SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

Appendix F

DESIGN OF GRADED

HETEROJUNCTIONS

FOR BIPOLAR TRANSISTORS

This appendix discusses the design of graded heterojunctions for bipolar transistors using an
example from the text (Example 5.3).

Consider four different n-p+Al 0. 3 Ga 0. 7 As/GaAs heterojunctions with ND=10^17 andNA=
5 × 1018. The AlGaAs in these junctions is graded fromx=0tox=0. 3 overXGrade=
0 (abrupt),XGrade= 100A ̊,XGrade= 300A ̊, andXGrade=1μm. Calculate and plot the
energy band diagrams for the above four cases. Assume the dielectric constant of AlGaAs to be
the same as that of GaAs.

Solution:Eg=1.8eVforAl 0. 3 Ga 0. 7 As, and Eg= 1.42 eV for GaAs. ΔEg= 0.374 eV,
ΔEC= 0.237 eV, andΔEV= 0.137 eV. On the AlGaAs emitter side, the conduction band
energy relative to the Fermi level far away from the junction is given by

φn=

EC−EF

e

=

kT

e

ln(

NC

n

)=0. 0323 V. (F.1)

Since the p-GaAs is degenerately doped, Joyce-Dixon statistics must be applied:

φp=EV−EF=

kT

e

(ln(

p

NV

)+A 1 (

p

NV

)+A 2 (

p

NV

)^2 )=0. 011 V. (F.2)

The built-in potential in the conduction band,φbiis given by

φbi=

1

e

(Eg(GaAs)+ΔEc)−(φp+φn)=1. 62 V. (F.3)

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