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Evaluation of Charge Injection Boundary Condition
10 5
-. . . . .. . . .
.
4.1.3
Case
Case
Case
Case
1
2
3
4
.... .............
100
C)
1n
20
30
40
50
60
70
80
F- n in kV
Figure 4-11: Charge injection term from equation (3.5) (see table 4.2 for cases).
Cases 1 through 3 for the charge injection parameters provide less variation in
the required current density to satisfy equation (3.30) compared to case 4.
The
high sensitivity to the normal electric field provided by case 4 results in a closer
approximation to the ideal charge injection boundary condition given by equation
(3.29) at the expense of stability since the derivatives with respect to the normal
electric field are very large.
The charge density corresponding to the cases in table 4.2 is assessed and solution
parameters are examined at the emitter surface. The solution parameters are also
evaluated for applied voltages ranging from 150 kV to 250 kV.
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