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Characteristics | Symbol | Units | Ge | Si | GaAs | Cu |
Effective Density of States | N c | Cm^ -3 | 1.04×10^ 19 | 2.8× 10^ 19 | 4.7×10^ 17 | |
N v | Cm^ -3 | 6.1×10^ 18 | 1.02× 10^ 19 | 7×10^ 18 | ||
Energy Gap | E g | eV | 0.68 | 1.12 | 1.42 | |
Intrinsic Carrier concentration | n i | Cm^ -3 | 2.25×10^ 13 | 1.15× 10^ 10 | 1.6×10^ 6 | 8.5× 10^ 22 |
Effective mass | m n (unit mass 9.11×10 -31 Kg) | 0.33 | 0.33 | 0.068 | ||
m p (unit mass 9.11×10 -31 Kg) | 0.31 | 0.56 | 0.56 | |||
Mobility | μ n | Cm^ 2 / (V-s) | 3900 | 1350 | 8600 | 44 |
μ n | Cm^ 2 / (V-s) | 1900 | 480 | 250 | ||
Dielectric Constant | ε r | 16.3 | 11.8 | 10.9 | ||
Atomic Concentration | Cm^ -3 | 4.42×10^ 22 | 5×10^ 22 | 4.42× 10^ 22 | 8.5× 10^ 22 | |
Breakdown Field | E BR | V/cm | 10^ 5 | 3×10^ 5 | 3.5×10^ 5 |
1.10.2.1. METALS ( with special reference to the mobility of conducting electrons and its implications for particle accelerators ).
Metal is a lattice of positive ions held together by a gas of conducting electrons. The conducting electrons belonging to the conduction band have their wave-functions spread through out the metallic lattice. The average kinetic energy per electron is (3/5)E _{F} (This will be a tutorial exercise). Hence
= 1.93
where m* is the effective mass of the electron but we will assume it to be the free space mass.
Therefore:
……………. 1.94
Where
This velocity is not thermal velocity but velocity resulting from Pauli’s Exclusion Principle which essentially is the result of the ferm-ionic nature of electrons. Electrons tend to repel one another when confined in a small Cartesian Space. Electrons are claustrophobic.
Therefore mean free path =
…… 1.95Where τ is mean free time.
Substituting the appropriate values for each metal, we get the mean free path for electron in their respective metals.
Table(1.10) Tabulation of the Fermi Energy, velocity, mean free time and mean free path of conducting electrons in their respective metals.
Metal | E F | Velocity(×10^ 5 m/s) | τ (femtosec) | L*(A°) |
Li | 4.7 | 9.96 | 9 | 90 |
Na | 3.1 | 8.08 | 31 | 250 |
K | 2.1 | 6.65 | 44 | 293 |
Cu | 7.0 | 12.15 | 27 | 328 |
Ag | 5.5 | 10.77 | 41 | 441.6 |
As we see from Table(1.10), the mean distance between two scatterers is 2 orders of magnitude greater than the lattice constant which is of the order of 5 A°. Hence lattice centers per se are not the scatterers but infact the disorderliness is what causes the scattering. The scatterers are thermal vibrations of lattice centers, the structural defect in crystal growth and the substitutional/interstitial impurities. This implies that with reduction in temperature mobile electrons will experience less scattering hence the metal will exhibit less resistivity leading to positive temperature coefficient of resistance. We will dwell upon this in Section (1.12).
1.10.2.2. SEMICONDUCTORS
Semiconductors are insulators initially. At low temperatures, all electrons are strongly bonded to their host atoms. Only at temperatures above Liquid Nitrogen that thermal generation of electron-hole pairs take place. So in semiconductors the situation is quite different as compared to that in metal. The conducting electrons and holes owe their mobility to thermal energy they possess in contrast to the conducting electrons in metal. On an average by Equipartition Law of Energy, the mobile carriers possess (1/2)kT thermal energy per carrier per degree of freedom. Since the carriers have 3 degrees of freedom hence they possess (3/2)kT average thermal energy per carrier.
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