V sb is the source bulk voltage f t lnn a n i is the

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V SB is the source-bulk voltage F = - T ln(N A /n i ) is the Fermi potential ( T = kT/q = 26mV at 300K is the thermal voltage; N A is the acceptor ion concentration; n i 1.5x10 10 cm -3 at 300K is the intrinsic carrier concentration in pure silicon) = (2q si N A )/C ox is the body-effect coefficient (impact of changes in V SB ) ( si =1.053x10 -10 F/m is the permittivity of silicon; C ox = ox /t ox is the gate oxide capacitance with ox =3.5x10 -11 F/m) 36/74
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Digital IC 2: Device I-V character in resistive or linear region Page 92 Linear dependence between V ds and I D L W t ε L W C L W k ox ox n ox n ' n = = = k n ox ox n ox n n DS DS T GS n DS DS T GS n D t C k V V V V k V V V V L W k I ' 2 2 ' 2 ) ( 2 ) ( 37/74
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Digital IC 2: Device nMOS Saturation Channel pinches off I ds independent of V ds We say current saturates Similar to current source + - V gs > V t n+ n+ + - V gd < V t V ds > V gs -V t p-type body b g s d I ds 38/74
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Digital IC 2: Device I-V relation under Saturation condition V ds V gs -V T ox ox n ox n ' n t ε u = C u = k 2 ) ( 2 ) ( 2 2 T GS n V V V DS DS T GS n D V V k V V V V k I T gs ds 39
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Digital IC 2: Device I-V characteristic of saturation ] ) ( [ ) ( T gs x o i V x V V C x Q W x Q x v I i n D ) ( ) ( dx dV x E x v n n n ) ( ) ( W V x V V C dx dV I T gs x o n D ] ) ( [ T GS V V T gs x o n L D WdV V x V V C dx I 0 0 ] ) ( [ Charge per unit area: 2 T GS ' n Dsat V - V L W 2 k = I 40/74
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Digital IC 2: Device Current-Voltage Relations Long-Channel Device 0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 6 x 10 -4 V DS (V) I D (A) VGS= 2.5 V VGS= 2.0 V VGS= 1.5 V VGS= 1.0 V Resistive Saturation V DS = V GS - V T Quadratic Relationship 41/74
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Digital IC 2: Device Another method for giving I-V Characteristics In Linear region, I ds depends on How much charge is in the channel? How fast is the charge moving? 42/74
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