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 experiment1, 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.
Physics Education • January − March 2007
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.
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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 Eph is emitted.2
⎡ hc ⎤
E ph = 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 (Ne) to the number of incident photons
per second (Np) is termed as the quantum yield
or efficiency of the PD and is denoted as qp.
292
qp = Ne / Np
(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 ri from the axis of the cone is
given by (2π ri a +π a2).
Suppose the PD is placed at a distance ri
from the axis of the cone which is the axis of
symmetry.
The current I(ri) in the PD (i.e. IPD) kept at
a distance ri from the axis of the cone is given
by
I (ri) = Ne e = Np qp e
(3)
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
energy hν) received per unit time by the PD, φ
(ri) is given by
φ (ri) = Np . hν
(4)
Using Eq. (3) to eliminate Np from Eq. (4), we
get
⎡ I ( ri ) ⎤
⎥ hν
⎢⎣ q p e ⎥⎦
φ(ri) = ⎢
(5)
Now the radiant power received over a strip
of radius ri and width a is
φstrip =
2
φ( ri )(2πra
i + πa )
2
a
Physics Education • January − March 2007
⎛ 2π ⎞
= ⎜ ⎟ φ( ri ) ri + πφ( ri )
⎝ a ⎠
Summing over all the strips gives the total
radiant power φT
Substituting for φ (ri), from Eq.(5) and for hν
from Eq.(1), we get
⎛ hc ⎞ ⎛ 2π
⎞
I ( r ) r + π∑ I ( ri ) ⎟ (6)
φT = ⎜
⎜ q eλ ⎟⎟ ⎝⎜ a ∑ i i
⎠
⎝ p ⎠
⎛ 2π ⎞
φT = ⎜ ⎟ ∑ φ( ri ) ri + π∑ φ( ri )
⎝ 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
photodiode I(ri) kept at a distance ri from the
axis of the cone to the total radiated power φT
emitted by the LED. (Implicit in the above
derivation is the assumption that the current
I(ri) is linearly proportional to the intensity of
light falling on it.)
Physics Education • January − March 2007
The efficiency η is given by
φ
η= T
PLED
(7)
where, φT is the total power radiated by the
LED and PLED is the electrical power (ILED
.VLED) supplied to it.
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The efficiency η of a LED is a function of
the current passing through it. For each LED
there is a particular value of ILED 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
(1/4n2)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
294
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.
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
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 qp = 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
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
−34
Planck’s constant, h = 6.63 × 10 J.s
The charge of an electron, e = 1.60 ×
−
10 19 C
The speed of light in vacuum, c = 3.00
−
× 108 m.s 1
For the LED
Physics Education • January − March 2007
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 ILED, VLED and IPD.
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 ILED. For each value of ILED record
VLED and IPD. Plot an appropriate graph to
obtain the value of ILED, at which efficiency is
maximum.
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Advice: The efficiency of LED is a ratio of the
radiant power φT to the electrical power PLED.
The current IPD is proportional to φT. Plot a
graph of [IPD . (PLED) −1] versus ILED.
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 ILED 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 (IPD) ½ versus d which shows the linearity of the PD.
Typical results
Part III
Part I:
VLED = 1.830 V, ILED = 20.06 . 10−3 A,
(Distance d between the LED and the PD is
varied from 0.03 m to 0.21 m and IPD is
recorded).
d = 0.15 m, VLED = 1.744 V,
ILED = 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 IPD is recorded.)
Part II
d = 0.01 m,
(ILED is varied from 1.05 . 10-3 A to 25.08 . 10-3
A and VLED and IPD are recorded.)
296
Results
From Figure 4, it can be observed that for a
range of intensity and wavelength of light used
in this experiment, the current IPD developed in
the photodiode is found to be linearly proporPhysics Education • January − March 2007
Figure 5. Graph of [IPD . (PLED) -1] versus ILED which shows an asymmetric maxima.
Figure 6. Graph of IPD versus ri 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
ILED = 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.
2.
298
C. Manilerd, International Physics Olympiads:
Problems and Solutions from 1967–1995,
(Rangsit University Press, Bangkok, 1996), p.
343.
S. M. Sze, Physics of Semiconductor Devices,
2nd ed. (Wiley Eastern Limited, New Delhi,
India, 1981), p. 689.
Physics Education • January − March 2007