3 . Consider a 300 um thick p-type silicon wafer with a doping density of NA = 1 x 1015 cm3. Light is illuminated on the surface as shown in Figure 2. Assume that the light is completely absorbed on the surface (x = 0), creating an excess minority carrier concentration, on(x = 0) = 1 x 1012 cm-3. (a) Calculate the minority carrier concentration, n(x). inside the semiconductor, x > 0. The minority carrier lifetime is to = 100 ns. (b) Calculate the electron current density, Jn (x), inside the semiconductor, x > 0. light p-type X O 300 um Figure 2. A p-type silicon under light illumination.Physical Constants and Material Properties Table B.2 | Conversion factors Prefixes 1 A (angstrom) = 10- cm = 10-10 m 10-15 1 pum (micrometer) = 10 *cm femto- 10 12 1 mil = 10- in. = 25.4 um pico- =P 10-9 2.54 cm = 1 in. nano- =n 10-6 1 ev = 1.6 X 10-" J micro- 10- 1 J = 10 erg milli- = m 10+3 kilo- =K mega- = M 10+9 giga- = G 10+12 tera = T Table B.3 | Physical constants Avogadro's number NA = 6.02 X 10+23 atoms per gram molecular weight Boltzmann's constant k = 1.38 x 10 23 J/K = 8.62 X 10 eV/K Electronic charge e = 1.60 X 10-19 C (magnitude) Free electron rest mass mo = 9.11 X 10- kg Permeability of free space Mo = 47 X 10 7 H/m Permittivity of free space 6) = 8.85 X 10 " F/cm = 8.85 X 10-12 F/m Planck's constant h = 6.625 X 10 * J-s = 4.135 x 10 15 eV-s 2 TT h = h = 1.054 x 10 # J-s Proton rest mass M = 1.67 X 10-2 kg Speed of light in vacuum c = 2.998 X 10" cm/s Thermal voltage (7 = 300 K) V, = KI = 0.0259 V KT = 0.0259 evTable B.A | Silicon, gallium arsenide, and germanium properties (7 - 300 K) Property SI Atoms (em ) GRAS Ge Atomic weight 5.0 X 1037 4.42 x 10" 4,42 x 10" Crystal structure 28.09 144.63 72.60 Density (glem' ) Diamond Zineblende Diamond Lattice constant (A) 2.33 5.32 5.33 Melting point ("C) 5.43 5.65 5.65 1415 Dielectric constant 1238 937 11.7 Bandgap energy (eV) 13,1 160 1.12 1.42 0.66 Electron affinity. X (V) 4.01 4.07 4.13 Effective density of states in 2.8 X 10" 4.7 X 10" 1.04 x 10 conduction band, N. (cm ') Effective density of states in 1.04 X 10 7.0 X 10' 6.0 X 10" valence band, N, (cm ') Intrinsic carrier concentration (em ) 1.5 X 10 1.8 X 10 2.4 X 10" Mobility (cm /V-5) Electron, #. 1350 8500 3900 Hole, Pp 480 400 1900 Effective mass (") Electrons m; = 0.98 0.067 1.64 m; = 0.19 0.082 Holes If = 0.16 0.082 0.044 my= 0.49 0.45 0.28 Density of states effective mass Electrons ma 1.08 0.067 0.55 Holes . 0.56 0.48 0.37 Conductivity effective mass Electrons m. 0.26 0.067 0.12 Holes 0.37 0.34 0.21