Determining Planck's constants constant with LEDS
http://technology.niagarac.on.ca/courses/phtn1300/Plancks.html
PHTN1300 : Lasers and Light Sources
Determining Planck's Constant
Introduction
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.
Prelab
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Read Csele sections 2.9-2.10 for a background on LED devices
Bring your electronics kit (with jumper leads and resistors) to the lab
Part A: Determining LED Characteristics
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).
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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. This
best-fit line MUST be shown on each graph submitted, and be sure to
show where it intercepts the axis as this is the bandgap voltage which
will be used in the rest of the experiment.
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 V gap 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, and this slope _is_
Planck's constant as required in this experiment.
When drawing the best-fit line in the analysis, you might have to omit the data point for the blue LED .... analyze your data
with, and without the blue LED to see how it "fits" (Blue LEDs use a quantum well structure and so the bandgap voltage
does not correspond to the freuency of the light emitted in the way other LEDs do). Analyze your data early and ask the
professor if required (but don't wait until the night before it is due to consider this).
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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.
Part B: Determining the wavelength of an unknown diode
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.
Lab Report
Hand In a WORD PROCESSED (not handwritten) lab report with contents as outlined below.
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 threehole 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:
1. A one-page summary of the experiment summarizing the method used to determine Planck's constant and the
application of this experimentally determined value to compute the emission wavelength of the unknown diode.
2. Include five graphs showing the V/I characteristic for each LED, identifying the bandgap voltage as found using
each graph. You can summarize all collected I/V data on a single graph with multiple curves and multiple
intercepts shown.
3. Show calculations of bandgap energies, converted into Joules. Include a single chart/table with the headings
"LED Colour", "BANDGAP VOLTAGE (V)", and "BANDGAP ENERGY (J)".
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4. Wavelength observations for each LED in the form of a single chart/table with the headings "LED Colour",
"WAVELENGTH (nm)", and "FREQUENCY (Hz)". Outline, briefly, in a single paragraph details of the calibration
procedure of the spectroscope as well.
5. The graph of gap energy vs. frequency used to determine Planck's constant, including the best-fit line and finally
Planck's constant as determined from this experiment (which is, of course, the slope of this line). Data points
must be shown in addition to the "best fit" line, and if the blue LED is eliminated, this must be explained (i.e. by
detailing the slope when the blue LED is included, and when it is eliminated).
6. The analysis of the unknown IR diode. Include the V/I graph, determination of the bandgap energy from this
graph (in eV and then Joules), calculation of the energy of maximum photon emissions (by adding thermal energy
as per chapter 2), and calculation of peak emission wavelength by using the value of Planck's constant you
determined in this experiment (NOT the accepted value).
Copyright (C) Niagara College, Canada, 2008-2012
A part of the PHTN1300 course in the photonics programs at Niagara College
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you are here->home->Physical Sciences->Modern Physics Virtual Lab->Determination of Planck's
Constant
Determination of Planck's Constant
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Theory
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Procedure
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Self Evaluation
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Simulator
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Assignment
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Reference
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Feedback
Aim
Determination of Planck’s constant.
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Apparatus
0-10 V power supply, a one way key, a rheostat, a digital milliammeter, a digital voltmeter, a 1 K
resistor and different known wavelength LED’s (Light-Emitting Diodes).
Theory
Planck’s constant (h), a physical constant was introduced by German physicist named Max Planck in
1900. The significance of Planck’s constant is that ‘quanta’ (small packets of energy) can be determined
by frequency of radiation and Planck’s constant. It describes the behavior of particle and waves at
atomic level as well as the particle nature of light.
An LED is a two terminal semiconductor light source. In the unbiased condition a potential barrier is
developed across the p-n junction of the LED. When we connect the LED to an external voltage in the
forward biased direction, the height of potential barrier across the p-n junction is reduced. At a particular
voltage the height of potential barrier becomes very low and the LED starts glowing, i.e., in the forward
biased condition electrons crossing the junction are excited, and when they return to their normal state,
energy is emitted. This particular voltage is called the knee voltage or the threshold voltage. Once the
knee voltage is reached, the current may increase but the voltage does not change.
The light energy emitted during forward biasing is given as ,
(1)
Where
c -velocity of light.
h -Planck’s constant.
λ -wavelength of light.
If V is the forward voltage applied across the LED when it begins to emit light (the knee voltage), the
energy given to electrons crossing the junction is,
(2)
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Equating (1) and (2), we get
(3)
The knee voltage V can be measured for LED’s with different values of λ (wavelength of light).
(4)
Now from equation (4), we see that the slope s of a graph of V
on the vertical axis vs. 1/λ on the horizontal axis is
(5)
To determine Planck’s constant h, we take the slope s from our
graph and calculate
using the known value
Alternatively, we can write equation (3) as
calculate h for each LED, and take the average of our results.
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