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MOSFET threshold voltage
This document summarizes the structure and operation of Metal Oxide Semiconductor Field Effect Transistors (MOSFETs). It describes the basic MOSFET structure with a semiconductor, metal oxide, and source/drain contacts. It explains MOSFET operation in different voltage regimes, including sub-threshold where there is low current, and above threshold where there is higher current. It discusses how the threshold voltage is defined and depends on factors like body bias and surface states. The key points covered are the inversion mechanism in MOSFETs and how the surface potential must reach 2fb for strong inversion and current flow.
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MOSFET threshold voltage
- 1. Metal Oxide Semiconductor FieldEffect Transistor (MOSFET) Structure: semiconductor metal oxide p+ n n S G D
- 2. MOSFET operation If VG=0Assuming VD=high, VS=0 G S D p+ n nNo current
- 3. MOSFET operation If VG=highNow if VD=high, there is a current flow between D and S G S D ++ ++
- 4. MOSFET structures andcircuit symbols p-type substr ate Si O2 n + Depletion r egion Gate Sour ce Dr ai n + Drain Drain Drain n Gate Bul k Sour ce Sour ce Sour ce Channel Substr ate (b) (c) (d) (a) (a) Schematic structure of n-channel MOSFET (NMOS) and circuit symbols for (b) MOSFET, (c) n-channel MOSFET, and (d) n-channel MOSFET when the bulk (substrate) potential has to be specified in a circuit.
- 5. Complementary MOSFET pairs Gaten-channel p-channel Dr ain Sour ce + Drain Drain + p n Si O2 n-type wel l Si O2 Gate Bul k p-type substrate Sour ce Sour ce Subst r ate Schematic structure of Complementary MOSFET (CMOS) and circuit symbols for p-channel MOSFET (PMOS). Minuses and pluses show the depletion regions.
- 6. Sub-threshold mode ofMOSFET operation •VG = 0; the MOSFET conducting channel VG = 0 is not formed higher VG Channel EcSource DrainEnergyFB EF Distance In the subthreshold regime, the MOSFET current is a small reverse current through the source • substrate and drain • substrate p-n junctions; Only a small number of electrons can pass over the potential barrier separating the drain and the source. ( B / kT - F ) n • n ×e ST Source
- 7. Sub-threshold mode ofMOSFET operation 10 2 0 10 VG2 -2 VG1 10 -4 10 -6 VG3 10 Source Drain -8 10 VG1<VG2<VG3 -10 10 Gate-source voltage (V) 1.81.41.00.60.2-0.2 0.05 V V ds = 3.0 V I t In the sub-threshold regime, the channel current is very low and increases exponentially with the gate bias. ( B / kT - F ) n • n ×e ST Source
- 9. 0.05 V V ds= 3.0 V I t 0.05 V V ds = 3.0 V I t MOSFET threshold voltage VG1<VG2<VG3 10 2 0 VG1 10 Source VG2 VG3 -2 10 -4 10 -6 10 Drain -8 10 -10 VT 10 -0.2 0.2 0.6 1.0 1.4 1.8 Gate-source voltage (V) At certain gate bias called the threshold voltage, the conductivity type under the gate inverts and the barrier between the Source and the Drain disappears. Electrons can enter the region under the gate to form a conducting n-channel. At the gate voltages above the threshold, the gate and the channel form a Metal-Insulator-Semiconductor (MIS) capacitor. 8
- 10. MOSFET above thethreshold voltage The free electron charge in the MOSFET channel (per unit area): Q1 = CGATE × (VG –VT) (assuming that at VG = VT the free electron concentration is zero) In MOSFETs, the gate and channel form a MIS-capacitor, hence the capacitance per unit gate area c =e / d =ee / d i ii ir 0 i ei = eir e0 is the total dielectric permittivity of the gate dielectric (usually, SiO2), eir is the relative dielectric permittivity of the gate dielectric. Total gate capacitance CG = ci ×A, where A is the gate area The sheet electron concentration above the threshold, nS is given by: qns = ci ( VGS - VT )= ciVGT
- 11. MOSFET above thethreshold voltage 1.81.41.00.60.2 0.05 V V ds = 3.0 V I t 10 2 0 10 -2 10 -4 10 -6 10 -8 10 -1010 -0.2 Gate-source voltage (V) qns = ci (VGS - VT ) = ciVGT Above the threshold, the sheet electron concentration and hence the channel current increase linearly with the gate bias VG.
