Materials in Electrical EngineeringElektrik-Elektronik Mühendisliği. Electromagnetic Spectrum...

LED (Light Emitting Diodes)and

LASERS (Light Amplification by Stimulated Emission of Radiation)

Sources: Optoelectronics and Photonics, S. O. Kasap. Materials for Engineers, W. F. Hosford.

Materials in Electrical Engineering

Karadeniz Teknik ÜniversitesiElektrik-Elektronik Mühendisliği

Electromagnetic Spectrum

Visible Spectrum


Refractive Index and Snell’s Law

• The index of refraction, n, of a material is the ratio of the velocity of light in a vacuum, vo, to that in the material: vm:

• When light passes from one material into another, it is refracted. Snell’s law states that the angles to the surface normal, φ, are given by


Refractive Index


The reflectivity, R, or fraction of the light that is reflected is directly related to n:

As light passes through a material, a fraction of it is absorbed. The intensity, I,decreases with distance, x:

Reflection and Absorption

α : absorption coefficient(is a function of wavelength anddepends on the property of medium)

source: pveducation.org


Direct and Indirect Bandgap Semiconductors

• The states yk(x) in the lower E–k curve constitute the wavefunctions for the valence electrons and thus correspond to the states in the valence band.

• Those in the upper E–k curve, on the other hand, correspond to the states in the conduction band since they have higher energies.

• According to the E–k diagram in figure when an electron and hole recombine, the electron simply drops from the bottom of the CB to the top of the VB without any change in its k value so that this transition is quite acceptable in terms of momentum conservation. The E–k diagram in Figure therefore for a direct bandgap semiconductor.

• In direct bandgap, the minimum of the CB is directly above the maximum of the VB. • The electron transition from the bottom of the CB to the top of the VB emits a photon.

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs is therefore a direct bandgap semiconductor.

(b) In Si, the minimum of the CB is displaced from the maximum of the VB and Si is an indirect bandgap semiconductor.

(c) Recombination of an electron and a hole in Si involves a recombination center.

▪ The minimum of the CB is not directly above the maximum of the VB, but it is displaced on the k-axis. Such crystals are called indirect bandgap semiconductors.

Direct and Indirect Bandgap Semiconductors

▪ The recombination process in indirect bandgapsemiconductors occurs via a recombination center at an energy level Er within the bandgap. These recombination centers may be crystal defects or impurities.

▪ The electron is first captured by the defect at Er. The change in the energy and momentum of the electron by this capture process is transferred to lattice vibrations, called as phonons.

▪ In some indirect bandgap semiconductors such as GaP, however, the recombination of the electron with a hole at certain recombination centers results in photon emission. (by the purposeful addition of nitrogen (N) impurities to GaP)


Light Emitting Diodes: Homojunction LEDs

• A light-emitting diode is essentially a pn junction diode typically made from a direct bandgap semiconductor. (for example, GaAs, in which the electron–hole pair recombination results in the emission of a photon)

• The emitted photon energy is approximately equal to the bandgap energy, hv ≈ Eg.

(a) The energy band diagram of a pn+ (heavily n-type doped) junction without any bias. Built-in potential Vo prevents electrons from diffusing from n+ to p-side. (b) The applied bias potential V reduces Vo and thereby allows electrons to diffuse, be injected, into the p-side. Recombination around the junction and within the diffusion length of the electrons in the p-side leads to spontaneous photon emission. (c) Quasi-Fermi levels EFp and EFn for holes and electrons across a forward-biased pn-junction.

▪ When a forward bias V is applied, the voltage drops almost entirely across the depletion region. Consequently, the built-in potential Vo is reduced to Vo - V, which then allows the electrons from the n+ side to diffuse into the p-side.

▪ The recombination of injected electrons in the depletion region as well as in the neutral p-side results in the spontaneous emission of photons.

▪ This recombination zone is usually called as ‘the active region’.▪ Because of the statistical nature of the natural recombination process between

electrons and holes, the emitted photons are in random directions; such randomly emitted radiation is called spontaneous emission.

▪ The LED structure has to be designed in a way that the emitted photons can escape the device without being reabsorbed by the semiconductor material. This means the p-side has to be sufficiently narrow. (or heterostructure devicescan be used)

▪ The emitted photon flux can be increased by increasing the carrier concentration which can be achievable by using heterostructures.

Light Emitting Diodes: Homojunction LEDs


Light Emitting Diodes: Heterojunction LEDs

The homojunction LEDs suffer from a number of drawbacks and has a low efficiency:

▪ The p-region must be narrow to allow the photons to escape without much reabsorption.

▪ When the p-side is narrow, some of the injected electrons in the p-side reach the surface by diffusion and recombine through crystal defects near the surface. This radiationless recombination process decreases the light output.

