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 need to 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, sketch 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 x-axis 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.  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 700-850nm.  After adjusting the x-axis you can auto-scale the y-axis to obtain a better view of the weaker peaks.  If the peaks are not visible, ask the instructor for assistance.  DO NOT ATTEMPT TO RE-ALIGN THE SYSTEM YOURSELF!
• Increase the integration time 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.
• 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 z₀ 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 650-850nm portion of the spectrum.  Normalize the 2 spectra by right-clicking on each y-column and selecting Normalize (normalizing means dividing all of the y-values by the maximum y-value).  Plot the 2 spectra together using a logarithmic y-scale 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 Maxwell-Boltzmann distribution (see Section 9.5 in the text).