09 Heterojunction FET Principles

8/10/2019 09 Heterojunction FET Principles

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MOSFET and HFET devices are both verysimilar to a plain capacitor

Let the area of the capacitor plates be A.

The induced charge Q can be expressed as

Q = q × A × ∆nS,

where q = 1.6 ×10-19 C is the electron charge,

∆nS is the SURFACE CONCENTRATION of induced electrons, ∆nS = Q / (q × A);

1x1 cm2

a

What is the surface concentration?

The bulk charge density, n

the layer thickness, a;

then the surface concentration,

nS = n × a

09 Heterojunction FET (HFET) principles

V

Metal

Semiconductor

d A



For the PLAIN CAPACITOR, C = ε ε0 ×A/d

Q = C × V = ε ε0 ×A×V/d,The induced concentration of electrons (which are negatively charged) in

the top (metal) plate:

∆nSM = - ε ε0 ×V/(q×d) <0;

in the bottom (semiconductor) plate:

∆nS = ε ε0 ×V/(q×d) >0;

For a given voltage, V, the induced charge increases as we decrease d

V

Metal

Semiconductor

d A

Estimation of induced charge



Suppose the semiconductor plate is doped with donor concentration ND;

The equilibrium electron concentration in the semiconductor, n0 = ND;

For the layer thickness, a, the surface concentration nS0 = ND ×a;

The voltage needed to deplete the entire active layer ( the semiconductor plate) is

referred to as the THRESHOLD VOLTAGE of the FET

For the n-doped layer the threshold voltage is negative in order to repulse the electrons.

The induced concentration at the threshold has to compensate the equilibrium one:

nST = ε ε0 ×VT /(q×d) = - nS0

Therefore,

VT = - q×d ×nS0 / (ε ε0)

The threshold voltage of FETs



At the threshold the net concentration in the channel is zero:

nST – nS0 = 0, where nST = ε ε0 ×VT /(q×d)

When the applied voltage is above the threshold, V > VT,

∆nS = ε ε0 ×V/(q×d)

nS = nS – nST = ε ε0 /(q×d) × (V – VT)

Note, ε ε0 /d = C1 the gap capacitance per unit area

Therefore,

nS = (C1 /q) × (V – VT)

The above model is referred to as “charge control model” of FETs

The charge control model of FETs



The channel current is then: I = V0 (q nS µ Z) /L = V0 q µ Z (C1/q) × (V – VT) /L

I = V0µ Z C1

× (V – VT) /L

FETs: general design considerations

The current through the channel is

RV I 0= where V0 is the voltage applied

between the DRAIN and the SOURCE

We are assuming that V0 << VT (we will see why, later on)

The channel resistance, R (Z is the device width):

Z nq

L

Z anq

L R

s µ µ ==

-

+G

Semiconductor

The gate length L

DS

+

-

V0

V

Low drain bias







Junction FET (JFET)

The gate-channel insulator consists of the DEPLETION REGION,

i.e. the same material as the channel.

For GaAs, ε ~ 12; for GaN ε ~ 9.

a0a

W

Different types of FETs



Metal-Semiconductor FET (MESFET)

The gate is formed by Schottky barrier to the semiconductor layer.

The gate-channel insulator consists of the DEPLETION REGION,

i.e. the same material as the channel. Very similar to the JFET

a0a

Different types of FETs



electrons

The Heterojunction Field-Effect Transistor (HFET)

The channel of HFETs is formed by 2D electron gas (2DEG)

induced channel (2DEG)

Channel

HFET JFET, MOSFET, MESFET



Effects of high drain bias on FET characteristics

VD

VG

+

+

DrainSource Gate

VD

VG

+

+

DrainSource Gate

The gate- to drain voltage difference depends on the position along the gate

So does the induced charge

JFETMOSFET



Effects of high drain bias on FET characteristics

The channel narrowing at the drain edge of the gate causes currentsaturation in the FETs

The particular range of the gate

voltage depends on the device

type





after T.A. Fjeldly, T. Ytterdal and M. Shur, 1998

Undoped active layer

Very high NS;

very high µ;

very high vS

(in sub-µ HFETs)

1960 - Accumulation layer prediction (Anderson)

1969 - Enhanced mobility of 2DEG prediction

(Esaki & Tsu)

1978 Enhanced mobility observed (Dingle et. al.)

1980 The first Heterojunction FET (HFET)

1991 The first GaN based HFET (A. Khan)

electrons


The channel of HFETs is formed by 2D electron gas (2DEG)

induced channel (2DEG)




1) Mobility depends on the interactions between electrons and phonons and impurities.

