light emitting diode (led) characterizationknown led’s wavelength, you should also be able to...

Ryerson University PCS 224 - Solid State Physics

Light Emitting Diode (LED) characterization

Physics Topics

If necessary, review the following topics and relevant textbook sections from Serway 9th Ed.and Neamen 4th Ed.

• Optical Devices (Serway 14.7)

• Ideal Diode Current (Neamen 8.1.5, especially equations 8.26, 8.27)

• LED basics (Neamen 14.5.1)

Lab Introduction

You are working as part of an engineering team to design a home security system which usesan LED. If a break-in occurs, a circuit will be completed, lighting up an LED which will bedetected by a photodetector setting off a silent alarm. So as not to alert the burgler, youwant to use an LED which emits infrared light (invisible to humans).

To test your prototype, you plan to use an infrared LED found in your company’s stock-room. Unfortunately, you don’t know the wavelength of this LED; you have been asked tocome up with a simple procedure to determine it. Luckily, you have several other visibleLEDs with known wavelengths which you can use. In the process of determining the un-known LED’s wavelength, you should also be able to measure a fundamental constant ofnature: Planck’s constant h.

Background

One photonic device which can be created using a p-n junction diode is the light emittingdiode (LED). Under (unbiased) equilibrium conditions, the majority carriers’ tendency todiffuse from high concentration to low concentration is balanced by the built-in electricpotential barrier and its associated electric field.

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When the p-n junction is forward biased,the potential barrier between the n and pregions is reduced, and electrons from then side are able to diffuse across the de-pletion region into the p side. (Similarly,holes from the p side are able to diffuseover to the n side). As this diffusion oc-curs, each side now has an excess of mi-nority carriers and as a result recombina-tion will occur. This recombination mayresult in the emission of a visible photon.

A pn junction LED circuit showing the emission of light afterrecombination. Note the direction of the current is counterclock-wise meaning that holes have diffused to the left across the deple-tion region and electrons have diffused to the right. From Dim-itrijev, Sima, Principles of Semiconductor Devices, (2nd Ed.)New York, NY: Oxford Univeristy Press, 2012.

Direct and Indirect Band Gap Semiconductos

Since free electrons in a semiconductor have energies within the conduction band, when theelectrons re-occupy a lower energy empty state in the valence band (when they recombinewith holes), some energy will be emitted. Certain semiconductors called direct bandgapsemiconductors allow this energy to be emitted as a photon with energy approximatelyequal to the gap energy

hc

λ= Eg. (1)

In other kinds of semiconductors called indirect bandgap semiconductors, the recombina-tion of charge carriers is a multi-step process in which energy is partially or fully emittedin phonons or vibrations of the material, not an optical photon. Thus only direct band gapsemiconductors are suitable for LEDs. It is interesting to note that the common semicon-ductors of silicon and germanium are indirect band gap semiconductors and are not suitablefor LED applications.

Even if a semiconductor is a direct band gap semiconductor, the emitted photon maynot have a wavelength in the visible range depending on the gap energy. For example,gallium-arsenide, another common semiconductor has a gap energy of 1.42eV leading tothe emission of infrared photons which are invisible to humans. Significant research wasconducted to develop semiconductors which are both made of direct bandgap materials andhave gap energies of the appropriate size to emit visible light∗. This engineering has led tothe development of red, green, and blue LEDs which are now in widespread use.

∗Examples of such materials are GaAs1−xPx and InxGa1−xN where x denotes the exact ratios of the ele-ments which can be adjusted leading to tunable optical properties. See Neamen 14.4.3 for more information.

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Beyond the Ideal Diode

The current in a diode as a function of the diode voltage can be expressed as

I = IS

[exp

(V

Vt

)− 1

](2)

Where Vt is a constant called the “thermal voltage” (more on this below). If the appliedvoltage is much larger than the thermal voltage V � Vt, the −1 term is negligible incomparison with the first term, leading to

I ≈ IS exp

(V

Vt

)(V � Vt) (3)

The reverse saturation current can, in turn, be expressed as

IS = B exp

(−Eg

eVt

)(4)

More details about the derivation of this expression can found in the Appendix. B is aconstant which depends on the temperature and specifics of the device. In this lab, we willassume that B is a universal constant common to all diodes, but whose particular value isnot important for this lab.

