We have derived the current-voltage relationship of ideal p-n junctions. One of the assumptions was that the quasi Fermi levels are constant across the depletion region. However this is contradictory to the requirement that there is a (constant) current across the depletion region

a. Write explicit expression for Jn and Jp in only terms of carrier density, mobility, and Quasi Fermi Level (derivative of QFL)

b. Compute the gradient(derivative) of the Electron and Hole QFL for a pn diode with Nd=2x10¹⁶ and Na=1x10¹⁷ cm-3, use mobilities for silicon and assume the current density is 10³ A/cm2.

c. Compute the width of the depletion region.

d. Determine the potential drop across the depletion region and thus explain why it is appropriate to make the assumption that the quasi Fermi levels are constant across the depletion region.

A silicon step np junction diode has ND=2x10¹⁶ and NA=5x10¹⁶

a. Draw, to scale, the energy band diagram of the junction at equilibrium. N side on the left, label all energy levels clearly

b. Determine the built-in voltage and compare to your sketch in part a)

c. Determine the junction width

d. Determine the junction capacitance (per ?m2)

e. Determine the width of both the n and p-side depletion regions

f. Accurately plot the electric field, identify the max electric field

g. Accurately plot the minority carrier injection current density versus bias Va=-2 to

+2V, use 300K Silicon material parameters where needed.