Physics 214 Assignment 13
Concepts:
Particle in a box
Atomic transitions and light emission
Harmonic oscillator
Hydrogen atom
Correspondence principle
Lasers
Uncertainty principle
Quantum tunneling
Reading:
Y&F, Vol. 3, Chapters 38, 39, 40 and 41.
Assignment:
Due Friday, May 2.
Please turn in this sheet stapled to the top of your work.
Physics Problems:
1. Y&F, Chapter 40, Question 11
2.
Y&F, Chapter 40, Question 14
3.
Semiconductor quantum wells and dots.
The formulas derived for electrons in
boxes can be applied to electrons and holes in semiconductors, with one important
correction:
the electrons and holes in the semiconductor each have an effective mass
m
eff
that is different than the mass of a free electron. It is this mass that must be used in
all formulas.
(a) Semiconductor lasers are usually formed from multiple layers of semiconductor,
each layer having a different composition.
One or more of these layers is often made
very thin to create a quantum well, which can increase laser efficiency (photons
out/electrical energy in).
In an AlGaAsGaAs quantum well laser, the electrons are
confined in a 10 nm wide GaAs layer, in which m
eff,e
=0.067m
e
.
What is the ground state
energy E
1,e
of an electron in this well?
(b) The transitions that give rise to laser light are between the quantum well states in the
conduction band and in the valence band, not between quantum well states within the
same band. The energy of the emitted photons is hf = E
g
+ E
1,e
+ E
1,h
, where E
g
is the
separation between the conduction and valence band of bulk GaAs, E
1,e
is the amount
by which confinement raises the ground state energy of electrons in the conduction
band, and E
1,h
is the amount by which confinement lowers the ground state energy of
holes in the valence band. Thus, confinement increases the emitted light frequency.
What is the ratio (E
1,e
+ E
1,h
)/E
g
?
Use E
g
= 1.43 eV, E
1,e
from (a), and calculate E
1,h
using m
eff,h
=0.45 m
e
. This roughly gives the fractional increase in photon energy due to
confinement in the quantum well.
Physics 214, Spring 2008
1
Cornell University
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(c) The brightly colored liquids shown in lecture contain colloidal CdSe
semiconductor nanocrystals.
By carefully timing the growth of these crystals from
solution, crystals of well defined and controllable size can be obtained.
The resulting
quantum confinement increases the energy of the emitted photons compared with bulk
CdSe, as in the case of quantum wells.
For CdSe, E
g
= 1.73 eV,
m
eff,e
=0.13m
e
and
m
eff,h
=0.45 m
e
.
What must be the diameter of a nanocrystal to produce light emssion at
600 nm (red), 560 nm (yellow) and 490 nm (blue)?
4. YF Chapter 40, Problem 56.
Add: (d) Take the limit U
0
→
∞
in your equation from
part (c) and show that the allowed k’s and energies are what we already found for the
infinite well.
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 Spring '08
 THORNE
 Energy, Light, Cornell University

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