Problemsamling

Calculate the band gap under the assumption that the variation in the
conductivity is partly caused by the increase in the density of charge
carriers and partly arises from the mobility, µ, of the charge carriers being
temperature dependent because of the thermal vibrations of the atoms.
Assume that µ ∝ T -3/2 in the relevant temperature interval.
3. Determine the maximum concentration (atomic fraction) of donor atoms
that can be allowed in the substances in the table below for intrinsic
conduction to dominate at room temperature. Is it possible to realise this
practically in any of these cases?
Substance Bandgap [eV] Density [kg/m 3 ]
Diamond 5.33 3.51 x 10 3
Silicon 1.14 2.42 x 10 3
Germanium 0.62 5.35 x 10 3
4. A silicon crystal is doped with Sb atoms to a concentration of 10 21 m -3 .
The impurity level lies 0.04 eV from the nearest band edge. Assume that
the band gap at 450 K is Eg = 1.14 eV. Calculate the conductivity at T = 450
K. Approximate the effective masses with the free electron mass and
assume that all impurity centres are ionised at room temperature. The
mobilities are: µe = 0.13 m 2 /Vs and µ h = 0.05 m 2 /Vs.
5. Calculate the concentration of electrons and holes in a p-type
semiconductor if the conductivity σ = 10 (Ωm) -1 , the mobilities are µ h =
0.2 m 2 /Vs and µe = 0.4 m 2 /Vs and the concentration of intrinsic carriers
is ni = 2.2 x 10 19 m -3 .
6. A silicon crystal is doped with 5 x 10 20 As atoms/m 3 . The donor level
lies 0.05 eV from the edge of the conduction band, and the band gap is
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