Memory Aid “a hairpin is lighter than a frying pan” light m* (larger d2E/dK2) heavy m* (smaller d2E/dK2)

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Presentation transcript:

Memory Aid “a hairpin is lighter than a frying pan” light m* (larger d2E/dK2) heavy m* (smaller d2E/dK2)

f(E) = 1/{1+exp[(E-EF)/kT]} EF E T=0 oK T1>0 T2>T1 0.5 All energy levels are filled with e-’s below the Fermi Energy at 0 oK

Putting the pieces together: for electrons, n(E) f(E) 1 EF E T=0 oK T1>0 T2>T1 0.5 EV EC S(E) E n(E)=S(E)f(E)

Putting the pieces together: for holes, p(E) fp(E) T=0 oK 1 T1>0 T2>T1 0.5 S(E) E EV EF EC p(E)=S(E)f(E) hole energy

Finding no and po the effective density of states in the conduction band

NA -> NA-ND = NA’ = ppo ND -> ND-NA = ND’ = nno

w=(2εV/qNB)1/2

Lasers

p n+ n++ L W (x) Ec(y) with VDS=0

Increasing VGS decreases EB EF ~ EC y L

Band diagram of triode and saturation

Threshold Voltage Definition VGS = VT when the carrier concentration in the channel is equal to the carrier concentration in the bulk silicon. Mathematically, this occurs when fs=2ff , where fs is called the surface potential

Quantum Effects on Threshold Voltage

(Maybe not so good for GaAs!) This is very confusing, because this effective mobility is being used to describe the velocity of carriers when the concept of mobility is not applicable!

Most Simple Model: Constant Field Scaling E = VDD/L after scaling becomes E = (VDD/a)/(L/a) …where a>1 next

Subthreshold Current (revisited) VDD scaling  VT scaling

High-K gate insulator reduces tunneling current by allowing a thicker insulator 0.8 nm

Junction Leakage Current Tunneling current due to highly doped Drain-Body junctions EV W D IJE Recall: tunneling T = Kexp(-2kW)

Total Stand-by Power Poff = VDD(Ig + IJE + Ioff)

Scaling Directions (I) SOI (DST, depleted substrate transistor) Very thin body region (Tsi = L/3) makes the source and drain spreading resistance (RS) large. Raised S/D improves ID (next) Improves subthreshold slope, S and decreases Ioff Also decreases CjE …and IJE

Scaling Directions (II) The “FinFET” moves from a single gate to double and triple gate structures and also multiple channels.

(Equation 2.111)

Effect of recombination currents. High injection effects also shown. Note: recombination does not contribute to Ic!

General behavior of β (hFE) as a function of collector current (from Sze). Low currents: Recombination currents dominate (just as in diode). High currents: High injection effects (increases effective base doping) and series resistance effects increase.