1                       EE 560               MOS TRANSISTOR THEORY                                               PART 1Ken...
2     TWO TERMINAL MOS STRUCTURE                                                    VG (GATE VOLTAGE)     GATE    OXIDE   ...
3ENERGY BAND DIAGRAM FOR p - TYPE SUBSTRATE                                               qΧ = electron affinity of Si    ...
4                 ENERGY BAND DIAGRAMS FOR                COMPONENTS OF MOS STRUCTURE       METAL (Al)       OXIDE        ...
VG = 0                        5        Equilibrium                                                 Oxide                  ...
MOS SYSTEM WITH EXTERNAL BIAS                                           7     Accumulation Region VG < 0                  ...
MOS SYSTEM WITH EXTERNAL BIAS                                      8                         VG > 0 (small)   Depletion Re...
MOS SYSTEM BIASED IN DEPLETION REGION                                    9                                VG > 0 (small)  ...
MOS SYSTEM WITH EXTERNAL BIAS                                       10                         VG > 0 (large)   Inversion ...
G                                                     G                                                                   ...
B            S                G                           D                   12                                          ...
B            S      G          D                   D           G          S         B              13                 p+  ...
VGS > VTn             INVERSION REGION                                            14                                      ...
MOS Capacitance C = WLC , C = ε ox                                              15                                        ...
16             Threshold Voltage for MOS Transistors   n-channel enhancement  For VSB = 0, the threshold voltage is denote...
17            Threshold Voltage for MOS Transistors    n-channel enhancement    For       : the threshold voltage is denot...
18             Threshold Voltage for MOS Transistors                             n-channel -> p-channel         ****BE CAR...
19             Threshold Voltage for MOS Transistors                                                      VT0             ...
20   EXAMPLE 3.2 Calculate the threshold voltage VT0 at VBS = 0, for   a polysilicon gate n-channel MOS transistor with th...
QB 0 Q ox        21   EXAMPLE 3-2 CONT.                               VT 0 = ΦGC − 2φF(sub) −     −                       ...
EXAMPLE 3.3 Consider the n-channel MOS transistor with the 22    following process parameters:           substrate doping ...
23   EXAMPLE 3-3 CONT.        where                       VT 0 = 0.38V (from EX 3-2)                        γ = 0.85V1 /2 ...
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Transcript of "Ee560 mos theory_p101"

  1. 1. 1 EE 560 MOS TRANSISTOR THEORY PART 1Kenneth R. Laker, University of Pennsylvania
  2. 2. 2 TWO TERMINAL MOS STRUCTURE VG (GATE VOLTAGE) GATE OXIDE SiO2SUBSTRATE tox p-type doped Si (NA = 1015 to 1016 cm-3) VB (SUBSTRATE VOLTAGE) EQUILIBRIUM: n p = ni2 (ni ≈ 1.45 x 1010 cm-3) Let SUBSTRATE be uniformy doped @ NA n i2 np 0 ≈ and pp0 = NAKenneth R. Laker, University of Pennsylvania NA (BULK concentrations)
  3. 3. 3ENERGY BAND DIAGRAM FOR p - TYPE SUBSTRATE qΧ = electron affinity of Si E F − Ei φF = q Work Function q ΦS = q χ + (E c − E F ) kT n i (N >> n ) kT N D φFp = ln A i φF n = ln (ND >> ni) q NA q nini = 1.45 x 10-10 cm-3 @ room temp,k = 1.38 x 10-23 J/oK, => kT/q = 26 mV @ room tempq = 1.6 x 10 C-19Kenneth R. Laker, University of Pennsylvania
