Modulation Doping HEMT/HFET/MODFET · V DS I DS 1 2 𝑔 3 = 𝑑𝐼 𝑑 » ¼ º « ¬ ª ' ( )...

Lecture 7: High Electron Mobility Transistor

2014-01-30 1 Lecture 7, High Speed Devices 2014

• Modulation Doping

• HEMT/HFET/MODFET

• Device structure • Threshold voltage • Calculate the current using drift • Effect of velocity saturation

Fundamental MESFET Problems


d

nN

1

Semi-insulating

Vgs (negative) Source Gate Drain

y

a Nd b

Depletion Region

00

1

gsbindm

V

L

aNg

2

002

aqN

s

d

High doping degrades mobility and causes gate leakage!

Depletion thickness (a-b) must be large (~ 50 nm) to avoid tunneling! Lg ≈≥ 3×a to avoid ”short channel effects”

gmmax,mesfet ~ 0.3 mS/µm gmmax,HEMT ~ 2.7 mS/µm High doping increases 00!

Heterostructure FET


Nd

InAlAs AlGaAs AlSb

(In)GaAs

d Nd~0

Nd~0

Ef

Ec

Electrons accumulate in the (In)GaAs

Gate

tb

tb

+ µn can be very large – no channel doping + High electron concentration in channel + InGaAs channel – higher mobility + InAlAs barrier (Eg=1.5 eV) – large B

+ tb thin (5-10 nm!)– large bandgap ”barrier” limits tunneling leakage (Lg>3tb) - More advanced design – requires heterostructure growth ND is used to tune the threshold voltage/access resistance.

y

Two dimensional electron gas


Nd WG

NG

d Nd~0

Nd~0

Ef

Ec

E1

E2

Part of wavefunction that penetrates into WG should also be kept away from any impurities d

y

• Electrons are confined in the y-direction

• Forms an quantum well! (Triangular or square) – 2-dimensional electron system system

• 2D density of states!

Modulation Doping II: 2D Density of states


0

, fEEfEdEDn

DEEEE

mED

DEEmh

ED

DEmm

ED

n

n

n

D

n

nD

D

12

24

32

*

1

*

22

32

**

3

kT

EEDkT

kT

EEDkTn

ff

s

21exp1lnexp1ln

f(E,Ef) – Fermi-Dirac

32212

21

1

1

2

00

EEEEEDEED

EEE

EE

EEDn

ff

f

f

fs

*

2

4 m

hD

For T=0K – Fermi Dirac is a step function

E1 E2

D

2D

Ef

𝑛𝑆 = 𝑁2𝐷𝐹0(𝜂𝐹,𝑖)

𝑁2𝐷 =4𝜋𝑘𝑇

ℎ2𝑚Γ∗

2 minute excercise


ns

Ef EC E1 E2

EC

E1

E2

Plot ns as Ef is varied in the quantum well T=0K

EF

Modulation Doping III: Energy Levels


E1

E2

xqV i 2,~ s

si

qn

2,

3/2

2,*

2

4

1

2

3

28

nq

m

hE in

kT

nkEDkTn

sf

s

3/2

1exp1ln

Triangular Well: En depends of charge in well.

Square well: En almost independent of ns

AlGaAs

AlGaAs

InGaAs

E1

E2

tw

2

22

*8 w

ntm

nhE Infinite square well

kT

EEDkTn

f

s

1exp1ln

Ef

Ef vs ns for a QW


0 1 2 3 4 5 6 7

x 1016

0

0.05

0.1

0.15

0.2

0.25

ns (m-2)

E f (eV

)

T=300K

T=10K

1st subband

2nd subband Ef

Ef0

Ef(ns)-Ec=Ef0+ans

01 fss

f ED

nE

D

nE 2D QW

Electron concentration: ns(Vg)


AlGaAs

GaAs

d

tb

qB

-qVGB

qG,1

DEc Ef

y

tb

d

Charge

Nd,1

Nd,1 Nd,2≈0

y

s

dqN

x

1,

ns

s

si

qn

bt

G dxxqq0

1,

fGBBcG EqVqEq D 1,

D BGB

sfc

b

s

d

b

ss V

q

nEEt

qN

tqn d

)(

2

21,

0 (ref. level)

