic process [6]. In this Letter, a model of stress-dependent growth is presented to account for new experimental observations of stress-dependent growth kinetics in conjunction with the current understanding of the atomistic nature of growth.The current model used to describe the influence of a stress state, ij , on the macroscopic velocity, v, of an advancing growth interface is given by the activation strain tensor, V ij kT@ lnv=@ ij , given bywhere v0 is the stress-free velocity, kT has the usual meaning, and i and j refer to axes in the coordinate frame of reference [6]. By convention, 1 and 2 are the in-plane directions, 3 is the growth direction, and positive (negative) elements of ij are tensile (compressive). The basis for Eq. (1) is the observation that for many solid-solid phase transformations, v0 v 0 expÿG =kT over a wide temperature range where v 0 is a temperature-independent prefactor and G is the activation energy for macroscopic growth as given by transition state theory (TST) [7,8]. However, Eq. (1) assumes a single, unspecified atomistic process is responsible for growth thus contradicting current understanding of solid-solid phase transformations [4,5]. Hence, it is assumed V ij V n ij V m ij , where V n ij and V m ij are the activation strain tensors associated with nucleation and migration processes [6]. The use of V ij is accepted for stressed solid phase epitaxial growth (SPEG) of (001) Si amorphized via ion-implantation [1,6,9,10]. However, using new results of stressed SPEG of (001) Si as a model system, a model of stressed solid-solid phase transformations is advanced which isolates the nucleation and migration processes. The results suggest that coordinated atomic motion may play a role in island ledge migration.In this study, a polished 50 m-thick (001) Si wafer was Si -implanted at 50, 100, and 200 keV to doses of 1 10 15 , 1 10 15 ...

Dopant-stress synergy in Si solid-phase epitaxy

“…10 In conjunction with recent work 11,12 where the stress-free growth velocity was shown to be given by =2⌬x n ͑0͒ −1 , where ⌬x is the monolayer spacing ͑0.14 nm͒, Eq. ͑1͒ may be rewritten as = 2⌬x ͑0͒ is the intrinsic ij = 0 time for ledge migration along 1 and ⌬V 11 m,11 is the activation volume for ledge migration along 1 in the 1 direction.…”

“…1͑b͒-1͑d͒, 83Ϯ 25, 64Ϯ 14, and 57Ϯ 10 nm of growth occurred which is less than the 11 = 0 case. The growth interface was observed to roughen significantly with 11 Ͻ 0, presumably due to kinetically driven instabilities. 11,13 In contrast, annealing with 11 = 0.5 and 1.0 GPa, shown in Figs.…”

“…The growth interface was observed to roughen significantly with 11 Ͻ 0, presumably due to kinetically driven instabilities. 11,13 In contrast, annealing with 11 = 0.5 and 1.0 GPa, shown in Figs. 1͑g͒ and 1͑h͒, produced nominally the same amount of growth as the 11 = 0 case.…”

“…These observations are qualitatively consistent with recent studies of intrinsic stressed SPEG. 11,12 The ␣-Si thickness as a function of anneal time was measured for different 11 as shown in Fig. 2.…”

“…2 indicating a peak C B of ϳ3.0ϫ 10 20 cm −3 ϳ200 nm deep. In cases of 0  ഛ 11 ഛ 1.0 GPa, the ␣-Si thickness versus time behavior was nominally the same for all 11 in this range and thus only the 11 = 0 set of data is reported for clarity. The growth kinetics for 11 Ͻ 0 were greatly retarded compared to the 0 ഛ 11 cases.…”