Homework 1: Solutions
1. Consider how the de Broglies suggestion might explain some properties of the hydrogen atom. a. Show that the assumption h p = m = and the quantization condiction that the length of a circular orbit be an integer multiple of the le
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1. Problem. Find the resistivity (in ohm-cm) for a piece of Si doped with both acceptors (NA = 1019 cm3 )
and donors (ND = 1016 cm3 ). Since the electron and hole mobilities depend on the concentration of the
dopants, use the following empriric
Homework 2: Solutions
1. Problem. We have approximated the conduction band of many semiconductors with an isotropic, parabolic
expression of the form:
However, this approximation fails at some large k. A rst correction to this express
1. Problem. Derive Eq. (171) of the Lecture Notes, Part 2, expressing the density of a system of electrons
conned in two dimensions as a function of Fermi level.
Solution. The derivation has been shown in class: The density in 2D can be obtaine
1. Problem. Following closely the derivation of the rate for scattering with ionized impurities (see Lecture Notes,
pages 65-68), derive the associated momentum relaxation rate:
h V 2 (2)3
[E(k ) E(k)] ,
Metal-Oxide-Semiconductor Field-Eect Transistors (MOSFETs)
The gure below illustrates schematically the MOSFET structure (an n-channel MOSFET or nFET - is
shown. p-channel devices or pFETs are doped in a complementary manner): Heavily n-dop