The configurational energy gap between amorphous and crystalline silicon

Abstract

The crystallization enthalpy of pure amorphous silicon (a-Si) and hydrogenated a-Si was measured by differential scanning calorimetry (DSC) for a large set of materials deposited from the vapour phase by different techniques. Although the values cover a wide range (200 -480 J/g), the minimum value is common to all the deposition techniques used and close to the predicted minimum strain energy of relaxed aSi (240 ± 25 J/g). This result gives a reliable value for the configurational energy gap between a-Si and crystalline silicon. An excess of enthalpy above this minimum value can be ascribed to coordination defects.In contrast to glasses, whose lower energy states can be accessed by either cooling the liquid at lower rates or by thermal annealing [1], the energy of amorphous tetrahedral semiconductors must be lowered by thermal annealing [2]. Among them, amorphous silicon (a-Si) has been extensively studied due to its technological relevance and because it is usually taken as a model material for covalent amorphous networks.We have recently shown [3] that after thermal annealing, the rms deviation from the tetrahedral angle, Δθ, is approximately 9° for a broad range of pure and hydrogenated a-Si materials. This "relaxed state" of pure a-Si (no H-atoms remain after annealing) gives support to the theoretical prediction [4] that it is not possible to build stable amorphous models below minimum bond-angle dispersion. In other words, there is a 'configurational gap' between a-Si and c-Si that ensures higher entropy in the amorphous state. This discontinuity makes it impossible for the material to evolve from one state to the other by continuously varying its short-range order.The bond-angle dispersion entails a built-in strain energy that is released during crystallization [5] and currently detected by differential scanning calorimetry (DSC) as an exothermic peak [6]. By measuring the crystallization enthalpy, ΔH cryst , we can, thus, determine the value of the 'configurational energy gap' between a-Si and c-Si. To date, the only systematic measurements of ΔH cryst have been taken from a-Si obtained by ion implantation of c-Si [6] (measurements on hydrogenated thin films being very scarce [7]). Since the experimental values felt within a narrow range (see the right side of Fig. 1), it is generally accepted that they correspond to the minimum energy of a-Si.However, since this method of synthesis is very far from equilibrium, there is good reason to suspect that, even after thermal annealing, the material has not reached its lowest energy level. In fact, we suggested [8] that one half of ΔH cryst of this material was due to high concentration of coordination defects and, consequently, predicted that the crystallization enthalpy could be reduced by this factor in defect-free materials.Recent studies of organic glasses [9] have shown that, thanks to a higher molecular mobility at the film free surface [10], deposition from the vapour phase is a way to achieve low-energy amorphous states. This behaviour could also apply ...

Can the crystallization rate be independent from the crystallization enthalpy? The case of amorphous silicon

“…They argued that the interface velocity (essentially, r n ) was dominated by the regions which are less enthalpic between the defects, which would account for most of the a-Si volume. Since our interpretation of the crystallization enthalpy variations from sample to sample relies on varying densities of point defects [10], the argument of [13] could be translated to the absence of any systematic variation of the growth rate of our samples.…”

“…These nucleation zones could also be the result of the inhomogeneous spatial distribution of structural defects. In fact, in our recent paper devoted to quantifying h c [10], we proposed that the excess of enthalpy above the minimum value common for all deposition techniques was due to different densities of structural defects. Nucleation could occur in those better ordered regions, free of defects.…”

“…to a minimum value of the crystallization enthalpy around 240 J g −1 (the configurational energy gap between a-Si and c-Si) [10] that would determine the g c value of the defect-free microscopic regions where nucleation occurs.…”

“…It is argued that nucleation would be easier in these regions. We have recently shown [10] that the crystallization enthalpy of a-Si varies within a factor of 2 for a large set of a-Si materials grown by different techniques. Since the classical theory of nucleation states that both nucleation and growth depend on the free energy of the amorphous state [1], one would expect a clear dependence of the crystallization rate on the crystallization enthalpy.…”

Measurement of the specific heat and determination of the thermodynamic functions of relaxed amorphous silicon

“…3 Determination of a-Si thermodynamic functions needs its entropy and enthalpy at a given temperature and its specific heat to be determined. The enthalpy at the crystallization temperature has recently been shown to vary between 5.6 and 13.5 kJ/mol for relaxed a-Si, depending on the particular a-Si material, 4 with the minimum value being below 1 = 2 the value usually taken as standard. 5 All calculations made so far 6,7 rely on this "standard" value, on a theoretical value of the entropy at 0 K (Ref.…”