Calorimetric evidence for structural relaxation in amorphous silicon

Abstract

Differential scanning calorimetry of amorphous silicon (<z-Si) prepared by ion implantation shows a one-time low-temperature heat release, equal to one-third of the heat of crystallization. This heat release is direct evidence for structural relaxation of cr-Si. It is in agreement with predictions made on the basis of Raman spectrometry.PACS numbers: 61.40.+b, 44.60.+k, 64.60.My, 78.30.Ly The structure of amorphous silicon (a-Si) has been the subject of study for many years and the emerging picture is that of a covalently bonded continuous random network. * On the average, the angles between bonds diverge 7°-12° from the ideal tetrahedral angle in a perfect crystal, yet there is only short-range order due to a large freedom in rotation around the axes parallel to the bonds. 1,2 It is generally assumed that the bond lengths are only slightly distorted. The strain energy associated with tetrahedral bond angle distortions is thought to constitute the main portion of the excess enthalpy of a-Si relative to crystalline Si (c-Si). 3 Ball and stick models 1,2 as well as computer simulations 4 " 6 indicate that changes in network topology coincide with changes in average bond angle distortion (AG), and consequently with changes in the excess free energy of a-Si. A decrease in A6 upon annealing is known as structural relaxation.Experimental indications that structural relaxation does indeed occur in a-Si came from Raman spectroscopy. 7 " 9 In these measurements the phonon density of states is probed, and changes in the phonon spectrum after thermal annealing treatments can be related to changes in A0. These changes consist essentially of a decrease in the width and a shift in the position of the firstorder transverse-optic-like (TO) peak. The width is thought to be approximately linearly dependent on AG. 2, Although there is little doubt that this interpretation of Raman spectra is qualitatively correct, 3,9 " 14 there is no general agreement on the quantitative relation between Raman spectra and bond angle distributions. In addition, the force constant in Si which relates bond bending to strain energy is not exactly known. 3 Estimates of the minimum and maximum obtainable strain energy were originally 12 and 40 kJ/mol. 7 Although these are values for the strain energy at 0 K, they may be used to estimate the heat of relaxation A// re iax. It follows that AH re i ax may be as high as 28 kJ/mol. More recent estimates for AH r eiax are 9 kJ/mol 3 and 4 kJ/mol. 14 A calorimetric study of crystallization in a-Si and a-Ge showed that both materials release a considerable

Mechanisms of boron diffusion in silicon and germanium

“…[22][23][24][25] Both the coordination defects and the bond angle distortion depend on the process history of a-Si, since it was widely shown that as-implanted a-Si, if annealed, undergoes a structural relaxation, with a heat release measured by differential scanning calorimetry at temperatures below the onset of crystallization. 26 In the mid nineties, after investigation through Raman spectroscopy, x-ray techniques, and photocarrier lifetime measurements, the origin of this relaxation was attributed to the recombination of the coordination defects, decreasing from $0.5% to 0.05%, and to the reduction of the bond angle distortion, from 12 to 9 . 20,27 Such a process was shown to be reversible, even if with an hysteresis loop, since ion implantation (leading to a damage level larger than $0.1 displacements per atom) performed on relaxed a-Si reproduces the same strain status as in the asimplanted a-Si.…”

Quantification of the bond-angle dispersion by Raman spectroscopy and the strain energy of amorphous silicon

“…23 Experiments have shown that during relaxation, the bond-angle dispersion and the density of point defects diminish. 5,8,12,24,25 This evolution has been simulated by molecular dynamics, too.…”

“…An interesting prediction of our analysis is that the heat of crystallization of a-Si may be lower than the reported values of 11-14 kJ/mol. 23,38,39 If the density of defects were lower, Q cryst could be as low as 6.6 kJ/mol. In fact, the first crystallization experiments of a-Si reported a value of 9.2 kJ/mol.…”

Growth-in-place deployment of in-plane silicon nanowires

“…1(a), arises from the difference in Gibbs energy between hydrogenated amorphous Si (a-Si:H) and crystalline Si. 11 A unique feature of the in-plane growth lies in that the movement of catalyst drops can be guided by simple surface features, like a single edge step. This allows to determine the position and the growth path of the SiNWs 7,8,10,12 and offers an exciting opportunity to position the in-plane SiNWs during their growth without interrupting the vacuum.…”