Microelectronics Technology Class Activity 10 February 25, 2011 1. Consider three semiconductors: Ge, Si, and GaAs. Each one is doped with 1018 cm‐3 acceptors. Assume the hole binding energy (or ionization energy) is 0.03 eV. What will be the value of the hole concentration p in each semiconductor at 300 K ? (Hint: Compare the ionization energy to the value of kT at 300 K; is p approximately the same in all semiconductors or will it be different ?). 2. The diagram below shows the bandgap values of several semiconductors. Suppose you want to detect 1.5‐m radiation. Which of the semiconductors shown below can you use? Explain your reasoning. (Hint: The semiconductor has to absorb the radiation to work as a detector) 3. A Si-sample is doped with NA=1016 cm-3 and ND=1016 cm-3. Determine the hole concentration in this sample at 300 K. Where is the position of the Fermi level ? What is the hole concentration at 0K? 4. What is the difference between a degenerately and non-degenerately doped semiconductor ? (Hint: Fermi-level position) 5. An n-type Si sample is doped such that the doping concentration increases exponentially from 1015 cm-3 to 1017 cm-3 as x increases from zero to x1. The magnitude of the electric field inside Si between x = 0 and x = x1 is (choose ND (cm‐3) one): (a) linearly decreasing 1017 (b) linearly increasing (c) constant (d) exponentially decreasing (e) zero 0 x1 x 6. The hole mobility in a Si sample is measured to be 500 cm2/Vs at 400 K. What is the hole diffusion coefficient at 400 K ? 7. Consider two uniformly doped p-type Si bars, A and B, both with NA=1017 cm-3 and same cross-sectional area A = 1cm2 and length. Let us assume by injecting electrons to the left and extracting them on the right, steady-state excess minority carrier concentration profiles in A and B are maintained as shown in the figure below. If bar A has a higher diffusion current density Jn,diff for electrons at x = 0, identify which of the two concentration profiles belongs to A. Justify your answer with a brief explanation. (Note: There is no generation of charge carriers taking place inside the bar.) n 12 ‐3 10 cm 0 0 x 8. Assume the Fermi‐level is 4 kT below the conduction band edge Ec. Determine the probability that an electron will occupy a state at EC at 300 K. (Hint: Fermi‐function). 9. Consider a 1016cm‐3 donor doped Si piece as shown which has a cross section of 1cm2. If you apply a voltage of 10V to the right end with respect to the left end, how much current will flow? Assume electron mobility of 1200cm2/Vs. Draw the band diagram when 10V is applied. x=0 x=1000um 9. GaAs is a semiconductor with a band gap of 1.42 eV. The intrinsic carrier concentration in GaAs is 2 × 106 cm‐3 at 300 K and 1012 cm‐3 at 500 K. A particular wafer of GaAs is doped with ND = 1017 cm‐3 donors and NA = 5 × 1016 cm‐3 acceptors. Assume the following for the free carrier mobilities: n = 7000 cm2/(Vs) and p = 500 cm2/(Vs). a) This wafer is (n‐type, p‐type, intrinsic: choose one) ? What is the hole and electron concentration at 300 K in this semiconductor? b) Calculate the resistivity of the above wafer at 300 K: c) Draw an energy band diagram showing the Fermi‐level position. Mark clearly EC, EV, Ei, and EF. Indicate the numerical values of EC – EV, EC – Ei, and EF – Ei in the diagram. d) Suppose the wafer is heated to 500 K. Determine the hole and electron concentrations at this temperature.
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