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04 Heterojunctions (continued)
Example for the class work
Construct a band diagram for a (p) GaAs/(N) Al0.35Ga0.65As
heterojunction at
thermal equilibrium.
The doping level and relevant material parameters are:
for the p-side GaAs, NA = 3 x 1019 cm-3;
and for the N-side AlGaAs, ND = 1 x 1016 cm-3.
For these doping levels the Fermi level positions (with respect
to the valence and
conduction band edges) are ΦP = -0.103 eV and Φ N = 0.093
eV
This slide and others in this lecture after:
Liu, William. Fundamentals of III-V devices: HBTs, MESFETs and
HFETs/HEMTs, Wiley-Interscience 1999
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04 Heterojunctions (continued)
1. First we need to find the built-in potential, φ bi
The energy gap of the narrower gap material (GaAs), is Egp
=1.424 eV.
In order to find ∆Ec we need to know the bandgap of AlGaAs
and
the bandgap offsets with respect to GaAs
x = ξ = Al mole fraction (!)
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04 Heterojunctions (continued)
∆Ec= 0.244 eV
From:
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2. We now need to find the built-in potentials on the p- and n-
sides
φn0 = =
GaAs (p-side): ε ε0 = 13.18 AlGaAs (p-side): ε ε0 = 12.09
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3. The depletion region widths on the n- and p-sides
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3. The band diagram
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Simple rule to determine the built-in voltage:draw the band
diagram at the flat-band condition
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04 Heterojunctions (continued)
p – N+
GaAs / Al0.35Ga0.65As heterojunction
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04 Heterojunctions (continued)
n+
– P GaAs / Al0.35Ga0.65As heterojunction
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04 Heterojunctions (continued)
n– P+
GaAs / Al0.35Ga0.65As heterojunction
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04 Heterojunctions (continued)
Graded heterojunctions
“Flat-band” Thermal equilibrium
Short grading
Long grading
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04 Heterojunctions (continued)
Heterojunction under bias
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Heterojunction under bias
The voltage drop across the n-side:
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04 Heterojunctions (continued)
Heterojunction under bias
GaAs/AlGaAs,
forward bias
GaAs/AlGaAs,
reverse bias
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04 Heterojunctions (continued)
Heterojunction current
Similar to the Schottky contact
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04 Heterojunctions (continued)
Heterojunction current
Current mechanism is the thermionic emission over the
barrier
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04 Heterojunctions (continued)
Heterojunction current
Current mechanism is the thermionic emission over the
barrier
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04 Heterojunctions (continued)
Heterojunction current
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04 Heterojunctions (continued)
Heterojunction current
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04 Heterojunctions (continued)
Heterojunction current
04 H t j ti ( ti d)
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04 Heterojunctions (continued)
Electron/hole current ratio
after J. P. Colinge, C. A. Colinge PHYSICS OF SEMICONDUCTOR
DEVICES,
©2002 Kluwer Academic Publishers New York, Boston, Dordrecht,
London, Moscow
