ALBERT

Notes: The effects of hydrostatic pressure on the solid-phase epitaxial growth (SPEG) rate v of intrinsic Ge(100) and undoped and doped Si(100) into their respective self-implanted amorphous phases are reported. Samples were annealed in a high-temperature, high-pressure diamond anvil cell. Cryogenically loaded fluid Ar, used as the pressure transmission medium, ensured a clean and hydrostatic environment. v was determined by in situ time-resolved visible (for Si) or infrared (for Ge) interferometry. v increased exponentially with pressure, characterized by a negative activation volume of −0.46Ω in Ge, where Ω is the atomic volume, and −0.28Ω in Si. The activation volume in Si is independent of both dopant concentration and dopant type. Structural relaxation of the amorphous phases has no significant effect on v. These and other results are inconsistent with all bulk point-defect mechanisms, but consistent with all interface point-defect mechanisms, proposed to date.A kinetic analysis of the Spaepen–Turnbull interfacial dangling bond mechanism is presented, assuming thermal generation of dangling bonds at ledges along the interface, independent migration of the dangling bonds along the ledges to reconstruct the network from the amorphous to the crystalline structure, and unimolecular annihilation kinetics at dangling bond "traps.'' The model yields v = 2 sin(θ)vsnr exp[(ΔSf + ΔSm)/k] exp− [(ΔHf + ΔHm)/kT], where ΔSf and ΔHf are the standard entropy and enthalpy of formation of a pair of dangling bonds, ΔSm and ΔHm are the entropy and enthalpy of motion of a dangling bond at the interface, vs is the speed of sound, θ is the misorientation from {111}, and nr is the net number of hops made by a dangling bond before it is annihilated. It accounts semiquantitatively for the measured prefactor, orientation dependence, activation energy, and activation volume of v, and the pressure of a "free-energy catastrophe'' beyond which the exponential pressure enhancement of SPEG cannot continue uninterrupted due to a vanishing barrier to dangling bond migration. The enhancement of v by doping can be accounted for by an increased number of charged dangling bonds, with no change in the number of neutrals, at the interface. Quantitative models for the doping dependence of v are critically reviewed. At low concentrations the data can be accounted for by either the fractional ionization or the generalized Fermi-level-shifting models; methods to further test these models are enumerated. Ion irradiation may affect v by altering the populatio

Notes: With rapid solidification following pulsed laser melting, we have measured the dependence on interface orientation of the amount of solute trapping of several group III, IV, and V elements (As, Ga, Ge, In, Sb, Sn) in Si. The aperiodic stepwise growth model of Goldman and Aziz accurately fits both the velocity and orientation dependence of solute trapping of all of these solutes except Ge. The success of the model implies a ledge structure for the crystal/melt interface and a step-flow mechanism for growth from the melt. In addition, we have observed an empirical inverse correlation between the two free parameters ("diffusive speeds'') in this model and the equilibrium solute partition coefficient of a system. This correlation may be used to estimate values of these free parameters for other systems in which solute trapping has not or cannot be measured. The possible microscopic origin of such a correlation is discussed.

Notes: A thermodynamic formalism is developed for illuminating the predominant point defect mechanism of self- and impurity diffusion in silicon and is used to provide a rigorous basis for point defect-based interpretation of diffusion experiments in biaxially strained epitaxial layers in the Si–Ge system. A specific combination of the hydrostatic and biaxial stress dependences of the diffusivity is ±1 times the atomic volume, depending upon whether the predominant mechanism involves vacancies or interstitials. Experimental results for Sb diffusion in biaxially strained Si–Ge films and ab initio calculations of the activation volume for Sb diffusion by a vacancy mechanism are in quantitative agreement with no free parameters. Key parameters are identified that must be measured or calculated for a quantitative test of interstitial-based mechanisms. © 1997 American Institute of Physics.

Notes: We have investigated the effect of hydrostatic pressure on interdiffusion in multilayers composed of alternating layers of amorphous Si (2.7 nm) and Ge (3.1 nm). Samples were annealed at 420 °C at pressures between 0 and 2.8 GPa in an externally heated diamond anvil cell. Interdiffusion was measured by monitoring the decay with annealing time of the intensity of the first-order x-ray reflection resulting from the effects of composition modulation. The decay curves for all pressures could be made to coincide by scaling the annealing times. This made it possible to separate the effects of pressure on the interdiffusivity from those of composition and structural relaxation. The interdiffusivity increased with applied pressure, with an activation volume of −5.0 cm3/mole, or −0.42 times the atomic volume of crystalline Si. © 1996 American Institute of Physics.

