2.5.2 Simulation of an n⁺p Diode

In the second example AVC scans of an n⁺p diode are simulated for the same beam currents as in the first example. The AVC potential $\varphi_{\mathrm{AVC}}^{}$ is plotted in Fig. 2.14. In this case the AVC potential on the lower doped p-side shows a much stronger dependence on the beam current than for the p⁺n diode. For beam currents up to 500 pA the potential drop across the junction is quite considerable when compared to the maximum potential drop in thermal equilibrium and the slope is steepest near the junction.

For higher beam currents the difference of the AVC potential across the pn-junction is very low and the slope is no longer steepest near the pn-junction. Near the junction on the n-doped side the AVC potential is even higher than the built-in potential.

The second derivative of the AVC potential is plotted in Fig. 2.15. For beam currents up to 500 pA the location where the second derivative of the AVC potential equals zero is shifted towards the higher doped n-side and the shift reduces with increasing beam current. At higher beam currents the shift towards the higher doped n-side increases again as can be seen from Fig. 2.16.

The high number of secondary electron-hole pairs is generated in a very small region which results in a strong concentration gradient especially on the lower doped side of the junction. This causes a strong diffusion of the secondary carriers away from the location of the generation. When the minority carriers reach the space charge region they are pulled across the junction by the built-in electric field (see Fig. 2.17) and the potential difference across the pn-junction is reduced. The electron mobility in silicon is approximately three times higher than that of holes. Therefore the diffusion current is higher and the reduction of the potential difference is much higher when the minorities on the lower doped side are electrons.

Figure 2.14: AVC potential of a n⁺p diode.

Figure 2.15: Second derivative of the AVC potential of a n⁺p diode. The metallurgical junction is located at x = 0.4 $\mu$m.

Figure 2.16: Shift of the location where the second derivative of the AVC potential of a n⁺p diode equals zero as function of the electron beam current.

Figure 2.17: Secondary electrons and holes diffuse away from the injection location. When the minority carriers reach the space charge region they are pulled across the junction by the built-in electric field.