1.11 Light emitting diode

Let's talk about the recombining electrons for a minute. When the electron falls down from the conductionband and fills in a hole in the valence band, there is an obvious loss of energy. The question is; where does that energygo? In silicon, the answer is not very interesting. Silicon is what is known as an indirect band-gap material . What this means is that as an electron goes from the bottom ofthe conduction band to the top of the valence band, it must also undergo a significant change in momentum. This all comes aboutfrom the details of the band structure for the material, which we will not concern ourselves with here. As we all know,whenever something changes state, we must still conserve not only energy, but also momentum. In the case of an electrongoing from the conduction band to the valence band in silicon, both of these things can only be conserved if the transitionalso creates a quantized set of lattice vibrations, called phonons , or "heat". Phonons posses both energy and momentum, and their creation upon the recombination of an electron and hole allowsfor complete conservation of both energy and momentum. All of the energy which the electron gives up in going from theconduction band to the valence band (1.1 eV) ends up in phonons, which is another way of saying that the electron heats up thecrystal.

In some other semiconductors, something else occurs. In a class of materials called direct band-gap semiconductors , the transition from conduction band to valence band involves essentially no change in momentum.Photons, it turns out, possess a fair amount of energy (several eV/photon in some cases) but they have very little momentumassociated with them. Thus, for a direct band gap material, the excess energy of the electron-hole recombination can either betaken away as heat, or more likely, as a photon of light. This radiative transition then conserves energy and momentum by giving off light whenever an electron and holerecombine. This gives rise to (for us) a new type of device, the light emitting diode (LED). Emission of a photon in an LEDis shown schematically in .

It was Planck who postulated that the energy of a photon was related to its frequency by a constant, which was later namedafter him. If the frequency of oscillation is given by the Greek letter "nu" ( $\nu$ ), then the energy of the photon is just $h\nu$ , where $h$ is Planck's constant, which has a value of $4.14E-15\mathrm{eV}\mathrm{seconds}$ .

As you no doubt notice, a number of the important LEDs are based on the GaAsP system. GaAs is a direct band-gap semiconductorwith a band gap of 1.42 eV (in the infrared). GaP is an indirect band-gap material with a band gap of 2.26 eV (550 nm, or green). Both As and P are group V elements. (Hence thenomenclature of the materials as III-V compound semiconductors .) We can replace some of the As with P in GaAs and make a mixed compound semiconductor $\mathrm{Ga}{\mathrm{As}}_{\text{1-x}}{P}_x$ . When the mole fraction of phosphorous is less than about 0.45 the band gap is direct, and so we can "engineer" thedesired color of LED that we want by simply growing a crystal with the proper phosphorus concentration! The properties of theGaAsP system are shown in . It turns out that for this system, there are actually two different band gaps, as shown in the inset . One is a direct gap (no change in momentum) and the other is indirect. In GaAs, thedirect gap has lower energy than the indirect one (like in the inset) and so the transition is a radiative one. As we startadding phosphorous to the system, both the direct and indirect band gaps increase in energy. However, the direct gap energyincreases faster with phosphorous fraction than does the indirect one. At a mole fraction $x$ of about 0.45, the gap energies cross over and the material goes from being a direct gapsemiconductor to an indirect gap semiconductor. At $x=0.35$ the band gap is about 1.97 eV (630 nm), and so we would only expect to get light up to the red using the GaAsPsystem for making LED's. Fortunately, people discovered that you could add an impurity (nitrogen) to the GaAsP system, whichintroduced a new level in the system. An electron could go from the indirect conduction band (for a mixture with a mole fractiongreater than 0.45) to the nitrogen site, changing its momentum, but not its energy. It could then make a direct transition tothe valence band, and light with colors all the way to the green became possible. The use of a nitrogen recombination center is depicted in the .

If we want colors with wavelengths shorter than the green, wemust abandon the GaAsP system and look for more suitable materials. A compound semiconductor made from the II-VIelements Zn and Se make up one promising system, and several research groups have successfully made blue and blue-green LEDsfrom ZnSe. SiC is another (weak) blue emitter which is commercially available on the market. Recently, workers at atiny, unknown chemical company stunned the "display world" by announcing that they had successfully fabricated a blue LEDusing the II-V material GaN. A good blue LED has been the "holy grail" of the display and CD ROM research community for a numberof years now. Obviously, adding blue to the already working green and red LED's completes the set of 3 primary colorsnecessary for a full-color flat panel display (Hang a TV screen on your wall like a picture?). Using a blue LED or laser in aCD ROM would more than quadruple its data capacity, as bit diameter scales as $\lambda$ , and hence the area as $\lambda ^2$ .