Experiments with -emitting Yaakov Kraftmakhera) Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel (Received 15 February 2011; accepted 16 May 2011) The radiant and luminous power spectra, efficiency, and luminous efficacy of commercially available light-emitting diodes (LEDs) are measured. The output radiant power is determined with a from its typical spectral response. A calculation of the radiant power spectra and the luminous power spectra is demonstrated. The response of the LEDs is determined in the range 10–107 Hz. For the white LED, the frequency response of the primary blue emission and the green-yellow phosphorescence is measured separately, and the phosphorescence time constant is estimated. The ratio h/e is estimated using the emission and the “turn- on” voltages. VC 2011 American Association of Physics Teachers. [DOI: 10.1119/1.3599072]

I. INTRODUCTION II. THE SETUP A light-emitting (LED) is a device Three color LEDs and one white LED from HuiYuan Opto- with a p-n junction that emits when electric cur- Electronic20 were used in the experiments: LB-P200R1C-H3 rent passes through it.1–3 The semiconductor crystal is (red), LB-P200Y1C-H3 (yellow), LB-P200B2C-H3 (blue), doped to fabricate an n-type region and a p-type region, and LB-P20WC3-60 (white). The input current of the LEDs one above the other. Forward electrical bias across the indicated by the supplier is 0.75 A. In the experiments we will LED causes the holes and to be injected from discuss, the maximum input current is 0.1 A, and the input opposite sides of the p-n junction into the active area, power does not exceed 0.3 W. where their recombination results in emission of photons. Two types of white LEDs are available. One type com- The of the emitted photons is approximately the bines two or three LEDs of appropriate colors. With such a band-gap energy of the semiconductor. The band-gap device, a spectrum similar to that of daylight is achievable. energy of ternary and quaternary semiconductor com- Modifications of the light from “warm white” to “cool pounds can be adjusted in a certain range by varying their daylight” are possible by varying the contributions of the composition. components. In the other type a suitable is posi- The first LEDs were homojunction diodes in which the tioned onto a blue LED, so that the output light contains blue material of the core layer and that of the surrounding clad light and a Stokes-shifted phosphorescence band. The white layers are identical. Then heterostructures with layers having LED we used is of the second type. a varying band-gap and refractive index were recognized as An important characteristic of a source is the advantageous. Contemporary LEDs are more complicated color (see, for example, Ref. 21). The color tem- double heterostructure diodes. perature does not mean that the spectrum of a light source is LEDs are efficient light sources for many applications, similar to that of a blackbody of equal temperature. Fluores- including indicators, large-area displays, and opto-couplers. cent lamps and LEDs are designed to emit only visible light. Holonyak4 pointed out that the LED is an ultimate light Therefore, their spectra differ radically from those of thermal source. Mayer5 has considered the current status and pro- sources governed by Planck’s distribution, which unavoid- spective of -state lighting, where the LED is an excel- ably include intensive emission. The spectrum of a lent alternative to incandescent and fluorescent light bulbs. lighting source can be characterized by the blue-to-red ratio, LEDs are easily modulated sources and are widely used in which can be made to be equal to that of a blackbody at a optical with optical fibers.6 The possibility given temperature. This ratio determines the color tempera- to modulate LEDs in a broad frequency band is crucial for ture of the source. The green band in the spectrum is needed simultaneously transmitting many or audio pro- for attaining high luminous efficacy of lighting sources (see grams through a single optical fiber. To correctly reproduce the following). For the white LED we used, the supplier the programs, the characteristic should claims that the is in the range 6000–7000 be linear. K. This value is typical for “cool daylight” lamps. For “warm LEDs can be used to demonstrate their basic properties7–15 white” lamps, the color temperature is in the range 2700– and as auxiliary tools for many experiments and demonstra- 3300 K. tions.16–19 The experiments described in the following can be The input and power, radiant output considered as an addition to those published earlier.7–15 Im- power, and efficiency of the LEDs can be measured or calcu- portant topics are the determination of the output radiant lated, and then displayed versus the voltage applied to the power, the radiant and luminous power spectra, and the lumi- device or versus the current passing through it. With a data- nous efficacy of LEDs. For a white LED, the frequency acquisition system, the are possible in a short response of the primary blue emission and of the green-yellow time. We use the ScienceWorkshop data-acquisition system phosphorescence is measured separately. The value of h/e is with DataStudio software from PASCO.22 The LED of inter- calculated from the emission wavelengths and the “turn-on” est is connected in series with a 10 X limiting to the voltages. generator in the ScienceWorkshop 750 Interface. The