For the phonon scattering, the dependence of mobility on temperature:

A.k.a. High electron mobility FETs: why?

For the impurity scattering, the dependence of mobility on impurity concentration, N:

When the dependence on both temperature and impurities is taken into account,




Concentration dependence of electron mobility

T = 300 K




Electron Drift velocity

mnvn max2

2= E n − E o ≈ hω l

The electron accelerates in the electric field until it gains enough energy to excite lattice

vibrations:

where vnmax is the maximum electron drift velocity. Then the scattering

process occurs, and the electron loses all the excess energy and all the drift

velocity. Hence, the electron drift velocity varies between zero and vnmax,

and average electron drift velocity (vn = vnmax/2) becomes nearlyindependent of the electric field:

vn ≈hω l

2mn

= vsn

Typically, vsn ≈ 105 m/s. Indeed, the measured drift

velocity becomes nearly constant in high electric fields




Electron Drift velocity

electric field (kV/cm)

e l e c t r o n v e l o

c i t y ( 1 0 0 , 0

0 0 m / s )

T = 300 K

Si

GaAs

InP

InGaAs

3

2

1

0

0 5 10 15 20

In the heavily doped materials the peak electron velocity is lower

Heavily doped



The HFET basics

qφb

di

qVFB

qϕb

∆Ec

Ec

GaAs

qVN

AlGaAsmetal

EFi

EFp

Ec

Ev

Considering first the band diagram of an AlGaAs/GaAs HFET with flat bands in the

GaAs buffer . As can be seen from this figure, the flat-band voltage is given by

V FB = φb − V N − ∆ E c + ∆ E F ( )/ q





The HFET basics

Band diagram Charge and field profiles

From the Poisson equation,s

si

qnF

ε ε 0=

Fi

F

At the threshold, ns~0 --> Fi ~0

qV N



The HFET basics

HFET threshold voltage

V N = q N d ( x)

εi ( x) x dx

0

d i∫

When ns is close to zero, the Fermi level in the

GaAs is close to the bottom of the conductance

band. Therefore,

V T ≈ φb −qN d d i

2

2εi

− ∆ E c / q

For non-uniform doping profile,

V T ≈ φb − qnδd δ / εi − ∆ E c / q

For the “delta-doped” barrier layer,



The HFET basics

HFET I-V characteristics

qns = ci V GT − V x

Above the threshold the HFET is similar to MOSFET, i.e.

where VGT = VG - VT

I d = W µnqns F = W µnci V GT − V dV

dx

The drain current:

I d =

W µnci

L ×

V GT V DS − V DS 2 / 2 , for V DS ≤ V SAT

V GT 2 / 2 , for V DS > V SAT

⎧

⎨

⎪

⎩⎪

where VSAT = VGT



The HFET basics


gm

=dI

d

dV GS V DS

The transconductance,

gm =βV

DS , for V

DS ≤ V

SAT

βV GT

, for V DS

> V SAT

⎪⎨⎪⎩

where β = W µ nci /L is called the transconductance parameter.



The HFET basics


Velocity saturation in HFETs

v F ( =µF , F < F s

vs , F ≥ F s

⎧⎨⎩

A two-piece model is a simple, first approximation to a realistic velocity-field

relationship:

More realistic velocity-field relationships :

v F ) =µF

1+ µF / vs( m

1/m

where m = 1….2 0.0

0.4

0.8

1.2

3210

Normalized Field

m = 1

m = 2

m =

Th HFET b i



The HFET basics



I d = W µnci

L× V GT V DS − V DS

2

/ 2 , for V DS ≤ V SAT

V L2 1 + V GT V L

2 − 1⎡⎣⎢

⎤⎦⎥

, for V DS > V SAT

⎧

⎨⎪

⎩⎪

V SAT = V GT − V L 1+ V GT / V L2 − 1⎡⎣⎢ ⎤⎦⎥

where V L = F s L.

For V L >> V GT , we arrive to the same expression as with the constant mobility case.

Th HFET b i



The HFET basics



I d

=W µnci

L×

V GT V DS − V DS 2 / 2 , for V DS ≤ V SAT

V L2 1 + V GT V L 2 − 1⎡⎣⎢ ⎤⎦⎥

, for V DS > V SAT

⎧

⎨⎪

⎩⎪

V SAT = V GT − V L 1+ V GT / V L2 − 1

⎡

⎣⎢

⎤

⎦⎥where V L = F s L.

In the opposite limit, when V L << V GT , we obtain V SAT ≈ V L

I sat ≈ βV LV GT

where β = W µ nci /L is the transconductance parameter.

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09 Heterojunction FET Principles

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