EC

-field

Channel Charge Equation


D

D B

fc

b

s

d

GB

bb

ss

q

EEt

qNV

ttqn d

021,

2

Ef –Ec0needs to change as ns changes

01 fss

f ED

nE

D

nE Quantum well, T=0K

D BGB

sfc

b

s

d

b

ss V

q

nEEt

qN

tqn d

21,

2

*

2

2 4 m

h

qt sb

D

Triangular well needs numerical approximation, Dtb~68Å for GaAs, Ef0 ~ 0.058 eV

2Å (Si) 24Å (GaAs) 74Å (InAs)

TGBoxs VVCqn '

Identical to that of an MOSFET!

A HEMT without doping in the barrier is essential equivivalent to a FD-SOI Si MOSFET

Dtb ? - Semiconductor (Quantum) Capacitance


Triangular well needs numerical approximation, Dtb~68Å for GaAs, Ef0 ~ 0.058 eV

MIM Capacitor:

VCn oxs DDSemiconductor quantum well

DqC

Dqn

EEqDn

q

fs

fs

2

2

1

DD

Cox

Cq

There must be a voltage drop over the oxide and the semiconductor!

𝐶𝑜𝑥′ =

𝜖𝑠𝑡𝑏 + Δ𝑡𝑏

𝐶𝑜𝑥′ =𝜖𝑠𝑡𝑏

Ordinary parallell-plate capacitor MOS capacitor

HEMT Structure – IV Calculation


Wide bandgap Nd

Wide bandgap intrinsic

Wide bandgap, S.I or intrinsic

Vgs Source Drain

Small bandgap, triangular or square well

VDS

),()(,' ' txvVtvCtxq csTGSoxch

x

x=0 x=L

x

Charge (cm-2)

Total potential difference over wide bandgap region: (Vgs-VT)-Vchannel(x)

This is the same fundamental equation as for an ordinary

MOSFET!

HEMT on-Current – drift only


),()(,' txvVtvtt

txq csTGS

bb

sch

D

D '

00

0

q

EEV

fc

BT

21,'

002

d

b

s

dt

qN'

oxC

2

2

2'

,

2'

)(

)0(

'

0

TGSnoxsatD

DSDSTGS

noxD

LV

V

cscsTGSnox

L

D

VV

L

WCI

VVVV

L

WCI

dVVVVL

WCdxI

cs

cs

satDSDS

satDSDS

VV

VV

,

,

satDSDS

satDSDS

satDS

DS

satDD

VV

VVV

V

II

,

,

,

2

,

0

11

TGSsatDS VVV ,

Long channel current saturates when qch(L)=0

Written using saturation index

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

Voltage (V)

Cu

rre

nt (m

A)

Vgs-VT=2V

Vgs-VT=1.33V

Vgs-VT=0.67V

Channel potential - DC


),(

),()(),(

txuxU

txvVtvtxu

chch

csTGSch

2

0

2

22'22' LUU

L

WCLUxU

xL

WCI CHCHnoxCHCHnox

D

0

0

CHCH

TGSCH

ULU

VVU

2110 L

xUxU CHCH

We will use this extensively for the AC-analysis of the HEMT

x

xUx

xUCtxq

chch

choxch

','

Assuming drift only – simple analytical expressions for qch and ch is obtained!

Short Channel Effects – Velocity Saturation


TGSnox

m VVL

WCg

'

High gm: Decrease L!

𝜀 𝑥 =𝑈𝐶𝐻 0

𝐿1 − 𝛼2

1

1 −𝑥𝐿 1 − 𝛼

2

Channel Electric Field

Dri

ft V

elo

city

(V

/cm

)

Vsat

Epeak ~ 4x103 V/cm

(x)>c! Electron velocity does not increase. Very important correction for modern devices.