825 Am. J. Phys. 79 (8), August 2011 http://aapt.org/ajp VC 2011 American Association of Physics Teachers 825 Fig. 1. General scheme of the experiments: (a) output radiant power and ef- ficiency; (b) emission spectra; and (c) frequency response. PD represents Fig. 2. (Color online) Input current and power consumed by the LEDs ver- photodiode. sus the applied voltage. Red (R), yellow (Y), blue (B), and white (W). The turn-on voltage increases with the energy of the emitted photons. Output voltage is the Positive ramp up voltage linearly increasing from zero to a maximum value set to achieve the maximum desired current through the LED. The period of spectral response of the photodiode taken from such a graph the Output voltage is 20 s. The Signal generator operates in can be represented as Auto mode: it starts to generate the Output voltage after start- R k I=P A=W 1:2 103 k 300 ; (1) ing a run. The option Automatic stop is used for automati- ð Þ¼ ð Þ¼ ð Þ cally ending each run. where k is the in nanometers. With minor modi- The output radiant power of the LEDs is determined with fications, Eq. (1) holds for all silicon . This a silicon photodiode by using its typical spectral response. approach is not as precise as a with a The radiant power spectra are obtained with a diffraction based on the thermal action of absorbed light. However, it is grating and converted to the luminous power spectra by much simpler and satisfactory for our purposes. using the standard luminosity function. The frequency DataStudio displays the output characteristics of an LED response of a LED is determined by sine-wave modulation versus the input current (Fig. 3). The output radiant power is of the feeding current. Setups used in the experiments are nearly proportional to the input current, and thus the rapid schematically shown in Fig. 1. increase of the input current or power indicates the threshold of the LED emission. III. MEASUREMENTS AND RESULTS For the color LEDs, the wavelengths for Eq. (1) are taken A. Radiant Power and Efficiency to be at the peaks of the radiant power spectra (see the fol- lowing). For the white LED, the mean wavelength is taken The input current i of the LEDs is measured directly as the as 550 nm. This simplification introduces an additional Output current of the Signal generator. DataStudio calcu- uncertainty to our results. For 100 mA input currents, the lates the voltage applied to the LED as the Output voltage output radiant power of the LEDs ranges from 13 mW (yel- minus the Output current times the resistance of the limiting low) to 53 mW (white). The efficiency is the ratio of the out- resistor, 10 X. The input electric power is calculated from put radiant power to the input electric power. For the LEDs the input current and applied voltage. Immediately after a tested, the efficiency ranges from 0.065 (yellow) to 0.19 run, DataStudio displays the input current and power versus (white). For input currents in the range of 10–40 mA, the ef- the applied voltage (see Fig. 2). ficiency of the white LED is even higher and is 0.21. To determine the output radiant power of an LED, its light In an ideal LED every -hole recombination pro- is directed onto a silicon photodiode (United Tech- duces one output of energy nearly equal to the band- nology, PIN-10D) positioned adjacent to the LED. The sensi- gap energy. The external quantum efficiency of such an LED tive area of the photodiode is about 1 cm in diameter, so that thus equals unity. Similarly, an ideal photodiode produces the light from the LED is almost fully utilized. The Voltage one electron for every incident photon, and hence its external sensor acquires the voltage on a 100 X load resistor of the quantum efficiency also equals unity (see Ref. 4). For the photodiode. combination of an ideal LED and an ideal photodiode, the ra- The output radiant power (radiant flux) of an LED is cal- tio of the current produced by the photodiode to the input culated from the photoelectric current and the spectral current of the LED thus should be one. For real devices, this response of the photodiode R(k), that is, the wavelength de- current ratio shows how close the LED is to this ultimate pendence of the ratio of the photodiode current I to the inci- limit. The external quantum efficiency of LEDs is much dent radiant power P. Usually, the function R(k) is given by lower than their internal efficiency because of the difficulty manufacturers as a graph. In the range 400–800 nm, the of extracting light from the device. The current ratio for the

826 Am. J. Phys., Vol. 79, No. 8, August 2011 Yaakov Kraftmakher 826 Fig. 4. (Color online) (a) Measured radiant power spectra of the LEDs and (b) normalized spectra. The measured spectra are normalized to make the in- tegral of every spectrum equal to the total radiant power determined with the silicon photodiode.

