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VE320 Intro to Semiconductor Devices
Summer 2024 – Problem Set 5
Due: 11:59pm, July 7th
In all problems, assume the temperature is 300K and all are completely ionization.
1. Define the built-in potential voltage and describe how it maintains thermal equilibrium.
2. Consider the equation 
where 
and 
and τn0 = 5 × 10−7s. Also let n ′ = p ′ = ni = 1015cm −3. Assume very low injection that δn ≪ ni. Calculate R/δn for a semiconductor which is (a) n-type (n0 ≫ p0), (b) intrinsic (n0 = p0 = ni), and (c) p-type (p0 ≫ n0).
3. Consider ann-type semiconductor as shown in the figure, doped at Nd = 1016cm −3 and with a uniform excess carrier generation rate equal to g ’ = 1021cm-3s-1. Assume that Dp = 10cm2/s and τp0 = 10−7s. The electric field is zero. (a) Determine the steady-state
excess minority carrier concentration versus x if the surface recombination velocity at x=0 is (i) s=0, (ii) s=2000cm/s, and (iii) s=∞ . (b) Calculate the excess minority carrier concentration atx=0 for (i) s=0, (ii) s=2000cm/s, and (iii) s=∞ .
Figure 1. Diagram for problem 3
4. Consider ap1-p2 “isotype” step junction shown in the figure below:
Figure 2. Diagram for problem 4
(a) Draw the energy band diagram of the junction assuming that the doping is non-degenerate throughout. Assume an energy gap of 1.4eV.
(b) Derive an expression for Vbi that exists across the junction in equilibrium.
5. AGe diode has ap-side doping of Na = 5×1016cm-3 and ann-side doping of half that value.
(a) Calculate depletion widths on both sides of the junction and draw the equilibrium energy level diagram as a function of position. Carefully label all energy levels (Ec, Ev andEf) and boundaries of the depletion region.
(b) Now apply a reverse voltage 0.1V and repeat part a. Include a sketch of the approximate positions of the quasi-Fermi energies.
6. Calculate the capacitance and plot c2/1 vs VR for the following Sin+p junctions:
Na = 1015cm-3
(a) Reverse bias voltage = 1V; (b) reverse bias voltage = 5V.
(For n+p junctions, Nd ≫ Na. Use a suitable approximation in your calculation.)
7. In the diagram below (the material is Si) :
Figure 3. Diagram for problem 7
(a) Is the diode under equilibrium or forward biased or reverse biased? If biased, what is the bias voltage?
(b) Determine the built-in potential of the diode under equilibrium.
(c) Determine Na and Nd.