In an ideal diode, we know that V idealt = kBT/e. Real diodes are are more complicated

and do not perfectly obey the ideal diode model for at least two reasons:

1.) The physical diode in the lab has an internal resistance. Due to the internal resistance,the measured voltage drop across the diode is actually Vmeasured = V − IRinternal, whereV is the “ideal” voltage drop appearing in the ideal diode equation. This effect becomesonly significant if the current through the diode is large; thus we can still use the idealdiode equation as long as we keep our current as small as possible (roughly 20mA orless, depending on the diode).

2.) Electrons and holes sometimes recombine in the depletion region, they don’t alwaysmake it all the way across, this fact is not accounted for in the ideal diode model. Thiseffect can be incorporated into the model by treating Vt as an unknown parameter tobe determined by fitting the data. Important: therefore in this lab we do NOTuse the ideal thermal voltage Vt 6= V ideal

t . Instead, we will determine Vt byfitting the data. Each LED will have a different value of Vt!.

Pre-Lab Questions

Please complete the following questions prior to coming to lab. You are required to take ashort quiz on D2L which is heavily based on one (or more) of these questions. Your instructorand/or TA will provide more details about when and how you will take the quiz.

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1.) Read through the entire lab manual before beginning

2.) What is the specific goal of this lab? Exactly what specific question are you tryingto answer? Be as specific as possible. (“To learn about topic X...” is not specific!)

3.) What specific measurements or observations will you make in order to answer thisquestion?

4.) The tertiary semiconductor compound In0.2Ga0.8As has a photon emission wavelengthof 1180 nm. What is its band gap energy in units of eV?

5.) What two conditions must be met for a semiconductor to emit visible light underforward bias?

6.) Of the three main semiconductor materials we study in this course (Si, Ge, GaAs),which (if any) emit light under forward bias?

7.) Of the three main semiconductor materials we study (Si, Ge, GaAs), which (if any)emit visible light under forward bias? .

8.) Using a single LED, if you measure the current I through the diode and the voltageV across the diode, assuming V � Vt, how could you plot your data so that the resultis a straight line?

9.) Assuming you have linearized your data (see the previous question) and determinedthe line of best fit:

(a) How could you determine Vt from your line of best fit?

(b) How could you determine IS from your line of best fit?

10.) Suppose now you have measured Vt and IS for a set of diodes, and you also know thewavelength of each diode. Show that plotting Vt ln(IS) on the y-axis and 1/λ on thex-axis, should result in a linear plot. In other words, show that

Vt ln(IS) = m

(1

λ

)+ b (5)

(a) What do you predict for the slope of the line, m? (Give your answer as anexpression.)

(b) What do you predict for the intercept of the line b? (Give your answer as anexpression.)

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Apparatus

• Arduino microcontroller (USB Boarduino, Adafruit Metro Mini, or suitable alternativeversion)

• Adafruit MCP4745 12-bit 5V DAC breakout board

• Adafruit INA219 DC High-Side Current Sensor breakout board

• MCP6002 dual op-amp (CMOS)

• TIP41C or 2N3904 BJT transistor (note different pinouts), or equivalent.

• Electrical prototyping board

• Jumper wires

• Red, Yellow, Green, Blue, Violet LEDs (with clear plastic casing)

• Infrared LED (with blue plastic casing)

To characterize an LED, it is necessary to measure the voltage across it and the currentrunning through it. We will use an Arduino microcontroller to control two “breakout boards”in order to perform these measurements. The assembly is shown below

MCP4725 DAC supplies a 0-5V voltage to an MCP6002 op-amp isolation buffer. Voltageout of the MCP6002 is routed through a BJT transistor current source. An INA219 currentsensor measures the current and voltage across the LED.

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Note: Some lab setups will use a slightly different circuit configuration. An alternativesetup is shown in Appendix B.

A simple Arduino program will be provided to tell the DAC to slowly increase voltage insmall steps from 0V to 5V. The program turns the voltage on only briefly for each step andthen resets it to 0V so that the LED does not overheat.

Procedure

1.) Ensure that your board is configured as shown in the figure. If there is an LED insertedinto the board remove it now, carefully noting where it was inserted as you will needto replace it several times during this lab.

2.) Plug in the Arduino into your computer’s USB port.

3.) The program to run the Arduino should be provided on D2L or on the physics labwebsite. Download and open this program so it runs in the Arduino software.

4.) Click the checkmark “verify” button to compile the code. If there are any errorsin compilation, please see Appendix A - Troubleshooting.

5.) Click the “Upload” button to run the code on the Arduino. If there are any errors,please see Appendix A - Troubleshooting.