- 12. MOSFET Threshold Voltage semiconductor metaloxide p+ n n S G D DrainSource
- 13. Band Diagram atthe MOS interfaces Before Contact Vacuum level oxide metal p+ n n q .ox EC qfm q qq ..s ss Ei qfs EC EFm E g EFs EV EV METAL OXIDE SEMICONDUCTOR
- 14. Metal and semiconductorFermi levels align by After Contact electron transfer. Bending is the result of the presence of transferred electron p+ n n EC EC EC E EEV VV EC Ei E EEFm FmFm EFs Ei EV EFs EV METAL OXIDE SEMICONDUCTOR
- 15. p + n n p + n n Flat band Voltage VG Gatevoltage making the band flat EC VFB= fm-fs EC EFm Ei VG EFs EV EV EC EC EFm Ei VG EFs EV VG EFm EV VG=VFB EC EC
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- 17. Conductivity conversion inMOSFET p + n n Less holes at the VG VG interface, more bending p + n n Less p type p type EC EC Ei Ei EFs EFs EV EV VG . VG=0 More depletion
- 18. p + n n p + n n p + n n VG VG Less p typep type Less p type p type EC EC Onset of Channel Channel Ei Ei creation created EFs EFs EV EV VG .. VG ... n type Inversion n type Strong Inversion
- 19. Inversion condition inMOSFET EC EV EFs Ei qfb Equilibrium hole concentration in the bulk of semiconductor qVs qfb kT pne = i qfb is the Fermi level offset from the mid-gap in the bulk material Surface potential Vs is controlled by the gate voltage Accumulation Depletion Onset of inversion Inversion V<0 V<fb V=fb V>fb sss s Strong Inversion When Vs = 2fb, n-concentration at the surface is the same as p-concentration in the bulk Vs>2fb
- 20. Surface potential requiredto reach the MOSFET threshold qfbqfb kTipne= EC EV EFs Ei VsT=2fb fbfbkTinne= When Vs = 2fb, n-concentration at the surface is the same as p-concentration in the bulk
- 21. Surface potential andgate voltage • VG is the gate voltage, as source is grounded, Vi VG=VGS • Vi is the voltage drop across the oxide/insulator • Vs is the surface potential VG EFm V = V + V + V GS FBsi EC Vs EC Ei EFs EV EV
- 22. Voltage drop acrossthe oxide layer V = V + V +V GS FB si Vi Vi is the voltage drop across the oxide/insulator Gate electrode and semiconductor form the VG plates of the MOS capacitor. EFm Voltage drop across the capacitor: Q d V = i C i EC Ei EFs EV EV EC where Qd is the capacitor charge and Ci is the capacitance. Since the charges on the metal and semiconductor plates are the same, Qd can be calculated as the charge in semiconductor. The semiconductor charge is formed by the charge of the depletion region
- 23. Voltage drop acrossthe oxide layer Vi The relation between the depletion region width W and the applied voltage Vs: qN W 2 a Vs = VG2es 2eVs EFm Form this, W = qN a The depletion region charge (per unit area) : EC Ei EFs EV EV 2eVs Q = qN W = qN . Q = 2e qN da
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- 25. Voltage drop acrossthe oxide layer Q Vi d V = i c i where,Q = 2e qN V d sas VG is the depletion region charge per unit area, EFm ci is the MOS-capacitor capacitance per unit area: e i c = i d i di is the thickness of the oxide film under the gate EC Ei EFs EV EV
- 26. MOSFET threshold voltage(cont.) The MOSFET threshold voltage is defined as the Gate voltage leading to the strong inversion, i.e. Vs = 2fb TV= V + At the onset of strong inversion: 2esqNa GS FBs ()()22 bbff+ 2e qN V s as V = V + V + c i FB c i Finally, the threshold voltage, V = V + 2. +. 2. TFB b b
- 27. N where the bodyeffect constant, .= N 2 saiqNc/e
- 28. Effect of BodyBias VG p+ n n VS VD VBS .0 the Threshold voltage, V = V + 2. +. T FB bN ( )BSb V2 -.
- 29. Effect of SurfaceStates p+ n n VS VD VBS .0 bonds are created that contributes to wanted trapped charges at the interface + + + + + + + + + + VG During the oxide growth on Si, dangling the Threshold voltage, VT = VFB + iCssQ+ 2.b +.N (2.b - VBS ) Qss : surface state charges per unit area