Quantum Electronics Lecture 2
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This document summarizes a lecture on quantum wells as a deviation from ideal particle-in-a-box structures. It begins with reviewing the particle-in-a-box model and posing questions about its limitations. It then discusses how quantum wells are physically realized using different material compositions and potential profiles. The key concepts of exciton formation, electron motion in one to three dimensions, and the Schrodinger equation for quantum wells are presented. Finally, it covers two-dimensional electron gases, multiple quantum wells, superlattices, and the difference between the two structures.
![Introducing Schrödinger Equation
for V=V0
( )
*2
02 2
2 ( )( )
( ) ( ) 0bm zd z
E z V z
dz
ψ
ψ+ − =
[ ]*
0
2 2
2 ( )bm z E V
κ
−
=
2
2
22
( )
( ) ( ) 0
d z
z z
dz
ψ
κ ψ+ =
material parameter
5/9/2020 13
Arpan Deyasi, designed for Dept of Elec.Sc,
A.P.C.C on 9th May 2020](https://image.slidesharecdn.com/q-200509094341/85/Quantum-Electronics-Lecture-2-13-320.jpg)
Quantum Electronics Lecture 2
- 1. Course: Quantum Electronics-II Lecture: 2 Arpan Deyasi Topic: Quantum Well – A Deviation from Ideal Structure 5/9/2020 1 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 2. Recapitulation: ‘Particle in a Box’ problem 2 2 * 2 ( ) ( ) ( ) ( ) 2 d V z z E z z m dz ψ ψ ψ− + = for 0<z<L, V(z) = 0 for z≤0 & z≥L, V(z) = ∞ L 2 2 2 * 2 2 n n E m L π = 5/9/2020 2 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 3. Q1: What is the material outside of the well? Q2: How can the potential barrier be infinite? Is it practically realizable? Q3: How the electron effective mass inside and outside the material be same? Q4: How step potential configuration be physically realizable? Queries 5/9/2020 3 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 4. how a quantum well is really formed 5/9/2020 4 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 5. how a quantum well is really formed 5/9/2020 5 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 6. Exciton how carriers are trapped 5/9/2020 6 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 7. Electron motion in a Quantum well Two dimensions are unrestricted Only one dimension is restricted 5/9/2020 7 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 8. 5/9/2020 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020 8 Electron motion in a Quantum wire Only one dimension are unrestricted Two dimensions are restricted
- 9. 5/9/2020 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020 9 Electron motion in a Quantum dot All the three dimensions are restricted
- 10. Introducing Schrödinger Equation 2 2 * 2 ( ) - ( ) ( ) ( ) ( ) 2m ( ) d z V z z E z z z dz ψ ψ ψ+ = 2 1 ( ) - ( ) ( ) ( ) ( ) 2 *( ) d d z V z z E z z dz m z dz ψ ψ ψ + = 5/9/2020 10 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 11. Introducing Schrödinger Equation for V=0 2 1 ( ) - ( ) ( ) 2 *( )w d d z E z z dz m z dz ψ ψ = for V=V0 2 0 1 ( ) - ( ) ( ) ( ) 2 *( )b d d z V z E z z dz m z dz ψ ψ ψ + = 5/9/2020 11 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 12. Introducing Schrödinger Equation for V=0 *2 2 2 2 ( )( ) ( ) ( ) 0wm zd z E z z dz ψ ψ+ = * 1 2 2 ( )wm z E κ = 2 2 12 ( ) ( ) ( ) 0 d z z z dz ψ κ ψ+ = material parameter 5/9/2020 12 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 13. Introducing Schrödinger Equation for V=V0 ( ) *2 02 2 2 ( )( ) ( ) ( ) 0bm zd z E z V z dz ψ ψ+ − = [ ]* 0 2 2 2 ( )bm z E V κ − = 2 2 22 ( ) ( ) ( ) 0 d z z z dz ψ κ ψ+ = material parameter 5/9/2020 13 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 14. Introducing Schrödinger Equation κ1: wave-vector of quantum well, i.e., for lower bandgap material κ2: wave-vector of quantum barrier, i.e., for higher bandgap material κ1 = f(mw *) ------ material parameter dependence κ2 = f(mb *) ------ material parameter dependence 5/9/2020 14 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 15. Where is the physics of semiconductor device? ( ) 2 2 2 * 1 ....... 2 E E E m κ α β+ + + = band non-parabolicity of second order band non-parabolicity of first order 5/9/2020 15 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 16. Two-Dimensional Electron Gas (2DEG) Wave nature Electrons in CB are considered Quantum well Electrons confined in conduction band of quantum well 5/9/2020 16 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 17. Multiple Quantum Well/Superlattice 5/9/2020 17 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 18. Q. What is the difference between MQW & Superlattice? Superlattice is a type of Multiple Quantum Well structure where wavefunctions between adjacent quantum wells can help carrier transfer through quantum-mechanical tunneling process 5/9/2020 18 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020
- 19. Superlattice MQW but not superlattice 5/9/2020 19 Arpan Deyasi, designed for Dept of Elec.Sc, A.P.C.C on 9th May 2020 Thickness of the sandwich barrier is critical for tunneling process