TRAP

Set coefficients of interstitial traps.

SYNOPSIS

trap
( silicon | oxide | poly | oxynitr | nitride | gas | aluminum | photores )
[ enable ] [ total = n ] [ frac.0 = n ] [ frac.E = n ]

DESCRIPTION

This statement allows the user to specify values for coefficients of the interstitial traps. The statement allows coefficients to be specified for each of the materials. SUPREM-IV has default values only for silicon. Polysilicon has not been characterized as extensively, and its parameters default to those for silicon.

The trap reaction was described by Griffin[1]. This model explains some of the wide variety of diffusion coefficients extracted from several different experimental conditions. The trap equation is:

where CT is the total trap concentration, KT is the trap reaction coefficient, e* is the equilibrium trap occupancy ratio. Instead of the reaction, the time derivative is used in the interstitial equation because it has better properties in the numerical calculation. The equation is derived from a simple interaction of an interstitial and a trap. To achieve balance in equilibrium, e* is defined to be CET / CT, the equilibrium number of empty traps divided by the total traps.

silicon, oxide, poly, oxynitr, nitride, gas, aluminum, photores
These parameters allow the specification of the material for which the parameters apply.

enable
This indicates that material specified has a finite number of traps.

total
This floating point parameter is used to specify the total number of traps, in cm-3. The default for silicon is 2.0E18 cm-3. This value is appropriate for Czochralski silicon material.

frac.0, frac.E
These floating point parameters allow the specification of the equilibrium empty trap ratio, e*. The default for these parameters is 2.39E5 cm-3 and 1.57 eV for the pre-exponential and activation energy for silicon.

EXAMPLES

trap silicon total=2.0e18 frac.0=0.5 frac.E=0.0 enable
This statement turns on interstitial traps and sets the total to 2.0E18 and the fraction to a half.

BUGS

There are no known bugs in this model. However, the model used here is involved in ongoing research, and may by out of date at any time. Further, experimental verification is difficult. The trap concentration will depend on the thermal history of the wafer, starting material, stress and temperature.

REFERENCES

  1. P. B. Griffin and J. D. Plummer, "Process Physics Determining 2-D Impurity Profiles in VLSI Devices," International Electron Devices Meeting, Los Angeles, p. 522, 1986.

SEE ALSO

The interstitial and vacancy statements.