6.) Within the Arduino software go to Tools → Serial Monitor. If your program isrunning successfully, the text “Press ENTER to do a data run” should appear. Don’tpress ENTER until you have completed the next step. If you cannot get the programto run successfully, please see Appendix A - Troubleshooting.

7.) Insert an LED into the board as shown in the figure. The shorter pin of the LED(cathode) should be closer to the bottom part of the board as shown in the figure.Another way to identify the cathode is by locating the flat section on the LED’s clearplastic base. This flat section should be facing the bottom part of the board as shownin the figure. Insert the LED into the board gently, taking care not to bend or damagethe pins.

8.) Press ENTER to collect a set of data of current vs. voltage. You should see numbersappearing in the serial monitor in two columns; the first column is the voltage acrossthe diode (in volts), the second columns is the current through the diode in milliamps.While the data is being taken, you should see the LED light up briefly. Be sure to notethe color of the LED.

9.) If you need to re-take data, simply click the “Upload” button again, and then pressENTER when prompted.

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10.) Once you are satisfied with your data run, copy and paste the data into an Excelspreadsheet. If the data pastes into a single column, you can make it into two columnsby going to Data → Text to Columns. A dialog box will appear; select Delimitedand then click Next. On the following screen, make sure the box next to Space ischecked. Then click Finish. The data should now be separated into two columns.

11.) Repeat steps 5 - 10 to take voltage and current data for each of the five visible LEDs.Keep your data in a single spreadsheet

12.) Finally, repeat steps 5 - 10 with the infrared LED which has a blue plastic casing. TheLED is not in the visible range and so will not shine as the data is taken. Add thisdata to your spreadsheet.

13.) Disconnect your Arduino and return the LEDs to the proper places so that the nextlab group may use them.

Analysis

1.) For each data set, plot your data such that the resulting plot is a straight line (youshould have determined how to do this in the Pre-Lab questions). Below are somefurther tips for doing so

(a) Since you’ll need to use the natural logarithm, you’ll want to exclude any data-points with negative (or zero) current. One way to do this is to sort the data setin Excel from low to high current. (Select the data, right click on it, then chooseSort → Custom Sort).

(b) As explained in the Background section, the LED will only obey the ideal diodeequation as long as the current is not too large. For some LEDs, the curve will notbe linear once the current reaches ∼30mA, though some other LEDs may have alarge linear range. Try to exclude data which does not fit the linear model, andonly plot the linear portion of your data.

(c) Add all 6 data sets to your plot; add a title, and label the axes.

2.) Fit a line to each dataset. Use your best fit lines to determine the value of Vt and ISfor each LED. Record your results in your notebook and/or lab report.

3.) You should now have a measurement of Vt, and IS for all 6 LEDs. The wavelength ofthe 5 visible diodes are shown in the figure below.

Combining equations (1) and (4), create a second linear plot which uses your datapoints of Vt, λ and IS for each of the 5 visible LEDs. This plot should have 5 datapoints, one for each of the visible LEDs. You may need to refer to the Pre-Lab question10.

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4.) The 5 data points from the previous step should be approximately linear (if plottedcorrectly). Find the line of best-fit to these 5 data points and record the equation inyour notebook and/or lab report.

5.) Using your best-fit line to these 5 data points, determine Planck’s constant h. Make aquantitative comparison to the accepted value. [Watch out for units!]

6.) Assuming the infrared LED would also lie on this line; use your line of best fit, as wellas the measurement of Vt and IS for the infrared LED to determine its wavelength.

Wrap Up

The following questions are designed to make sure that you understand the physics implica-tions of the experiment and also to extend your knowledge of the physical concepts covered.Each member of your group should be able to answer any/all of these questions. Your TAwill check that this is the case; please check out with your TA before exiting lab.

1.) When plotting ln(I) vs. V , the ideal diode equation predicts a linear plot. Your plotsprobably start off linear, but then eventually curve and flatten out. Why isn’t the plotperfectly linear as predicted by the diode equation?

2.) In the analysis of the first plot, you should have measured Vt for all 6 diodes. If thediodes were ideal, the value of Vt should be equal to kBT/e. For each diode, by howmuch (give a multiplicative factor) is your measured value of Vt different from the idealvalue? In light of your answer (pun intended), is it acceptable to model these LEDs asideal diodes?

