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Transcript
Current Density [A/M 2
X 10
lVpl[C/M4]
0.4
14
0.4
0.3
0.03
0.3
12
0.025
0.2
0.2
10
0.1
0.1
E
8
0
-0.2-0.3
-
0.015
6
-0.1
4
-0.2
2
'0.02
0
0.01
-0.3
0.005
-0.4
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
-0.4
0.4
0.3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
(b) Current density.
(a) Charge density gradient.
Figure 4-10: Charge density gradient and current density solution for V
Po = 1 x 10-4 Crn-3.
150 kV,
density gradient in figure 4-10a exhibits some faceting. The impact of the discontinuous charge density solution is minimal since the diffusion coefficient D is small in the
definition of the current density (see equation (3.5)). The charge density gradient is
maximized at the 6 o'clock location on the emitter since the charge density decreases
rapidly with distance from the emitter (see figure 4-9b).
The solutions for the axisymmetric case and the offset emitter case have used a
uniform charge density applied to the emitter as a Dirichlet boundary condition. The
dependence of the electric field at the emitter for various values of po indicates that
there are orders of magnitude for po where the normal electric field is affected strongly
or minimally. Table 4.2 lists the choices for p,-ef and Eref which are investigated in
the next section. The range is based on solutions where V = 150 kV. Case 4 consists
of arbitrarily chosen parameters.
Table 4.2: Choices for Pref andrEe,
Cases 1 Pref C/M3
10-4
j
1
2
3
4
10-5
1o-6
10~6
57
Erej kV /
12.14
32.58
39.96
1
111