SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

APPENDIX F. DESIGN OF GRADED HETEROJUNCTIONS 549

Quasi E-field

Quasi E-field

Effective field Effective field

WN 0

xgrade

xgrade^0

Electrostatic

field

Negative

Electric field

WN

Figure F.1: Electric field in a graded heterojunction. If the grading distance is too short (Right),
the quasi-electric field can cause the effective electric field to reverse direction, leading to a
barrier in the conduction band. When designed correctly, the quasi-electric field magnitude is
lower than the electrostatic field (Left).

Assuming xD 1 and xD 2 are the depletion thicknesses in the n and p regions, and solving,

NDxD 1 =NAxD 2 (F.4)

e

2 

(NDWn^2 +NAWp^2 )=φbi (F.5)

Wn=1.5× 10 −^5 , and Wp=3.0× 10 −^7.
Since Wnand Wpare known, the electrostatic potential can now be calculated. The band
profiles are found by superimposing the electrostatic and quasi-electric fields. The quasi electric
field is given by−exΔgradeEC for the conduction band, andexΔgradeEV for the valence band.

In the 100A ̊and 300A ̊cases, we can assume that the depletion width is much larger than the
grading distance. The electric field in the conduction band is given by the following equations: