240ln03 - FIELD EFFECT TRANSISTORS LN #3 VGS D VDS MOSFETS...

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1 FIELD EFFECT TRANSISTORS LN #3 MOSFETS n+ n+ p V DS S D G V SB =0 V GS UPON THE APPLICATION OF MORE +VE GATE BIAS THE DEPLETION REGION UNDER THE GATE INCREASES space V GS =0 Φ ms =0 metal semiconductor work function difference E Fm E c E v E i E Fs add oxide φ s semiconductor band bending E c E i E Fs E v E Fm V GS tox + - ε ENERGY DIAGRAMS a)No bias b)Moderate bias φ s =2 φ F semiconductor band bending at threshold E c E i E Fs E v E Fm V GS =V T tox + - ε b)Strong bias Inversion THRESHOLD CONDITION φ F φ F The width of the depletion region in general is given by x d With further increase in V GS , the band Bending reaches 2 φ F and the width of the depletion region reaches a maximum value of 2 / 1 2 = φ ε A d qN x 2 / 1 max 2 2 = F A d qN x This happens because the increase of charge in the channel begins to be supplied by the increase in the free carriers in the channel instead of the increase in the depletion charge. As a result the depletion charge reaches a saturated value. The gate voltage when this occurs is labeled THRESHOLD VOLTAGE THRESHOLD RELATIONS
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2 1/2 0 2 2 [ 2] 1 [2 2 ] T F ox ox ox ox ox ox Bo A F A Bo ox A F ox ox V V V t Q qN qN Q hence qN ε φ εφ εε = + = Ε ⇒Ε = = ⇒Ε = = Thus ox ox ox ox Bo F Bo ox ox F T t C C Q Q t V = + = + = 2 2 0 Due to other non-ideal effects which are a)fixed interfacial charge Q ss , b)non zero value of Φ the actual value of V ms T0 becomes Φ = Φ + + = ox ss ms FB ox ss ms ox Bo F T C Q V C Q C Q V ] 2 [ ' 0 Φ ms Q represents the difference in the work function between the metal gate and the semiconductor. The work function is defined as the energy required to lift the electron from the Fermi energy to free space (to remove the electron from the material) ss represents charge at the interface in the oxide which results from the change in lattice structure at the semiconductor-insulator interface. NOTE: In the case of a finite substrate bias, the substrate charge Qs (see above) is modified to [ ] [ ] 0 ' 2 2 |2 1 22 2 SB Bo ss B Bo B A F SB T V F ms ox ox ox T To F SB F A ox Q Q QQ Q qN V V C CC V V V where qN C γφ γ  = + = + +Φ − +   = + + −−−−−−> −−− = It is useful now to substitute some numbers
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3 n+ n+ p V SB =0 S D G N A =10 16 cm -3 T=300K t ox = 100Å Si | SiO 2 ε Si = 11.8 , ε ox = 3.9 V T0 = 2 φ F + Q B | C ox | φ =2 φ F a) φ F = (kT/q) ln (N A /n i ) = 0.0259 ln (10 16 /1.5x10 10 ) = 0.347 2 φ F = 0.6946 b) Q B = [2 ε qN A ] 1/2 = [4 ε qN A φ F ] 1/2 = [1.6x10 -19 *11.8*8.85x10 -14 *10 16 *0.347] 1/2 = 4.82x10 -8 C/cm 2 c) C ox = ε ox /t ox = (3.9*8.85x10 14 )/100x10 -8 = 3.453x10 -7 F/cm 2 d) V To = 0.6946 + 4.82x10 -8 /3.45x10 -7 = 0.695 + 0.139 V To = 0.834 V IN A REAL MOS STRUCTURE, NON-IDEAL EFFECTS WILL SET IN AND V T = V To + V FB where V FB = Φ ms – Q ss /C ox Q ss b) Interface charge is composed of a) Fixed oxide charge 10 14 10 18 Φ ms (V) -.2 -.5 Al/n-Si n+ poly/n - Si -.8 -1.2 Al/p-Si n+ poly/p-Si Gate Material Φ m - X Ag 0.73 Au 0.82 Cr -0.06 Cu 0.63 Mg -1.05 Sn -0.83 Vacuum Φ m Φ m X Φ s E Fs E FM Φ Ms = Φ M – X – ( E c - E Fs )
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4 Example:
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240ln03 - FIELD EFFECT TRANSISTORS LN #3 VGS D VDS MOSFETS...

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