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3.) Roughly what range of wavelengths (in nanometers) are visible to the human eye?Roughly what range of wavelengths (in nanometers) correspond to infrared light?(When completing your analysis, it’s a good idea to check that your results for theIR wavelength pass this basic check!)

Appendix A - Arduino Troubleshooting

The Arduino Code has errors on compilation

If you cannot get your code to compile without errors, try these steps:

1.) Connect the Arduino to the computer via USB cable

2.) Select Tools→Manage Libraries and search for the following two libraries necessaryto run the breakout boards:

(a) Search for Adafruit MCP4725. If the library is not installed, select Install

(b) Search for Adafruit INA219. If the library is not installed, select Install

3.) Under Tools → Board, ensure that Arduino/Genuino Uno is selected.

4.) Try re-compiling your code. If this does not fix the problem, ask your lab TA.

The Arduino Code does not upload correctly

If your code compiles, but you cannot upload it to the board, try the following steps:

1.) Connect the Arduino to the computer via USB cable

2.) Under Tools → Board, ensure that Arduino/Genuino Uno is selected.

3.) Under Tools → Port, set the port to the last entry listed. If the program fails toupload, try selecting a different port and re-uploading.

4.) You can also try connecting the Arduino to the computer via a different USB port.Upon re-connecting it, see if any new ports are available in the Tools → Port menu.If so, select the new port and try re-uploading.

5.) Return to step 4 of the Procedure section of this manual and try again to upload thecode to the board. If you find that you are still unable to get the code to run, ask yourTA for help.

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The Arduino Code runs, but the LED does not light up

If your code compiles and uploads, but your LED does not light up during the data run,check the following:

1.) Ensure that your LED is inserted exactly as shown in the figure in the lab manual.

2.) Ensure that your LED is not inserted backwards (follow the instructions in the labmanual for how to insert the LED correctly)

3.) Are you using an infrared LED? The infrared LED will not light up visibly (you cantell the IR LEDs because they have a blue plastic casing).

4.) Is your LED burned out? Try a different LED (with clear plastic casing).

5.) If none of these steps work, ask your TA for help.

Appendix B - Alternative Board Configuration

Some lab setups may use an alternative circuit configuration, using an “USB Boarduino”Arduino. This configuration is show below

Appendix C - Derivation of Equation (4)

The reverse saturation current IS can be expressed as - see Neamen (8.26)

IS = A|q|[Dppn0

Lp

+Dnnp0

Ln

](6)

where A is the cross sectional area of the device, pn0 is the equilibrium hole concentrationon the n side of the junction, np0 is the equilibrium electron concentration on the p side ofthe junction.

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Dp and Dn are electron/hole diffusion constants which contain information about howquickly electrons/holes can diffuse through the material. The Einstein relation, Neamen(5.47) relates these constants to mobility and charge:

Dp =kBTµp

|q|(7)

Dn =kBTµn

|q|(8)

The diffusion lengths are defined as

Ln =√Dnτn0 =

√kBTµn

|q|τn0

(9)

Lp =√Dpτp0 =

√kBTµp

|q|τp0

(10)

where τp0 and τn0 are the average times before recombination for holes and electrons respec-tively.

Using the four equations above, the fundamental semiconductor equation

nn0pn0 = n2i (11)

np0pp0 = n2i (12)

and assuming strong doping, nn0 ≈ Nd and pp0 ≈ Na, we can rewrite (6) as

IS = A√kBT |q|

(1

Nd

√µp

τp+

1

Na

√µn

τn

)n2i (13)

Finally, inserting the definition of the intrinsic carrier concentration:

IS = A√kBT |q|

(1

Nd

√µp

τp+

1

Na

√µn

τn

)NCNV e

−Eg/kBT (14)

Inserting this formula into the idea diode equation we have

I = Be−Eg/kBT[e|q|V/kBT − 1

](15)

where B is a constant which depends on the temperature, material properties and devicespecifics:

B ≡ ANCNV

√kBT |q|

(1

Nd

√µp

τp+

1

Na

√µn

τn

)(16)

the exact value of B is not needed for our purposes. Variations in B among the different colorLEDs is not significant compared to the exponential dependence on Eg, thus it is acceptablein this lab to treat B as a constant common to all LEDs.

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Reference

The procedure in this lab is based on the article by Roger Morehouse, “Measuring Planck’sconstant by means of an LED”, American Journal of Physics 66, 12 (1998);https://doi.org/10.1119/1.19034

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light emitting diode (led) characterizationknown led’s wavelength, you should also be able to...

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