Threshold Voltage for an MOS Junction At threshold, the concentration of electrons at the surface equal to the concentration of holes in the bulk: 0psurfacepn= At threshold, Bsψψ2=. It is assumed that all the charge in the semiconductor is due to the depletion region. BToxBToxTHdEVVψψ22,,+=+= BTsoxSEdψεε2,+= Boundary: oxoxssEEεε= BoxDCQψ2+= By Gauss’s Law DssQE =ε With dCoxoxε=: Oxide Capacitance per unit Area BoxDTHCQVψ2+= For a real MOSFET, FBTHTHVVV −=′ oxDoxssmsTHCQCQV ±±−=ψϕ2 (+ for p-type, - for n-type) where ssQis the charge trapped at the oxide/semiconductor interface.EI EF EV EV BqψBqψBSqqψψ2=MOSFET (Metal Oxide Semiconductor Field Effect Transistor) Subthreshold 0(0) [ / ]psnnExpqkTψ= 0]/)([)(0≅−= kTVqExpnLndsspψTdsnndiffusiondsdriftdsVVLLnnqDEnqJJ≅−=)()0(,,µ ⎥⎦⎤⎢⎣⎡∝kTqVExpJgsds Vgs’ Cox CdVox sψGate Semiconductor′+=gsDoxoxsVCCCψ VgsVdsSGDpn+ n+L 0 W dOhmic Mode (Triode) ))(()( xVVVCxQTHgsoxn−−= With dCoxoxε= 0)0( =V and dsVLV=)( Resistance of a length dx: SxqndxSdxdRn)(µρ==` Sxqn )(=Charge per unit length in x direction=)(xWQn WxQdxdRnn)(µ= dRIdVD= ∫∫=−−LdVdsTHgsoxndxIdVxVVVWC00))((µ ⎥⎥⎦⎤⎢⎢⎣⎡−−=2)(2dsdsTHgsoxndVVVVCLWIµ VgsVds pn+ n+ L 0 x dxdSaturation Mode (Pinch-Off) ))(()( xVVVCxqnTHgsox−−=)()(dsTHgsoxVVVCLqn −−= For dssatTHgsdsVVVV =−≥, 0)(=Ln: the channel is pinched-off near the drain Further increase of dsVdoesn’t increase the source-drain current ∫∫′=−−LdVdssatTHgsoxndxIdVxVVVCW00))((µ dsatdssatoxnTHgsoxndIVCLWVVCLWI ≡≅−′=222)(2µµ dIdsVgsV2dsV∝Saturation Mode Ohmic Mode 1gsV2gsV3gsV4gsVTHgsVV−1VgsVds SGDpn+ n+ L 0 x dxdL’Types of Noise Thermal Noise (Johnson Noise) Caused by thermal random motion of the current carriers Spectral Density: ()4vSf kTR= Noise Voltage: ()24nvBVSfdfkTRB==∫ where 2nV is the mean-squared thermal noise, T is the absolute temperature in K, B is the bandwidth, and R is the real part of the impedance. Example 21 kΩ100 KHz300 K1.3 VnRBTVµ===⇒= Flicker Noise (1f noise) ()nvfmVSf Kf= In semiconductors this noise is mostly due to random trapping and detrapping of charges at the Si-SiO2 interface and associated changes in carrier mobility due to Coulombic scattering. Proposed Hooge’s formula