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PHYSICS THROUGH TEACHING LABORATORY – VII

Efficiency of a Emitting

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 device used in a variety of applications, instruments and circuits. When current is passed through a forward biased LED, it emits light in visible, or 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 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 in a higher energy level recombines square shaped sensitive area of the PD. and falls back to a lower energy level, a 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 of the light emitted by the LED. by The wavelength of the light depends on the I (r ) = N e = N q e (3) 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 (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.

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⎛⎞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.

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The efficiency η of a LED is a function of (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 (≈ 1 KΩ), one fixed value one) can be moved horizontally in X and Y (≈ 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

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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 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. /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. Use three separate digital multimeters for should always be connected in series with the measurement of ILED, VLED and IPD. the load/resistance and a multimeter when Advice: A LED can be treated as a point used as a voltmeter should always be source of light. We know that the intensity of connected in parallel with the light originating from a point source varies load/resistance. inversely as square of the distance (inverse 3) While measuring the intensity of light square law). Thus changing the distance emitted by the LED using a photodiode, between the LED and the PD will change the to incorporate the correction due to intensity. This can be used to study the ambient light, measure the current in the linearity of the PD. Plot an appropriate graph to photodiode with the LED ON and LED obtain a straight line. OFF and record the corrected value of the photodiode current. Part II: Variation of efficiency of the LED: Useful constants and data Design and carry out the necessary experiment Planck’s constant, h = 6.63 × 10−34 J.s to study the variation of the efficiency with the The charge of an electron, e = 1.60 × current passing through it. Keep the distance between the LED and the PD constant and vary 10−19 C the current ILED. For each value of ILED record The speed of light in vacuum, c = 3.00 VLED and IPD. Plot an appropriate graph to 8 −1 × 10 m.s obtain the value of ILED, at which efficiency is maximum. For the LED

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Advice: The efficiency of LED is a ratio of the Advice: Adjust ILED to a value at which the radiant power φT to the electrical power PLED. efficiency of LED is maximum. Choose an The current IPD is proportional to φT. Plot a appropriate distance between the PD and LED −1 graph of [IPD . (PLED) ] versus ILED. and record the current in the photodiode by scanning the part of the circular cross section Part III: Maximum efficiency: perpendicular to the axis of the cone in the Design and carry out the necessary experiment steps of 2 mm (i.e. a). In this part, the ambient to determine the total radiant power emitted by light will add significantly to the light from the the LED and calculate its maximum efficiency. LED and hence it is necessary to incorporate the correction due to the ambient light.

½ Figure 4. Graph of (IPD) versus d which shows the linearity of the PD.

Typical results Part III

Part I: d = 0.15 m, VLED = 1.744 V, −3 -3 VLED = 1.830 V, ILED = 20.06 . 10 A, ILED = 7.53 . 10 A, (Distance d between the LED and the PD is (The position of the LED is kept fixed and the varied from 0.03 m to 0.21 m and IPD is photodiode is moved in Y direction in steps of recorded). 0.002 m and IPD is recorded.)

Part II Results d = 0.01 m, From Figure 4, it can be observed that for a (I is varied from 1.05 . 10-3 A to 25.08 . 10-3 LED range of intensity and wavelength of light used A and VLED and IPD are recorded.) in this experiment, the current IPD developed in the photodiode is found to be linearly propor-

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-1 Figure 5. Graph of [IPD . (PLED) ] versus ILED which shows an asymmetric maxima.

Figure 6. Graph of IPD versus ri which shows the variation of intensity along the Y axis.

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tional to the intensity of light falling on it. Acknowledgements Please note that the straight line does not pass through the origin. This is because the LED The authors are thankful to Profs. H. C. chip is encapsulated and is at a distance from Pradhan, D. A. Desai and V. A. Singh for their the top of the dome lens which is used as a help and suggestions. This work was supported reference for the distance measurements. by the National Initiative on Undergraduate From Figure 5, it can be observed that the Science (NIUS) programme undertaken by the efficiency of the LED is maximum for Homi Bhabha Centre for Science Education, -3 ILED = 7.53 . 10 A. On performing the Tata Institute of Fundamental Research, necessary calculations the value of the Mumbai, India. 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.

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, 2nd ed. (Wiley Eastern Limited, New Delhi, India, 1981), p. 689.

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