Extended Point Defects in Crystalline Materials: Ge and Si

Abstract

B diffusion measurements are used to probe the basic nature of self-interstitial 'point' defects in Ge. We find two distinct self-interstitial forms -a simple one with low entropy and a complex one with entropy ~30 k at the migration saddle point. The latter dominates diffusion at high temperature. We propose that its structure is similar to that of an amorphous pocket -we name it a morph. Computational modelling suggests that morphs exist in both self-interstitial and vacancy-like forms, and are crucial for diffusion and defect dynamics in Ge, Si and probably many other crystalline solids.A vast array of crystalline material properties arises from the behavior of atomic-scale 'point'defects, yet these defects are poorly understood. Knowledge of simple point defects -single atoms added interstitially to, or missing from, an otherwise undisturbed lattice -is well established from quantum theoretical calculations and low-temperature experiments, but diffusion experiments hint that more complex entities may be involved at high temperatures relevant to industrial processing [1][2][3][4][5]. This Letter provides the first definitive evidence for these elusive complex defects and presents a specific physical model for their structure and diffusion. 2 Recent interest in Ge-based nano-electronics has led to basic studies on diffusion [5][6][7][8][9] and implantation defects [10,11] in crystalline Ge. Most dopants in Ge are found to diffuse by vacancy mechanisms, with activation energies below that of vacancy-mediated self-diffusion (≈ 3.1 eV), but boron diffusion is an exception with an activation energy of ≈ 4.65 eV [6,12].Experiments [5,[7][8][9] show that boron diffuses via the reaction B + I  BI, where 'B' represents substitutional boron, 'I' the self interstitial, and 'BI' a mobile dopant-interstitial complex. The energetics involved is illustrated in Figure 1.The reduction in free energy on forming BI enables it to migrate a mean projected distance λ before dissociating to B and I. The mean number of jumps before dissociation depends on the energy difference between migration and dissociation of BI and the diffusional entropies of I and BI. In general,A is the impurity (here, boron), X the point defect driving AX diffusion (here, I), a the capture radius for the forward reaction, f AX the diffusion correlation factor (~1), E AX , S AX , E self,X , S self,X the activation energies and entropies of impurity diffusion and self-diffusion via the species AX and Fig. 1. Schematic of total energy versus configuration for the reaction mediating B diffusion in Ge. Also shown are energies inferred from previous experiments. E BI and E self,I are the respective energies of BI and I at their migration saddle points, relative to that of substitutional B. Under RED conditions (dashed curve) the fitted values of E λ shift 0.025 eV in the negative direction. This could be accounted for by a reduction of 0.05 eV in the migration energy of BI under H irradiation. T (°C)4To test this idea we have repeated the experiments...

Ultrafast Generation of Unconventional{001}Loops in Si

“…Energy plateaus are indicative of the presence of disordered I-clusters, whose dominance at high temperatures is favored with respect to ordered structures due to their high configurational entropy [31]. The existence of these high entropy amorphous configurations of Is at high temperatures is in line with the "morph" postulated by Cowern and coworkers to explain high-temperature diffusion experiments in Si and Ge [32]. Even though disordered I-clusters in our simulations may involve tens of excess Is and even hundreds of DAs, we observe that they are highly mobile and rapidly grow by interacting with other mobile disordered aggregates or immobile tetra-Is.…”

Diffusion of point defects in crystalline silicon using the kinetic activation-relaxation technique method

“…Even for such a simple symmetry, the number of low-energy pathways associated with adatom diffusion turns out to be remarkably large, with concerted diffusion taking place, as discovered later by Henkelman and Jonsson, over a range of atomic distances [2]. Similar complexity is also observed in bulk systems such as silicon [3][4][5][6][7] and iron [8][9][10], as demonstrated by extensive searches for defect structures and pathways. Understanding these microscopic mechanisms is crucial then for the characterization of long-time defect diffusion and structural evolution.…”

Diffusion ofn-type dopants in germanium

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