(Solved): Silicon has an energy band diagram shown in Figure 2(a) and a first Brillouin zone shown in Figure ...

Silicon has an energy band diagram shown in Figure 2(a) and a first Brillouin zone shown in Figure 2(b). (b) Figure 2. (a) Energy band diagram for silicon. (b) First Brillouin zone for silicon. a. The density of states effective mass for electrons in silicon is $m_n^{\ast }=1.08\cdot m_0$. On page 409 of your textbook, it shows the constant-energy ellipsoids near the conduction band minima in silicon have $m_{\Vert }^{\ast }=0.98\cdot m_0$ and $m_{\perp }^{\ast }=0.19\cdot m_0$. Show how these single ellipsoid parameters, $m_{\Vert }^{\ast }$ and $m_{\perp }^{\ast }$, are used to obtain the density of states effective mass of $m_n^{\ast }=1.08\cdot m_0$. b. The density of states effective mass for holes in silicon is $m_p^{\ast }=0.549\cdot m_0$. On page 411 of your textbook, it shows the constant-energy surfaces near the valence band maxima in silicon have a light hole and a heavy hole band, see Figure $2(a),m_{lh}^{\ast }=0.16\cdot m_0$ and $m_{hh}^{\ast }=0.49\cdot m_0$. Show how these single band parameters, $m_{lh}^{\ast }$ and $m_{hh}^{\ast }$, are used to obtain the density of states effective mass of $m_p^{\ast }=0.549\cdot m_0$. c. Explain the difference between the density of states effective mass and the conductivity effective mass. What are the values of these for conduction band electrons in silicon?