Question

The depletion layer width for different junctions is given by the following equations: w = het w = jane te pare VO w = (1280XL) Intrinsic carrier concentration of silicon, n., is 9.65 x 10 cm 1) The expressions for minority carrier diffusion length and diffusion coefficients and thermal velocity are as follows (for n-and p-type materials). L. - (Dpt) La = (Dat)* Và = To 1/NA in p-type material 1 - 1/(RexNA), where Re is the recombination And the density of bulk recombination centres is and bulk recombination centre density of 102 cm and the effective mass of holes mois 0.69 m, and of electrons is 0.98 me a) Use the appropriate equations to determine the minority carrier diffusion lengths for the following materials: i) Silicon doped with 10 cm Boron, electron capture cross-section of o. - 4 x 10 cm and minority (electrons) carrier mobility values of: 800 cm s!, 1500 cm v sand 1800 cm Vs ii) Silicon doped with 5 x 10 cm. Phosphorus atoms, - 10cm mobility values of up is 50 cm Vs' and 400 cmvls, respectively. and with hole ili) Cate with the usual doping mechanism, at a concentration of 10 cm and a direct recombination coefficient, Re, of 10-10 cm's and an electron mobility of 10 cm Vs b) Use the appropriate equations to determine the depletion layer width lengths for the following materials (The permittivity of free space (F ) can be taken to the 3 decimal places and the dielectric constant for silicon is 12.1).

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Answer 1

diffussion lengths D.Ia) The minority carrier i Lp = (0, 2)2 Now Dp = (kt up since when silicon doped with Boron then P-type material formed. Here first we have to calculate the value 6. = 2ne Jц, ц, 2 me= 4 neuen

for Me - doo Hp : (4 x1014) 4x (9.65x10")*(1 6X10') doo Up = 2.097 X10-13 cm?v's Dp - J26*10* *2- 0971's - 26mV at T = 210 De = 7.383 x10-8 LP = (Dp 21% 45 (7.3837109 x bona sio [p = 3.50x10thm For sn= 1500 cm³ 5 5 Mp= (4x101912 4x( 4.65 x10') < (1-6*10^)2 x 1500 Mp3 1.118x10-13 cm' s

26x103 x 1.118 x1013 Dp = 5-39x10-8 le= (P. til 1: {5.39-410 r 'o2 5 xics )" = 2.99x1016 cm similarly for den= 1800 alp = (4x10-14) ² 4x(9.65X10%) x( 16x10') x 1800 Mp = 9.321810-14. Op = k des Dp = 26x10²x 9.321x1019 Dp = 4.9 22x10 - 8

(p= (Dp T ad LP: (4.922x100 x 602681d")" 11p: 2.85 x1046cm (ii). In this case n-type material formed Mp = 50 cm v smo Mn= 6.² 4 ne² up der (101s)? 4x(9.65x109) (1.6x1019) 2x 50 = 10-30 4x (9.65 x 18² x (1.6x10 197 ²450 Mn = 2.097x10-15 cm² vs. 26*10* 2.097X10 DA K n = 26x10*x 2.097410's Da = 7. 384 X10-9 (Dn T')'2 L

La =(7.38 4x10 a . 6.02 3X10²3 - 1. 10 7x10 16cm Similarly for rep= 400 cm Vs Mo – (1030) 4x(9.65 x109? x (1.6x1079)2 7400 den - 2.62x1016 cm² vagn Du 26x10² x 2.62x 1016 Du = 2.61810-9 Lai (Dn 2)² De 2² - (2.618109x 2 I 6.023x1023 In - 6.583x10llam.

b) u depletion layer width is given by W = /2 E, C ( Nat No) v.. and V. kr en (No Here NA= 5x105 cm3 No= 5x108 cm3 V. 26x103 en (5x108x5x10' (9.6 5 x10912) Vo = 0.923 V W: J2x12.1x 8-854x10^2(Sxvdesmi@J 20.923 2x 12.1x 8.854 x 1072/5x10 & 5x10181 I 5xlobulx0.923 W=6.32x10 17 cm. 6. Vo = 0.923. W= |2412-148-854x10" (s 20" x 5 x 0"* ) <0-913 W: 2.812x16'7cm