Optical Spectroscopy IV
Semiconductor Quantum Wells
Objective:
We will study a semiconductor sample containing alternating
layers of GaAs and AlGaAs, which yield finite square well potentials along the
axis perpendicular to the layers. The layers are thin enough to exhibit quantum
confinement, so the ground state energy depends on the thickness of the well.
We will measure the emission energy of these quantum wells, and compare our
results with theoretical predictions using both infinite and finite square well
analysis. We also seek to understand the shape of the high energy tail on
our emission peaks in the context of thermal energy and the Boltzmann
distribution.
Background:
We will investigate the structure shown (not to scale!) below:
GaAs layers are sandwiched between AlGaAs layers,
which have a higher conduction band energy. Hence, when electrons are
excited by the laser, they get trapped in the thin GaAs layers, and quantum
confinement shifts their emission energies as shown to the right of the
structure. The GaAs emission energy without quantum confinement is 1.512eV
at 77K. A peak near this energy should be evident in your measured spectrum.
You should also observe 3 emission peaks above this energy which correspond to
the 3 quantum wells in the structure. The ground state energy of electrons in each
quantum well is the difference between the measured peak energy and the energy
without quantum confinement (~1.512eV). These measured energies should be
compared with the predictions of infinite and finite square well theories.
Please note that electrons in GaAs behave as if they were lighter than free
electrons so you will need to adjust the mass as follows: m* = 0.067m_{e}
(m* is the effective mass in GaAs, and m_{e} is the free electron mass).
For the finite square well predictions, you will need the AlGaAs
energy (1.933eV at 77K) to determine the barrier height.
Procedure:
Emission from the quantum wells is weak at room temperature, so we will eventually cool
the sample with liquid nitrogen to 77K. When you are ready to start the
lab, your instructor will take you through this process. Please note that
it takes approximately 1 hour for the system to cool to 77K. In the
meantime, draw a block diagram of the experimental setup (here's
an image of the cryostat) and review the instructions below.
 Begin
by running the Ocean Optics SPECTRASUITE control software. Ensure that the I2J2362
spectrometer is configured properly by comparing the xaxis scale to the
range indicated on the spectrometer and noting whether spectra are being
collected. Note the room light
spectrum and then turn the room lights off.
CAUTION: THE Nd:YAG LASER
EMITS INTENSE RADIATION AND EXPOSURE TO THE EYES AND SKIN MUST BE AVOIDED. PAY
PARTICULAR ATTENTION TO REFLECTIONS OF THE LASER BEAM, AS THESE ARE SOMETIMES
DIFFICULT TO PREDICT.
 PUT
LASER SAFETY GLASSES ON and then turn the key switch on the laser. The
Ready indicator light will flash while the laser system stabilizes
the temperature. When the indicator stops flashing, press the Ready
button to start the laser. The output power will ramp up to 200mW which is too much laser power because it will heat the sample. Reduce the output power of the laser to 5075mW. Open the shutter on the laser. If the
system is aligned properly, you should see a very strong peak at
approximately 870nm (due to the InGaAs QW#0) and several weak peaks at higher energies (between 700
and 850nm). The green Nd:YAG laser light is attenuated by the long wavelength
pass filter (RG665) in front of the detector. Since we are only
interested in these weaker (GaAs QW) peaks, adjust the
Spectrum Scale under the View menu. A good spectral range is
700850nm. After adjusting the xaxis you can autoscale the yaxis to
obtain a better view of the weaker peaks. If the peaks are not
visible, ask the instructor for assistance. DO NOT ATTEMPT TO REALIGN
THE SYSTEM YOURSELF!

Increase the integration time and boxcar (no more than a value of 4) settings to obtain a nice, smooth spectrum (with maxima
just below the upper limit of 4000 counts). Now close the shutter on
the laser and record a dark spectrum (press the grey lightbulb button).
Subtract the dark spectrum, then open the shutter and record the emission
spectrum. Save the result.
 Cool the sample to 77K. Change the integration time to obtain a nice spectrum. Make sure you retake the dark spectrum and subtract it from the spectrum. Record and save the spectrum.
 Now
set the temperature to 200K and switch the temperature controller to AUTO.
Watch how the peaks lose intensity with increasing temperature.
Excited electrons in semiconductors can release their energy by emitting
either light or heat, and the emission of heat becomes more favorable
(relative to the emission of light) as the temperature is increased.
After the temperature reading has stabilized at 200K, wait another 5 minutes
or so to ensure that the sample has thermalized with its environment.
Now adjust the integration time to obtain maxima with ~ 4000 counts, collect
a new dark spectrum, and record the 200K emission spectrum.
Analysis:
 For
the 77K spectrum, measure the peak energy associated with each quantum well
and determine each ground state energy.
 Determine the theoretical ground state energy for each well using the
infinite square well approximation. Compare the theoretical values
with your experimental results.
 Are the measured energies bigger or smaller than the theoretical
predictions? Why?
 How
does the percent error depend on the well width? Explain.

Determine the ground state energy for each well using the finite square well
theory. Start by computing z_{0} for each quantum well.
Then solve each transcendental equation for z using the FindRoot function on Mathematica.
Finally, use these results to compute the ground state energies.
Compare the theoretical values with your experimental results.

Which theory (finite or infinite square well) works better? Why?
 Copy your 77K and
200K data into Origin and delete the rows above and below
the 650850nm portion of the spectrum. Normalize the 2 spectra by
rightclicking on each ycolumn and selecting Normalize (normalizing
means dividing all of the yvalues by the maximum yvalue). Plot the 2 spectra together using a logarithmic yscale for your plot.
 Do
the emission peaks broaden on the high energy side with increasing
temperature? Why?
 Is
the high energy tail exponential? (If it is, it will look ~ linear on a
logarithmic plot.) Explain your answer in the context of the MaxwellBoltzmann
distribution (see Section 9.5 in the text).