Lecture 6: III-V FET DC I - MESFETs

Metal- Junction Basic MESFET Operation

2014-01-28 Lecture 6, High Speed Devices 2014 1 Field Effect

V Lg g W Gate Source Drain V y DS

N+ N+

x

• The gate electrode controls the carrier concentration in the channel • Source/Drain set the potential at the source/drain side

• Electrons flow from source to drain  IDS and n(x,y) depend on geometry and transport properties. • 2D problem (in x and y)

2014-01-28 Lecture 6, High Speed Devices 2014 2 Field Effect Transistors

V =1V Bulk MOSFET g SOI, Quantum Well MOSFET Metal Metal VD=1V Oxide Oxide - n+ n+ n+ n n+ p-type Oxide or wide bandgap Semicondudctor p-type, S.I. Insulating

MESFET Vg=-1V Metal HEMT Metal Depletion Wide band region semiconductor n+ n+ n+ n+ - n n Wide band semiconductor p-type, S.I. Insulating p-type, S.I. Insulating

2014-01-28 Lecture 6, High Speed Devices 2014 3 Si vs. III-V Field Effect Transistors (FETs)

• Si: µ ≤ 1300 Vs/cm2. v ≈ 8×106 cm/s III-V are difficult to n sat fabricate 2 7 • Alternative: Semiconductor InGaAs µn ≈ 14000 cm /Vs! vsat ≈ 2×10 cm/s to isolate the gate from the SiO2-Si excellent interface channel • InGaAs- GaO InO AsO – poor interface Simple: MESFETs x x x • Better: HEMTs or III-V MOSFETs

SiO2/HfSiO2 Schottky

Barrier

n+ n+ n+ GaAs n n+ Si p-type GaAs Semi-Insulating

An Si MOSFET uses an oxide (SiO2, A III-V Metal-Semiconductor FET (MESFET) SiHfO2) to isolate the gate

2014-01-28 Lecture 6, High Speed Devices 2014 4 Metal-Semiconductor Junction

Similar to a p+N junction!

qcs qfm

qfn Fb fbi Fb

qfb  qfm  qcs height

Fn Too simplistic! f  f  Build in potential bi b q

However, now we ignored that we terminated the crystal and created a lot of surface states....

2014-01-28 Lecture 6, High Speed Devices 2014 5 Metal-Semiconductor Junction II

Experiments show only a very weak

dependence of fb as a function of metal work function fb

qfb

fm

Surface reconstruction and surface defects create a large Fn number of states in the bandgap, which “pins” the Fermi- fbi  fb  energy q The energy position of these surface states sets the

Schottky barrier height. For GaAs, fb≈0.7-0.8V fb is a material InP fb ≈ 0.3V, InAs fb ≈ -0.1V, In0.53Ga0.47As fb ≈ 0.1V parameter!

2014-01-28 Lecture 6, High Speed Devices 2014 6 MESFET Structure – simplest FET

Vgs (negative) Source Gate Drain x Depletion Region: n≈0 a Nd b y

Semi-insulating

•Schottky depletion under gate modulates channel thickness b

•VDS causes current to flow from source to drain, which can be

modulated by Vgs

2014-01-28 Lecture 6, High Speed Devices 2014 7 Metal-Semiconductor Junction III

d q  Nd dy  s  q df  y  N X  y s (X )   (X )  0 r d dep dep dep

 s dy q  y 2  f y  N  X y   Ref. s   d  dep  fs (0)  0 X  s 2 potential

dep  

a

y

2 s Depletion thickness, maximum Xdep=a X dep  fbi Va  qNd

Potential needed to fully qNd 2 f00  a deplete down to a 2 s

2014-01-28 Lecture 6, High Speed Devices 2014 8 2 minute exercise – part 1

Depletion Edge

Vgs=0 Vgs=-1V A B

C D

Black – Vg = 0V

Which green plot corresponds to Vgs=-1 V?

