Problem: p-n Junctions

  
Figure 7.4: (a) Energy levels for an unbiased p-n junction. The contact potential (the energy level shift at the p-n interface) is given by ; is the Fermi energy. (b) Energy levels of an unbiased heavily doped junction where tunneling can now occur.

         (a) The junction between a p-type and an n-type semiconductor is regularly used as an electronic device; the energy levels for such a device are drawn in Figure 7.4(a).

The zero bias diffusion currents for electrons and holes are defined as

where the superscript denotes electron (e) or hole (h) current and the subscript denotes the direction of the current, p to n (pn) or n to p (np). The net current must be zero when the bias is zero, so we know that

 

   If we now bias the junction with voltage V (by putting the positive voltage lead on the p side and the negative lead on the n side) the majority carrier currents will become

while the minority carrier currents remain unchanged. We are assuming that . Plot the total current for this junction as a function of V (for both positive and negative voltages). What is this device?

  (b) When semiconductors are very heavily doped, the depletion region at the junction can become quite narrow. In such a situation, as shown in Figure 7.4(b), tunneling will occur when possible.

Without any calculations, plot the I-V curve for such a device.