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# Memory Aid “a hairpin is lighter than a frying pan” - PowerPoint PPT Presentation

light m * (larger d 2 E/dK 2 ). heavy m * (smaller d 2 E/dK 2 ). Memory Aid “a hairpin is lighter than a frying pan”. 1. T=0 o K. T 1 >0. f (E). T 2 >T 1. 0.5. 0. E. E F. f (E) = 1/{1+exp[(E- E F )/ kT ]}. All energy levels are filled with e - ’s below the Fermi Energy at 0 o K.

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## PowerPoint Slideshow about ' Memory Aid “a hairpin is lighter than a frying pan”' - hilary-crawford

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Presentation Transcript

(larger d2E/dK2)

heavy m*

(smaller d2E/dK2)

Memory Aid“a hairpin is lighter than a frying pan”

T=0 oK

T1>0

f(E)

T2>T1

0.5

0

E

EF

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

T=0 oK

T1>0

T2>T1

S(E)

0.5

0

E

EV

EF

EC

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

E

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

Putting the pieces together:

for holes, p(E)

fp(E)

T=0 oK

1

T1>0

T2>T1

0.5

0

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

p

n+

n+

W

L

(x)

Ec(y) with VDS=0

Increasing VGS decreases EB

EB

EF ~ EC

y

0

L

Band diagram of triode and saturation

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 fsis called the surface potential

on Threshold Voltage

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

Subthreshold Current (revisited)VDD scaling  VT scaling

E a thicker insulatorC

EV

W

Junction Leakage CurrentTunneling current due to highly doped Drain-Body junctions

B

D

IJE

Recall: tunneling

T = Kexp(-2kW)

Total Stand-by Power a thicker insulatorPoff = VDD(Ig + IJE + Ioff)

Scaling Directions (I) a thicker insulatorSOI (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) a thicker insulatorThe “FinFET” moves from a single gate to double and triple gate structures and also multiple channels.

(Equation 2.111) a thicker insulator

General behavior of a thicker insulatorβ (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.