PHTN1300 Principles of Light Sources and Lasers
Determining Planck's Constant (2011F)
In photonics, few constants are so widely utilized as Planck's constant, the constant which relates the energy of a photon to it's frequency according to E=hν where E is the photon's energy in Joules, h is Planck's constant, and ν is the photon's frequency. By observing the wavelength of light emitted from semiconductor LEDs, and knowing the energy lost by electrons in the downward transition, this constant may be accurately determined.
In the case of this experiment, we will exploit the fact that for a light-emitting semiconductor diode, the energy of an emitted photon is related to the energy required to jump the bandgap between the semiconductor materials.
In the case of a diode, the bandgap energy is seen as the constant voltage across the device while current is flowing. If the voltage across the device is below that of the bandgap, no current flows (and in the case of an LED, no light is emitted). If we increase the voltage gradually, we will reach a point where we have supplied electrons with enough energy to jump the gap: current will flow and an LED will emit light.
Knowing the voltage required to cause photon emission, and knowing the frequency of the light (i.e. by measuring the wavelength of this emission using a spectroscope), we can calculate the energy of photons emitted and then Planck's constant.
Wire a red LED in series with a 1000 Ohm resistor to an Agilent 3620A variable power supply (set its meter to V1). An external digital voltmeter must be connected directly across the LED in order to measure the bandgap voltage directly. Set the voltage control on the power supply to zero volts and turn ON the supply. Note the voltage across the device at which light first appears (despite the fact that current will read zero at this point) and then increase the voltage gradually so that current increases in steps of 1mA. To measure current accurately flip one meter lead so that it measures voltage across the resistor - in effect measuring current (1 volt across the resistor = 1mA of current flow), then flip the lead to measure voltage across the LED accurately.
Note the voltage and current at each step (Read both as voltages from the meter which is directly across the LED device or the resistor - not the ones on the power supply which are not particularly accurate).
You will note that at a certain voltage, the LED begins to light but below that, no light is emitted. Continue recording V & I (with current in steps of 1mA: 1V on the meter when measuring voltage across the LED) until a current of 10mA flows through the LED at which point the LED will glow brightly. Calibrate a spectroscope using a mercury lamp (in the same manner as you did in lab #1) - you only need to do this once before determining the spectra of all the LEDs used in this lab. Mount the LED in a suitable 3-point holder on the breadboard, point it towards the slit on the spectroscope, and observe the output wavelength of the LED. It will be required to adjust the alignment of the LED as well as the slit on the spectroscope. Observe the longest and shortest wavelengths of emission as seen in the spectroscope (record the angles, and convert to wavelength as you did in the first lab). Observe the output qualitatively as well: you might well observe the skewed curve as discussed in class and in the text (i.e. the sharp cutoff in the longer wavelength {red} side of the emission curve).
Repeat this procedure of graphing I&V and determining the emission wavelength for five 'regular' visible LEDs (Red, Orange, Yellow, Green, and Blue). Note that the BLUE LED is static sensitive and can be destroyed by stray charges: be sure to ground yourself before touching these components and carry the device with both terminals shorted.
Graph voltage vs. current for each LED in a manner similar to that seen to the left (the same as that outlined in Csele section 2.9). You will notice the 'knee' in the curve where light first appears. This is the voltage at which photons are emitted - the gap voltage. Find the gap voltage accurately by drawing an asymptote (line) to the linear (upper) part of the I/V curve and extrapolating to the zero intercept on the y-axis.
Each photon produced originates from the downward transition of a single electron. That electron, with electronic charge e, acquires an energy of V volts. The energy of each electron is therefore Vgap in electron-volts as discussed in section 2.10 and in class (an exact match is not expected though due to thermal energy and the distribution of charge carriers, as discussed in the lectures). Convert each gap energy in eV (one for each LED) into Joules.
Now, convert the longest wavelength observed (that will be the closest emission expected from the edges of the bands as seen in figure 2.10.1 of the text) to a frequency (in Hz) and plot bandgap energy in J on the y-axis (as obtained from voltage observations) and frequency on the x-axis (as obtained from spectral observations). The slope (rise/run) will have units of Joules/Hz or Joule-seconds, the units in which Planck's constant is usually expressed.
When drawing the best-fit line in the analysis, you might have to omit one set of data points if it lies far outside the normal range .... analyze your data early and ask the professor if required (but don't wait until the night before it is due to consider this).
Note, too, that your value of Planck's constant will be somewhat different than the accepted value since the procedure used does take thermal energy into account (this is a more-or-less constant value for all of these similar types of LEDs). Refer to chapter 2 of Csele for details.
In the report include five graphs showing the V/I characteristic for each LED, the bandgap voltage as found using each graph (and subsequent conversion from eV to Joules), the wavelength observations for each LED (including brief details of the calibration procedure as well), the graph of gap energy vs. frequency used to determine Planck's constant, and finally report Planck's constant as determined from this experiment.
You have been given an infrared LED as well - these come in a variety of wavelengths ranging from 700nm to 1500nm - record the serial number on your IR LED as there are several types in the class, identified only by this number. Measure the V/I characteristics of this diode in the same manner as you did for Part A. Determine the voltage at the 'knee' and using the method above and, using the value for Planck's constant which you determined in Part A (not the "accepted" value, since your value compensates for thermal energy effects), report a predicted wavelength (in nm) for this LED. The wavelength you predict will be the longest wavelength though (at the edge of the bandgap): Predict the PEAK emission wavlength according to that outlined in 2.10 of Csele by adding a thermal energy to the determined energy of the bandgap - assume a temperature of 300K. Peak emission wavelength is how commercial LEDs are rated.
The FIRST PAGE must be a title page containing nothing more than the title of the lab, the course, and the student's name and ID number
Answer each question as "1", "2", etc with each new question starting on a NEW PAGE so that question 2 starts on the top of a new page and question 3 starts at the top of a different page, etc. You'll have, therefore, at _least_ seven pages in this report.
The lab must be submitted in a report cover (preferably either a three-hole punched cover or one with a clamp on the left side), NEVER as a stapled mass of loose papers
Failure to follow this simple outline, used for all condensed labs in this course, will result in deduction of marks
LAB SUBMISSION:
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