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Laboratory exercise: Light-emitting diodes
Kilian [email protected]
February 4, 2014
Light-emitting diodes (LEDs) are semiconductor devices with a p-n junction in which in-jected carriers recombine radiatively. LEDs are efficient light sources for many applications,including indicators, large-area displays, and opto-couplers. Furthermore are LEDs an ex-cellent alternative to incandescent and fluorescent light bulbs. LEDs are easily modulatedsources and are widely used in optical communications with optical fibers.
In This laboratory exercise we will demonstrate some basic properties of LEDs. Importanttopics are the determination of the output radiant power, the radiant and luminous powerspectra, and the luminous efficacy of LEDs. To determine these properties we measure theluminosity function.
Radiant power and efficiency
To determine the output radiant power of an LED, its light is directed onto a silicon photo-diode adjacent to the LED. The sensitive area of the photodiode is about 1 cm in diameter,so that the light from the LED is almost fully utilized. But, to get reliable and comparableresults the position of the detector must be adjusted to maximize the photoelectric current.
Task:
• Measure the I-V characteristics and the dependence of the photoelectric current on theapplied LED current
The output radiant power (radiant flux) of an LED is calculated from the photoelectric currentand the spectral response of the photodiode R(λ), that is, the wavelength dependence of theratio of the photodiode current Ipd to the incident radiant power Popt. Figure 1 shows thespectral response of a typical silicon photodiode. For very accurate measurements we wouldmeasure the spectral response of the photodiode but for this lab we will assume a lineardependence in the visible wavelength region
R(λ) =IpdPopt
= m(λ− 200) (1)
where λ is the wavelength in nanometers and m is the slope and a characteristic of the pho-todiode. To determine the photodiode specific m we can measure the photoelectric currentfor a laser-pointer with known emitted light power and wavelength.
Figure 1: Spectral response of a typical silicon photodiode and linear fit in the visible wave-length region.
• plot the output radiant power of the LEDs versus input current
• plot the efficiency of the LEDs versus input current. What is the maximum efficiency?
Radiant and luminous power spectra
The emission spectra of the LEDs are determined with the Avantes USB fiber spectrometer.The measurement data are acquired in a broad wavelength range from the ultraviolet to theinfrared. The emission spectra are radiant power spectra (in arbitrary units). For most LEDsthe dominant wavelength of the spectrum depends on the applied current and therefore itshould be measured for more than one applied current.
• What could be the reason for the dependence of the emitted wavelength on the appliedcurrent? Is the dependence the same for all measured LEDs?
To calculate the true radiant power spectra of the LEDs, the radiant power spectrum of eachLED (in arbitrary units) must be integrated over all wavelengths and then normalized to makethe integral equal to the output radiant power determined with the silicon photodiode. Thisoperation provides the true radiant power spectra, that is, the wavelength dependency of theradiant power per unit wavelength, Pλ(λ) (mW/nm).
• plot the measured radiant power spectra of the LEDs and the same spectra normalizedwith the output radiant power.
The next step is the conversion of the radiant power spectra to luminous power spectra.The radiant power spectrum is an insufficient characteristic of a lighting source because thehuman eye is not equally sensitive to the light of different colors. The typical human eyespectral response is given by the standard luminosity function S(λ) established by the Inter-national Commission on Illumination. For light-adapted vision, this function has a maximumat 555 nm and can be approximated by a simple equation proposed by Agrawal et al.1
S(λ) = exp(−88x2 + 41x3) (2)
2
Figure 2: Standard luminosity function2 and approximated equation.
where x = λ/555− 1, and λ is the wavelength in nanometers.
We will try to measure the spectral response of our eyes with the color LEDs by tuning thecurrent of two LEDs until both seem to have the same intensity. This task is quite tricky withthe simple setup we have here. It might be helpful to cover the LEDs with a piece of paper toget more diffuse light sources. The sense of brightness is approximately proportional to thelogarithm of the stimulus and therefore it is better to use lower brightnesses to compare theintensities. Measure more than once. Remember: The emitted wavelength may depend onthe applied current and for the spectral response you need to know the emitted wavelength.
• Determine the spectral response of your eyes and compare it with the standard lumi-nosity function.
The spectral response of the human eye is a crucial factor for providing effective and qual-itative (similar to daylight) lighting. The two requirements are in obvious contradiction:qualitative lighting assumes the presence of blue and red bands, which is ineffective becauseof the nature of human vision. Initially, the base unit of luminous intensity, the candela(cd), was based on a ”standard candle.” The present-day definition of this unit adopted in1979 says: ”The candela is the luminous intensity, in a given direction, of a source thatemits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensityin that direction of 1/683 watt per steradian.”3 The frequency 540 × 1012 Hz correspondsto λ = 555 nm, while the factor 1/683 was chosen to match the original definition of thecandela. The lumen (lm) is defined as 1lm = 1 cd sr. A light source of one candela pro-vides a total luminous power (luminous flux) of 4π ∼= 12.57 lm. By definition, one watt ofelectromagnetic radiation at λ = 555 nm produces a luminous power of 683 lm. The ratioof the total luminous power from a light source to the electric power consumed is called theluminous efficacy. The maximum possible luminous efficacy of a light source thus equals683 lm/W, while much lower values should be expected when the emission includes blue andred optical bands.
The luminous power spectrum, that is, the wavelength dependence of the luminous powerper unit wavelength, Fλ(λ) (lm/nm), is obtained by multiplying the radiant power spectrumby 683 (lm/W) and then by the standard luminosity function.
• Calculate the luminous power spectra of the LEDs.
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LEDs as Lighting Sources
The total luminous power F from a light source is obtained by integrating its luminous powerspectrum,
F (lm) =
∫ ∞
0Fλ(λ)dλ. (3)
• What is the total luminous power from the LEDs?
Note that the luminous efficacy is in the range 10-20 lm/W for incandescent lamps and 30-110 lm/W for fluorescent lamps.4
The report
Remember to label and provide captions for all graphs. The figure captions should include allrelevant experimental settings. Try to draw conclusions from the experimental observationsand relate your findings, if possible, to the literature. The report should be handed in at thelatest one week after the experiment is finished.
References[1] D. C. Agrawal, H. S. Leff, and V. J. Menon, Efficiency and efficacy of incandescent lamps, Am. J. Phys. 64, 649-654
(1996).
[2] CIE Proceedings (1964) Vienna Session, 1963, Vol. B, pp. 209-220 (Committee Report E-1.4.1), Bureau Central de laCIE, Paris
[3] Bureau International des Poids et Mesures, The International System of Units (SI), 8th edition, STEDI MEDIA, 2006,ISBN 92-822-2213-6.
[4] S. K. Mayer, Bringing science policy into the optics classroom: Solid state lighting and United States lighting standards,Am. J. Phys. 78, 1258-1264 (2010).
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