EECS 170A Electronics I
Fall 2025
Homework #2
Submission deadline: October 22 2025
Q1) Figure 1 shows the parabolic E versus k relationship in the valence band for a hole in two
particular semiconductor materials. Determine the effective mass (in units of the free electron
(3pts)
mass) of the two holes.
Figure 1 E-k relationship in the valence band for a hole in semiconductor materials A and B
Q2) Figure 2(A) shows the result of removing an atom from the Si lattice. The bonding model for
GaAs is pictured in Figure 2B.
(a) Draw the bonding model for GaAs depicting the removal of the Ga and As atoms circled in
red in Figure 2B. (1pt)
Recall:Ga and As take their bonding electrons with them when they are removed from the lattice.
(b) Redraw the bonding model far GaAs showing the insertion of Si atoms into the missing
Ga and As atom sites. (2pts)
c) Is the GaAs doped p- or n-type when Si atoms replace Ga atoms? Explain. (2pts)
d) Is the GaAs doped p- or n-type when Si atoms replace As atoms? Explain. (2pts)
e) Draw the energy bond diagram for GaAs when the GaAs is doped with Si on (i) Ga
sites and (ii) on An sites. (2pts)
Figure 2 (A) Visualization of missing atom or point defect. (B) Bonding model of GaAs
Q3)
(a) Under equilibrium conditions and T > 0 K, what is the probability of an electron state being
(1pt)
occupied if it is located at the Fermi level?
(b) If EF is positioned at EC, determine (numerical answer required) the probability of finding
(2pts)
electrons in states at EC + kT.
(c) The probability a state is filled at EC + kT is equal to the probability a state is empty at EC +
(2pts)
kT. Where is the Fermi level located? (numerical answer not required)
Q4)
Determine the total number (#/cm3) of energy states in Silicon between Ec and Ec+2kT at T =
300K. For Si, mn* =1.08m0
(3pts)
Q5) Given a Ge semiconductor material at T = 300 K. Calculate the equilibrium electron and hole
concentrations for:​
15
−3
(a) 𝑁𝑑 = 2 × 10 𝑐𝑚 ; 𝑁𝑎 = 0
16
−3
(2 pts)
15
−3
(b) 𝑁𝑎 = 10 𝑐𝑚 ; 𝑁𝑑 = 7 × 10 𝑐𝑚
(2 pts)
Q6）
The carrier effective masses in a semiconductor are mn* = 1.21m0 and mp* = 0.70m0. Determine the
position of the intrinsic Fermi level with respect to the center of the bandgap at T= 300 K. (b)
Repeat part (a) if mn* =0.08m0 and mp* = 0.75m0.
(4pts)
Q7)
16
The value of 𝑝0in silicon at T=300 K is 2 × 10
−3
𝑐𝑚
(a) Determine 𝐸𝐹 - 𝐸𝑣. (b) Calculate the
value of 𝐸𝑐 - 𝐸𝐹. (c) What is the value of 𝑛0? (d) Determine 𝐸𝐹𝑖 - 𝐸𝐹.
(7pts)