Velocity Saturation II


Short channel transistors (Lg < 1µm) Modern FETs – Lg=16-50 nm – => c

Analytical modeling starts to become tricky

𝑣𝑑 =𝜇𝑛𝜀

1 +𝜀𝜀𝑐

𝐼𝑑 =𝑊𝐶𝑜𝑥′ 𝜇𝑛

1 +𝑉𝐷𝑆𝜀𝑐𝐿𝐿𝑉𝐺𝑆 − 𝑉𝑇 𝑉𝐷𝑆 −

𝑉𝐷𝑆2

2

2

2'

,TGSnox

satD

VV

L

WCI

𝑉𝐷𝑆,𝑠𝑎𝑡 = 𝑉𝐺𝑆 − 𝑉𝑇

1

1 + 1 +𝑉𝐺𝑆 − 𝑉𝑇𝐿𝜀𝑐

𝐼𝑑𝑠 ≈ 𝑊𝐶𝑜𝑥′ 𝜀𝑐𝜇𝑛 𝑉𝐺𝑆 − 𝑉𝑇 = 𝑊𝐶𝑜𝑥

′ 𝑣𝑠𝑎𝑡 𝑉𝐺𝑆 − 𝑉𝑇

2

2'

DSDSTGS

noxD

VVVV

L

WCI

TGSsatDS VVV ,

No velocity saturation – unphysical for Lg < 1 µm!

Triode Region

L0

Saturation Voltage

Velocity Saturation III


10-2

10-1

100

101

102

10-5

10-4

10-3

10-2

10-1

100

Gate Length (µm)

Curr

ent (m

A)

TGSsatoxD VVvWCI '

𝑣𝑑 =𝜇𝑛𝜀

1 +𝜀𝜀𝑐

VDS=2V VGS-VT=1V W = 1µm Cox’=1 µF/cm2

c= 4kV/cm µn=10000 cm2/Vs

Current at saturation

For gate lengths below ~ 1µm – velocity saturation is very important! For very short gate-lengths – quasi-ballistic transport!

Channel Length Modulation


Velocity saturarion occurs approximately when =dU/dx>sat

Vds=Vds,sat

VDS

IDS

1

vdrift

-field sat

vsat

𝜀 𝑥 =𝑈𝐶𝐻 0

𝐿1 − 𝛼2

1

1 −𝑥𝐿1 − 𝛼2

(x) < crit

qch(x)

x

qch(x)

x x

2 3

L L L

qch(x)

D

2

2

,

,

'satDS

satDSTGSnox

D

VVVV

LL

WCI

=sat at x=L DL

Low-field Velocity saturation

=sat at x=L-DL

Channel Length Modulation II


VDS

IDS

1 2 3 𝑔𝑑 =

𝑑𝐼𝐷𝑆𝑑𝑉𝐷𝑆

D

2)(

2

,

,

'satDS

satDSTGS

ds

noxD

VVVV

VLL

WCI

• Channel Length modulation causes output conductance!

• 2D electrostatic effects also gives a similar

• Very Important for short channel FETs!

Modern HEMT with Lg=30-50 nm Signs of velocity saturation: IDS almost independent of Lg

IDS ~ VGS-VT

gm/gd ~ 5-50

However – these devices are quasi ballistic

MESFET / HEMT Breakdown


Lateral FETs breakdown is due to high field in the gate-drain region. The high field causes impact ionization / tunneling breakdown. This limits the maximum VDS of the device Scales with band gap (Eg,channel & Eg,barrier)

Sou

rce

Dra

in

Ec

Ev

Vdg=Vds-Vgs

Impact Ionization Impact Ionization

Tunneling causes large gate leakage

Modulation Doping HEMT/HFET/MODFET · V DS I DS 1 2 𝑔 3 = 𝑑𝐼 𝑑 » ¼ º « ¬ ª ' ( )...

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Transcript of Modulation Doping HEMT/HFET/MODFET · V DS I DS 1 2 𝑔 3 = 𝑑𝐼 𝑑 » ¼ º « ¬ ª ' ( )...