Biomedical Engineering Reference
In-Depth Information
57:43 Split
L
ef
electron (Å)
L
ef
heavy hole (Å)
L
ef
light hole (Å)
Well
Width (Å)
Aluminum
Concentration
ψ
inf
=
E
fin
E
inf
=
E
fin
ψ
inf
= ψ
fin
E
inf
=
E
fin
ψ
inf
= ψ
fin
E
inf
=
E
inf
90
0.1
169.5
144.7
122.5
116.8
170
144.9
0.3
125
118.5
106.5
104.3
128
120.5
95
0.1
172.5
149.5
127.5
121.8
173
149.7
0.3
129.5
123.5
111
109.3
132.5
125.4
100
0.1
176
154.2
132
127
176.5
154.5
0.3
134.5
128.4
116
114.3
137
130.4
85:15 Split
L
ef
electron (Å)
L
ef
heavy hole (Å)
L
ef
light hole (Å)
Well
Width (Å)
Aluminum
Concentration
ψ
inf
= ψ
fin
E
inf
=
E
fin
ψ
inf
= ψ
fin
E
inf
=
E
fin
ψ
inf
= ψ
fin
E
inf
=
E
inf
90
0.1
150
134
145
121.3
283
191
0.3
117.5
113.2
117
112.7
169
144.4
95
0.1
154
139
149
136
281
195
0.3
122.5
118.2
121.5
117.6
172
149.2
100
0.1
157.5
143.8
153
141
279.5
200
0.3
127
123.2
126.5
122.6
175.5
154
FIGURE 3.24
Effective widths table.
Step A—The effective masses of the particles, the conduction-valence band
split, and the effective well widths are found as follows:
A1: The energy gap difference is used to determine the depths of the
conduction and the valence band wells. There are the values
V
e
and
V
h
. A
relatively arbitrary choice is made concerning the ratio of the conductance-
valence band split.
A2: Figure 3.20 is used to determine the effective masses of the electrons,
and light and heavy holes.
A3: Using the values determined in steps A1 and A2, along with the actual
width of the wells, the effective well widths are determined by the methods
previously described.
Step B—Values of
E
e
and
E
h
are found using the following steps.
B1: A “universal” curve is calculated using Equation 3.27. It is convenient
to keep these values as a look-up table since the solution requires an iterative
technique. This curve expresses the normalized energy w as a function of
the normalized filed
f
through Equation 3.27.
B2: With a knowledge of
w
(
f
) the actual energy of the particle
W
(which
is actually
E
e
or
E
h
) is found by use of the Equation 3.26 to produce
W
1,
F
1,
f
,
w
, and
W
.
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