APPENDIX F. DESIGN OF GRADED HETEROJUNCTIONS 551
The final potential is found by integrating the piecewise electric field function above. The
conduction band at the junction (x=0) is given by
φ(0) =φn+eNDWn^2
2 . (F.9)
The conduction band profile is given by the following equations.
0 <x<xgrade EC=φ(0)−eND
(x−x^2
2 Wn)+
ΔECx
exgrade(F.10)
xgrade<x<Wn: EC=φ(0)−eND
(x−x^2
2 Wn)+
ΔEC
e(F.11)
x>Wn: EC=φn (F.12)In the case where the AlGaAs is graded over 1μm, the quasi-electric field is very small
compared to the electrostatic field. The electrostatic depletion depth is therefore much smaller
than the grading distance. The junction behaves almost like a n-GaAs/p-GaAs homojunction,
and very little performance advantage is gained from using a heterojunction.
The band profiles for the three different grading conditions, (a) abrupt grade, (b) 100A ̊grade,
and (c) 300A ̊grade are shown in Figure 2.
The quasi-electric field can create an undesirable bump in the conduction band if not designed
correctly, as seen in Figure 2 for the abrupt and the 100A ̊case. The 300A ̊grade is best suited
for the HBT since it does not lead to a barrier to electron flow.