Physics 214 Assignment 13
Particle in a box
Atomic transitions and light emission
Y&F, Vol. 3, Chapters 38, 39, 40 and 41.
Due Friday, May 2.
Please turn in this sheet stapled to the top of your work.
1. Y&F, Chapter 40, Question 11
Y&F, Chapter 40, Question 14
Semiconductor quantum wells and dots.
The formulas derived for electrons in
boxes can be applied to electrons and holes in semiconductors, with one important
the electrons and holes in the semiconductor each have an effective mass
that is different than the mass of a free electron. It is this mass that must be used in
(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 AlGaAs-GaAs quantum well laser, the electrons are
confined in a 10 nm wide GaAs layer, in which m
What is the ground state
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
, where E
separation between the conduction and valence band of bulk GaAs, E
is the amount
by which confinement raises the ground state energy of electrons in the conduction
band, and E
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
= 1.43 eV, E
from (a), and calculate E
. This roughly gives the fractional increase in photon energy due to
confinement in the quantum well.
Physics 214, Spring 2008