# 固態電子元件導論 第三章習題 Introduction to Solid ```固態電子元件導論 第三章習題
Introduction to Solid-State Electronic Devices Homework #3

1.
The bandgap energy in a semiconductor is usually a slight function of temperature. In some
cases, the bandgap energy versus temperature can be modeled by
𝐸𝑔 = 𝐸𝑔 (0) −
𝛼𝑇 2
(𝛽 + 𝑇)
where Eg(0) is the value of the bandgap energy at T = 0 K. For silicon, the parameter values
are Eg(0) = 1.170 eV, α = 4.73 x 10-4 eV/K, and β = 636 K. Plot Eg versus T over the range 0
≦T≦600 K. In particular, note the value at T = 300 K.
2.
The forbidden bandgap energy in Ge is 0.66 eV. (a) Determine the minimum frequency of an
incident photon that can interact with a valence electron and elevate the electron to the
conduction band. (b) What is the corresponding wavelength?
3.
The energy band diagram for silicon is shown below. The minimum energy in the conduction
band is in the  direction. The energy in this one-dimensional direction near the minimum
value can be approximated by
𝐸 = 𝐸0 − 𝐸1 𝑐𝑜𝑠𝛼(𝑘 − 𝑘0 )
where k0 is the value of k at the minimum energy. Determine the effective mas of the particle
at k = k0 in terms of the equation parameters.
4.
The Fermi energy level for a particular material at T = 300 K is 5.50 eV. The electrons in this
material follow the Fermi-Dirac distribution function. (a) Find the probability of an electron
occupying the energy at 5.80 eV. (b) Repeat part (a) if the temperature is increased to T =
700K. (Assume that EF is a constant.) (c) Determine the temperature at which there is a 2
percent probability that a state 0.25 eV below the Fermi level will be empty of an electron.
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