MOS Physics lecture #3

2010-11-24 1MOS Physics 2010

• Frequency dependent capacitance

Read: 99-101104-124

125-139 includes fairly tricky derivations –

will try to summarize in class

140-156170-174

Clicker #1

2010-11-24 2MOS Physics 2010

How interesting was the hand in problemRate on a scale 1-5! (5 very, 1 not very)

1. Boring and unformative2. …3. Somewhat interesting4. …5. Interesting and exciting

Clicker #2

2010-11-24 3MOS Physics 2010

How difficult was the hand in problemRate on a scale 1-5! (5 very, 1 not very)

1. Easy easy!2. …3. Just about right!4. …5. Quite Hard!

Majority Carriers – Dielectric Relaxation time

2010-11-24 4MOS Physics 2010

2/1

2

nq

kT s

kT/q

Local potential fluctuation, kT/q

Decays over a distance equal to extrinsic debye lenght,

Induces electric field F = kT/q1/

Time for carriers to redistribute(dielectric relaxation time)

Majority carriers can follow a acsignal if fac<<1/(tmaj)

tmaj=/(µF)=s/(qµn)

Clicker # 3 – Shape of High-f curve

2010-11-24 5MOS Physics 2010

V

C

LF-curve

V

C

V

C

V

C C

A B

C DFor the p-typeLF MOS CV above – whichis the correspondingHF curve?

E - ???

A. AB. BC. C

D. D

E. E

Experimental Si Curves

2010-11-24 6MOS Physics 2010

•Accumulation and depletion –majority carrier response

•Inversion / Strong Inversion – needto generate holes!

•Shockley-Read-Hall

Si MOS, n-type

Clicker # 4: Interface Traps

2010-11-24 7MOS Physics 2010

Can an interface trap act as an efficient GR-centre in strong inversion?A. YesB. NoC. ???

Traps

2010-11-24 8MOS Physics 2010

Ec

Ev

ET

Electron Capture Electron Emission Hole Capture Hole Emission

ra rb rc rd

in(x,t)

dv(x,t)

Ef

Equivalent Circuit #1

2010-11-24 9MOS Physics 2010

GnDx

GpDx

CTDx

dv(x)dvs

Cox

CI

Cx Cw-x

VB

CB

Trap at distance x: Driven by dv(x) variation

Need to solve Possion eq.Integrate over 0 < x < w

Coupled Equations: (SdQ)•Majority Charge at w•Minority Charge CI

•Charge state of bulk traps

Only traps close to cross-overwill contribute significantly

dufp

Ec

Ev

ET

Efn

x=xc

Efp

w – depletionegde

Equivalent Circuit #2

2010-11-24 10MOS Physics 2010

Ggr

CTpx

Cox

CI

CD

VB

CB

Assume low trap density: nT

>> ND

CD: depletion capacitance

CI: Inversion charge capacitance

CTnx: Electrons stored at traps

CTpx: Holes stored at traps

Ggr: Generation/recombinationconductance

w – depletionegdeCTnx

w

xGxGxCj

xGxdxG

gr pnT

pnG0

Only pure capacitances and conductance at small !

Equivalent Circuit #3

2010-11-24 11MOS Physics 2010

CI

Ggr

CTpx

Cox

CD

CTnx

tt

ttt

ttbt

n

p

pnbtg

pn

btgr

CCH

CG

ln1

≈CDnT / ND : Bulk trap capacitance

cnno(xc) cppo(xc) << tn,tp

If tn=tp=t

Electron/hole capture time

11

0

1)1(

np

g

ffffjdfH

tt

CTnx << CD, CTpx << CI

Cox CD

CI

Ggr

Cox CD

Ggr

jwCI >> Ggr

Strong Inversion, CI >> Cox

ox

HF

ox

gr

mC

C

C

G1

Clicker #4

2010-11-24 12MOS Physics 2010

Which material have lowest transition frequency, assumuing mid-gap trap?

1. n-type InAs2. GaAs3. Si 4. GaN5. ??

ox

HF

ox

gr

mC

C

C

G1

Bulk Diffusion

2010-11-24 13MOS Physics 2010

Electron/Holes can be generated from bulk defects/back contacts

Diffuses to inversion layer throughneutral layer

Modeled as diffusion conductance, connecting conduction/valence band.

1

kTE

igr

kTE

dp

ip

d

g

g

enG

eNL

nqµG

2/

/2

Cox CD

CI

Ggr Gd

Full Conductance – MOSFET Structure

2010-11-24 14MOS Physics 2010

V

C

p

n n

Vg

LF A B

C

E - ???

D

f=5m

A p-type MOS Diode has a transistion frequency m.What is the corresponding CV-curve at f=5m for a MOSFET-diode?

A. AB. BC. CD. DE. ???

Deep Depletion

2010-11-24 15MOS Physics 2010

)(2

13

0

scmn

nvG iTthSRH

Et

Vg(t)

Efn

Efp

•If Vg(t) increases fast enough, GSRH can be too small to supplyenough charges for an inversion layer to form•Hole quasi fermi level not constant•No holes – depletion width increases until breakdown!

• CD,deep < CD

HF curve

C

VDeep depletion