Lecture 11: MOS TransistorLecture OutlineMOS CapacitorAccumulation: VGB < VFBDepletion: VFB<VGB < VTInversionThreshold VoltageInversion Stops DepletionQ-V Curve for MOS CapacitorNumerical ExampleNum Example: Electric Field in OxideNumerical Example: Depletion RegionMOS CV CurveC-V Curve Equivalent CircuitsMOSFET Cross SectionMOSFET LayoutPMOS & NMOSCMOSCircuit SymbolsObserved Behavior: ID-VGSObserved Behavior: ID-VDS“Linear” Region CurrentMOSFET “Linear” RegionMOSFET: Variable ResistorDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11Lecture 11: MOS TransistorProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadLecture OutlineReview: MOS Capacitors RegionsMOS Capacitors (3.8 − 3.9)–CV Curve–Threshold VoltageMOS Transistors (4.1 − 4.3):–Overview–Cross-section and layout –I-V CurveDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadMOS CapacitorMOS = Metal Oxide SiliconSandwich of conductors separated by an insulator “Metal” is more commonly a heavily doped polysilicon layer n+ or p+ layerNMOS p-type substrate, PMOS n-type substrateOxide (SiO2)Body (p-type substrate)Gate (n+ poly)011.7se e=03.9oxe e=Very Thin!~ 1nmoxtx0Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadAccumulation: VGB < VFBEssentially a parallel plate capacitorCapacitance is determined by oxide thickness:( )G ox GB FBQ C V V= -Body (p-type substrate)−+GB FBV V<++++++++++++++++++−−−−−−−−−−−−−−−−−−B GQ Q=( )xr( )xfDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadDepletion: VFB<VGB < VTPositive charge on gate terminates on negative charges in depletion regionPotential drop across the oxide and depletion regionCharge has a square-root dependence on applied biasBody (p-type substrate)+−GB FBV V>+ + + + + + + + + +( )B a d GBQ qN X V=-− − − − − − − − −− − − − − − − −( )G GB BQ V Q=-oxt( )xr( )xfDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadInversionThe surface potential increases to a point where the electron density at the surface equals the background ion densityAt this point, the depletion region stops growing and the extra charge is provided by the inversion charge at surfacesqkTs i an n e Nf= =Body (p-type substrate)+ + + + + + + + + ++−GB TV V=− − − − − − − − −− − − − − − − −sfoxtdepx( )xr( )xfDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadThreshold VoltageThe threshold voltage is defined as the gate-body voltage that causes the surface to change from p-type to n-typeFor this condition, the surface potential has to equal the negative of the p-type potentialApply KCL around loop:Gate (n+ poly)GS FB ox BSV V V V= + +12 2 ( 2 )Tn FB p s a poxV V q NCf e f= - + -oxV+-BSV+-+−GB TV V=− − − − − −2s BS pVf = =-sox ox ox ox soxV E t t Eee= =2 ( 2 )2a dep a pa ss ss s a sqN x qNqNEqNfefe e e-= = =Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadInversion Stops DepletionA simple approximation is to assume that once inversion happens, the depletion region stops growingThis is a good assumption since the inversion charge is an exponential function of the surface potentialUnder this condition:,max( )G Tn BQ V Q�-,max( ) ( )G GB ox GB Tn BQ V C V V Q= - -Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadQ-V Curve for MOS CapacitorIn accumulation, the charge is simply proportional to the applies gate-body biasIn inversion, the same is trueIn depletion, the charge grows slower since the voltage is applied over a depletion regionGQ( )GBV VTnVFBVinversionaccumulationdepletion,maxBQ-( )N GBQ V-Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadNumerical ExampleMOS Capacitor with p-type substrate:Calculate flat-band:Calculate threshold voltage:20nmoxt =16 35 10 cmaN-= �( ) (550 ( 402)) 0.95VFB pnV f+=- - =- - - =-12 2 ( 2 )Tn FB p s a poxV V q NCf e f= - + -13-63.45 10 F/cm2 10 cmoxoxoxCte-�= =�19 12 162 1.6 10 1.04 10 5 10 2 0.4.95 2( 0.4) 0.52VTnoxVC- -� � � � � � � �=- - - + =Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadNum Example: Electric Field in OxideApply a gate-to-body voltage:Device is in accumulationThe entire voltage drop is across the oxide:The charge in the substrate (body) consist of holes:2.5GB FBV V=- <562.5 0.55 ( 0.4) V8 102 10 cmGB pox noxox oxVVEt tf+-+ -- + - -= = = =- ��7 2( ) 2.67 10 C/cmB ox GB FBQ C V V-=- - = �Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadNumerical Example: Depletion RegionIn inversion, what’s the depletion region width and charge?,max2 0.8VB s p p p pV f f f= - =- - =- =2,max ,max12aB dsqNV Xe� �=� �� �,max,max2144nms BdaVXqNe= =7 2,max ,max1.15 10 C/cmB a dQ qN X-=- =- �Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadMOS CV CurveSmall-signal capacitance is slope of Q-V curveCapacitance is linear in accumulation and inversionCapacitance is depletion region is smallestCapacitance is non-linear in depletionGQ( )GBV VTnVFBV,maxBQ-( )N GBQ V-CGBVoxCoxCTnVFBVDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadC-V Curve Equivalent CircuitsIn accumulation mode the capacitance is just due to the voltage drop across toxIn inversion the incremental charge comes from the inversion layer (depletion region stops growing). In depletion region, the voltage drop is across the oxide and the depletion regionoxCoxCoxCdepCsdepdepCxe=11dep oxox oxtotdep s oxdep oxox depoxC CC CCC tC CxCee= = =+++Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 11 Prof. A. NiknejadMOSFET Cross SectionAdd two junctions around MOS capacitorThe regions forms PN junctions with substrateMOSFET is a four terminal
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