EEE4351C
Semiconductor Devices
Spring 2024
Diagnostic Exam 1
Chapters 3 – 6
Jan 26, 2024
Permitted Resources: pencil, eraser, brain.
Forbidden Resources: Calculator, anything else.
1. Consider Intrinsic Silicon at room temperature (T = 300 K).
a) What is the carrier concentration per cubic centimeter? 1010 cm-3
b) Name the process of adding elemental impurities to intrinsic silicon. Doping
c) Assume there is a 96% probability that an electron occupies a particular state. What is the probability of finding a hole in that state? Phole = 1 – Pelectron = 1 – 0.96 = 0.04 = 4%
d) If you add donor atoms, does the semiconductor become n-type or p-type? n-type
e) If you add acceptor atoms, does the semiconductor become n-type or p-type? p-type
f) Add impurity atoms to a concentration of Nd = 1015 cm-3. What’s the minority carrier concentration at thermal equilibrium?
At thermal equilibrium: ni = 1010, no = Nd and nopo = ni2 => p0 = ni2/no = 1020/1015 = 105 cm-3
g) Please draw and label the approximate Fermi energy level to complete the energy band diagram below.
2. An n-type Si sample has donor conc. of Nd = 1016 cm-3. The minority carrier hole lifetime is found to be tp0 = 20 μs.
- What is the lifetime of the majority carrier electrons?
- Determine the thermal-equilibrium recombination rate for electrons and holes in this material.
3. In an n-type silicon with ND= 1E16 cm-3, find nn, nn0, pn, pn0 when illumination in the steady-state condition resulted in (Del. N, excess electron concentration) dn = 5E6 cm-3
4. Consider Si at T = 300K doped with donor impurities at Nd = 5 x 1015 cm-3.
- Determine the thermal equilibrium hole concentration.
- The excess carrier lifetime is 2 x 10-7 s. Excess carriers are generated such that δn = δp = 1014 cm-3. What is the recombination rate of holes for this condition?
5. Consider a uniform block of n-type semiconductor with cross-sectional area A = 1 cm2 and length L = 1000q cm. The majority carrier concentration Nd = 1/q. One side is grounded but a light is generating charges to create a carrier density gradient. On the other side, we apply a known positive voltage. We don’t know the temperature, E field,or diffusion coefficient. Follow the steps below to find the total current flowing through the semiconductor. Assume thermal equilibrium.
a) Determine the diffusion coefficient given the carrier mobility: µn = 100q/KT
Dn = µn(KT/q) = 100 via Einstein Relation
b) What is the diffusion current density the electron concentration varies linearly from 1.1E17 cm–-3 to 1E16 cm-3 over a distance of 1.6 cm? Use the diffusion coefficient found above in part a).
Jn-diff = qDn(dn/dx) = qDn(n/x) = (1.6E-19)(100)[(1.1-0.1)E17]/(1.6 cm) = 1 A/cm2
c) What is the E-field when we apply KT volts across the length of the semiconductor? Leave your answer in terms of KT and q.
E = V/L = KT/1000q V/cm2
d) Assume the mobility is µn = 100q/KT. Calculate electron drift in A/cm2.
Edrift = qnµnEx = q(1/q)(100q/KT)(KT/1000q) = 0.1 A/cm2.
e) What is the total current flow due to both drift and diffusion found in parts b) and d)? Only consider the current flow as calculated from the majority carriers.
Jtotal = Jdiff + Jdrift = 1 + 0.1 = 1.1 A/cm2
f) In which direction is the current flowing with respect to the light?
Electrons are flowing towards the positive voltage and away from the light source. Current is flowing towards the light source away from the positive voltage (But in the direction the E field is pointing).
6. Consider the following graph. Notice the x-axis is in units of 1000K/T (1000 Kelvin per unit Temperature).
a) What is the intrinsic carrier concentration of Indium nitride (InN) at 500 K? (i.e., 1000/T ~ 2)
1010 cm-3
b) What is the approximate intrinsic carrier concentration of Indium nitride (InN) at room temperature? (i.e., 1000/T ~ 3.3) 104 cm-3
c) If 6H-SiC goes from 400K to 1000K during a process, by how much will the intrinsic carrier concentration change?
d) Using the same material and process as in part c, what is the density of holes and electrons at 400K and 1000K for 6H-SiC?