  4. 4. 4 ENERGY BAND DIAGRAMS FOR COMPONENTS OF MOS STRUCTURE METAL (Al) OXIDE SEMICONDUCTOR (Si)Eo qΦM = qχox= 0.95 eV qχm = 4.1 eV Ec qΦS qχSi = 4.15 eVEFm Ec band-gap: Eg = 1.1 eV band-gap: Ei Eg = 8 eV qφFp EFp Ev Ev ΦS > ΦM => p-type Si ΦM > ΦS => n-type SiKenneth R. Laker, University of Pennsylvania
  5. 5. VG = 0 5 Equilibrium Oxide p-type Si Substrate VB = 0Flat-band voltage:VFB = ΦM - ΦS volts Equilibrium Built-in potential: Ec qΦM qΦS Ei qφs qφF EFm EFp φs = surface potential Ev METAL (Al) OXIDE SEMICONDUCTOR (Si)Kenneth R. Laker, University of Pennsylvania
  6. 6. MOS SYSTEM WITH EXTERNAL BIAS 7 Accumulation Region VG < 0 EOX EOX Oxide holes ACCUMULATED on the Si surface p-type Si Substrate VB = 0 VG = 0 Equilibrium Oxide p-type Si Substrate VB = 0Kenneth R. Laker, University of Pennsylvania
  7. 7. MOS SYSTEM WITH EXTERNAL BIAS 8 VG > 0 (small) Depletion Region EOX EOX Oxide DEPLETION Region p-type Si Substrate VB = 0 Ec Ei qVG EFp EFm Ev METAL (Al) OXIDE SEMICONDUCTOR (Si)Kenneth R. Laker, University of Pennsylvania
  8. 8. MOS SYSTEM BIASED IN DEPLETION REGION 9 VG > 0 (small) EOX EOX Oxide 0 x DEPLETION xd d Region x p-type Si Substrate VB = 0 Mobile charge in thin layer parallel to Si surface Change in surface potential to displace dQ Depletion Region ChargeKenneth R. Laker, University of Pennsylvania
  9. 9. MOS SYSTEM WITH EXTERNAL BIAS 10 VG > 0 (large) Inversion Region EOX EOX Oxide xdm Electrons attracted to Si p-type Si Substrate surfaceInversion Condition VB = 0 φs = -φF 2ε Si | 2φF | x dm = x d φs = − φF = Ec qN A Ei EFp EFm qVG φs = -φF Ev METAL (Al) OXIDE SEMICONDUCTOR (Si)Kenneth R. Laker, University of Pennsylvania
  10. 10. G G 11 G G G GD S D S S DS D S D S B B B B B B n-channel enhancement p-channel enhancement I DS I DS IDS IDS -VTp -V Tp V VGS 0 GS V VGS 0 GS +VTn +V Tn n-channel depletion I DS G IDS I p-channel depletion I DS +VTp +VTp DS VGS V GS D S 0 B V VGS -VTn -V 0 GS Tn Kenneth R. Laker, University of Pennsylvania
  11. 11. B S G D 12 W L oxide n+ n+ conducting channel substrate depletion layer or bulk B pN-CHANNEL ENHANCEMENT-TYPE MOSFET nMOS Layout polysilicon gate active area metal contact area W L Kenneth R. Laker, University of Pennsylvania
  12. 12. B S G D D G S B 13 p+ p+ n+ n+ n-well p -substrateVGS < VTn CUT-OFF REGION DEPLETION REGION 0 < VGS < VTn VGS VDS G oxide B (G2) S D C CGC GC n+ n+ CBC n+ n+ CBC depletion region depletion region substrate substrate p or or bulk B bulk B p Kenneth R. Laker, University of Pennsylvania
  13. 13. VGS > VTn INVERSION REGION 14 VGS VDS G oxide B (G2 ) S D CGC C GC n+ n+ CBC n+ n+ CBC conducting channel substrate substrate depletion region or or or bulk B or bulk B inversion region inversion region p p Underneath Gate Ec VG = VTn Ei φF 2φF EFp EFm qVTn -φF Ev METAL (Al) OXIDE SEMICONDUCTOR (Si)Kenneth R. Laker, University of Pennsylvania
  14. 14. MOS Capacitance C = WLC , C = ε ox 15 [tox -> TOX in SPICE] GC ox ox t ox [Cox -> COX in SPICE] tox = 50 nm, εox = 0.34 pF/cm => Cox = 6.8 x 10-8 F/cm2 W x L = 50 µm x 50 µm => CGC = 170 fF Depletion Capacitance C BC = WLC j , C j = εSi xd [NSUB -> NSUB in SPICE] NSUB (p - substrate) kT n i ln φFp = q NANA = 3 x 1017 cm-3, ni = 1.45 x 1010 cm-3 => φF = -0.438 V (recall that at room temp or 27oC kT/q = 26 mV)VSB = 0 V, εSi = 1.06 pF/cm, q = 1.6 x 10-19 C, NA, φF => xd = 6.22 µm εSi, xd => Cj = 0.17 x 10-8 F/cm2 W x L = 50 µm x 50 µm => CBC = 42.5 fFKenneth R. Laker, University of Pennsylvania