▪ If the recombination occurs over a relatively large volume (or distance), due to long electron diffusion lengths, then the chances of reabsorption of emitted photons becomes higher; the amount of reabsorption increases with the material volume.


• LED constructions for increasing the intensity of the output light make use of the double heterostructure (DH) structure.

• In this example structure, the semiconductors are AlGaAs(AlxGa1-xAs) with Eg ≈ 2 eV and GaAs with Eg ≈ 1.4 eV. The double heterostructure in Figure (a) has an N+pheterojunction between N + -AlGaAs and p-GaAs. There is another heterojunctionbetween p-GaAs and P-AlGaAs.

• When a forward bias is applied, the majority of this voltage drops between the N+-AlGaAs and p-GaAs (i.e., across the depletion region) and reduces the potential energy barrier eVo, just as in the normal pn junction diode. This allows electrons in the CB of N+-AlGaAs to be injected (by diffusion) into p-GaAs as shown in Figure (c). These electrons, however, are confined to the CB of p-GaAs since there is a barrier ∆Ec between p-GaAs and P-AlGaAs.

• The wide bandgap AlGaAs layer therefore acts as a confining layer that restricts injected electrons to the p-GaAs layer.

• The recombination of injected electrons with the holes present in this p-GaAs layer results in spontaneous photon emission.

• Since the bandgap Eg of AlGaAs is greater than that of GaAs, the emitted photons do not get reabsorbed as they escape the active region and can reach the surface of the device.

Light Emitting Diodes: Heterojunction LEDs

A typical quantum well (QW) device has an ultra-thin, typically less than 50 nm, narrow bandgap semiconductor with a bandgap Eg1 sandwiched between twowider bandgap semiconductors with a bandgap Eg2. For example, this could be a thin GaAs (Eg1) layer sandwiched between two AlxGa1-xAs (Eg2) layers.

The wide bandgap layers are called confining layers.

Light Emitting Diodes: Quantum Well High Intensity LEDs


▪ A QW structure that shows the energy levels in the wells and how charge carriers that are brought in by the current fall into the lowest energy level in the well and then recombine, emitting a photon.

▪ The electrons at a particular energy level also have kinetic energies in the yz plane, which is not quantized. The electrons are therefore spread in energy above En as shown.

▪ The same notion also applies to holes in the ∆Ev well.

• The main problem with the single quantum well (SQW) heterostructure LEDs is that, under a sufficiently large current, the well can be flooded with charge carriers and can overflow. The advantages of the QW action would be lost.

• This problem can be resolved by using multiple quantum wells (MQWs), in which electrons are shared by a number of quantum wells. Not only is the overflow problem alleviated but more photon flux is generated due to more wells.

• Modern high intensity UV, violet, and blue LEDs use MQW heterostructures.

LED Materials and Structures

❑ There are various direct bandgap semiconductor materials that can be readily doped to make commercial p-n junction LEDs which emit radiation in the red and infrared range of wavelengths.

❑ The fabrication of an actual LED would require that the doped crystal layers with the required bandgap can be grown on a suitable substrate crystal.

❑ The substrate crystal and the LED material will have to be lattice matched, that is, they must have the same crystal structure and very close lattice parameters (a) to avoid creating dislocations at the interface.

❑ An important class of commercial semiconductor materials that cover the visible spectrum is the III–V ternary alloys based on alloying GaAs and GaP, which are denoted as GaAs1-yPy.

LED Structures

(a) A planar surface-emitting homojunction green GaP:N LED. (b) AlGaInP high-intensity heterostructure LED. (c) III-Nitride-based (GaN/InGaN) MQW LED for emission from the UV to green.

LEDs are typically fabricated by epitaxially growing doped semiconductor layers on a suitable substrate (e.g., GaAs or GaP) as illustrated above.


(a) Some of the internally generated light suffers total internal reflection (TIR) at the semiconductor–air interface and cannot be emitted into the outside. (b) A simple structure that overcomes the TIR problem by placing the LED chip at the centre of a hemispherical plastic dome. The epoxy is refractive index matched to the semiconductor and the rays reaching the dome’s surface do not suffer TIR. (c) An example of a textured surface that allows light to escape after a couple of (or more) reflections (highly exaggerated sketch). (d) A distributed Bragg reflector (DBR) under the confining layer (below the active region in grey) acts as a dielectric mirror and increases the extraction ratio. (e) An RCLED is an LED with an optical resonant cavity (RC) formed by two DBRs has a narrower emission spectrum

LASERS (Light Amplification by Stimulated Emission of Radiation)

Stimulated Emission and Population Inversion

The electron can undergo the downward transition by itself quite spontaneously, or it can be induced (stimulated) to do so by another photon.

