Find reverse and forward current densities in a silicon p-n diode used as a rectifier of AC voltage 0.5 V. The rectifier is made of silicon doped with phosphorus with a concentration of 2e16 cm 3 and boron with a concentration of 5e16 cm 3. The lifetime of the charge carries is 0.1 us. Question 1: DP current density : j = e.NcNv ZpNo + InNA expl - Ex-ev A / 2 L: diffusion length N: effective density of states D : diffusion constant Ey : band yup energy Ev : energy Room temperature properties of Si, Ge, GaAs, and GaN Quantity Symbol Si Ge GaAs GaN (Unit) Crystal structure D D Z W Gap: Direct (D) / Indirect (!) D D Lattice constant do = 5.431 5.646 5.653 5.185 (Co) Bandgap energy E. = 1.12 0.66 1.42 3.425 ev Intrinsic carrier concentration n= 1.0 x 1010 2.0 x 1013 2.0 x 106 1.9x10-10 cm Effective DOS at CB edge Nc = 2.8 x 1019 1.0 x 1019 4.4 x 1017 2.3x1018 cm 3 Effective DOS at VB edge 1.0 x 1019 6.0 x 1018 7.7 x 1013 1.8x1019 cm -3 Electron mobility Hn = 1500 3900 8500 1500 cm / (Vs) Hole mobility Ho = 450 1900 100 30 cm / (Vs) Electron diffusion constant 39 101 220 39 cm /s Hole diffusion constant 12 49 10 0.75 cm / s Electron affinity X = 4.05 4.0 4.07 4.1 Minority carrier lifetime 1= 10 6 10 6 10-8 10 Electron effective mass me* = 0.98 me 1.64 me 0.067 me 0.20 me Heavy hole effective mass mah* = 0.49 me 0.28 me 0.45 me 0.80 me Relative dielectric constant & = 11.9 16.0 13.1 8.9 Refractive index near Eg n = 3.3 4.0 3.4 2.5 Absorption coefficient near Es OL= 10 10 104 105 D = Diamond; Z = Zincblende; W = Wurtzite; DOS = Density of states; VB = Valence band; CB = Conduction band. The Einstein relation relates the diffusion constant and mobility in a non-degenerately doped semiconductor: D = H (kT/e) Minority carrier diffusion lengths are given by in = (Dntn)" and Lp= (Dp Tp) 1/2 The mobilities and diffusion constants apply to low doping concentrations (2 10" cm"). As the doping concentration increases, mobilities and diffusion constants decrease. The minority carrier lifetime t applies to doping concentrations of 10" cm" . For other doping concentrations, the lifetime is given by t = B" (n + p)", where Bs = 5 x 10"cm /s, Bee 2 5 x 10" cm /S, Beaks # 10 10 cm /s, and Bean = 10-10 cm /s. 28