![]() In linear scale, we have a quadratic dependence In log-scale, we have an exponential dependenceġ5 ( ) I = I e - e ( ) ( ) d n Dn = dx No recombination Dn = Ax + B l dnĢ n No recombination Dn = Dn = Ax + B dx 2 dn d D n 2 = D + G - R dt n dx 2 l y varies as kVG dn n - n (qDn / l) (e-(Y - Vs)/UT - e-(Y - Vd)/UT) J = qD = qD source drain = n dx n l ( ) ( ) ( ) k V - V / u k V - V / u I = I e - g S T e g d T Use subthreshold operation as the fundamental case Sub-VT operation simplifies this 2D problem to 2 1D problems Allows intuition across sub-VT and above-VT operationġ0 Channel Current Dependence on Gate Voltage (n-well) CMOS Process = nFETs and pFETs are available all p-n junction must be reversed bias We create a silicon-oxide “stencil” (or mask) We get highly repeatable gates because the gate acts as a stencil as well N-type ND P-type NA First-Principles Modelĥ A MOSFET Transistor Source Drain Gate Drain Gate Source SubstrateĦ Self-Aligned Process How do we make a basic transistor element? Ec qDV Ec E0 Ec Ef Case I: P(E) ~ exp( - E0 /kT) Case II: P(E) ~ exp( - ( E0 - qDV)/kT) Ratio of Case II to Case I = 1 P(E) = ~ e-(E-Ef)/kT 1 + e-(E-Ef)/kT exp( DV / UT ) UT = kT/qģ P-N Junctions Depletion Layer or Region N-type ND P-type NA qND Charge
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