EE 5340Semiconductor Device TheoryLecture 28 - Fall 2009

Professor Ronald L. Carterronc@uta.edu

http://www.uta.edu/ronc

L 28 Dec 1 2

e-e- e- e- e- + + + + + + + + + + + +

Implanted n-channel enhance-ment MOSFET (ohmic region)0< VT< VG

VB < 0

EOx,x> 0

Acceptors

Depl Reg

VS = 0 0< VD< VDS,sat

n+

n+

p-substrate

Channel

e- channel ele + implant ion

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Si & SiO2

AlSi3N4

Si Al & SiO2

Si3N4

Range

RP

Ion implantation*

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“Dotted box” approx**

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curve dottedunder area curve dashedunder area

iaiimpl XNdxN 0

'ox

iit

iait

CxqNΔV so

xand Nget implant to desired, as Vget To

FBTmaxd,i V V then , x xIf

dii

aiiiibeforessss xQQ

NNNN

qN 'impl ,

'

Calculating xi and VT

L 28 Dec 1 6

aiaiSBppsa

iai

msxdaiaid

a

aiips

ad

NNxqVqN

xqN

xqNxqNQ

NNx

qNx

22

,

2

2

2

If xi ~ xd,max

L 28 Dec 1 7

i

idiath

i

iaiathps

aiaiSBppsaOx

pspOx

iai

Ox

ssmsT

nxNNV

nxNNV

NNxqVqNC

CxqN

CQV

lnor , ln

21 22'

''

'

Calculating VT

L 28 Dec 1 8

Implanted VT

Vt per Eq. 9.1.23 in M&K for a MOSFET with an 87-nm-thick gate oxide, Qff/q = 1011 cm-2, N’ = 3.5 X 1011 cm-2, and Na = 2 X 1015 cm-3. Both VS and VB = Figure 9.8 (p. 441)

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Mobilities**

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Substrate bias effect on VT (body-effect)

pSBpOx

aSiSBT

SBTTa

SBpmaxd,

Ox

maxd,apFBST

T

2V2'CNq20VV

VVV so , qNV22x

where , 'CxNq2VVV

Source to relative be ncalculatio V Letting

L 28 Dec 1

Body effect dataFig 9.9**

11

L 28 Dec 1 12

M&K Fig. 9.9 (Eq. 9.1.23)

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Subthreshold conduction• Below O.S.I., when the total band-

bending < 2|p|, the weakly inverted channel conducts by diffusion like a BJT.

• Since VGS>VDS, and below OSI, then Na>nS >nD, and electr diffuse S --> D

tDS

tGS

subthresh,D VVexp1V

VexpI

Electron concentration at Source

Concentration gradient driving diffusion

L 28 Dec 1 14

M&K Fig.9.10 (p.443)

Band diagram along the channel region of an n-channel MOSFET under bias, indicating that the barrier qΦB at the source depends on the gate voltage.

L 28 Dec 1 15

M&K Fig. 9.11 (p.444)

Measured subthreshold characteristics of an MOS transistor with a 1.2 μm channel length. The inverse slope of the straight-line portion of this semilogarithmic plot is called the drain-current subthreshold slope S (measured in mV/decade of drain current).

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Subthreshold current data

Figure 11.4*Figure 10.1**

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Mobility variationdue to Edepl Figures 11.7,8,9*

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0eff

0eff EE

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Velocity saturationeffects

L2vf

vWCg E as vv So

vE1

vv limit" speed"

satT

satOxsat,msat

212

sateff

effthsat

Figure 11.10*

L 28 Dec 1 19

Based on figure 12.18*

n-type channel

L0

Junction Field-Effect Transistor (JFET)

Active channel

height, a

dbiSiqN

)y(VV2yh Ch to Substr D.R.

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Pinch-offVoltage

dCh

aChbipT

bipi

GChtbi

Si

dp

TGS

eff

GSbiSi

NNifNNif

VVV

VVenhmt

nNNVVaqNV

VVaShqN

VVSh

,

if ,ln ,2

opens channel the then , when ,ch. n ,NNN ch. p ,NNN

,2

2

2

dCheff

aCheff

Note: In depl mode devices, Vp0 > Vbi

L 28 Dec 1 21

Channel conductanceand drain current

D

S

V

VbichSichchch

DL

0D

D

chbiSi

chch

dVyVVqN2WWaqN

LIdyI

ygydVIqN

yVV2aWqNdyyg

L 28 Dec 1 22

N-ch. ohmic regdrain current soln.

TGSsatDS

dn

GSbiGSbiDSp

DSD

satDSDSTGS

VVVL

WaNqG

VVVVVV

GVGIin

VVVV

,

01

232301

011

,

at off-pinch Draincond. channel-open the ,

32

:region ohmic the i.e. ,0&0 For

L 28 Dec 1 23

Saturation draincurrent,

p

bi

p

biPPDSS

T

GSDSSsatDsatD

bip

N

NTSi

ap

pP

p

GSbi

p

GSbiPPsatD

VV

VVIII

VVIIIlawSquare

VVVaqNVVG

I

VVV

VVVIII

a

d

3213

1 :approx

, 2 ,3

3213

11

2

,,1

2011

11,1

TGSDS VVV

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Ideal JFET draincharacteristics

ID

VDSVDS,sat

ID,sat

Ohmic, ID1

Non-physical analytic extension of ID1

Saturated: ID,sat ~ID1,sat

L 28 Dec 1 25

n-channel JFET gatecharacteristic ID

VGSVp

IDSS

Saturated: ID,sat, approx.

Saturated: ID1,sat

pGSDS VVV

L 28 Dec 1 26

Small-signal para-meters: gds and gd

p

GSbi

VVDS

Dd

p

GSbiDS

ds

DVDS

Dds

VVVG

VIg

VVVVG

g

VIg

DSGS

GS

-1

Saturation ,0

Ohmic ,-1

,I for ,

010,

01

1

L 28 Dec 1 27

Graphical interpre-tation of gds and gd

ID

VDSVDS,sat

ID,satSlope = gds

Slope = gd

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Small-signal gainparams: gmL and gms

T

GS

T

DSS

p

GSbi

VGS

Dms

GSbip

DSit

V

GSbi

DS

p

GSbi

mL

DVGS

Dm

VV

VI

VVVG

VIg

VVVVG

VVV

VVVG

g

VIg

satDS

DS

DS

12-1

2

11

5 slide see (ohmic), ,I for So .

01

01lim

0

01

1

,

L 28 Dec 1 29

Based on figure 12.18*

n-type channel

L0

Channel ModulationCapacitances

Active channel

height, a

dbiSiqN

)y(VV2yh Ch to Substr D.R.

L 28 Dec 1 30

Application of JFET theory to MESFET• The channel material is often GaAs• The substrate is often semi-insulating

gallium arsenide (SI GaAs)• Vbi is replaced by Vn

bi, the band-bending in the semiconductor– Often limited by surface state pinning and

not determined exactly by s

• Neff is now exactly Nch

L 28 Dec 1 31

Final Exam• EE 5340 Section 001

– 8:00 to 10:30 AM– Tuesday, December 8 in – 108 NH– Cover sheet will be postedon web page

at http://www.uta.edu/ronc/5340/tests/• The Final is comprehensive

– 20% to 25% on Test 1 material– 20% to 25% on Test 2 material– Balance of final on material since Test 2

L 28 Dec 1

References* Semiconductor Physics & Devices,

by Donald A. Neamen, Irwin, Chicago, 1997.

**Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986

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