# Compact MOSFET Models for VLSI Design by A. B. Bhattacharyya

By A. B. Bhattacharyya

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Example text

T. k is related to the effective mass of the electron, which will be discussed in a later sub-section. 16) 2πn ∗ ∗ where u∗ (x) = u(x) exp −i( 2πnx a ), and kx = (kx + a ). It may be noted that u (x) is a product of two components, each of which has the same periodicity. Consequently, u∗ (x) also retains the same periodicity as that of the components, and kx and kx∗ are equivalent. 16) can as well be considered a solution of the Schr¨odinger equation. The entire range of the electron energy can, therefore, be embedded within the first Brillion zone, − πa ≤ kx ≤ πa .

In this region, the mobility, μ, which is given by the slope of the vdr –F curve, dvdr /dF is constant. This is also called the low-field region where Ohm’s law holds √ good. The thermal velocity of an electron at room temperature T is given by vth = 3kT/m (∼ 107 cm s−1 ), which is dependent on ambient temperature. At low field, the drift velocity is negligible compared to the thermal velocity of the carriers, and the low field mobility value is determined by lattice and coulomb scattering. r As the field is increased, the vdr –F curve deviates from linear behavior.

K is related to the effective mass of the electron, which will be discussed in a later sub-section. 16) 2πn ∗ ∗ where u∗ (x) = u(x) exp −i( 2πnx a ), and kx = (kx + a ). It may be noted that u (x) is a product of two components, each of which has the same periodicity. Consequently, u∗ (x) also retains the same periodicity as that of the components, and kx and kx∗ are equivalent. 16) can as well be considered a solution of the Schr¨odinger equation. The entire range of the electron energy can, therefore, be embedded within the first Brillion zone, − πa ≤ kx ≤ πa .