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(Metal-Oxide-Semiconductor) Capacitor Structure EE105 – Fall 2014 Microelectronic Devices and Circuits Prof. Ming C. Wu [email protected] 511 Sutardja Dai Hall (SDH) Lecture 8: MOSFET (1): physics 1 MOS (Metal-Oxide-Semiconductor) Capacitor Structure • First electrode - Gate: Consists of low-resistivity material such as metal or doped polycrystalline silicon • Second electrode - Substrate or Body: n- or p-type semiconductor • Dielectric - Silicon dioxide: stable high-quality electrical insulator between gate and substrate. Lecture 8: MOSFET (1): physics 2 1 MOS Capacitors in Three Bias Regions Accumulation Inversion Accumulation Depletion Depletion Inversion Threshold voltage: VTN • Total capacitance modeled as series combination of fixed Gate voltage: VG • Accumulation: V << V oxide capacitance and G TN voltage-dependent • Depletion: V < V G TN depletion-layer capacitance. • Inversion: VG > VTN Lecture 8: MOSFET (1): physics 3 NMOS Transistor Structure • 4 device terminals: Gate(G), Drain(D), Source(S) and Body(B). • Source and drain regions form pn junctions with substrate. • vSB, vDS and vGS always positive during normal operation. • vSB always < vDS and vGS to reverse bias pn junctions Lecture 8: MOSFET (1): physics 4 2 NMOS Transistor: Qualitative I-V Behavior • VGS << VTN : Only small leakage current flows. • VGS < VTN: Depletion region formed under gate merges with source and drain depletion regions. No current flows between source and drain. • VGS > VTN: Channel formed between source and drain. If vDS > 0, finite iD flows from drain to source. • iB = 0 and iG = 0. Lecture 8: MOSFET (1): physics 5 NMOS Transistor: Triode Region Characteristics Charge per unit length in channel: " Q'(x) = −WCox (vGS − v(x)−VTN ) [F/cm] v(x) : voltage of channel at position x i(x) = Q'(x)vx (x), vx (x) : electron velocity at x dv(x) v (x) = −µ E = −µ x n x n dx µn : electron mobility L L " dv(x) ∫ i(x)dx = ∫ WµnCox (vGS − v(x)−VTN ) dx 0 0 dx " !W $ Kn = µnCox # & vDS " L % " iDL = WµnCox (vGS − v(x)−VTN )dv(x) " ∫ Cox = εox Tox : oxide capacitance 0 per unit area # vDS & iD = Kn %vGS −VTN − (vDS εox = oxide permittivity (F/cm) $ 2 ' Tox = oxide thickness (cm) for vGS −VTN ≥ vDS ≥ 0 Lecture 8: MOSFET (1): physics 6 3 NMOS Transistor: Saturation Region • If vDS increases above triode region limit, the channel region disappears and is said to be pinched-off. • Current saturates at constant value, independent of vDS. • Saturation region operation mostly used for analog amplification. Lecture 8: MOSFET (1): physics 7 NMOS Transistor: Saturation Region (cont.) " µnCox W 2 iD = (vGS −VTN ) for vDS ≥ vGS −VTN 2 L vDSAT = vGS −VTN is termed the saturation or pinch-off voltage Lecture 8: MOSFET (1): physics 8 4 Transconductance of an MOS Device • Transconductance relates the change in drain current to a change in gate-source voltage ∂iD gm = ∂vGS Q − pt • Taking the derivative of the expression for the drain current in saturation region, € " W 2ID gm = µnCox (VGS −VTN ) = L VGS −VTN Lecture 8: MOSFET (1): physics 9 Channel-Length Modulation • As vDS increases above vDSAT, the length of the depleted channel beyond the pinch-off point, DL, increases and the actual L decreases. • iD increases slightly with vDS instead of being constant. " µnCox W 2 iD = (vGS −VTN ) (1+ λvDS ) 2 L λ = channel length modulation parameter Lecture 8: MOSFET (1): physics 10 5 Body Effect or Substrate Sensitivity • Non-zero vSB changes threshold voltage, causing substrate sensitivity modeled by V V v 2 2 TN = TO +γ( SB + φF − φF ) where VTO = threshold voltage for vSB = 0 γ = body - effect parameter ( V) 2 φF = surface potential (V) € Lecture 8: MOSFET (1): physics 11 NMOS Model Summary Lecture 8: MOSFET (1): physics 12 6 PMOS Transistors: Enhancement-Mode Structure • p-type source and drain regions in an n-type substrate. • vGS < 0 required to create p-type inversion layer in channel region • For current flow, vGS < VTP • To maintain reverse bias on source-substrate and drain -substrate junctions, vSB < 0 and vDB < 0 • Positive bulk-source potential causes VTP to become more negative Lecture 8: MOSFET (1): physics 13 PMOS Transistors: Output Characteristics • For vGS > VTP, transistor is off. • For more negative vGS, drain current increases in magnitude. • PMOS device is in the triode region for small values of VDS and in saturation for larger values. • Remember VTP < 0 for an enhancement mode transistor Lecture 8: MOSFET (1): physics 14 7 PMOS Model Summary Lecture 8: MOSFET (1): physics 15 8 .
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