LIGHT-EMITTING DIODES

the holes drifting from thepside to thenside recombine radiatively with electrons. On either side, of course, the emitted photons are produced when an electron makes a downward transition from a state of energyEfto one of energyEi. Not every recom- bination of an electron with a hole will be radiative because there are competing, nonradiative recombinations in which the energy lost by the electron appears in the form of crystal lattice vibrations. Although there are LEDs in which nearly every recombination process is radiative, the actual device efficiency is limited by other factors, as discussed below.

Interband recombination radiation has a distribution of wavelengths arising from the thermal distribution of electron energy within the conduction band. The maximum wavelengthl_maxgiven by (2.9.1), however, provides a good estimate of the peak wave- length. Thus, we can deduce from it that LEDs made from Si or Ge junctions will not generate much visible radiation.

Actually there are other types of radiative recombination that produce longer wavelengths than the interband maximum l_max. As noted in the preceding section, there are donor levels and acceptor levels associated with the impurities of a doped semiconductor, and these levels lie just below the bottom of the conduction band and just above the top of the valence band, respectively. Radiative recombination processes involving these impurity levels produce radiation of wavelengthsl_.l_max, as is clear from Fig. 2.27. In part (a) of the figure we indicate an interband radiative recombination transition, that is, a transition of an electron from the conduction band to the valence band. Part (b) shows a transition from a donor level to the valence band, while (c) shows a transition from the conduction band to an acceptor level. Finally, we show in (d) a transition from a donor level to an acceptor level. Processes (b) – (d) obviously lead to wavelengths greater than the interband process (a), and so LED wavelengths are often greater than the interband maximum (2.9.1). Because the differences Ec2EdandEa2E_vare small compared toEg, however, (2.9.1) provides a good estimate of the sort of wavelength that can be expected with a given semiconductor.

The question of wavelength is obviously an important one if an LED is to be used for visual display purposes. Silicon and germanium, for instance, are eminently useful electronically because of the relative ease with which they can be doped and fabricated as diodes, but their band gaps are too small to make them useful as LEDs for visible radiation. Moreover, Si and Ge are radiatively too inefficient to be used in LEDs. This is because they are indirect-band-gap semiconductors, for which the

hn E_d

E_a E_a

E_d

hn hn

hn

(a) (b) (c) (d)

Figure 2.27 Radiative recombination involving a transition from (a) the conduction band to the valence band, (b) a donor level to valence band, (c) the conduction band to an acceptor level, and (d) a donor level to an acceptor level.

interband radiative recombination rates are very low. GaAs, by contrast, is adirect-band- gapsemiconductor and is consequently a much more efficient radiator. Indirect-band- gap materials can be used in LEDs if there are efficient radiative pathways in addition to interband recombination.

† In the case of a direct band gap the minimum of theE2kcurve for the conduction band lies directly above the maximum of theE2kcurve for the valence band. (See the Appendix in this chapter for a discussion of a simplified one-dimensional model of electron wave functions and E2k curves in a crystal, and also Fig. 15.2.) This means that a “vertical”

transition can occur in which the electron energy (E) decreases by an amount equal to the energy of the emitted photon while there is no change in the k vector of the electron wave function. More precisely, the calculation of the transition rate leads to the kselection rule: the difference in the k vectors of the initial and final electron wave functions must be equal to the wave vector of the emitted photon; otherwise the transition is forbidden. But since the electron kvector has a much greater magnitude than the wave vector of the photon, this selection rule says that the electronkvector is approximately unchanged and momentum (hk) as well as energy is conserved in the transition.

For an indirect band gap, however, the maximum of theE2k curve for the valence band is offset from the minimum of the E2k curve for the conduction band, and the wave vectors of the initial and final electron wave functions are not the same. To conserve momentum, therefore, a radiative transition in this case must be accompanied by a change in the momentum of the crystal lattice. Crystal lattice vibrations are characterized approximately in terms of the equally spaced energy levels of a harmonic oscillator, and the particle-like excitations associated with these energy levels are calledphonons. Energy and momentum conservation in electron – hole recombination for an indirect band gap involves not only electrons and photons but also the phonons of the crystal lattice. As a consequence the rate and efficiency of the phonon- mediated, indirect-band-gap photon emission are generally much smaller than for direct-band-

gap emission. †

In addition to having a band gap large enough to produce visible radiation, a semi- conductor to be used in an LED must, of course, have bothp-type andn-type forms that can be made by suitable doping. As a rule of thumb, large-gap materials tend to have high melting points, making doping of a melt more difficult, and furthermore they tend to have low conductivities even when doped. Among the more commonly used LED materials is gallium arsenide (GaAs), with a band gap of 1.44 eV (and there- forelmax861 nm). Depending on the dopant, the dominant radiative recombination transition may be interband (Fig. 2.27a) or from the conduction band to an acceptor level (Fig. 2.27c).

