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Efficiency of a Light Emitting Diode 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: [email protected]) 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 The conversion efficiency of a LED is the ratio of output radiant power to the input electrical In this experiment1, we use two different types power. of semiconductor devices namely a light The LED chip is surrounded by a resin or emitting diode (LED) and a photodiode (PD). epoxy encapsulation (Figure 1). The dome lens A LED emits incoherent light when electrical and the small V shaped reflector dish (on energy is supplied to it through the process of which the chip is mounted) focus the emitted injection electroluminescence. Thus a LED light through the top of the LED to emerge in a converts electrical energy into light energy. cone. Physics Education • January − March 2007 291 It is interesting to note that a LED can also qp = Ne / Np (2) be used as a photo-detector. When light is incident on a LED, it develops a current proportional to the intensity of light. (However, Expression for Efficiency in this experiment; we shall limit our study to LED as a source of light.) 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 Theory symmetry as shown in the Figure 2. Light Emitting Diode (LED) The intersection of the cone (in which the LED emits light) and a plane perpendicular to In a LED, a part of the electrical energy the axis of the cone is a circular disc. We can supplied to it is used to excite electrons to divide this circular disc into number of circular higher energy levels. When such an excited strips of small width equal to the side a of the electron in a higher energy level recombines square shaped sensitive area of the PD. and falls back to a lower energy level, a photon 2 The area of each such circular strip which with energy Eph is emitted. is at a distance ri from the axis of the cone is 2 ⎡⎤hc given by (2π ri a +π a ). Ehph =ν= (1) Suppose the PD is placed at a distance r ⎣⎦⎢⎥λ i from the axis of the cone which is the axis of where h is the Planck’s constant, ν ( = c/λ) is symmetry. the frequency of the light emitted, c is the The current I(ri) in the PD (i.e. IPD) kept at speed of light in vacuum and λ is the a distance ri from the axis of the cone is given wavelength of the light emitted by the LED. by The wavelength of the light depends on the I (r ) = N e = N q e (3) band gap energy of the semiconductor material i e p p used for the LED. where e is the charge of an electron. Let the radiant power received by the PD be φ (ri). Since Np is the number of photons (of Photodiode energy hν) received per unit time by the PD, φ A Photodiode (PD) converts light energy into (ri) is given by electrical energy and hence can be used to φ (r ) = N . hν (4) measure the intensity of light. A photodiode is i p sensitive to the incident light for a certain Using Eq. (3) to eliminate Np from Eq. (4), we range of wavelength. The current developed in get the photodiode is linearly proportional to the intensity of light, up to a certain limit. When ⎡ Ir()⎤ φ(r ) = i hν (5) light falls on the sensitive area of a i ⎢ ⎥ ⎣⎢ qep ⎦⎥ semiconductor photodiode, some of the incident photons free some of the electrons Now the radiant power received over a strip within the semiconductor material. The ratio of of radius ri and width a is the number of free electrons generated per 2 second (Ne) to the number of incident photons φπ+π()(2rraaii ) φstrip = 2 per second (Np) is termed as the quantum yield a or efficiency of the PD and is denoted as qp. 292 Physics Education • January − March 2007 ⎛⎞2π Substituting for φ (ri), from Eq.(5) and for hν = ⎜⎟φ+πφ()rrii () r i ⎝⎠a from Eq.(1), we get Summing over all the strips gives the total ⎛⎞hc ⎛⎞2π φ=⎜⎟ I()rr +π Ir () (6) radiant power φ Tiii⎜⎟⎜⎟∑∑ T ⎝⎠qep λ ⎝⎠ a 2π ⎛⎞ φ=Tiii⎜⎟∑∑ φ()rr +π φ () r ⎝⎠i Figure 1. Photograph of a LED Figure 2. Schematic of the LED emitting light in a cone. This expression links the current in the The efficiency η is given by photodiode I(ri) kept at a distance ri from the φ η= T (7) axis of the cone to the total radiated power φT P emitted by the LED. (Implicit in the above LED derivation is the assumption that the current where, φT is the total power radiated by the I(ri) is linearly proportional to the intensity of LED and PLED is the electrical power (ILED light falling on it.) .VLED) supplied to it. Physics Education • January − March 2007 293 The efficiency η of a LED is a function of semiconductors (e.g. refractive index of GaAs the current passing through it. For each LED is 3.54). The escape cone for the light in a there is a particular value of ILED for which its semiconductor of refractive index (n) = 3.5 is efficiency is maximum. Also note that, the only about 16° as imposed by Snell’s law. This efficiency will reduce as the operating narrow escape cone covers a solid angle of temperature is increased. (1/4n2)4π sr. Thus only a small part (about 2%) of the internally generated light can escape Note: There is an important difference between and come out of the LED, the rest of the light the internal efficiency of a LED and its suffer total reflection and gets reabsorbed. external efficiency. This is due to the difficulty for light to escape from high refractive index Figure 3. Photograph of the acrylic mount board with LED (left) and PD (right) boxes. Apparatus and Y directions in which two plastic boxes can be mounted and moved (Figure 3). The One acrylic mount board, one light emitting LED and the PD are fixed on separate boxes diode (LED) fixed to a plastic box, one such that when they are mounted in the slot, photodiode (PD) fixed to a plastic box, three the center of PD lies on the axis of the LED. digital multimeters with cords, one DC power The LED box (left one) can be moved supply (15 V, 1 A) with connectors, one horizontally in X direction. The PD box (right potentiometer (≈ 1 KΩ), one fixed value one) can be moved horizontally in X and Y resistor (≈ 150 Ω), two measuring scales, one direction. One can use the scales fixed on the magnifying torch, six connecting cords. 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 Description of Apparatus with the aid of the small pins (pointers) fixed to 1) An acrylic mount board: This is a large these boxes using the magnifying torch. rectangular acrylic board with slots made in X 294 Physics Education • January − March 2007 2) Digital multimeter: Digital multimeters are Color of light emitted = red used for the measurement of DC voltage and The peak wavelength of the light current. Three input sockets marked COM, emitted λ = 635 × 10−9 m V/Ω, and A are used for the connections. The Spectral line width = 30 × 10−9 m value of the measured quantity is displayed on Size if the circular LED = diameter × the LCD screen. The central rotary switch is h = 0.01 m × 0.014 m used to choose the measurement function and range. The power switch is used to put ON or For the Photodiode OFF the multimeter. Quantum efficiency/yield qp = 0.80 (at 550 nm) 3) DC power supply: This instrument is to be Detection surface of the PD = h × w = used for supplying necessary DC power to the 0.002 m × 0.002 m LED. One may vary the power by using the V Spectral range of sensitivity = 350 − Coarse, V Fine, I Coarse and I Fine knobs. 820 × 10−9 m Warnings Procedural Instructions 1) While measuring voltage or current, wait Part I: Linearity of the photodiode till the digital multimeter displays a steady reading. If the last digit of the display Design and carry out the necessary experiment flickers between two consecutive numbers, to show that the current developed in the choose either the lower or the upper value photodiode is linearly proportional to the consistently throughout the experiment. intensity of the light falling on its sensitive 2) A multimeter when used as an ammeter area.
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