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# (Solved): Problem (50 Points): A Silicon Step Junction At T = 300 K Has Doping Concentrations Of NA = 5x1016 C...

Problem (50 points): A silicon step junction at T = 300 K has doping concentrations of NA = 5x1016 cm-3 and N, = 5x1015 cm-3. The cross-sectional area of the junction is 100 um?. Show all steps in your solution (a) (5 points) Calculate the Fermi energy on each side of the junction in the quasi-neutral regimes) with respect to the intrinsic Fermi level, i.e. Ef-E;. (b) (5 points) Calculate the resistivity of both n-type and p-type quasi-neutral regions. (c) (5 points) Calculate the built-in potential Vbi. (d) (5 points) Calculate the width of the depletion region under zero bias. What percentage of the depletion region is in the n-side of the junction? (e) (5 points) By what factor does the depletion region width increase if you reverse bias the junction by at VA = -25 V?
(1) (5 points) Calculate junction capacitance of p-n junction reverse biased at VA=-25 V. (g) (10 points) Now assume that the p-n junction is forward biased with VA = 0.5 V. Sketch, in log scale, the steady-state majority and minority carrier concentrations on both sides of the depletion region as a function of the position. Indicate the equilibrium level of minority carrier concentrations in your sketch. (h) (10 points) Calculate the current density flowing through the p-n junction in case of a forward- bias voltage of Va=0.5 V. Assume a minority carrier lifetime for holes and electrons of tn= Tp = 1 us. You might need: g = 1.6x10-19 C, K. = 11.8, Ep = 8.85x10-14 F/cm, KT = 0.026 eV at T = 300K E, = 1.12 eV, n = 1010cm-3 at T = 300K, use carrier mobilities from the graph below. Silicon T = 300 K Electrons 1000 Holes (395-A/zu15) ri1071 NA or Np (cm3) 1 x 1014.... 1 x 1015 Mode cm / V-SCC 1358 461 1357 460 1352 459 1345 458 1332 455 1298 448 1248 437 1165419 986 378 801 331 1 x 1016 1 x 1017 10 1014 1015 1018 1016 1017 NA or ND (cm-3)

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