Examples - 1 MOSCapacitor((1 MOS(Metal oxidesemiconductor...

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12/4/2010 1 MOS Capacitor (Metal Insulator Semiconductor junctions) (1) MOS (Metal oxide semiconductor) capacitors are made of two junctions between metal ( Ag , Au, Al , Heavily doped poly Si , etc), insulator ( SiO 2 , Si 3 N 4, etc) and semiconductors Here the thin oxide layer (insulator, 10nm 1 μ m) is sandwiched in between the metal and the semiconductor 12/4/2010 1 V G Gate An ideal MOS structure has following properties: Metallic gate is uniform & thick enough to distribute charge/voltage evenly across the oxide surface at any operational condition x GND Metal-Oxide-Semiconductor (MOS) capacitor Oxide is a perfect insulator with zero current flow Oxide layer is isotropic with uniform boundary at the semiconductor interface ( no local charge centers ) Semiconductor is uniformly doped and thick enough and any applied gate voltage (V G ) is only felt near the insulator boundary Ohmic contact at back side of the semiconductor to extract charges Work functions of metal and semiconductor are equal: ( ) S M C F at flat Band E E   Ex 1 MOS Capacitor R 1 V 1 V S V G =3V T Calculate V 1 values that put this MOS capacitor in inversion regime? (Logic in this example is relevant to the last example in lecture notes 6) In previous cases we assume substrate is grounded (V 0), no resistances. The presence of V1 and resistances change S x V G Gate 12/4/2010 2 R 2 GND the voltage drop across the cavacitor as V =V , ? GS G S G S V Here V is given V 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 3 ( , . . 0) 3 2 S GS G S T GS T G T S T T T R No current flow through capacitor V V R R R V V V V V R R To operate in inversion regime V V it is V V i R V f substrate is grounded i e V R V V V V R R R R MOSFET: I D V D Relationships (6) If we summarize our findings for an n channel MOSFET 12/4/2010 3 2 2 0 0 & 0 1 & 2 & 1 2 D Dsa N o G T D D D D Dsat O Dsat G T t G N o G T G o T T Z C V V V V Z C V V V V L I K W V V V V here V V V C L V x V Example 1 MOS Capacitor: An MOS capacitor at T=300K with oxide thickness of 200nm and a p type substrate (bulk silicon). The bulk silicon has a acceptor density of N A =10 16 cm 3 . Calculate the reference potential (voltage) with respect to doping ( φ F ), width of the space charge region (depletion region), W, surface electric field, E S , at threshold and the threshold voltage, V T . Remember the MOS capacitor 12/4/2010 4 16 10 1/2 1/2 14 0 19 16 ln( ) 0.026 ln(10 /10 ) 0.36 2 2 11.7 8.85 10 2 2 0.36 0.962 1.6 10 10 F A i S F A kT N n V V q K W m qN ln( ) ln( ) A i F D i kT N n p type q kT N n n type q