PHYSICS THROUGH TEACHING LABORATORY VII Efficiency of a Light Emitting Diode RAJESH B. KHAPARDE AND SMITHA PUTHIYADAN Homi Bhabha Centre for Science Education Tata Institute of Fundamental Research V. N. Purav Marg, Mankhurd, Mumbai 400088, India (e.mail: rajesh@hbcse.tifr.res.in) ABSTRACT Light emitting diode (LED) is a semiconductor device used in a variety of applications, instruments and circuits. When current is passed through a forward biased LED, it emits light in visible, infrared or ultraviolet region. In this article, an experiment on the external efficiency of a bright red LED is presented. We study the variation of efficiency of a LED with the current passing through it and find the value of current at which the efficiency is maximum. We then determine the total radiant power emitted by the LED and calculate its maximum external efficiency. Introduction In this experiment 1, we use two different types of semiconductor devices namely a light emitting diode (LED) and a photodiode (PD). A LED emits incoherent light when electrical energy is supplied to it through the process of injection electroluminescence. Thus a LED converts electrical energy into light energy. The conversion efficiency of a LED is the ratio of output radiant power to the input electrical power. The LED chip is surrounded by a resin or epoxy encapsulation (Figure 1). The dome lens and the small V shaped reflector dish (on which the chip is mounted) focus the emitted light through the top of the LED to emerge in a cone. Physics Education January March 2007 291
It is interesting to note that a LED can also be used as a photo-detector. When light is incident on a LED, it develops a current proportional to the intensity of light. (However, in this experiment; we shall limit our study to LED as a source of light.) Theory Light Emitting Diode (LED) In a LED, a part of the electrical energy supplied to it is used to excite electrons to higher energy levels. When such an excited electron in a higher energy level recombines and falls back to a lower energy level, a photon with energy E ph is emitted. 2 hc Eph = hν= λ (1) where h is the Planck s constant, ν ( = c/λ) is the frequency of the light emitted, c is the speed of light in vacuum and λ is the wavelength of the light emitted by the LED. The wavelength of the light depends on the band gap energy of the semiconductor material used for the LED. Photodiode A Photodiode (PD) converts light energy into electrical energy and hence can be used to measure the intensity of light. A photodiode is sensitive to the incident light for a certain range of wavelength. The current developed in the photodiode is linearly proportional to the intensity of light, up to a certain limit. When light falls on the sensitive area of a semiconductor photodiode, some of the incident photons free some of the electrons within the semiconductor material. The ratio of the number of free electrons generated per second (N e ) to the number of incident photons per second (N p ) is termed as the quantum yield or efficiency of the PD and is denoted as q p. q p = N e / N p (2) Expression for Efficiency Let us select a photodiode (PD) with a square shaped (with each side a) sensitive area. A LED emits light in a cone with cylindrical symmetry as shown in the Figure 2. The intersection of the cone (in which the LED emits light) and a plane perpendicular to the axis of the cone is a circular disc. We can divide this circular disc into number of circular strips of small width equal to the side a of the square shaped sensitive area of the PD. The area of each such circular strip which is at a distance r i from the axis of the cone is given by (2π r i a +π a 2 ). Suppose the PD is placed at a distance r i from the axis of the cone which is the axis of symmetry. The current I(r i ) in the PD (i.e. I PD ) kept at a distance r i from the axis of the cone is given by I (r i ) = N e e = N p q p e (3) where e is the charge of an electron. Let the radiant power received by the PD be φ (r i ). Since N p is the number of photons (of energy hν) received per unit time by the PD, φ (r i ) is given by φ (r i ) = N p. hν (4) Using Eq. (3) to eliminate N p from Eq. (4), we get φ(r i ) = I( r i ) h ν qe p (5) Now the radiant power received over a strip of radius r i and width a is 2 φ( ri)(2 π ra i +πa ) φ strip = 2 a 292 Physics Education January March 2007
