Chapter 16. MOS Fundamental Capacitance - Voltage ...

Chapter 16. MOS Fundamental

Capacitance - Voltage Characteristicsp gHigh- and low- frequency C-V characteristics.


• CV characteristic is of considerable practical importance.p

M O S

A

VG : Slowly changed∆ VG : AC signal ( high

+VG– +∆ VG– G g ( gfrequency/low frequency)


Q• Qualitative theory

Accumulation

GVQC

∆∆

≡– Accumulation

• The state of the system can be changed very rapidly. The majority carrier can equilibrate with a time constant on the order of 10-10 to 10-13 sec.q

• The small ac signal merely adds or subtracts a charge close to the edges of

an insulator.　 parallel-plate capacitor, CO.p p p

O

Μ O S

Go

o

AKCaccC

0

)()(ε

= ecapacitancoxideΜ O S

- Q

Q

∆Q

oxGo 0= Q

-∆Q

CCo


– Depletion

• Withdrawal of majority carriers• The charge state can be changed very rapidly.• The depletion width quasi-statically fluctuates

about its dc value 　 two parallel plate capacitors (C

oand C

s; oxide and semiconductor capacitance)

in series.↑ ↑ ↓• DC bias ↑ W ↑ C(depl)↓

Μ O S

( )O

OSOWK

CCC

CCdeplC =+

=+Q

+∆Q

W

OxS

OSOK

WKCC ++ 1- Q -∆Q

Co CS


– Inversion

• W = WT

• The charge fluctuation depends on the frequency of the AC signal

– Low frequency :

• Minority carriers can be generated or annihilated in response to the ac signal. Just as in accumulation, charge is added or subtracted close to the edges of insulator.

+∆Q

∆Q

Q

WT ( ) OLF CinvC =

Μ O S

-∆Q


– High frequency :

h l i l l i h i bi i• The relatively sluggish generation-recombination process can’t supply or eliminate minority carriers i h i l h b fin response to the ac signal. The number of minority carriers in the inversion layer remains fi d d h d l i id h fl b hfixed and the depletion width fluctuates about the W

Tdc value.　 Two parallel-plate capacitors in

iseries.• Since W

T=constant, C

HF(inv) = C(depl)

minimum=

T HF minimumconstant

Μ O S

+∆

( )

xTo

o

so

soHF

KWK

CCC

CCinvC+

=+

=1

WT

+∆Q

oxsK-∆Q


– For medium frequencyFor medium frequency

• A portion of the inversion layer can be created/annihilatedcreated/annihilated.

• CHF

(inv) < CMF

(inv) < CLF

(inv)

Μ O S

W

+∆Q

WT

-∆Q

-∆Q’


• Delta-Depletion Analysis (skip)• Delta-Depletion Analysis (skip)– Depletion bias

1/ 2

02 SS

KW ε φ⎡ ⎤

= ⎢ ⎥2A

SqN Wφ =

VV

KKW G

os

⎥⎤

⎢⎡

−+= 11x

SAqN

φ⎢ ⎥⎣ ⎦

2K N

02SS

WK

φε

Vh

δ

NKqVK

os

oo

⎥⎦

⎢⎣

x0

2x s AG S o S

o s

K qNVK K

φ φε

= +

V where δ εC

NK

qA

oo

os≡2 2 2

0 0

x 02

sA Ao G

s o s

KqN qNW W VK K Kε ε

+ − =

2

V

CCG

o

+=

1

2

02 x xs s so o G

o o A

K K KW VK K qN

ε⎛ ⎞=− ± +⎜ ⎟

⎝ ⎠

⎡ ⎤

δV+1

02x 1 1x

s s oo G

o A s o

K K KW VK qN K

ε⎡ ⎤= + + −⎢ ⎥

⎢ ⎥⎣ ⎦


the delta-depletion theory (x =0 01µm NA=1017/cm3 T=300K )(xo=0.01µm, NA=10 /cm ,T 300K )

1.0 Low frequency

0.8C/C

0.6C/Co

0 2

0.4High frequency

0 0.5 1.0 1.5 2.0-0.5-1.0

0.2

0 0.5 1.0 1.5 2.00.51.0


• Exact CalculationExact Calculation– Doping dependence

With increased doping the high-frequencyWith increased doping, the high-frequency inversion capacitance increases significantly and the depletion bias region widens substantiallythe depletion bias region widens substantially.


• Low frequency characteristics – Given modern-day MOS-Cs with long carrier lifetimes and low

carrier generation rates even freq as low as several Hz will yieldcarrier generation rates, even freq. as low as several Hz will yield high-freq. C-V.

– If a low-freq. characteristic is required, the quasi-static technique m st be emplo edmust be employed.

– The quasi-static displacement current flowing through the device is proportional to the low-freq. capacitance.

C QV

I tV

IV t

IR

= = = =∆∆

∆∆ ∆ ∆/

V V V t R∆ ∆ ∆ ∆/

(I : displacement current, R : voltage ramp rate)


• High frequency characteristics– Normal measurement frequency ~ 1MHz. – In the ramped-measurement, a deep-depletion phenomenon may

appear.


• Deep depletion• Deep depletion

Note that at even the slowest ramp rates one does not properly plot out the inversion portion of the high-freq. characteristic.the inversion portion of the high freq. characteristic.


In accumulation or depletion only majority carriers are– In accumulation or depletion, only majority carriers are involved 　Charge configuration rapidly reacts to the changing gate biaschanging gate bias.

– In inversion region, minority carriers should be generated– The generation process is sluggish and has difficulty

supplying the minority carriers needed for the structure to equilibrate.


– Deep depletion : the nonequilibrium condition where there is a deficit of minority carriers and a depletion width in excess of W

T　 C < C

HF(inv)

– Ramp rate ↑ C ↓Ramp rate ↑ C ↓– The limiting case occurs when the semiconductor is

ll d id f i i i ll d d l dtotally devoid of minority carriers - totally deep depleted.

CC CV G

=+

0

1 Same form as simple depletion case V

+1δ

p p


Non-equilibrium charge configuration inside an p-type MOS-CNon equilibrium charge configuration inside an p type MOS C

Q+∆Q

WT

W>WT

Q

WT

WQ

- Q-∆Q

(a) under deep depletion (b) under total deep depletion

Missing electrons

(a) under deep depletion (b) under total deep depletion

Chapter 16. MOS Fundamental Capacitance - Voltage ...

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