Fundamentals of Physical Vapor Transport Process

Abstract

The crystal growth of physical vapor transport (PVT) transforms the original source material powder into the final form of compound semiconducting crystal in a closed ampoule. The vapor species were transported from the source at one end of the ampoule to the crystal at the other end because of the applied temperature gradient between the source and the crystal. To understand the fundamentals of PVT, one of the most important parameters during PVT, the partial pressures of the vapor species in equilibrium with the compounds as a function of temperature with different stoichiometry, have been measured by optical absorption technique to establish the three-phase curve. Then using an associated solution model for the liquid phase, which is assumed to consist of certain atomic/molecular species, the Gibbs energy of mixing for the liquid can be expressed in terms of the interaction parameters between these species. After the establishment of the best-fit parameters, the complete phase diagram and thermodynamic properties of the system can be generated for the applications of crystal growth experiments. The thermodynamic analysis has been applied to binary, ternary and quaternary systems such as Hg–Te, Cd–Te and Hg–Cd–Te as well as In–Sb, Ga–Sb and In–Ga–Sb, Hg–Cd–Zn–Te, Zn–Se and Zn–Se–Te. Then, a one-dimensional diffusion model, which includes the vapor species in equilibrium with a binary compound and the residual inert gases, was established to identify the critical growth parameters such as the heat treatment conditions, the thermal field for the growth process, the composition of the grown (ternary) crystal as well as the growth rate. From the results of the one-dimensional diffusion analysis, four experimentally adjustable parameters: the source temperature, the deposition temperature, the partial pressure ratio over the source and the residual gas pressure, determine the diffusive mass flux in a PVT system. However, two of these four parameters, the partial pressure ratio over source and the residual gas pressure, are more critical than the others.

Appendix

2.1.1 A.1 Thermophysical Properties of Vapor Phase

2.1.1.1 A.1.1 Viscosity

The viscosity of a one-component gas phase can be calculated by assuming a Lennard-Jones 6-12 intermolecular potential between species as:

$$\varPsi \left( r \right) = 4\varepsilon \left( {\left( {\frac{\sigma }{r}} \right)^{12} - \left( {\frac{\sigma }{r}} \right)^{6} } \right)$$

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The two interaction parameter, ε and σ, are, respectively, the potential well depth and the intermolecular distance at Ψ = 0. The viscosity μ is then given by:

$$\mu = 26.69\frac{{\sqrt {MT} }}{{\sigma^{2} \varOmega_{\upsilon } }}$$

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where μ is in micro-poise, T in K, σ in $\dot{A}$ and

$$\varOmega_{\upsilon } = \frac{A}{{T_{r}^{B} }} + \frac{C}{{\exp (DT_{r} )}} + \frac{E}{{\exp (FT_{r} )}}$$

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where T_r = kT/ε and A = 1.16145, B = 0.14874, C = 0.52487, D = 0.77320, E = 2.16178, F = 2.43787.

The viscosity of a gas mixture, μ_m, at low pressure is given by:

$$\mu_{m} = \sum\limits_{i = 1}^{n} {\frac{{y_{i} \mu_{i} }}{{\sum\limits_{j = 1}^{n} {y_{j} \varphi_{ij} } }}}$$

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where

$$\phi_{ij} = \frac{{\left( {1 + \left( {\mu_{i} /\mu_{j} } \right)^{1/2} \left( {M_{j} /M_{i} } \right)^{1/4} } \right)^{2} }}{{\left( {8\left( {1 + M_{i} /M_{j} } \right)} \right)^{1/2} }}$$

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and μ_i, and y_i are the viscosity of pure-component i and mole fraction of species i, respectively.

2.1.1.2 A.1.2 Thermal Conductivity

The thermal conductivity of a gas system, κ, is related to its viscosity, μ, by the Eucken factor, f_Eu:

$$f_{Eu} = \frac{\kappa M}{{\mu C_{\upsilon ,m} }} = 1.32 + 1.77\left( {\frac{R}{{C_{\upsilon ,m} }}} \right)$$

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where M is the molar weight, C_υ,m the molar heat capacity at constant volume and R the gas constant.

2.1.2 A.2 Thermophysical Properties of a Typical ZnSe PVT Growth System

T (source)	1160 ℃	μ (viscosity)	4.3 × 10−4 poise (g/s cm)
T (crystal)	1130 ℃	ν (kinematic viscosity) = μ/ρ	36 stoke (cm2/s)
PZn	0.11 atm	a (radius)	0.75 cm
PSe2	0.0007 atm	L (length)	10 cm
Presidual gas (36% CO2, 26% CO 26% N2 and 12% H2)	0.01 atm	g0 (gravitational acceleration)	980 cm/s2
β = 1/T (thermal expansion)	7.1 × 10−4 K−1	κ (thermal conductivity)	5.42 × 10−4 J/cm s K
ρ (density)	1.2 × 10−5 g/cm3	Cν (heat capacity)	0.76 J/g K