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.