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XV. What do the different terms refer to in the above Integral Equation? Answer: N(E)=density of states per unit volume per unit energy, P(E) →Fermi-Dirac Statistics or the probability of occupancy at energy E by Fermions. dE → elemental energy, m*→effective mass of electron in the conduction band.X 0 →Fermi Level in Metal with respect to the bottom edge of the Conduction Band i.e.X 0 =E F - E C .[1/10+1/10+1/10+1/10+1/10=1/2 Points]
XVI.
In the adjacent equation and in Question XV, X _{0} is the same parameter. What is this parameter. Answer: X 0 =E F - E C .[1/2 Point]XVII.
What are the different parameters and what are their units ? Answer: E g is Band-Gap in eV and λ is the wavelength of the photon emitted accompanying the radiative transition from Conduction Band to the Valence Band.[1/4+1/4=1/2]XVIII. Define the parameters and give the units ?
Semiconductor | E _{g} | n _{i} | ε _{r} (DC) | ? | ρ _{i} (300K) | N _{C} | N _{V} |
---|---|---|---|---|---|---|---|
Si | 1.12 | 1×10 ^{10} | 11.7 | 5×10 ^{22} /cc | 3.2×10 ^{5} | 3.2×10 ^{19} /cc | 1.8×10 ^{19} /cc |
Ge | 0.67 | 2×10 ^{13} | 16.2 | 4.4×10 ^{22} /cc | 48 | 1×10 ^{19} /cc | 5×10 ^{18} /cc |
GaAs | 1.424 | 2.1×10 ^{6} | 12.9 | 4.42×10 ^{22} /cc | 3.3×10 ^{8} | 4.7×10 ^{17} /cc | 7×10 ^{18} /cc |
Answers: E _{g} (eV) , n _{i} (#/cc), ε _{r} (DC) rel.permittivity (Dimensionless ), #density of atoms in the crystal , ρ _{i} (300K) Intrinsic Resistivity in Ω-cm, N _{C} _ Effective Density of States at E C, N _{V} _ Effective Density of States at E V [1/14+1/14+1/14+1/14+1/14+1/14+1/14=1/7]
XIX.
Define the terms and give the units. v = 10 ^{7} cm/s. What is this velocity. Answers: v drift = electric drift velocity(m/s), μ(mobility) (cm 2 /(V-s)), q=electric charge(Coulombs), τ scattering (Mean Free Path or Relaxation Time)(sec),m* e =effective mass of electron(Kg)[1/28,1/28,1/28,1/28,1/28,1/28,1/28, 1/28,1/28,1/28,1/28,1/28,1/28,1/28,=1/2]XX.
This rule is called Matthiessen’s Rule. Define the parameter and give the units of the parameter. Answers:μ effective ,→ effective mobility, μ imp ,→mobility due to impurity scattering, μ lattice ,→mobility due to lattice scattering, cm 2 /(V-s), [1/8+1/8+1/8+1/8=1/2]XXI.
What are these power laws. Answers: lattice scattering inverse 3/2 power law , impurity scattering 3/2 power law [1/4+1/4=1/2 points]XXII. σ = qμn Define the terms and give the units. Answers: σ →conductivity(Siemens/cm), q→electronic charge(Coulomb),μ→mobility(cm 2 /(V-s),n→conducting electron number density[1/16+1/16+1/16+1/16+1/16+1/16+1/16+1/16=1/2 Points]
XXIII. What special information is given by this Table.
Metal | Au | Cu | Ni | Pt |
---|---|---|---|---|
Effective Mass/Free Mass of electron | 1.1 | 1.01 | 28 | 13 |
Answers: Ni and Pt are heavy Fermionic Metals [1/4+1/4=1/2]
XXIV. What is the basic difference about electron transport reflected by the Table below ?
Element | E _{F} | τ(femtosec) | L(Angstrom) | W _{F} | v _{e} ^{1} (×10 ^{5} m/s) |
---|---|---|---|---|---|
Li | 4.7 | 9 | 90 | 9.96 | |
Na | 3.1 | 31 | 250 | 2.3 | 8.08 |
K | 2.1 | 44 | 293 | 2.2 | 6.55 |
Cu | 7.0 | 27 | 328 | 12.15 | |
Ag | 5.5 | 41 | 441.6 | 10.77 | |
Ge | E _{V} +E _{G} /2 | 2217 | 2106 | 1.16 | |
Si | E _{V} +E _{G} /2 | 767.6 | 729 | 1.16 | |
GaAs | E _{V} +E _{G} /2 | 4890 | 4645.5 | 1.16 |
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