Self consistent solution for the wave functions AlGaAs 0.3- GaAs Self-Consistent Solution 0.2- ENERGY ev Ninv-5 E11/cm² Ndepi-5 E10/cm² (NA-1.6 E14/cm³ ND-5 E17/cm³ spacer 50 ang 300 Kelvin 0.1- 0.0+ -100 0.0 100 300 400 500 200 DISTANCE (angstroms) Triangular-well approximation V (z) = q Feffz z > O Feff= = ndepl ar uni If the barrier height is sufficiently large, we can neglect the penetration of the envelope function in that region and assume that Qn(z) = 0 for z < 0 CnAi 2mz 1/3 (q Feffz – En)}. :)" - 4n (2) = C A { (12²² ) ( 9 F 2 – h2q2F2 2/3 n- n = 1, 2,... (-) (→) En 2m 1/3 2 Exercise 5: Derive these equations.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 68E
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Self consistent solution for the wave functions
AlGaAs
0.3-
GaAs
Self-Consistent Solution
0.2-
ENERGY
ev
Ninv-5 E11/cm²
Ndepi-5 E10/cm²
(NA-1.6 E14/cm³
ND-5 E17/cm³
spacer 50 ang
300 Kelvin
0.1-
0.0+
-100
0.0
100
300
400
500
200
DISTANCE (angstroms)
Triangular-well approximation
V (z) = q Feffz
z > O
Feff=
=
ndepl
ar
uni
If the barrier height is sufficiently large, we can neglect the
penetration of the envelope function in that region and assume
that
Qn(z) = 0 for z < 0
CnAi
2mz
1/3
(q Feffz
– En)}.
:)"
-
4n (2) = C A { (12²² ) ( 9 F 2 –
h2q2F2
2/3
n-
n = 1, 2,...
(-) (→)
En
2m
1/3
2
Exercise 5: Derive these equations.
Transcribed Image Text:Self consistent solution for the wave functions AlGaAs 0.3- GaAs Self-Consistent Solution 0.2- ENERGY ev Ninv-5 E11/cm² Ndepi-5 E10/cm² (NA-1.6 E14/cm³ ND-5 E17/cm³ spacer 50 ang 300 Kelvin 0.1- 0.0+ -100 0.0 100 300 400 500 200 DISTANCE (angstroms) Triangular-well approximation V (z) = q Feffz z > O Feff= = ndepl ar uni If the barrier height is sufficiently large, we can neglect the penetration of the envelope function in that region and assume that Qn(z) = 0 for z < 0 CnAi 2mz 1/3 (q Feffz – En)}. :)" - 4n (2) = C A { (12²² ) ( 9 F 2 – h2q2F2 2/3 n- n = 1, 2,... (-) (→) En 2m 1/3 2 Exercise 5: Derive these equations.
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