Your Name: ECEN 3320 Semiconductor Devices Final exam - Sunday December 17, 2000 1. Review questions a) Illustrate the generation of a photocurrent in a p-n diode by drawing an energy band diagram. Indicate the photo-generated carriers and their direction of motion. (5 points) b) How does recombination in the base-emitter depletion region affect the emitter, base and collector current? (5 points)
c) Draw an MOS flatband diagram. Indicate the work function of the metal and the semiconductor as well as the flatband voltage. Draw it approximately to scale using Φ M = 4.1 V, χ = 4.05 V, E g = 1.12 ev (silicon) and N a = 10 16 cm -3. (5 points) d) Name the three bias regimes of an MOS capacitor and explain what happens in the semiconductor in each of these bias modes. (5 points)
e) Why is the high frequency capacitance constant in inversion? (5 points) f) Which device has most positive threshold voltage a depletion mode p-type MOSFET or an enhancement mode p-type MOSFET? Explain. (5 points)
2. An aluminum-silicon Schottky diode has a breakdown voltage of 5 V. The silicon is p-type with a doping N a = 10 18 cm -3. Calculate the breakdown field and the depletion layer width. (Φ M = 4.0 V) (15 points)
3. Consider a silicon bipolar transistor with N E = 10 18 cm -3, N B = 10 17 cm -3 and N C = 10 16 cm -3 The quasi-neutral width in the emitter and base are w E = 1 µm and w B = 0.2 µm. a) Calculate the majority as well as the excess minority carrier charge per unit area in the base region. (V BE = 0.65 V, V BC = 0 V) b) Find the minority carrier lifetime in the base for which the transistor has a current gain of 100. Use µ n = 1000 cm 2 /V-s and µ p = 300 cm 2 /V-s. (25 points)
4. The gate length of a silicon nmosfet is reduced from 0.18 µm to 0.13 µm. At the same time the doping density of the substrate is increased from 8 x 10 17 cm -3 to 1.2 x 10 18 cm -3 and the gate oxide thickness is reduced from 6 to 4 nm. By what amount must the charge density (per unit area) at the interface be changed to reduce the threshold voltage from 0.15 V to 0.1 V? Indicate whether the charge density must be increased or decreased. The gate material is heavily doped n-type poly-silicon with a work function of 4 V. (30 points)
Extra credit problem: Find the threshold voltage of the 0.13 µm device (Problem 4) if the bulk-to-source voltage equals 4 V. (5 points)
Appendix 2: Physical constants Avogadro's number Bohr radius Boltzmann's constant Electronic charge Free electron rest mass Permeability of free space Permittivity of free space Planck's constant Reduced Planck's constant Proton rest mass Rydberg constant Speed of light in vacuum Thermal voltage (at T = 300 K) N A a 0 k q m 0 6.022 x 10 23 atoms per mole 52.9177 picometer 0.529177 Angstrom 1.38 x 10-23 Joule/Kelvin 8.62 x 10-5 electron Volt/Kelvin 1.602 x 10-19 Coulomb 9.11 x 10-31 kilogram 5.69 x 10-16 ev s 2 cm -2 µ 0 4π x 10-7 Henry/meter ε 0 h h M R c V t 8.854 x 10-12 Farad/meter 8.854 x 10-14 Farad/centimeter 6.625 x 10-34 Joule second 4.134 x 10-15 electron Volt second 1.054 x 10-34 Joule second 1.67 x 10-27 Kilogram 2.17991 x 10-18 Joule 13.6058 electron Volt 2.998 x 10 8 meter/second 2.998 x 10 10 centimeter/second 25.86 millivolt
Appendix 3: Material Parameters Name Symbol Germanium Silicon Gallium Arsenide Bandgap energy at 300 K E g (ev) 0.66 1.12 1.424 Breakdown Field E br (V/cm) 10 5 3 x 10 5 * 4 x 10 5 Effective density of states in the conduction band at 300 K Effective density of states in the valence band at 300 K N c (cm -3 ) 1.02 x 10 19 2.82 x 10 19 4.35 x 10 17 N v (cm -3 ) 5.65 x 10 18 1.83 x 10 19 7.57 x 10 18 Intrinsic concentration at 300 K n i (cm -3 ) 2.8 x 10 13 1.0 x 10 10 2.0 x 10 6 Effective mass for density of states calculations Electrons m e * / m 0 0.55 1.08 0.067 Holes m h * / m 0 0.37 0.81 0.45 Electron affinity χ (V) 4.0 4.05 4.07 Mobility at 300 K (undoped) Electrons µ n (cm 2 /V-s) 3900 1400 8800 Holes µ p (cm 2 /V-s) 1900 450 400 Relative dielectric constant ε s / ε 0 16 11.9 13.1 Thermal conductivity at 300 K χ (W/cmK) 0.6 1.5 0.46 Refractive index at 632.8 nm wavelength n 5.441 * See also section 4.5.1: Breakdown field in silicon at 300 K - i 0.785 3.875 - i 0.0181 3.856 - i 0.196 µ µ µ = µ max min min + α N 1+ ( ) N r Arsenic Phosphorous Boron µ min (cm 2 /V-s) 52.2 68.5 44.9 µ max (cm 2 /V-s) 1417 1414 470.5 N r (cm -3 ) 9.68 x 10 16 9.20 x 10 16 2.23 x 10 17 α 0.68 0.711 0.719