2. Consider a Si pin junction at room temperature. The n-type region is infinitely long, has a doping density of ND = 1.0 x 1016 cm and the minority carrier (hole) lifetime To = 106 s. The p-type doping density is much greater than the n-type doping, NA > > ND. Suppose that we make another pin junction with the same doping density. The n-type region is also infinitely long. But the second diode is made of a hypothetical semiconductor material whose properties are identical to those of silicon (e.g., effective mass, mobility, diffusion coefficients, etc.) except the bandgap. The bandgap of the hypothetical material is 10% larger than that of silicon. How does the current density J of this second diode compare with the current density of the original one? Specify your answer by calculating the current density ratio, Jsecond / Joriginal.Physical Constants and Material Properties Table B.2 | Conversion factors Prefixes 1 A (angstrom) = 10 8 cm = 10-10m 10-15 I pum (micrometer) = 10 4 cm femto- = f 10-12 1 mil = 10 ' in. = 25.4 um pico- =P 10-9 2.54 cm = 1 in. nano 10-6 1 ev = 1.6 X 10-19 J micro- = u 10-3 milli- 1J = 10' erg m 10+3 kilo- = K 10 6 mega- = M 10+9 giga- EG 10+12 tera ET 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 10-5 eV/K Electronic charge e = 1.60 X 10-19 C (magnitude) Free electron rest mass mo = 9.11 X 10-31 kg Permeability of free space Mo = 47 X 10-7 H/m Permittivity of free space 6 = 8.85 X 10-14 F/cm = 8.85 X 10-12 F/m Planck's constant h = 6.625 x 10-34 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 37 kg Speed of light in vacuum c = 2.998 X 10" cm/s Thermal voltage (T = 300 K) e V. = KL = 0.0259 V AT = 0.0259 evTable BA | Silicon, gallium arsenide, and germanium properties (7 = 300 K) Property Si Atoms (cm) GaAs Ge 5.0 X 1022 Atomic weight 4.42 X 1022 4.42 x 10% 28.09 Crystal structure 144.63 72.60 Density (g/cm) Diamond Zincblende Diamond 2.33 Lattice constant (A) 5.32 5.33 5.43 Melting point ("C) 5.65 5.65 1415 1238 937 Dielectric constant 11.7 13.1 16.0 Bandgap energy (eV) 1.12 1.42 0.66 Electron affinity. x (V) 4.01 4.07 4.13 Effective density of states in 2.8 X 1019 4.7 X 10" 1.04 X 109 conduction band, N. (cm '). Effective density of states in 1.04 X 1019 7.0 X 1018 6.0 X 10 valence band, N. (cm ) Intrinsic carrier concentration (im ) 1.5 X 1010 1.8 X 10 2.4 X 1033 Mobility (cm /V-s) Electron, An 1350 8500 3900 Hole, Mp 480 400 1900 Effective mass m* Electrons m; = 0.98 0.067 1.64 m; = 0.19 0.082 Holes n, = 0.16 0.082 0.044 my = 0.49 0.45 0.28 Density of states effective mass Electrons (m. 1.08 0.067 0.55 Holes mo 0.56 0.48 0.37 Conductivity effective mass Electrons m. 0.26 0,067 0.12 Holes ma 0.37 0.34 0.21