1. A diffused silicon p-n junction has a linearly graded junction on the p-side with a = 10¹⁹ cm^-4, and a uniform doping of 3 x 10¹⁴ cm^-3 on the n-side. If the depletion layer width of the p-side is 0.8μm at zero bias, find the total depletion layer width, built-in potential and maximum field at zero bias.

2. Determine the n-type doping concentration to meet the following specifications for a Si p-n junction:

N_A = 10¹⁸ cm^-3, δ_max = 4 x 10⁵V/cm at V_R = 30 V, T = 300 K.

3. For a silicon linearly graded junction with a impurity gradient of 10²⁰ cm^-4, calculate the built-in potential and the junction capacitance at reverse bias of 4 V (T = 300 K).

4. Calculate the applied reverse-bias voltage at which the ideal reverse current in a p-n junction diode at T = 300 K reaches 95% of its reverse saturation current value.

5. Calculate the theoretical barrier height and built-in potential in a metal-semiconductor diode for zero applied bias. Assume the metal work function is 4.55 eV, the electron affinity is 4.01 eV, and N_D = 2 x 10¹⁶cm^-3 at 300 K.

6. Copper is deposited on a carefully prepared n-type silicon substrate to form an ideal Schottky diode. Φ_m = 4.65 eV, the electron affinity is 4.01 eV, N_D = 3 x 10¹⁶ /cm³, and T = 300 K. Calculate the barrier height, the built-in potential, the depletion-layer width, and the maximum field at a zero bias.

7. The capacitance of a Au-n-type GaAs Schottky barrier diode is given by the relation 1/C² = 1.57 x 10⁵ - 2.12 x 10⁵ V_a, where C is expressed in μF and V_a is in volts. Taking the diode area to be 10^-1 cm², calculate the built-in potential, the barrier height, the dopant concentration, and the work function.