Fundamental Mechanisms for Hg Vacancy and Interstitial Modeling in Mercury Cadmium Telluride
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Mat. Res. Soc. Symp. Proc. Vol. 389 0 1995 Materials Research Society
influenced by both diffusion down a concentration gradient, represented by the usual Fickian diffusion equations, and defect interactions through the Frenkel mechanism. That is, Hg interstitials and vacancies are generated and recombined in proportion to the rate constants g and kiv respectively, as seen in Eq. 1. The rate of generation and recombination at a certain point also depends on the concentration of defects at that point. If the Hgi or VHg are below their equilibrium values, Hg atoms will leave the cation lattice to generate more defects. Eq. 1 will be driven in the forward direction. The chemical reaction will be driven in the reverse direction when the defects are above their equilibrium values. Eqs. 2 and 3 give the coupled continuity equations for Hgi and VHg that SUMerCad solves to model type conversion. 4 Di and Dv are the diffusion coefficients for Hg interstitials and vacancies respectively.
dHgi
Hg
,
D
2
- --= dVHg
D
Hg
+
(1)
Hg__,
2 -•-
+g- vHgVi + g- kiHgV
(2) (3)
The algorithm developed discretizes the coupled partial differential equations using an iterative Crank-Nicolson discretization scheme. 5 Eq. 4 is used to solve for the flux of interstitials at the front and back boundaries. The first term is negative for the front surface and positive for the back. The assumption is made for the type-conversion problem that there is no flux of vacancies at the boundaries. (In other words, no material is etched or grown.) ±dHg +
dx
his ,rf( 2)Hgi =
isurf(3)
(4)
The algorithm uses a menu based input to allow the user to control the starting material's properties and the anneal conditions. SUMerCad creates a graphical output of the diffusion profile as a function of depth for each step in time. The discretizations in space are simply made by dividing the sample thickness by the number of specified resolution points. The time step is automatically increased by a factor proportional to the current time step and the maximum relative concentration change. Determination of parameters in SUMerCad The accuracy of the SUMerCad process model depends on the precision of the parameters used by the simulator. In order for SUMerCad to be an effective tool in predicting the effect of anneals on the type conversion junction, the following parameters must be determined: the equilibrium concentrations of Hgi and VHg, the point defect diffusion coefficients (Di and Dv), the rate constants (g and kiv) and the boundary condition constants (hisurf(2) and hisurf(3)). Because the Hg vacancies are doubly ionized, their concentration can be measured fairly easily using techniques such as differential Hall. The equilibrium vacancy concentration in
48
SUMerCad was obtained from the experimental data of Schaake 6 and Vydyanath 7 under Hg rich and Te rich anneal conditions, Fig. 1. The vacancy concentration used differs from that predicted by Vydyanath at low temperatures under Te rich conditions. Vydyanath's data was experimentally deter
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