In the first example AVC scans of a p+n diode are simulated for beam
currents varying from
10 pA up to
1 nA. The AVC potential
extracted from these simulations is shown in Fig. 2.11. For
comparison the built-in potential is shown in this plot too. The equilibrium
potential is nearly identical to the potential for a beam current of
10 pA or
100 pA.
For increasing beam currents the number of electron-hole pairs generated by the
injected electrons becomes much higher than the equilibrium carrier
concentration on the lower doped n-side of the diode. The secondary electrons
and holes are separated very quickly by the strong electric field in the
vicinity of the pn-junction. Recombination in the depletion region can be
neglected because the extension of the depletion region is below
1 m
and the average carrier velocities are of the order of
106 m s- 1.
This gives a time constant of approximately
1 ps which is much smaller
than the average recombination time for
Si which is approximately
1
s. The holes which are the minorities on the lower doped n-side
are pulled across the junction by the built-in electric field leaving back the
electrons. This causes a reduction of the potential difference across the
pn-junction and of the slope at the pn-junction.
On the higher doped side of the pn-junction the perturbation of the majority carrier concentration is negligible. Therefore the potential shows only a small change.
The second derivative of the AVC potential is shown in Fig. 2.12. From this figure it can be seen that the location where the second derivative equals zero shifts towards the lower doped side with increasing beam current. Fig. 2.13 shows the shift of the location where the second derivative of the AVC potential equals zero as function of the beam current.
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