(c) (5%)

(b) Find the position of Fermi level Ef with respect to the intrinsic Fermi level Ei, (i.e. Ef - Ei). (5%)

(c) The sample is used to make an integrated circuit resistor. The width and beight of the sample are 10 um and l um, respectively, and the length of the sample is 20 um. Calculate the resistance of the sample. (5%)

(a)(5%)

(b) .(5%)

Diodes and BJT 3.Please qualitatively plot the steady-state depletion region widths and the minority carrier concentration profiles in a pn junction under forward bias, zero bias, and reverse bias. Assume that the p-type doping concentration is larger than that of n-type. (15%)

4.The common-base current gain a of an NPN BJT can be expressed as a = γaTδ where a is the emitter injection efficiency factor, aT  is the base transport factor, andδ is the recombination factor. To have an a as large (close to 1) as possible, cach of these factors must be close to l as well. For these three factors, respectively, what about device design and/or operation bias must be done to make them large? (15%) If is increased, will a increase or decrease? Why? (5%)

(a) Given that the work function of the Al is slightly larger than , the electron affinity of Si, and assumed that the oxide is perfect (completely insulating, no fixed charge/interface states within the oxide and at the interface), please plot the band diagrams of the MOS capacitor when the MOS capacitor is biased at equilibrium and threshold, respectively. You have to include (vacuum level), Ec (conduction band edge), Ei (intrinsic level) , Ev (valence band edge) and EF (Fermi level) in you plots. Please also indicate on you plot the condition that the MOS structure reaches threshold. (10%)

(b) Denote the work function of Al as ΦM. If there is now fixed charges density (per unit area) (QF) at the SiO2/Si interface, write down, without derivation, the threshold voltage for the MOS capacitor. Note that you have to express the work function of Si in term of. (6%)

(c) Repeat (b), i.c., write down , for an Al/ SiO2 /n -Si structure, albeit with NA replaced by ND. Denote again the metal work function asΦM and express the work function of Si in tem of . (6%)

(d) Explain the difference between enhancement type and depletion type, for both n-channel MOSFET and p-channel MOSFET, in term of threshold voltage. If the Al / SiO2 / p - Si MOS structure in (a) is part of an MOSFET, is this MOSFET enhancement type or depletion type? Repeat for the Al / SiO2 /n- Si MOS structure in (c). (3%, 2%,2%)