生长在砷化镓基板上的圆锥形砷化铟量子点的电子状态仿真
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2 | CONICAL QUANTUM DOT
This application computes the electronic states for a quantum-dot/wetting-layer system.
It was inspired largely by the work of Dr. M. Willatzen and Dr. R. Melnik (Ref. 1) as well
as B. Lassen.
Introduction
Quantum dots are nanoscale or microscale devices created by confining free electrons in a
3D semiconducting matrix. The tiny islands or droplets of confined “free electrons” (those
with no potential energy) present many interesting electronic properties. They are of
potential importance for applications in quantum computing, biological labeling, and
lasers, to name only a few.
Scientists can create such structures experimentally using the Stranski-Krastanow
molecular beam-epitaxy technique. In that way they obtain 3D confinement regions (the
quantum dots) by growth of a thin layer of material (the wetting layer) onto a
semiconducting matrix. Quantum dots can have many geometries including cylindrical,
conical, or pyramidal. This application studies the electronic states of a conical InAs
quantum dot grown on a GaAs substrate.
To compute the electronic states taken on by the quantum dot/wetting layer assembly
embedded in the GaAs surrounding matrix, you must solve the 1-band Schrödinger
equation in the effective mass approximation:
where h is Planck’s constant, Ψ is the wave function, E is the eigenvalue (energy), and m
e
is the effective electron mass (to account for screening effects).
Model Definition
The model works with the 1-particle stationary Schrödinger equation
h
2
8π
2
---------
∇
1
m
e
r()
---------------
Ψ r()∇
⋅
– Vr()Ψr()+ EΨ r()=
∇
h
2
8π
2
m
---------------
∇Ψ
⋅– VΨ+ EΨ=
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