09 Heterojunction FET principles - ee.sc.eduee.sc.edu/personal/faculty/simin/ELCT882/09 Heterojunction FET...1980 The first Heterojunction FET (HFET) 1991 The first GaN based HFET

MOSFET and HFET devices are both very similar to a plain capacitor

Let the area of the capacitor plates be A. The induced charge Q can be expressed asQ = 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, nthe layer thickness, a;then the surface concentration,nS = n × a

09 Heterojunction FET (HFET) principles

V

Metal

Semiconductor

dA

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

dA

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 areaTherefore,

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 = V0 µ 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):

ZnqL

ZanqLR

s µµ==

-+ G

Semiconductor

The gate length L

DS

+-

V0

V

Low drain bias

The main factors affecting FET performance (for any FET type):

µ I and gm

I = V0 µ Z C1 × (V – VT) /L

The transconductance, gm = dI/dV;The gm is the “responsivity” of FET.In the linear mode under consideration (V0 << V),

gm = V0 µ Z C1 /L

FETs: general design considerations

-+ G

Semiconductor

The gate length L

DS

+-

V0

V

L I and gm

Carrier mobility in the channel and the gate length are crucial parameters of any FET

Low drain bias

Different types of FETs

Metal - Oxide - Semiconductor FET (MOSFET)

d

W

The gate-channel insulator is made out of dielectric (SiO2), ε = 3.9

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


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

a0 a


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 gateSo does the induced charge

JFETMOSFET


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

The particular range of the gate voltage depends on the device type


Velocity saturation due to high electric field in the channel also results in the I-V saturation

Electron velocity saturation due to high electric field in the channel

The average electric field in the channel, Eav ~ V0 /L

Can be extremely high for small L

I = V0 µ Z C1 × (V – VT) /L I = vS Z C1 × (V – VT)

v = µ × E ~ µ × V0 /L

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,

The Heterojunction Field-Effect Transistor (HFET)Concentration dependence of electron mobility

T = 300 K


Electron Drift velocity

mnvn max2

2= En − Eo ≈ 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 nearly independent of the electric field:

vn ≈

hω l2mn

= 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)

elec

tron

vel

ocity

(100

,000

m/s

)

T = 300 K

Si

GaAs

InP

InGaAs3

2

1

00 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

VFB = φb − VN − ∆Ec + ∆EF( )/ q

The HFET basics

The HFET basics

Band diagram Charge and field profiles

From the Poisson equation, s

si

qnFεε0

=

Fi

F

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

qVN

The HFET basics

HFET threshold voltage

VN = qNd (x)εi (x)

x dx0

di

∫

When ns is close to zero, the Fermi level in the GaAs is close to the bottom of the conductance band. Therefore,

VT ≈ φb −qNd di

2

2εi− ∆Ec / q

For non-uniform doping profile,

VT ≈ φb − qnδdδ / εi − ∆Ec / q

For the “delta-doped” barrier layer,

The HFET basics

HFET I-V characteristics

qns = ci VGT − V x( )[ ]Above the threshold the HFET is similar to MOSFET, i.e.

where VGT = VG - VT

Id = Wµnqns F = Wµnci VGT − V( ) dV

dx

The drain current:

Id =Wµnci

L×

VGT VDS − VDS2 / 2[ ], for VDS ≤ VSAT

VGT2 / 2 , for VDS > VSAT

⎧ ⎨ ⎪

⎩ ⎪

where VSAT = VGT

The HFET basics


gm =dId

dVGS VDS

The transconductance,

gm =βVDS , for VDS ≤ VSATβVGT , for VDS > VSAT

⎧⎪⎨⎪⎩

where β = Wµnci /L is called the transconductance parameter.

The HFET basics


Velocity saturation in HFETs

v F( ) =

µF , F < Fsvs , F ≥ Fs

⎧ ⎨ ⎩

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

3210Normalized Field

m = 1

m = 2

m = �

The HFET basics



Id =Wµnci

L×


VL2 1 + VGT VL( )2 − 1⎡

⎣ ⎢ ⎤ ⎦ ⎥ , for VDS > VSAT

⎧

⎨ ⎪

⎩ ⎪

VSAT = VGT − VL 1+ VGT / VL( )2 − 1⎡

⎣ ⎢ ⎤ ⎦ ⎥

where VL = Fs L.

For VL >> VGT, we arrive to the same expression as with the constant mobility case.

The HFET basics



Id =Wµnci

L×


VL2 1 + VGT VL( )2 − 1⎡

⎣ ⎢ ⎤ ⎦ ⎥ , for VDS > VSAT

⎧

⎨ ⎪

⎩ ⎪

VSAT = VGT − VL 1+ VGT / VL( )2 − 1⎡

⎣ ⎢ ⎤ ⎦ ⎥

where VL = Fs L.

In the opposite limit, when VL << VGT, we obtain VSAT ≈ VL

Isat ≈ βVLVGT

where β = Wµnci /L is the transconductance parameter.

Documents

09 Heterojunction FET principles - ee.sc.eduee.sc.edu/personal/faculty/simin/ELCT882/09 Heterojunction FET...1980 The first Heterojunction FET (HFET) 1991 The first GaN based HFET