• In spontaneous emission, the electron falls down in energy from level E2 to E1

and emits a photon of energy hv = E2 - E1 in a random direction.• In stimulated emission, an incoming photon of energy hv = E2 - E1 stimulates

the whole emission process by inducing the electron at E2 to transit down to E1. The emitted photon has the same energy, since hv = E2 - E1, it is in phase with the incoming photon, it is in the same direction, and it has the same polarization.

• Stimulated emission is the basis for obtaining photon amplification since one incoming photon results in two outgoing photons which are in phase.

▪ When a collection of atoms are considered to amplify light, majority of the atoms must beat the energy level of E2. Otherwise, the incoming photons would be absorbed by the atoms at E1. When there are more atoms at E2 than at E1, it is called a population inversion.

▪ Under normal equilibrium conditions, as a result of Boltzmann statistics, most of the atoms would be at E1, and very few at E2. Therefore atoms need to be excited for population inversion to obtain stimulated emission (which can be done with at least three energystates).

❑ In an example of ruby laser, energy levels of E1, E2, and E3 correspond to the energies of the chromium ions (Cr 3+) in a crystal of Al2O3 (a corundum crystal); E1 is the ground energy of the Cr 3+ ion.

❑ Suppose that an external optical excitation causes the Cr 3+ ions in the crystal to become excited to the energy level E3. This is called the pump energy level, and the process of exciting the Cr 3+ ions to E3 is called pumping. In the present case, optical pumping is used, and we need a pump source with a photon energy of hv13 = E3 - E1.

❑ From E3, the Cr 3+ ions decay rapidly to an energy level E2 by emitting phonons, that is, lattice vibrations (heat).

❑ Thus, the transition from E3 to E2 is a radiationless transition.❑ The energy level E2 happens to correspond to a state that does not rapidly and

spontaneously decay to the lower-energy state E1. In other words, the state at E2 is a long-lived state.

❑ With ample pumping, sufficient Cr 3+ ions can be accumulated at E2 to cause a population inversion between E2 and E1, as pumping takes more and more Cr 3+ ions to E3 and hence E2. Population inversion is shown in Figure (c).

❑ When a Cr 3+ ion at E2 decays spontaneously, it emits a photon (a “random photon”) which can go on to a neighboring Cr 3+ ion and cause that to execute stimulated emission.

❑ The photons from the latter can go on to the next Cr 3+ ion at E2 and cause that to emit by stimulated emission and so on. The result is an avalanche of stimulated emission processes with all the photons in phase, in the same direction, and with the same polarization, so that the light output is a large collection of coherent photons as in Figure (d).

❑ At the end of the avalanche of stimulated emission processes, the Cr 3+ ions at E2

would have dropped to E1 and can be pumped again to repeat the stimulated emission cycle. The emission from E2 to E1 is called the lasing emission.

❑ The system we have just described for photon amplification is a laser, an acronym for Light Amplification by Stimulated Emission of Radiation.

• Stimulated emissions can be increased by increasing the number of photons, i.e., the radiation intensity, within the crystal inasmuch as more photons cause more stimulated emissions. The ends of the ruby crystal, which is normally a rod, are silvered to reflect back and forward the stimulated radiation, that is, to form an optical cavity with mirrors at the ends.

A four-energy-level laser system. Highly simplified representation of Nd3+:YAG laser

Principle of the Laser Diode

(a) The energy band diagram of a degenerately doped pn with no bias. eVo is the potential energy barrier against electron diffusion from the n+-side to the p+-side. Note that (EFn - Ec) and (Ev - EFp) are small compared with eVo.

(b) Band diagram with a sufficiently large forward bias to cause population inversion and hence stimulated emission.


• In addition to population inversion, an optical cavity is also needed to implement a laser oscillator to build up the intensity of stimulated emissions by means of an optical resonator. This would provide a continuous coherent radiation as output from the device.

• The pn junction uses the same direct bandgap semiconductor material throughout, for example GaAs, and hence has the name homojunction.

• The ends of the crystal are cleaved to be flat and optically polished to provide reflection and hence form an optical cavity. Photons that are reflected from the cleaved surfaces stimulate more photons of the same frequency and so on. This process builds up the intensity of the radiation in the cavity.

A schematic illustration of a GaAs homojunction laser diode. The cleaved surfaces act as reflecting mirrors


Typical output optical power vs. diode current (I) characteristics and the corresponding output spectrum of a laser diode. Ith is the threshold current and corresponds to the extension of the coherent radiation output characteristic onto the I-axis.

Other structures explained in LED part of the slides (heterostructures, QW structure etc.) can also be applied for laser applications by achieving stimulated emission and population inversion.


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