Notes: We have measured the effect of pressure on As diffusion in Ge. Diffusion anneals on ion-implanted samples were carried out in a high-temperature diamond anvil cell using fluid argon as a clean, hydrostatic pressure medium. At 575 °C over the pressure range 0.1–4 GPa, pressure slightly enhances the diffusivity, characterized by an activation volume of −1.7±1.4 cm3/mole or −0.12±0.10 times the atomic volume. The results call into question the prevailing view that diffusion of groups III, IV, and V elements are mediated entirely by vacancies. If diffusion of As is mediated entirely by vacancies then either the vacancy formation volume must be unexpectedly low or the energy of vacancy migration must be unexpectedly high. © 1996 American Institute of Physics.

Notes: The diffusivity of B in Si is enhanced by pressure, characterized by an activation volume of V*=−0.17±0.01 times the atomic volume; V* is close to the formation volume of the self-interstitial determined by atomistic calculations. The results for hydrostatic pressure are used to make predictions for the effect of biaxial strain on diffusion. Assuming an interstitial-based mechanism and a range of values for the anisotropy in the migration volume, comparison is made between our results, the atomistic calculations, and the measured dependence of B diffusion on biaxial strain. We find a qualitative consistency for an interstitial-based mechanism with the measured strain effect on diffusion in Si–Ge alloys, but not with the measured strain effect in pure Si. Experiments and calculations to determine the origin of this discrepancy are discussed. © 1999 American Institute of Physics.

Notes: We report a comparison between theory and experiment for a general stress-induced morphological growth instability that is kinetically rather than energetically driven. Stress variations along a perturbed planar growth front result in variations in interfacial mobility in a manner that is destabilizing under one sign of the stress state and stabilizing under the opposite sign, even for a pure material. Investigation of solid-phase epitaxial growth at a corrugated Si(001) interface under both compression and tension results in good agreement between experiment and theory with no adjustable parameters, demonstrating that this mobility-based mechanism is dominant in determining morphological evolution in this system. © 2000 American Institute of Physics.

Notes: The diffusivity of Sb in Si is retarded by pressure, characterized at 860 °C by an activation volume of V*=+0.07±0.02 times the Si atomic volume. V* is close to values inferred from atomistic calculations for a vacancy mechanism. Our results for hydrostatic pressure are used to predict the effect of biaxial strain on Sb diffusion. The prediction matches measured behavior for Sb diffusion in biaxially strained Si and Si–Ge films. This work lends additional support to the predominance of the vacancy mechanism for Sb diffusion and demonstrates the first steps in the development of a capability for predicting the effect of nonhydrostatic stress on diffusion. © 1999 American Institute of Physics.

Notes: A high-temperature pressure calibration technique using Sm-doped Y3Al5O12 (Sm:YAG) crystal as the pressure calibrant has been developed by studying its Y1 through Y10 fluorescence peaks (frequencies from 15 600 to 17 200 cm−1) at pressures (p) from 1 bar to 19 GPa and temperatures (T) from 20 to 850 °C in externally heated diamond anvil cells. The entire spectrum was fit to a sum of ten Lorentzians plus a linear background. The positions, relative intensities and widths were represented by empirical functions of p and T. Several fitting routines for p determination were created based on these dependences, and were tested on various high-p and high-T experimental Sm:YAG fluorescence spectra. The p values obtained from the fitting routines are compared with those obtained from the ruby and the nitrogen (N2) vibron pressure scales. A fitting routine is proposed that can determine p from 20 to 850 °C within an estimated uncertainty of 0.4 GPa. © 1998 American Institute of Physics.

Notes: We have measured the crystal growth rate u of B2O3-I in the amorphous phase, as it varied over five orders of magnitude with changes in temperature and pressure. We eliminated the crystal nucleation barrier by seeding the surface of boron oxide glass with crystals. u became measurable only when the pressure exceeded a threshold level near 10 kbar. Using the published thermodynamic information on the B2O3 system and a crude free-energy model for the crystal and glass phases, we account qualitatively for our results with the theory of crystal growth limited by the rate of two-dimensional nucleation of monolayers. The constants for the prefactor, activation energy, activation volume, and ledge tension are determined by fitting. By adjusting the thermodynamic parameters to a set of values that are well within the ranges delineated by their experimental uncertainties, we account quantitatively for the measured growth rates from 300 to 500 °C and from 0 to 30 kbar with the following relation: u(T,P)=(785 m/s)[||ΔGm||/(RT)]1/6 ×exp[π×3 A(ring)(420 erg/cm2)2(28 cm3/mole)/(3 kTΔGm)]exp[−10 366 cal/mole/(RT)] ×exp[−P×16 cm3/mole/(RT)]×{1−exp[ΔGm/(RT)]}2/3, with the driving free energy given by ΔGm(T,P)=(13 cm3/mole) [PM(T)−P] and the melting curve given by PM(T)=(T−450 °C)/(42.6 K/kbar). The "B2O3 crystallization anomaly'', that crystals have never been observed to grow at atmospheric pressure, is explained, since according to our model, the frequency of two-dimensional nucleation is negligible at all temperatures at pressures less than 10 kbar.