# Tutorial 6

Tutorial 6

1. For a PN junction with NA = 1017 and ND = 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 ni = 1.5 * 1010/cm3
2. For a PN junction with NA = 1017/cm3, and ND = 1016/cm3, operating at T = 300 , find
3. a) Value of Cj0 per unit area and
4. b) Capacitance Cj at a reverse bias voltage of 2V, assuming the junction area of 2500 µm2 , use ni = 1.5 * 1010/cm3, m = ½ and the value of V0 is 0.728
5. Calculate the intrinsic carrier density ni at 250K, 300K and 350K
6. Consider an n –type silicon in which the dopant concentration ND 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 NA = 10/cm3. Use ni = 1.5 * 1010 /cm3, assume that for intrinsic silicon µn = 1350cm2/V-s. and µp = 480 cm2/V-s and for doped Silicon µn = 1110 cm2/V.s and µp = 400 cm2/V.s [ Note that doping results in reduced carrier mobilities]
8. A diode has NA = 1017/cm3, ND = 1016/cm3, ni= 1.5 * 1010/cm3, Lp = 5 µm, Ln =10 µm, A = 2500 µm2, Dp = 10cm2/V.s and Dn = 18 cm2/V.s . The diode is forward biased and conducting current I = 0.1 mA. Calculate
9. a) IS
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

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