SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.5. CHARGE CONTROL MODEL FOR THE MODFET 387

assumeΔnpar=

∫ 0

−dn(AlGaAs)dx→^0. From equation 8.5.9, we have

ns(VG)=

(

Nd−Nd^0

)

dδ−/e[VG−(φb−ΔEc/e)]

D

(8.5.22)

From this expression, we can solve forΔΔVnGs:

Δns

ΔVG

=

1

D

[

−

ΔN^0 d

ΔVG

·dδ+



e

]

(8.5.23)

Inserting this into equation 8.5.11 gives us the following expression for the modulation effi-
ciency:

ME(VG)=1−

e



ΔNd^0

ΔVG

·dδ=1−

Cp,ef f

Cp

(8.5.24)

where

Cp,ef f=

eΔNd^0

ΔVG

Cp=



dδ

Again, if the change in charge density in the AlGaAsΔNd^0 is negligible, thenCp,ef f→ 0 and
ME→ 1. Finding an expression forCp,ef frequires solving for the conduction band occupancy
in the AlGaAs as a function ofVG. This must be done numerically and is left as a problem for
the reader.

Example 8.1Consider ann-type GaAs/Al 0. 3 Ga 0. 7 As MODFET at 300 K with the

following parameters:

Schottky barrier height, φb =0.9V

Barrier doping, Nd =10^18 cm−^3

Conduction band discontinuity, ΔEc =0.24 eV

Dielectric constant of the barrier, b =12. 2

Spacer layer thickness, ds =30A ̊

Barrier thickness, d = 350A ̊

Calculate the 2DEG concentration atVG=0andVG=−0.5V.

The parameterVp 2 of this structure is given by

Vp 2 =

eNd

b

(d−ds)^2 =

(

1. 6 × 10 −^19 C

)(

1018 cm−^3

)(

320 × 10 −^8 cm

) 2

12 .2(8. 85 × 10 −^14 F/cm)

=1.52 V

The threshold voltageVof fis given by

Vof f=0. 9 − 0. 24 − 1 .52 =− 0 .86 V