Fig. 3. (Color online) Output characteristics of the LEDs versus input cur- rent: (a) output radiant power, (b) efficiency, and (c) current ratio, a measure and Automatic stop options, the measurement data are of the quantum efficiency of the LED–photodiode combination. The output acquired in the wavelength range from 350 to 750 nm. The radiant power is nearly proportional to the input current. spectra may be distorted because the efficiency of diffraction gratings depends on wavelength, and for the grating we used, LEDs that we tested ranges from 0.045 (yellow) to 0.16 this dependence is unknown. (white). Because the external quantum efficiency of a silicon The emission spectra corrected by the use of Eq. (1) are photodiode is sufficiently high (see, for example, Ref. 23), radiant power spectra (in arbitrary units). The spectra of the the low values of the current ratio are caused mainly by the color LEDs have one peak near the center of the emission low external quantum efficiency of the LEDs. band: 465 nm (blue), 585 nm (yellow), or 625 nm (red). The It is easy to find a relation between the external quantum full width of the spectra at half a maximum is nearly 30 nm efficiency of a LED, g1, and of a photodiode, g2, and the cur- (see Fig. 4). rent ratio of the LED–photodiode combination. We assume The radiant power spectrum of the white LED has a peak that the energy of photons emitted by the LED, h, equals in the blue band and a wide green-yellow phosphorescence the bang-gap energy, eVg (e is the electron charge), and that band with a maximum at 555 nm. To make the phosphores- the emission occurs when the voltage applied to the LED is cence evident, it is sufficient to illuminate the LED by blue Vg, and the current is i. The power consumed by the LED is light from outside. With the blue LED we used, the green- iVg, and the output radiant power is P ¼ g1nh ¼ g1iVg, yellow phosphorescence is clearly seen. This observation where n ¼ i/e is the number of electrons passing through the confirms that the LEDs can be used for observing phospho- LED per unit of time. The external quantum efficiency of the rescence spectra. For instance, when we focus the light from LED thus equals its electrical efficiency. The external quan- the blue LED on the screen of a -ray tube, the spec- tum efficiency of a photodiode is the ratio of the number of trum of the phosphorescence is observable by looking at the electrons N2 ¼ I/e produced per unit of time to the number of screen through a diffraction grating. The spectrum can be incident photons N1 ¼ P/h ¼ P/eVg. Therefore, g2 ¼ N2/N1 compared with the spectrum of the ¼ (I/P)Vg ¼ R(k)Vg. The current ratio I/i of the LED–photo- screen (see, for example, Ref. 24). diode combination thus equals g1g2. To calculate the true radiant power spectra of the LEDs, the radiant power spectrum of each LED (in arbitrary units) 25 B. Radiant Power Spectra is integrated over all wavelengths with Origin software. Then each spectrum is normalized to make the equal The emission spectra of the LEDs are determined with the to the output radiant power determined with the silicon pho- PASCO Educational spectrophotometer (OS-8537), two todiode. This operation provides the true radiant power spec- lenses, and a diffraction grating with 600 lines per milli- tra, that is, the wavelength dependency of the radiant power meter. The PASCO Light sensor (CI-6504A) and the Aper- per unit wavelength, Pk(k) (mW/nm). The next step is the ture bracket (OS-8534A) are also used. Initially, the sensor conversion of the radiant power spectra to luminous power is set at the zero diffraction angle. With the Delayed start spectra.