Even if every charge carrier injected across the junction gave rise to an emitted photon, the efficiency of an LED would still be much less than 100%. An important reason for this is a phenomenon well known in classical optics: total internal reflection.

For a quick review of this effect, recall that the refraction of light at an interface of two media is governed by Snell’s law:

n1sinu₁¼n2sinu₂, (2:9:2) wheren₁andn₂are the refractive indices on the two sides of the interface, andu₁andu₂ are the corresponding angles of incidence, as in Fig. 2.28a. Now ifn1.n2, it is possible for light propagating from medium 1 to medium 2 to be reflected back into medium 1 instead of penetrating the interface and going into medium 2. This total internal

2.9 LIGHT-EMITTING DIODES 51

reflection occurs at angles of incidenceu₁greater than the critical valueu_cfor which u_2¼908:

n₁sinu_c¼n₂sin 908¼n₂, (2:9:3) or

u_c¼sin¹ n₂

n1 : (2:9:4)

This is illustrated in Fig. 2.28b.

Any light emerging from an LED and propagating into air is passing from a medium of higher index to a medium of lower index. This means that light approaching the LED – air interface at an angle greater than the critical angleu_c will be reflected back into the LED instead of emerging as useful output radiation. In fact, the refractive indices of LED materials are often quite large, making the critical angle for total internal reflection rather small. In GaAs, for instance, n3.6, so that u_c168 for the GaAs – air interface.

The deleterious effect of total internal reflection is minimized in the common LED design shown in Fig. 2.29. The junction is enclosed in a plastic case of refractive indexn1.5. This reduces the effect of total internal reflection at the emitting surface because the critical angle for total internal reflection (2.9.4) is increased over that appropriate to a diode – air interface. Of course, there is still total internal reflection at the plastic – air interface, but this is minimized by shaping the plastic into the form of a hemispherical or similarly shaped dome. With this geometry, most of the light rays at the plastic – air interface have angles of incidence less than the critical angle for total internal reflection, and as a result the emission efficiency can typically be increased by10 (Problem 2.6). The shape of the plastic enclosure also determines the extent to which the light emission is directional. A tubular shape, for example, can increase directivity as a result of side reflections. Alternatively, it is desirable in some applications to have a more diffuse emission, which can be accomplished by using a “diffusing lens”

design in which tiny glass particles embedded in the plastic casing scatter the light from thepnjunction and thereby produce a wider angular spread of radiation from the LED.

q₁ n₂

(a) (b)

n₁

q₂

qc

a

a

b b

n₂ n₁

Figure 2.28 (a) Geometry for Snell’s law ifn₁,n₂. (b) Total internal reflection occurs at the inter- face ifn1.n2and the angle of incidence exceeds the critical angleu_cgiven by (2.9.4).

There are two other effects that lower LED emission efficiency. One is simply the absorption of light, which can be significantly reduced by using a transparent material as the substrate for thepnjunction. The other is the “Fresnel loss” due to reflection at the interface between the LED and the surrounding medium, which of course occurs even if total internal reflection is effectively eliminated. For light normally incident at an interface between the LED with refractive indexn and a medium with refractive indexn⁰, for example, the power reflection coefficient is given by the Fresnel formula [Eq. (5.A.6)] r¼(n2n⁰)²/(nþn⁰)². Some of the reflected light can be retrieved by using a reflecting layer or cup at the “bottom” of thepnjunction.

A wide range of LED colors has been realized by “band gap engineering” of mixed compound semiconductors such as gallium aluminum arsenide (GaAlAs) and gallium arsenide phosphide (GaAsP). For example, the band structure of GaAs12xPx, wherex is the mole fraction of P, is such that there is a direct band gap that monotonically increases with x from 1.44 eV when x¼0 (GaAs) to 2.1 eV when x¼0.45.

GaAs0.6P0.4, for example, has a peak emission wavelength of 650 nm and is used in red LEDs. Atx¼0.45 the compound has anindirectband gap and is nonradiative. It turns out, however, that doping the indirect-band-gap material with nitrogen allows direct-band-gap and therefore radiative electron – hole recombination. Thus, N-doped GaAs0.15P0.85, for example, has a peak emission wavelength of 589 nm and is used in yellow LEDs.

Blue LEDs based on gallium indium nitride (GaInN) became widely available in the 1990s. Together with red and green LEDs, they made it possible to produce any (visible) color by combining the light from three LEDs with appropriately adjusted currents and therefore output light intensities. White light is also produced using single, blue LEDs coated with wavelength-converting phosphors or “quantum dot” nanostructures that confine electrons to regions of linear dimension2 – 10 nm and act in some respects as “artificial atoms” with electron transition energies that vary with the size of the dot.