2π = φ ( ri) ri +πφ ( ri) a Summing over all the strips gives the total radiant power φ T 2π φ T = φ ( ri) ri +π φ( ri) i Substituting for φ (r i ), from Eq.(5) and for hν from Eq.(1), we get hc 2π φ T = I( ri) ri +π I( ri) qe p λ a (6) Figure 1. Photograph of a LED Figure 2. Schematic of the LED emitting light in a cone. This expression links the current in the photodiode I(r i ) kept at a distance r i from the axis of the cone to the total radiated power φ T emitted by the LED. (Implicit in the above derivation is the assumption that the current I(r i ) is linearly proportional to the intensity of light falling on it.) The efficiency η is given by φt η= (7) P LED where, φ T is the total power radiated by the LED and P LED is the electrical power (I LED.V LED ) supplied to it. Physics Education January March 2007 293
The efficiency η of a LED is a function of the current passing through it. For each LED there is a particular value of I LED for which its efficiency is maximum. Also note that, the efficiency will reduce as the operating temperature is increased. Note: There is an important difference between the internal efficiency of a LED and its external efficiency. This is due to the difficulty for light to escape from high refractive index semiconductors (e.g. refractive index of GaAs is 3.54). The escape cone for the light in a semiconductor of refractive index (n) = 3.5 is only about 16 as imposed by Snell s law. This narrow escape cone covers a solid angle of (1/4n 2 )4π sr. Thus only a small part (about 2%) of the internally generated light can escape and come out of the LED, the rest of the light suffer total reflection and gets reabsorbed. Figure 3. Photograph of the acrylic mount board with LED (left) and PD (right) boxes. Apparatus One acrylic mount board, one light emitting diode (LED) fixed to a plastic box, one photodiode (PD) fixed to a plastic box, three digital multimeters with cords, one DC power supply (15 V, 1 A) with connectors, one potentiometer ( 1 KΩ), one fixed value resistor ( 150 Ω), two measuring scales, one magnifying torch, six connecting cords. Description of Apparatus 1) An acrylic mount board: This is a large rectangular acrylic board with slots made in X and Y directions in which two plastic boxes can be mounted and moved (Figure 3). The LED and the PD are fixed on separate boxes such that when they are mounted in the slot, the center of PD lies on the axis of the LED. The LED box (left one) can be moved horizontally in X direction. The PD box (right one) can be moved horizontally in X and Y direction. One can use the scales fixed on the acrylic mount board to measure the distance between the LED and the PD. One can adjust the position of the LED box and the PD box with the aid of the small pins (pointers) fixed to these boxes using the magnifying torch. 294 Physics Education January March 2007
2) Digital multimeter: Digital multimeters are used for the measurement of DC voltage and current. Three input sockets marked COM, V/Ω, and A are used for the connections. The value of the measured quantity is displayed on the LCD screen. The central rotary switch is used to choose the measurement function and range. The power switch is used to put ON or OFF the multimeter. 3) DC power supply: This instrument is to be used for supplying necessary DC power to the LED. One may vary the power by using the V Coarse, V Fine, I Coarse and I Fine knobs. Warnings 1) While measuring voltage or current, wait till the digital multimeter displays a steady reading. If the last digit of the display flickers between two consecutive numbers, choose either the lower or the upper value consistently throughout the experiment. 2) A multimeter when used as an ammeter should always be connected in series with the load/resistance and a multimeter when used as a voltmeter should always be connected in parallel with the load/resistance. 