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MOSFET Transistor Basics AVLSI Workgroup Paul Hasler

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Diffusion of Charge over Barrier EcEc EcEc EfEf EcEc AB P(E) = ~ e -(E-Ef)/kT 1 1 + e -(E-Ef)/kT Case I: P(E) ~ exp( - E 0 /kT) q V E0E0 Case II: P(E) ~ exp( - ( E 0 - q V)/kT) Ratio of Case II to Case I = exp( V / U T ) U T = kT/q

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P-N Junctions N-type N D P-type N A Depletion Layer or Region Charge Density qN D -qN A Band Diagram

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P-N Junctions --- Diodes N-type N D P-type N A First-Principles Model

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A MOSFET Transistor Gate Source Drain Source Substrate Gate Drain

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Self-Aligned Process How do we make a basic transistor element? We create a silicon-oxide stencil (or mask) We get highly repeatable gates because the gate acts as a stencil as well

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CMOS Process Cross Section (n-well) all p-n junction must be reversed bias CMOS Process = nFETs and pFETs are available

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MOS Transistor Operation Use subthreshold operation as the fundamental case Allows intuition across sub-V T and above-V T operation Sub-VT operation simplifies this 2D problem to 2 1D problems

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Water Analogy of a MOSFET

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Channel Current Dependence on Gate Voltage In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

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MOSFET Channel Picture

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MOS Capacitor Picture

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MOSFET Channel Picture

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Calculation of Drain Current

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No recombination 0 2 2 dx nd DnDn n dn qDJ l nn qD drainsource n 0 l varies as V G n = Ax + B RG dx nd D dt dn n 2 2 0 00 (qD n / l) ( e -( - Vs)/UT - e -( - Vd)/UT ) eeII uVVuVV TdgTSg / / 0

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MOSFET Current-Voltage Curves 1 /)( 0 //)( 0 / // 0 TSG TdSTSG TD TSTG uVKV uVuV uV uVu DS eI eeI eeeII eeII uVVuVV TdgTSg // 0 1 / / 0 TSd TSg uVV uVV eeI

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Channel Current Dependence on Gate Voltage In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

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Channel Current Dependence on Gate Voltage In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependence

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Determination of Threshold Voltage 0.40.50.60.70.80.91 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Gate voltage (V) Drain current / subthreshold fit V T = 0.86

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Drain Current --- Source Voltage

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Origin of Drain Dependencies Increasing Vd effects the drain-to-channel region: increases depletion width increases barrier height

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Cause of DIBL

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Drain Characteristics

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Current versus Drain Voltage

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Not flat due to Early effect (channel length modulation)

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Current versus Drain Voltage Not flat due to Early effect (channel length modulation) In BJTs --- Base Modulation Effects

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Current versus Drain Voltage Not flat due to Early effect (channel length modulation) I d = I d (sat) (1 + (V d /V A ) ) or I d = I d (sat) e Vd/VA In BJTs --- Base Modulation Effects

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Drain Induced Barrier Lowering Data taken from a popular 1.2 m MOSIS process Data taken from a popular 2.0 m MOSIS process

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MOSFET Operating Regions End on mobile charges in channel End on fixed ions in bulk Field Lines from gate charges Below ThresholdAbove Threshold Channel current flows DiffusionDrift Charge boundary condition at source Set by Fermi Distribution C ox ( (V g -V T )-V s ) = ln( 1 + e ) ( (V g - V T ) - V s )/U T Q s = e ( - V s )/U T Approximate surface potential V g ln(Q s ) (EKV modeling)

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MOS-Capacitor Regions Q s = ln( 1 + e ) ( (V g - V T ) - V s )/U T Q s = e ( - V s )/U T Depletion ( (V g - V T ) - V s < 0) Q s = e ( (V g - V T ) - V s )/U T Inversion ( (V g - V T ) - V s > 0) Q s = ( (V g - V T ) - V s )/U T Surface potential moving from depletion to inversion

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Band-Diagram MOSFET Picture Band-diagram picture moving from subthreshold to above-threshold Conduction band bends due to electrostatic force of the electrons moving through the channel

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Physics Based Models: Channels Utilizing the physics of physical medium (Si) to efficiently implement computation n + p-substrate n + l = Channel Length DepletionLayer V ds E c E c What if Hodgkin and Huxley had known / understood MOSFET transistors when developing the original modeling….. +- V Outside Inside + - - - - - - - - - - - - - - - - + ++ ++ ++ + + ++ ++ ++ Gate DrainSource E K E Na C V mem M Na M K [Farquhar and Hasler, 2004]

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