SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

550 APPENDIX F. DESIGN OF GRADED HETEROJUNCTIONS

-0.2 -0.1 0.0 0.1

-2

-1

0

1

2

AlGaAs GaAs

Energy (eV)

Distance from junction (μm)

-0.2 -0.1 0.0 0.1

-2

-1

0

1

2

100 Å

AlGaAs GaAs

Energy (eV)

Distance from junction (μm)

-0.2 -0.1 0.0 0.1

-2

-1

0

1

2

AlGaAs 300 Å GaAs

Energy (eV)

Distance from junction (μm)

(a) (b)

(c)

Figure F.2: Calculated band profiles for the graded heterojunctions with (a) abrupt, (b)100A ̊, and
(c) 300A ̊grade. There is no bump in the 300A ̊case.

0 <x<xgrade E=−

eND



(1−

x

Wn

)+

ΔEC

exgrade

(F.6)

xgrade<x<Wn: E=−

eND



(1−

x

Wn

) (F.7)

x>Wn: E=0 (F.8)

The equations describing the valence band potential are similar except thatΔECis replaced
by−ΔEV.