Electronic devices
EGRE 303 Electronic Devices Spring 2024 Homework #4 Due on 10/15/2021, Friday 11:59pm. Show your work clearly to receive credit! 1. The majority carrier drift velocity in a GaAs semiconductor measured as a function of the electric field is shown on the right. Note that this is a log-log plot! a) Determine the type of carrier (electron or hole) this measurement is conducted for. Explain why. b) Determine the doping level for all possible doping configurations. Explain your reasoning. 2. In HW#3, you calculated the resistivity for intrinsic GaAs. a) Calculate the room temperature equilibrium resistivity for GaAs doped with NA = 1 x 107 cm-3 and show that it is larger than that of the intrinsic GaAs. (ni = 2.25 x 106 cm-3) b) This shows that you do not have the maximum resistivity for the intrinsic material. Derive an expression for the carrier concentration required for maximum resistivity in any semiconductor. Start from the expression for resistivity! Note: You may use values of µn = 8,000 cm2/Vs and µp =400 cm2/Vs for lightly doped GaAs, since the mobility values change very little at low Nd and Na. 3. A Silicon sample of length L maintained at 300 K is characterized by the energy band diagrams shown. Answer the following questions and explain how you arrived at your answers. Make your plots for the whole range from x = 0 to x = L. a) Is the sample under equilibrium? Explain why. b) Is the material degenerate at any position(s) x? If yes, where (x = ?) and what is the majority carrier type at these positions? c) Sketch the kinetic energy of the electron as a function of position x if it moves back and forth between x = 0 and x = L without changing its total energy. d) Sketch the kinetic energy of the hole as a function of position x if it moves back and forth between x = 0 and x = L without changing its total energy. e) Sketch the potential energy of the electron in part c as a function of position x. f) Sketch the electrostatic potential V inside the semiconductor as a function of x. g) Sketch the electric field E inside the semiconductor as a function of x. h) Roughly sketch on the same plot log(n) and log(p) as a function of x. i) Roughly sketch on the sample plot the electron drift current density JN|drift and electron diffusion current density JN|diff inside the Si sample as a function of x. Make sure to graph the proper polarity of the current densities at all points and clearly label the two components. 4. Use energy band diagrams to show how one visualizes a) photogeneration, b) direct thermal generation, c) generation via R-G centers, d) impact ionization, e) band-to-band recombination, f) recombination via R-G centers, g) Auger recombination, h) an n-type semiconductor under illumination (non-equilibrium). 5. A Germanium sample (uncompensated) under equilibrium is illuminated and reaches steadystate. The energy band diagrams before and after illumination are shown. a) Calculate n0 and p0 (equilibrium values) b) What is the dopant density and type? c) Calculate the carrier concentrations under illumination at steady state d) What can you say about the perturbation, are “low-level injection” conditions satisfied? Explain e) Calculate the resistivity before and after illumination. (Use Figure 3.5 in Pierret textbook when needed). Is the resistance increased or decreased under illumination?
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