Although (red and green) LEDs became commercially available in the 1960s, research and development remained at a rather low level for a quarter-century. The recent advances have stemmed in considerable part from work on semiconductor lasers, including experimentation with different materials and dopants, progress in pure wafer fabrication and bonding techniques, and the development of suitable sub- strates for efficient extraction of radiation.

pn junction

Plastic capsule

Electrical contacts

Figure 2.29 More light is extracted from an LED when there is a transparent plastic enclosure in the form of a hemispherical dome to reduce total internal reflection at the plastic – air interface.

2.9 LIGHT-EMITTING DIODES 53

Their use in cell phones resulted in a dramatic increase in the commercial production of light-emitting diodes in the 1990s and early 2000s. Infrared LEDs had already become ubiquitous in television remote controls and similar applications, while LEDs in the visible had replaced incandescent lamps in applications demanding compactness, low power consumption, and a high degree of reliability. For such purposes they are used either singly or in arrays. In the latter case a pattern or message can be conveyed when some of the LEDs are switched on. A simple and familiar example is the digital display used in clock radios and calculators. These commonly employ the seven-segment dis- play shown in Fig. 2.30 in which each segment is an individual LED. The numerals 0 – 9 are displayed by turning on only certain of these LEDs at a time.

The energy efficiency and robustness of LEDs compared to incandescent or fluores- cent glass lamps have made them increasingly important. It is estimated that in 2000 lighting accounted for 6 – 7% of the total power consumption in the United States.

Incandescent lamps (like the everyday lightbulb) are notoriously inefficient: Only about 5% of the electrical power consumed is converted to light, with the rest wasted as heat. Efficiencies of fluorescent lights are 4 – 5 times greater but do not approach the 90% efficiencies possible with LEDs. Low power consumption, compactness, long life (tens of years or more), and resiliance under jolts and vibrations make LED arrays ideal as light sources for traffic signals, for instance, and in the mid-1990s some cities in the United States began replacing incandescent traffic signal lights with LEDs. It is expected that in the near future most traffic lights will employ LED arrays. LED arrays were first used in automobile rear-center brake lights in the late 1980s, and front-end lights employing white-light LEDs were introduced as early as 2004. High-brightness LED arrays make possible the huge outdoor television screens that can be clearly seen even in daylight. Some industry analysts predict that by about 2015 most home lighting in the United States will employ LEDs.

† In applications in which only a very small amount of power from a small battery is available, such as in digital wrist watches and many pocket calculators, theliquid-crystal display, or LCD, is used instead of the LED. LCDs consume less power because they do not generate any light of their own but use ambient light. Their operation is based on the properties of certain organic liquids of rod-shaped molecules. The molecules can take on certain organized relative alignments (hence the termliquid“crystal”) in such a way that the polarization of an incident light wave is rotated by 908 in passing through the LCD cell. The cell is a liquid-crystal layer, typically ,10 mm thick, sandwiched between two clear plates whose inner surfaces are coated with a Figure 2.30 Seven-segment display format used with LEDs and LCDs. The ten digits 0 through 9 may be displayed by lighting selected segments.

transparent conducting material arranged in a certain pattern. When a voltage is applied between the plates, the molecular alignment is altered and the polarization of incident light is no longer rotated by 908. By using orthogonally oriented polarizing sheets in front of and behind the cell, and a mirror at the back, we can arrange for incident light to be reflected when there is no applied voltage, but for no light to be reflected from those areas where there is an applied voltage.

Then we see the familiar black-and-white alphanumeric display patterns.

Liquid-crystal displays used in flat-screen televisions and laptop computers, for instance, are transmissive, or “backlit,” rather than reflective, but the principle of operation is the same. The backlighting is done with very small fluorescent tubes or LEDs, together with a white panel behind the LCD that scatters light from the tubes to produce a uniform illumination of the

LCD. The light from the screen is strongly polarized. †

The light-emitting material in organic light-emitting diodes (OLEDs) consists of large organic molecules or polymers in a very thin layer, typically only a few hundred nanometers thick. The emitting layer is sandwiched between a cathode array and an anode array, with additional conductive layers serving to facilitate the injection of electrons and holes into the emitting layer. The color and brightness of the light pro- duced by electron – hole recombination in the emitting layer depend on the type of organic molecules used and on the strength of the applied current. The electrode layers are anode and cathode strips, and the emitting pixels (picture elements) are at the intersections of these strips. The application of different current levels to different pixels determines which pixels are on or off for display or video. The emitting layers for OLEDs can be produced in large and flexible sheets, suggesting applications such as foldable electronic “newspapers” that can be updated minute by minute.

Transistors, consisting basically of two adjacentpnjunctions (pnpornpn), are the most important application of semiconductor junctions, and their operation may be understood within the electron – hole framework we have used to discuss LEDs.