827 Am. J. Phys., Vol. 79, No. 8, August 2011 Yaakov Kraftmakher 827 C. Luminous Power Spectra The radiant power spectrum is an insufficient characteris- tic of a lighting source because the human eye is not equally sensitive to the light of different colors. The typical human eye spectral response is given by the standard luminosity function S(k) established by the International Commission on Illumination. For light-adapted vision, this function has a maximum at 555 nm and can be approximated by a simple equation proposed by Agrawal et al.26

SðkÞ¼expð88x2þ41x3Þ; (2) where x ¼ k/555 – 1, and k is the wavelength in nanometers. For our purpose, this approximation is satisfactory. However, one should use the original numerical data for precise calculations. The spectral response of the human eye is a crucial factor for providing effective and qualitative (similar to daylight) lighting. The two requirements are in obvious contradiction: qualitative lighting assumes the presence of blue and red bands, which is ineffective because of the nature of human vision. Initially, the base unit of , the can- dela (cd), was based on a “standard .” The present-day definition of this unit adopted in 1979 says: “The is Fig. 5. (Color online) (a) Standard luminosity function S(k) and (b) lumi- nous power spectra of the LEDs. The latter are equal to the radiant power the luminous intensity, in a given direction, of a source that spectra times S(k) and 683 (lm/W). emits monochromatic radiation of frequency 540 1012 Hz and that has a radiant intensity in that direction of 1/683 per .”27 The frequency 540 1012 Hz corresponds power of the LEDs and their tolerances. With mean values to k ¼ 555 nm, while the factor 1/683 was chosen to match of the supplier’s data, the efficacy should be 32 (red), 34 the original definition of the candela. The (lm) is (yellow), 11 (blue), and 67 lm/W (white). The agreement defined as 1 lm ¼ 1 cd sr. A light source of one candela pro- between the two sets of data confirms that our experiments vides a total luminous power (luminous flux) of 4p % 12.57 are free of significant errors. Note that the luminous efficacy is in the range 10–20 lm/W for incandescent lamps and 30– lm. By definition, one watt of electromagnetic radiation at 5 k ¼ 555 nm produces a luminous power of 683 lm. 110 lm/W for fluorescent lamps. The ratio of the total luminous power from a light source to the electric power consumed is called the luminous effi- E. The Frequency Response cacy. The maximum possible luminous efficacy of a light source thus equals 683 lm/W, while much lower values The frequency response of LEDs is very important for op- should be expected when the emission includes blue and red tical . Infrared light is commonly used with optical bands. optical fibers due to its less attenuation and dispersion. The The luminous power spectrum, that is, the wavelength de- signal encoding is typically simple intensity modulation. For pendence of the luminous power per unit wavelength, F (k) teaching purposes, modulated LEDs have been employed in k a simple telemetric system28 and for transmitting video sig- (lm/nm), is obtained by multiplying the radiant power spec- 29 trum by 683 (lm/W) and then by the standard luminosity nals through a light guide. The setup for measuring the frequency response of the function S(k). This conversion significantly changes the 29 spectra (see Fig. 5). The luminous power spectrum of LEDs is similar to that used earlier. A dc supply and a the white LED has only one maximum at 555 nm; however, , Hewlett-Packard 33120A, each with an X the blue emission is evidently pronounced. additional 100 resistor at the output, are connected in par- allel to the LED, and the limiting 10 X resistor is excluded. The output voltage of the dc supply is set to obtain a 100 mA current through the LED. With two lenses, the light from the D. LEDs as Lighting Sources LED is focused on the sensitive area of a fast photodiode The total luminous power F from a light source is obtained (United Detector , PIN-5D) operated with a 9 V by integrating its luminous power spectrum, . The signal on a 150 X load resistor of the photodiode ð is observed with an , Kenwood CS-4025. The ac 1 voltage applied to the LED is sufficiently small, and there- FðlmÞ¼ FkðkÞdk: (3) 0 fore the ac signal from the photodiode is nearly sinusoidal. The frequency response was determined in the range of 10– In our case, the integration is performed with Origin soft- 107 Hz. The characteristics are similar for all the LEDs ware. Among the LEDs tested, the white LED produces the tested. The frequency response is constant up to 103 Hz and maximum luminous power of nearly 15 lm. slightly decreases up to 106 Hz, and then rapidly falls. The luminous efficacy of the LEDs appears to be 33 (red), Because the LEDs have an internal resistance, , 33 (yellow), 12 (blue), and 55 lm/W(white). The supplier and even inductance,30 the actual voltage across the p-n junc- gives values of the applied voltage and the total luminous tion is unknown, and becomes frequency dependent at high

828 Am. J. Phys., Vol. 79, No. 8, August 2011 Yaakov Kraftmakher 828 Table I. Parameters of the LEDs for 100 mA input currents. The frequency

f0.5 corresponds to 50% response. The value of h/e ¼ VFk/c.

