HOMEWORK

Please note that unless you show work in the derivations and solutions you will get no credit for the answers. Obviously copied answers from study partners or other sources, etc., will also receive no credit. Please do all parts of all six problems. You may want to make a copy of your homework in case it cannot be returned before Exam 3 (solutions will be provided).

Problem #1

An abrupt silicon pn junction at zero bias and T=300K has dopant concentrations of N_A = 2x10¹⁶/cm³ and N_D = 1X10¹⁶/CM³.

a) Calculate the Fermi level on each side of the junction with respect to the intrinsic Fermi level.

b) Sketch the equilibrium energy band diagram for the junction and determine Vbi from the diagram and the results of part a).

c) Now calculate V_bi using Equation (7.10) and compare to the result found in part b).

d) Determine x_n, x_p and the peak electric field for this junction.

e) Show how the energy band diagram will change (qualitatively) under both forward and reverse bias on a duplicate of the sketch obtained in part b). What will happen (qualitatively) to the results found in part d) for both forward and reverse bias?

Problem #2

We are going to design a GaAs pn junction to meet some certain specifications. The diode is at 300K with a cross-sectional area of 10^-4 cm². At a reverse bias of 4V, we want 20% of the total space charge region width to lie in the p-region and the total junction capacitance to be 0.6 pF. Determine a reasonable set of N_D, N_A, V_bi, and W to make this diode meet specification.

Problem #3

An abrupt silicon pn junction at T=300K under equilibrium conditions has a p-side doping of of N_A = 3x10¹⁵/cm³ and an n-side doping of N_D = 2x10¹⁵/cm³.

(i) Compute:

a) V_bi

b) x_n, x_p, and W

c) the electric field at x=0

d) the voltage at x=0

(ii) Sketch the following as a function of position: a) charge density, b) electric field, electrostatic potential.

(iii) Repeat parts (i) and (ii) if everything is kept the same except of N_A = 10¹⁷/cm³.

Problem #4

An abrupt silicon pn junction diode is to be designed to operate at T = 300K such that the diode current is I = 10 mA at a forward biased diode voltage of 0.75V. The ratio of electron current to hole current is to be 0.1 and the maximum current density is to be no more than 20 A/cm². Use the following parameters: N_A = N_D = 10¹⁶/cm³ , D_n = 25 cm²/s, D_p = 10 cm²/s, τ_p0= τ_n0 = 0.5 gs, ε_r = 11.7.

Problem #5

A symmetrically doped abrupt silicon pn junction has doping concentration of N_A = ND = 5x10¹⁶/cm³. If the peak electric field of in the junction at breakdown is 4 x 10⁵ V/cm, determine the breakdown voltage of the junction.

Problem #6

A silicon pn junction diode at T=300K has the following parameters: N_A = 5 x 10¹⁶ /cm³, N_D = 1 x 10¹⁶ /cm³, D_n = 25 cm²/s, D_p = 10 cm²/s, n_i = 1.5 x 10¹⁰ /cm³, τ_n0 = 5 x 10^-7 s, τ_p0= 1 x 10^-7 s, A = 10^-3 cm². The forward bias voltage is 0.625 V.

Find: a) the minority electron diffusion current at the space charge edge;

b) the minority hole current at the space charge edge;

c) the total current in the pn junction.

d) the electron and hole currents at x = x_n, x = x_n + L_p, and x = x_n + 10L_p.