Calculate the resistivity of Silicon at given that its resistivity at
is
.
The resistivity of intrinsic semiconductors like silicon varies with temperature according to the relation: [ \rho(T_2) = \rho(T_1) , e^{\frac{E_g}{2k} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)} ] where: * (\rho(T_1)) is the resistivity at temperature (T_1) * (E_g) is the energy band gap of silicon ((E_g \approx 1.12 , \text{eV})) * (k) is Boltzmann's constant _____ __________ ________ _______ ______ _____ _______ ________.
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A metallic crystal has an fcc lattice with a lattice constant . Explain whether the following planes are allowed or forbidden for X-ray diffraction:
(100), (111), (210), (220)
Calculate the X-ray diffraction angles for the allowed planes. Assume that diffraction occurs in the first order and the X-ray wavelength is .
Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
For the energy dispersion relation:
calculate the inverse mass tensor.
In an n-type semiconductor the Fermi level lies below the conduction band at
. Calculate the position of the Fermi level when the temperature is raised to
.
For Chromium () vapour at
with a number density of atoms
calculate:
i) The Larmor diamagnetic susceptibility assuming the atomic radius to be 1.2 A.
ii) The Curie paramagnetic susceptibility.
Show that the reciprocal lattice of a bcc lattice is an fcc lattice. Calculate the magnitude of the shortest non-zero reciprocal lattice vector.
Calculate the temperature at which the lattice contribution to the specific heat and the electronic contribution to the specific heat become equal in a metal which has a Debye temperature of and a Fermi energy
.