Design an ideal abrupt silicon PN-junction at 300 K such that the donor impurity concentration in the n-side N_d = 5×10¹⁵/cm³ and the acceptor impurity concentration in the p-side N_a = 061 ×10¹⁵/cm^3. Use the diode parameters: diode area = 2×10^-3 cm², n_i = 10¹⁰/cm³, D_n =25 cm²/s, D_p =10 cm²/s, τ_n = τ_p = 5×10^-7 s, ε_r =11.8, µ_n = 1350 cm²/V.s, µ_p = 450 cm²/V.s

Determine the following when a forward bias of 0.6 V is applied to the diode:

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1. The contact potential V_c (in V).

2. The values (in µm) of the depletion width at the p-side xp and the depletion width at the n-side x_n.

3. The electric field (V/cm) at a distance of 0.2 × x_n away from the metallurgical junction in the n-side.

4. Minority carrier hole diffusion current in mA at the n-side depletion edge I_p (x_n)

5. Minority carrier electron diffusion current in mA at the p-side depletion edge I_n (−x_p)

6. The total diode current I in mA.

7. The junction capacitance Cj in F

Summarize your answers in a Table in your answer sheet for Q1 to Q7 as follows:

Contact potential Vc (V)		Ip (xn) in mA
Depletion width xp (µm)		In (−xp) in mA
Depletion width xn (µm)		Diode current, I (mA)
Electric field (V/cm)		Capacitance Cj (F)

8. Roughly, sketch the carrier distribution across the junction under forward bias. Label clearly.

9. Calculate and prove that the magnitude of electric field far away from the depletion region is small compared to that in the space charge region.

10. For the same forward bias of 0.6 V, an application requires higher diode current than that calculated in Part 6. If you have a choice to change the dopant concentration in one side of the junction (either p-side or n-side) to achieve this higher current, state whether you will increase or decrease the dopant concentration in the chosen side? Briefly explain your answer.

11. If the PN-junction diode is made of GaAs semiconductor instead of Silicon, do you expect the total diode current I to remain the same, decrease or increase for the same forward bias of 0.6 V? Explain briefly without doing any calculation.

12. Assume that the Silicon PN junction with E_G = 1.12 eV is redesigned such that it is heavily doped on both p- and n-sides. If the built-in voltage for this device is determined to be 0.8 V, how much reverse bias voltage is required to be applied to facilitate Zener breakdown of this junction? Explain.

13. Compare the material properties of Ge and Si semiconductors. Choose one property and explain why Si is better than Ge, and choose another property and explain why Ge is better than Si.