SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.10. TAILORING ELECTRONIC PROPERTIES 75

GeSi

SiC

SiOGaN 2

AlNInN

GaAsInAs

ZnOInP

ZnOZnS

GaPAlP

AlAsAlSb

GaSbInSb

ZnSeCdS

CdSeZnTe

CdTe

SiH 32 NO 4

BaTiOTB 2 O 53

550-BaTiOBaZrO 33

SrTiOSrTiO 3

SrO

HfOZrO 22

AlY 22 OO 33

ZrSiOPrO 43

a-Si

-10-9-8-7-6-5-4-3-2-1 0

Band Alignment

eV

Material

Figure 2.31: Bandedge lineups in a variety of materials.

If the barrier potentialVcis not infinite, the wavefunction decays exponentially into the barrier
region, and is a sine or cosine function in the well. By matching the wavefunction and its
derivative at the boundaries one can show that the energy and the wavefunctions are given by the
solution to the transcendental equations (see Section 2.2)

αtan

αW

2

= β

αcot

αW

2

= −β (2.10.5)

where

α =

√

2 m∗E

^2

β =

√

2 m∗(Vc−E)

^2