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]}

All energy levels are filled with e-’s below the Fermi Energy at 0 oK

f(E)

1

0EF

E

T=0 oKT1>0T2>T1

0.5

Putting the pieces together:for electrons, n(E)

f(E)

1

0EF

E

T=0 oKT1>0T2>T1

0.5

EV EC

S(E)

E

n(E)=S(E)f(E)

Putting the pieces together: for holes, p(E)

fp(E)

1

0EF

E

T=0 oK

T1>0T2>T1

0.5

EV EC

S(E)

p(E)=S(E)f(E)

hole energy

Finding no and po

2/3

2

*

/

2/3

2

*

2(min)

0

22...]/)(exp[

2

2

1)()(

kTmNwherekTEEN

dEeEEm

dEEfESp

dshVVFV

kTEEEv

Vdsh

Ev

Ev

pF

2/3

2

*

/

2/3

2

*

2

(max)

0

22...]/)(exp[

2

2

1)()(

kTmNwherekTEEN

dEeEEm

dEEfESn

dseCFCC

kTEE

Ec

Cdse

Ec

Ec

F

the effective density of statesin the conduction band

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

w=(2εV/qNB)1/2

Lasers

pn+n+

n++

LW

Ec(y) with VDS=0

(x)

Increasing VGS decreases EB

EB

y0 L

EF ~ EC

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 s=2f ,

where s is called the surface potential

Quantum Effectson 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/)/(L/)

…where >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 CurrentTunneling current due to highly doped Drain-Body junctions

EC

EV

W

Recall: tunnelingT = Kexp(-2kW)

IJE

D

B

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

Scaling Directions (I)SOI (DST, depleted substrate transistor)

Improves subthreshold slope, Sand decreases Ioff

Also decreases CjE …and IJE

Very thin body region (Tsi = L/3) makes the source and drain spreading resistance (RS) large.

Raised S/D improves ID (next)

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.