3) While measuring the intensity of light emitted by the LED using a photodiode, to incorporate the correction due to ambient light, measure the current in the photodiode with the LED ON and LED OFF and record the corrected value of the photodiode current. Useful constants and data Planck s constant, h = 6.63 10 34 J.s The charge of an electron, e = 1.60 10 19 C The speed of light in vacuum, c = 3.00 10 8 m.s 1 For the LED Color of light emitted = red The peak wavelength of the light emitted λ = 635 10 9 m Spectral line width = 30 10 9 m Size if the circular LED = diameter h = 0.01 m 0.014 m For the Photodiode Quantum efficiency/yield q p = 0.80 (at 550 nm) Detection surface of the PD = h w = 0.002 m 0.002 m Spectral range of sensitivity = 350 820 10 9 m Procedural Instructions Part I: Linearity of the photodiode Design and carry out the necessary experiment to show that the current developed in the photodiode is linearly proportional to the intensity of the light falling on its sensitive area. Use three separate digital multimeters for the measurement of I LED, V LED and I PD. Advice: A LED can be treated as a point source of light. We know that the intensity of light originating from a point source varies inversely as square of the distance (inverse square law). Thus changing the distance between the LED and the PD will change the intensity. This can be used to study the linearity of the PD. Plot an appropriate graph to obtain a straight line. Part II: Variation of efficiency of the LED: Design and carry out the necessary experiment to study the variation of the efficiency with the current passing through it. Keep the distance between the LED and the PD constant and vary the current I LED. For each value of I LED record V LED and I PD. Plot an appropriate graph to obtain the value of I LED, at which efficiency is maximum. Physics Education January March 2007 295
Advice: The efficiency of LED is a ratio of the radiant power φ T to the electrical power P LED. The current I PD is proportional to φ T. Plot a graph of [I PD. (P LED ) 1 ] versus I LED. Part III: Maximum efficiency: Design and carry out the necessary experiment to determine the total radiant power emitted by the LED and calculate its maximum efficiency. Advice: Adjust I LED to a value at which the efficiency of LED is maximum. Choose an appropriate distance between the PD and LED and record the current in the photodiode by scanning the part of the circular cross section perpendicular to the axis of the cone in the steps of 2 mm (i.e. a). In this part, the ambient light will add significantly to the light from the LED and hence it is necessary to incorporate the correction due to the ambient light. Figure 4. Graph of (I PD ) ½ versus d which shows the linearity of the PD. Typical results Part I: V LED = 1.830 V, I LED = 20.06. 10 3 A, (Distance d between the LED and the PD is varied from 0.03 m to 0.21 m and I PD is recorded). Part II d = 0.01 m, (I LED is varied from 1.05. 10-3 A to 25.08. 10-3 A and V LED and I PD are recorded.) Part III d = 0.15 m, V LED = 1.744 V, I LED = 7.53. 10-3 A, (The position of the LED is kept fixed and the photodiode is moved in Y direction in steps of 0.002 m and I PD is recorded.) Results From Figure 4, it can be observed that for a range of intensity and wavelength of light used in this experiment, the current I PD developed in the photodiode is found to be linearly propor- 296 Physics Education January March 2007
Figure 5. Graph of [I PD. (P LED ) -1 ] versus I LED which shows an asymmetric maxima. Figure 6. Graph of I PD versus r i which shows the variation of intensity along the Y axis. Physics Education January March 2007 297
tional to the intensity of light falling on it. Please note that the straight line does not pass through the origin. This is because the LED chip is encapsulated and is at a distance from the top of the dome lens which is used as a reference for the distance measurements. From Figure 5, it can be observed that the efficiency of the LED is maximum for I LED = 7.53. 10-3 A. On performing the necessary calculations the value of the maximum external efficiency η of the given LED is found to be 0.0459 (i.e. 4.59 %). It is interesting to note the intensity distribution (Figure 6) in the cone along the Y axis. Acknowledgements The authors are thankful to Profs. H. C. Pradhan, D. A. Desai and V. A. Singh for their help and suggestions. This work was supported by the National Initiative on Undergraduate Science (NIUS) programme undertaken by the Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai, India. References 1. C. Manilerd, International Physics Olympiads: Problems and Solutions from 1967 1995, (Rangsit University Press, Bangkok, 1996), p. 343. 2. S. M. Sze, Physics of Semiconductor Devices, 2 nd ed. (Wiley Eastern Limited, New Delhi, India, 1981), p. 689. 298 Physics Education January March 2007