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3. Consider a Schottky contact between gold and n-type Si which has a uniform doping density of ND = 5.0 x 1015 cm-3. The work function of gold is pm = 5.1 V and the electron affinity of Si is Xsi = 4.01 V. Sketch the equilibrium (zero bias) energy band diagram for this Schottky contact. What are the values of the barrier height and built-in voltage?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