  15. 15. 16 Threshold Voltage for MOS Transistors n-channel enhancement For VSB = 0, the threshold voltage is denoted as VT0 or VT0n,p T0 -> VT0 in SPICE] [V QB 0 Q ox VT 0 = ΦGC − 2φF − − C ox C oxThreshold Voltage factors: (+ for nMOS and - for pMOS) [2φ F = PHI in SPICE]-> Gate conductor material;-> Gate oxide material & [N A = NSUB in SPICE] thickness;-> Channel doping;-> Impurities in Si-oxide interface; ΦGC = φF(substrate) -φM metal gate ΦGC = φF(substrate) -φF (gate) polysilicon gate-> Source-bulk voltage Vsb;-> Temperature. [Qox = qNSS in SPICE]Kenneth R. Laker, University of Pennsylvania
  16. 16. 17 Threshold Voltage for MOS Transistors n-channel enhancement For : the threshold voltage is denoted as VT or VTn,p QB Q ox VT = ΦGC − 2φF − − C ox C ox Q B 0 Q ox Q B − Q B0 = ΦGC − 2φF − − − C ox C ox C ox where VT0 (γ = Body-effect coefficient) [γ = GAMMA in SPICE] +Kenneth R. Laker, University of Pennsylvania
  17. 17. 18 Threshold Voltage for MOS Transistors n-channel -> p-channel ****BE CAREFULL*** WITH SIGNS • φF is negative in nMOS, positive in pMOS • QB0, QB are negtive in nMOS, positive in pMOS • γ is positive in nMOS, negative in pMOS • VSB is negative in nMOS, positive in pMOS C BC NOTE: γ ∝ C GCKenneth R. Laker, University of Pennsylvania
  18. 18. 19 Threshold Voltage for MOS Transistors VT0 3V nMOS NBULK = NA 14 16 NBULK NA 10 10 pMOS NBULK = ND -3V VT 16 3V (nMOS 10 /cm 3 ) 14 (nMOS 3 x10 /cm 3 ) 0 VBS V SB 3 6 16 (pMOS 10 /cm3 ) -3VKenneth R. Laker, University of Pennsylvania
  19. 19. 20 EXAMPLE 3.2 Calculate the threshold voltage VT0 at VBS = 0, for a polysilicon gate n-channel MOS transistor with the following parameters: substrate doping density NA = 1016 cm-3, polysilicon doping density ND = 2 x 1020 cm-3, gate oxide thickness tox = 500 Angstroms, oxide-interface fixed charge density Nox = 4 x 1010 cm-2. QB 0 Q ox VT 0 = ΦGC − 2φF(sub) − − C ox C ox φF(sub), ΦGC: ΦGC = φF(sub) − φF(gate) kT n i  1.45x10  10 φF(sub) = ln = 0.026Vln  = −0.35V q NA  10 16  kT N D  2 x10 20  φF( gate) = ln = 0.026 Vln  10  = 0.60 V q ni  1.45x10  ΦGC = φF(sub) − φF(gate) = -0.35 V - 0.60 V = -0.95 VKenneth R. Laker, University of Pennsylvania
  20. 20. QB 0 Q ox 21 EXAMPLE 3-2 CONT. VT 0 = ΦGC − 2φF(sub) − − C ox C ox QB0: = − 2(1.6x10 −19 C)(1016 cm −3 )(1.06 x10 −12 Fcm −1 ) | 2 x 0.35V| F = C/V -8 2 = - 4.87 x 10 C/cm Cox: ε ox 0.34 x10 −12 Fcm −1 −8 C ox = = = 6.8x10 F/cm 2 t ox 500 x10 −8 cm Qox: Q ox = qNox = (1.6x10 −19 C)(4 x1010 cm −2 ) = 6.4 x10 −9 C/cm 2 Q B 0 −4.87x10 C/cm −8 2 Q ox 6.4 x10 −9 C/cm 2 = = −0.716 V = −8 2 = 0.094 V −8 2 Cox 6.8x10 F/cm C ox 6.8x10 F/cm VT 0 = −0.95V− (−0.70 V) − (−0.72 V) − (0.09V) = 0.38VKenneth R. Laker, University of Pennsylvania
  21. 21. EXAMPLE 3.3 Consider the n-channel MOS transistor with the 22 following process parameters: substrate doping density NA = 1016 cm-3, polysilicon doping density ND = 2 x 1020 cm-3, gate oxide thickness tox = 500 Angstroms, oxide-interface fixed charge density Nox = 4 x 1010 cm-2. In digital circuit design, the condition VSB = 0 can not always be quaranteed for all transistors. Plot the threshold voltage VT as a function of VSB. γ - Body-effect coefficient: F = C/V 2 qN A e Si 2(1.6 x10 −19 C)(1016 cm −3 )(1.06 x10 −12 Fcm −1 ) γ= = −8 C ox 6.8x10 F/cm 2 5.824 x10 −8 C/V −1/ 2 cm 2 = −8 = 0.85V1/ 2 6.8x10 C/Vcm 2Kenneth R. Laker, University of Pennsylvania
  22. 22. 23 EXAMPLE 3-3 CONT. where VT 0 = 0.38V (from EX 3-2) γ = 0.85V1 /2 VT(Volts) 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 VSB(Volts) -1 0 1 2 3 4 5 6Kenneth R. Laker, University of Pennsylvania
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