Remember: negative bias increases the potential energy of an electron!! 2014-01-28 Lecture 6, High Speed Devices 2014 9 2 minute exercise – part 2

Depletion Vsub=1V Vgs Vgs=-1V egdes + Vsub -

Black plot – Vg and Vsub = 0V

Which red plot corresponds to Vgs=-1 V and Vsub = 1V?

2014-01-28 Lecture 6, High Speed Devices 2014 10 MESFET Operation

+ VDS - Vgs

I Id d

Vcs=0 Vcs(x) Vcs=Vds Resistive voltage drop along channel

DV DV DVgs gs gs

VDS

The potential under the gate is set by the channel-gate potential Vcs(x)

2014-01-28 Lecture 6, High Speed Devices 2014 11 Calculation of the current

V + DS f - Vgs s(x,0)=0 퐽푛 = 푞휇푛푛훻푉 훻 ∙ 퐽푛 = 0 휕2휙 휕2휙 −푞 2 + 2 = ∆푉 = 푁푑 − 푛 Id 휕푥 휕푦 휀푠

Complicated 2D problem!

x y GCA – Gradual Channel approximation: d2f/dx2<

휕2휙 −푞 2 = 푁푑 휕푦 휀푠 Xdep(x) varies slowly with x 휕휙(푥, 푏) Electric field in x-direction is ‘small’ 퐽 = 푞휇 푛 푛 푛 휕푥 푑퐽푛(푥)/푑푥 = 0

2014-01-28 Lecture 6, High Speed Devices 2014 12 Drift Current

ich x  qWNd n xbx Drift current Gradual channel approximation b(x) varies slowly with x ich f  0  i x  I Continuity b(x) is determined by solving s(y) x ch D f x  f x  X  a s bx  a  X  a1 s  Depletion dep dep  f  f00  00  f x f x f V V (x) x   s E-field s bi gs cs x

L L  f x  f x fL f   s    s    s  I Ddx  qWNd na 1  dx  qWNd na 1 dfs  x   f x   x  f00  x   f00 

2014-01-28 Lecture 6, High Speed Devices 2014 13 Saturation Voltage, Pinch-off

Vds=0V Vds>0>VDS,sat Vds=VDS,sat Vds>VDS,sat

At pinch-off, the depletion region reaches the S.I region

Our 1D-decoupled model breaks down: (d2f/dx2>>0) we need to solve 2D possion equation, Dfs(x,y) (numerical solutions needed)

Result: Channel of finite thickness forms at channel edge. Increased Vds drops inside this VDS ,sat f00 fbi Vgs region, or between channel-drain.

Current remains independent of Vds after Vds,sat

2014-01-28 Lecture 6, High Speed Devices 2014 14 Current-Voltage Characteristics

f x f 0 f L u(x)  s s  s d  s f V f00 f00 f00 s  bi gs f 00

qWNd naf00  2 3/ 2 2 3/ 2  fbi Vgs VDS I D  d  s  d  s  d  V  V L  3 3  DS DS ,sat f 00

fbi Vgs VDS ,sat 0.16 d  1 VDS  VDS ,sat f 00 0.14 Vgs=0 0.12 qNd 2 0.1 f00  a 0.08 2 s 0.06 Ids - arb units arb - Ids V <0 gs V  f f V Pinch-off voltage 0.04 DS ,sat 00 bi gs

0.02 Threshold Voltage VT  fbi f00 0 0 0.5 1 1.5 2 2.5 3 Vds Vgs=-|VT| 2014-01-28 Lecture 6 High Speed Devices 2014 15 MESFET limitations

qWNd naf00  1 2 3/ 2  I D,sat    s  s  L  3 3 

dI qWN  a  f V  g  D,sat  d n 1 bi gs  m dV L  f  gs  00 

• We want a high gm – but:

• Positive gate-voltage – very high gate leakage!

• From electrostatics: a

• Increase ND – but this lowers µn due to impurity scattering and increases gate leakage!

• Increase µn by material choice: Need to have a high Schottky barrier! (InGaAs, InAs can’t be used!)

• We can do better using heterostructures or MOSFETs! 2014-01-28 Lecture 6, High Speed Devices 2014 16