LED Red Yellow Blue White

k (nm) 625 585 465 460

VF (V) 1.8 1.85 2.6 2.6 Input power (mW) 185 200 290 280 Output radiant power (mW) 32 13 37 53 Efficiency 0.17 0.065 0.13 0.19 Luminous power (lm) 6.15 6.6 3.6 15.5 Luminous efficacy (lm/W) 33 33 12 55

f0.5 (MHz) 3 h/e (10–15 J s/C) 3.75 3.60 4.05 4.00

experiment. With LEDs of different color, results obtained in these experiments are close to the correct value, usually, to within 6 10%.31–33 This approach raises doubts34,35 because of the assumptions that are made. It was shown experimen- tally15 that the of photons emitted by four color LEDs were 7%–20% smaller than the band-gap energies, and the turn-on thresholds appeared to be significantly lower than the photon energies. Precise values of h/e cannot be expected from such measurements, but it is worthwhile to look for LEDs that yield results close to the true value. In any case, students should be familiarized with the problem. An additional decision is the appropriate wavelength to be used in the calculations. Usually, the wavelength relates to the peak in the radiant power spectrum. Because the spectral peaks are 30–50 nm wide, the uncertainty in the wavelength may be several percent. We used the relation Fig. 6. (Color online) (a) Frequency response of the white LED: ( ) pri- mary blue band, ( ) green-yellow phosphorescence band. (b) With an enlarged scale, the lag of the phosphorescence at high is clearly h=e ¼ VFk=c: (4) seen.

The VF values were found by linearly extrapolating to zero the plots of input current versus applied voltage shown in frequencies. The frequency response presented here relates Fig. 2, and the uncertainty is nearly 0.05 V. The wavelengths to the ac voltage at the output of the function generator. k were taken at the peaks in the radiant power spectra shown By measuring the frequency response it is possible to dis- in Fig. 4, and the uncertainty of these values is nearly 10 nm. tinguish the primary blue emission and the green-yellow For the white LED, the wavelength is taken at the peak in phosphorescence of the white LED. The two optical bands the blue part of the spectrum. However, the validity of were separated with color filters, and the frequency response Eq. (4) based on the turn-on voltage remains doubtful. For for each band was determined independently. The time con- the LEDs studied, the calculated h/e values appeared to be stant of the phosphor is very short, and thus the phosphores- lower than the true value with the blue and white LEDs pro- cence well follows the primary light modulation up to about 6 viding the best results. The properties of the LEDs and the 10 Hz. From the data obtained, only a rough estimation of calculated h/e values are given in Table I. the time constant of the phosphor is possible and was found to be of the order of 10–8 s (see Fig. 6). For frequencies up to 106 Hz, all the LEDs tested provide IV. CONCLUSION nearly 100% light modulation. Therefore, they can be employed for determining the time constant of , The experiments described here involve quantum mechan- for which their radiation is sufficient to activate the ics, , human vision, efficiency and efficacy, phosphorescence. optical communications, and provide good opportunities for experimentation. The experiments are accessible to under- graduate students and can be used as laboratory exercises F. Determination of h/e and demonstrations. Optical emission from LEDs appears when the applied voltage reaches a definite value VF, the forward “turn-on” ACKNOWLEDGMENT voltage. This threshold is assumed to be close to Vg. The energy of emitted photons is hc/k, where c is the speed of Many thanks to Eliezer Perel for providing me with the light, and h is Planck’s constant. By taking this energy equal LEDs for the measurements and to a referee for useful to eVF or eVg, it is possible to determine h/e by a simple suggestions.

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