course230B3

course230B3 - nMOSFET Schematic Four structural masks Field...

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nMOSFET Schematic ± Four structural masks: Field, Gate, Contact, Metal. 2/3/2010 1 ,, , ± Reverse doping polarities for pMOSFET in N-well.
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nMOSFET Schematic polysilicon gate gate xide V g ± Source terminal: round potential. oxide V ds Ground potential. ± Gate voltage: V g ± Drain voltage: V ds ± Substrate bias y n source + n drain + 0 L z voltage: V bs x depletion gion inversion ¾ ψ ( x , y ): Band bending at any point ( x , y ). Quasi ermi p-type substrate region channel W ¾ V ( y ): Quasi-Fermi potential along the channel. 0) = 0 2/3/2010 2 -V bs ¾ V ( y =0) = 0, V ( y = L ) = V ds .
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Drain Current Model Electron concentration: nxy n e i qV k T (,) () = 2 ψ Electric field: N 2 2 N a + + = = kT q e e N n kT q e kTN dx d y x kT q kT qV a i kT q si a ε ) 1 ( 1 2 ) , ( / / 2 / 2 E Condition for surface inversion: 02 yV y B = + Maximum depletion layer width at inversion: [ ] Wy Vy N dm si B = + 22 εψ 2/3/2010 3 qN a
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Gradual Channel Approximation Assumes that vertical field is stronger than lateral field in the channel region, thus 2-D Poisson’s eq. can be solved in terms f 1 vertical slices of 1-D vertical slices. Current density eq. (both drift and diffusion): V Integrate in x - and z -directions, J x y qn x y dV y dy nn (,) ( ) = − μ V V where is the inversion charge/area. I y W dV dy Q y W dV dy QV ds eff i eff i () = − = − μ Qy q nxyd x i x i =− 0 Current continuity requires I ds independent of y , integration with respect to y from 0 to L yields V s 2/3/2010 4 ( ) I W L Q V dV ds eff i ds = ( ) 0
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Pao-Sah’s Double Integral Change variable from ( x , y ) to ( ψ , V ), n 2 nxy n V N e i a q V kT ( , ) ( , ) ( )/ = = = = s B d e N n q d dx V n q V Q kT V q a i i ) / ( ) , ( ) ( / ) ( 2 Substituting into the current expression, B s V d ) , ( E ds s V kT V q a i V e N n W / ) ( 2 ) / ( here is solved by the gate voltage eq for a = B eff ds dV d V L q I 0 ) , ( μ E where s ( V ) is solved by the gate voltage eq. for a vertical slice of the MOSFET: VV Q V kTN q n e gf b s s fb s si a si qV k T s =+− =++ + ψψ ε 2 2 2 12 () / / 2/3/2010 5 C C kT N ox ox a
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Charge Sheet Model Assumes that all the inversion charges are located at the silicon surface like a sheet of charge and that there is no potential drop across the inversion layer. ± Depletion charge: s a si d a d qN W qN Q ψ ε 2 = = ± Inv. charge: s a si s fb gs ox d s i qN V V C Q Q Q 2 ) ( + = = ± Change variable: () = d s s s s s s i eff ds d d dV Q L W I , , ) ( μ 2 2 2 ± Note that: ± And: = kT q kTN V V C n N q kT V s a si s fb gs ox i a s 2 ) ( ln 2 a si s fb gs ox qN V V C kT dV ) ( 2 2 + 2/3/2010 6 d s a si s fb gs ox s qN V V C q d 2 ) ( 1 2 2 + =
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Charge Sheet Model + + + = d s s s s s a si s fb gs ox a si s fb gs ox s a si s fb gs ox eff ds d qN V V C qN V V C q kT qN V V C L W I , , 2 ) ( ) ( 2 2 ) ( 2 ψ ε μ Further approximation: for the last term in the bracket.
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course230B3 - nMOSFET Schematic Four structural masks Field...

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