Tutorial 6

Tutorial 6

1. For a PN junction with N_A = 10¹⁷ and N_D = 10¹⁶ /cm³, find at T =300K, the built in voltage, the width of the depletion region, and the distance it extends in the p side and in the n side of the junction. Use n_i = 1.5 * 10¹⁰/cm³
2. ^{For a PN junction with N}_A ^{= 1017/cm3, and N}_D ^{= 1016/cm3, operating at T = 300 , find}
3. ^a) Value of C_j0 per unit area and
4. b) Capacitance C_j at a reverse bias voltage of 2V, assuming the junction area of 2500 µm² , use n_i = 1.5 * 10¹⁰/cm³, m = ½ and the value of V₀ is 0.728
5. ^{Calculate the intrinsic carrier density n}_i ^{at 250K, 300K and 350K}
6. ^{Consider an n –type silicon in which the dopant concentration N}_D ^{is 1017/cm3. Find the electron and hole concentrations at 250K, 300K and 350 K. Use the results obtained in the previous question}
7. ^{Find the resistivity of (a) intrinsic Silicon and (b) p –type Silicon with N}_A ^{= 10/cm3. Use n}_i ^{= 1.5 * 1010 /cm3, assume that for intrinsic silicon µ}_n ^{= 1350cm2/V-s. and µ}_p ^{= 480 cm2/V-s and for doped Silicon µ}_n ^{= 1110 cm2/V.s and µ}_p ^{= 400 cm2/V.s [ Note that doping results in reduced carrier mobilities]}
8. ^{A diode has N}_A ^{= 1017/cm3, N}_D ^{= 1016/cm3, n}_i^{= 1.5 * 1010/cm3, L}_p ^{= 5 µm, L}_n ^{=10 µm, A = 2500 µm2, D}_p ^{= 10cm2/V.s and D}_n ^{= 18 cm2/V.s . The diode is forward biased and conducting current I = 0.1 mA. Calculate}
9. ^a) I_S
10. _b) The forward bias voltage V
11. c) The component of current I due hole injection and that due to electron injection across the junction
12. d) _{τp and τn}
13. _{e) The excess hole charge in the n region Qp}
14. _{f) The excess electron charge in the p region Qn}
15. _{g) Total minority stored charge Q}
16. _{h) Transit time τT}
17. _{i)The diffusion capacitance}

Answers:

1. 728 mV ; 0.32 µm ; 0.03 µm ; 0.29 µm

2. 0.32 fF/ µm² ; 0.41 pF

3. 1.5 * 10⁸ /cm³ ; 1.5 * 10¹⁰/cm³ ; 4.18 * 10¹¹/cm³

4. 10¹⁷; 2.25 * 10^-1 ; 10¹⁷ , 2.25 * 10³ , 10¹⁷ , 1.75 * 10⁶ (all per cm³)

5. 2.28 * 10⁵ Ω-cm ; 1.56 Ω-cm

6. 2*10^-15 A; 0.616V; 91.7 µA ,8.3 µA ;25ns , 55.6 ns; 2.29 pC;0.46 pC ;2.75 pC ;27.5 ns; 110 pF

References

Q1 - Q6 -- "Microelectronics" by Sedra and Smith