Description

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
𝛼𝑇2
𝐸𝑔 =𝐸𝑔(0)−
𝛽+𝑇
where 𝐸𝑔(0) is the value of the bandgap energy at 𝑇=0𝐾. For silicon, the parameter values are 𝐸𝑔(0)=1.170𝑒𝑉, 𝛼=4.73×10−4𝑒𝑉/𝐾, and 𝛽=636𝐾. Plot 𝐸𝑔 versus T over the range 0≤𝑇≤600𝐾. In particular, note the value at 𝑇=300𝐾. 2. The E versus k diagram for a particular allowed energy band is shown in Figure P3.15. Determine (a) the sign of the effective mass and (b) the direction of velocity for a particle at each of the four positions shown.

3. The figure below shows the parabolic E versus k relationship in the conduction band for an electron in two particular semiconductor materials, A and B. determine the effective mass (in units of the free electron mass) of the two electrons.

4. (a) The forbidden bandgap energy in GaAs is 1.42 eV. (i) Determine the minimum frequency of an incident photon that can interact with a valence electron and elevate the electron to the conduction band. (ii) What is the corresponding wavelength? (b) Repeat part (a) for silicon with a bandgap energy of 1.12 eV.
5.