110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:固態電子元件#104944

(b) .(5%)

(c) (5%)

4.The common-base current gain a of an NPN BJT can be expressed as a = γa_Tδ where a is the emitter injection efficiency factor, a_T  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 E_F (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 Φ_M. If there is now fixed charges density (per unit area) (Q_F) 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 N_A replaced by N_D. Denote again the metal work function asΦ_M and express the work function of Si in tem of . (6%)