# 9. Optoelectronics

## 9.1 General Concerns

### 9.1.1 Semiconductors and Light

Basic Questions

| Optoelectronics here means the coupling of optics, i.e. light (including all relevant wavelengths from the far infrared to the deep ultraviolet) and electronics, and that this is somehow done with semiconductors. We have two basic possibilities.
|  | 1. The input is light, the output is an electrical signal or electrical power. 2. The input is electrical power and the output is light
|  | If we go for less orthodox definitions, we may also consider 3. Electrical input switches light on or off or, more generally, modulates light.
| Let's look at a few examples:
|  | For the first point we have solar cells, if you like, although few people would count then among optoelectronics proper. The paradigm for this field is the optical sensor, sitting, e.g., at the end of a fibre optics cable and converting the signal coming in in the form of light being on or off to electrical signals. A more ubiquitous product example is the "CCD" chip in your digital 8 Megapixel camera, that contains no less then 8 Mio optical sensors in a matrix.
|  | For the second point we have two paradigmatic products. LED's - light emitting diodes and LASER diodes. Both devices are closely related technologically, but quite a bit apart from their working principles.
|  | The third example could include flat panel displays in the form of "LCD's" and all the light manipulating MEMS devices we already considered in the MEMS context. Nobody would list those devices under optoelectronics proper, but we do have a connection between light and semiconductors.
| As far as this lecture course is concerned, we can just touch upon the basic principles of LED's and Lasers. So let's look at a few general points in the context of producing light in a semiconductor by running a current through it. This brings us to the first major point:
| 1. Generating light takes power - current I times voltage U.
|  | Just having almost powerless voltage swings, which are (almost) all you need for processing information, will not suffice. There is some energy h · n contained in the light generated that we want to flow out of the system, and thus some energy I · U · t must flow into the system.
|  | That means we always have some efficiency h (measured in %) associated with the process of light generation; and h, as always, should be as large as possible. In fact, with LED's we can achieve rather large efficiencies > 50 % (compare that to to a light bulb with » 7 %!), if everything is done just right.
| 2. LED's generate light with just one wavelength l (of course with some ±Dl ).
|  | The wavelength l (or the frequency n) of the light generated is more or less determined by the band gap. We already looked at the possibilities we have for bandgap-engineering in our "master diagram"; the basic relation is
l | = | c n | = | h · c h · n | = | h · c0 n · Eg
--- | --- | --- | --- | --- | --- | ---
|  | with Eg=band gap energy, and c=speed of light in the medium the light is propagating, i.e. c=co/n with co=speed of light in vacuum, and n=index of refraction =(er)½; er is the relative dielectric constant of the material.
|  | There - you have elementary optics coming in as you should have suspected when the "opto"electronics came up. In other words, the dielectric constant and with it the index of refraction of our semiconductors enters the game here, a property we have hardly noticed so far.
|  | Most semiconductors, actually, have a rather large index of refraction; some values are given in the table below. In case you wonder why materials that are not transparent to light should have an index of refraction, keep in mind All semiconductors are perfectly transparent to light with h · n < Eg; so at least for small enough wavelengths an index of refraction makes perfect sense. In that part of optoelectronics where we want to produce light, we must work with wavelengths where the semiconductor is at least semitransparent. Otherwise no light could possible come out of the material. If we cool any semiconductor down to a sufficiently small temperature, it will be a good insulator for which we can easily define a dielectric constant and thus an index of refraction.
|  | In fact, looking ahead to somewhat more advanced material science, everything contained in notions like electric conductivity, dielectric constant, index of refraction, or absorption coefficient are just special aspects of a so-called (complex) dielectric function, which is nothing but the (complex) dielectric "constant" as a function of frequency; more to that in the link.
| 3. A third point of general interest is the absolute intensity, or even more specific, the intensity density we can produce. In other words, when we generate a certain "amount" of light as given by energy in times efficiency, from what kind of volume is it coming from.
|  | From a "point source" as we like it (in text books) for doing optics with lenses; from some finite volume like in a real light bulb, from some elongated structure like in a fluorescent tube, or from a large area like - ???.
|  | Well, with "normal" light sources you have a problem if you need two-dimensional light sources. You just can't throw a light switch and have a whole wall of your room start glowing uniformly - until you go for (future) LED's, that is.
|  | Whatever, we have an important point here that we need to address if we want to use LED's for making light.
| If we take points 1 - 3 and remember that a photon in an LED will only be produced if an electron and a hole recombine in a process that transfers their energy to a photon (and not to the lattice or to something else) we have our task cut out: Recombine as many electrons and holes as you need per second (Þ current) for the amount of light you want to produce (Þ intensity) with as many recombination events as possible producing light (Þ efficiency) in a defined volume (Þ intensity density) and get the light produced out of the semiconductor (Þ efficiency once more).
|  | In simple and straight terms, we need to consider how we can handle massive recombination in a given volume. We need to do this for a number of different semiconductors because we need different wavelengths.
|  | This is new! So far we tried to either avoid recombination (e.g. in solar cells) or to ignore it (e.g. in the simple standard version of the diode equation). Now recombination is in the focus of what we need to optimize.
|  | What is also new to some extent is that we are now using (electrical) power=UI. It you want to produce a lot of light (=energy), you must provide power. You can't get much light out of 1 W light bulb and you can't get much light out of just a 1 W LED either. This is new to some extent because in microelectronics (=communication and signal processing) we avoided power as much as we could - we had voltage swings, but no current if possible.

Material Issues

Color | Wavelength (nm) | Typical Semiconductor
Infrared | 880 | GaAlAs/GaAs
Red | 660 - 633 | GaAlAs/GaAs
Orange to Yellow | 612 - 585 | AlGaInP GaAsP/GaP GaAsP/GaP
Green | 555 | GaP AlInGaP
Blue to Ultraviolet | 470 - 395 | AlInGaPN GaN/SiC GaN/SiC InGaN/SiC
|  |  | As already pointed out above, we need several suitable semiconductors to cover all aspects of optoelectronics.
|  |  | It also became clear that we have to look at more properties than we did so far : For example, dielectric constants and recombination mechanisms are now prime parameters we must consider.
|  |  | The value of the band gap, too, is now of prime importance (In contrast, we wouldn't have cared much about the precise value of the bandgap for Si technologies!).
|  | Besides appreciating the material overview given in the table at the right, let's look a bit closer at major semiconductors and their properties in detail: The same table but with more entries concerning properties we have not yet encountered can be found in the link.
|  |  |  | Interesting points that can be found in this table are Indirect semiconductors like GaP are listed! A strange recombination mechanism ("exciton - band") is listed A strange semiconductor (In0,53Ga0,47As) is listed

| Here is a table with a lot (but not all by far) interesting properties of some semiconductors:
Properties | Si | Ge | GaAs | InP | InSb | In0,53Ga0,47As | GaP | GaN | SiC | Diamond | Remarks
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Crystal
Unit weight [mol] | 29,09 |  | 144,63 | 145,79 |  | 168,545 |  |  |  |  |
Density [g/cm3] | 2,33 |  | 5,32 | 5,49 |  | 5,49 |  |  | 3.166 (cubic) 3.211 (hex) | 3,51 |
Crystal structure | Diamond | Diamond | Sphalerite | Sphalerite | Sphalerite | Sphalerite |  |  | Many variants cubic, hex, rhombohedral | Diamond |
Lattice constant [nm] | 0,5431 | 0,565 | 0,565 | 0,587 | 0,648 | 0,5867 |  |  | a=0,30 c many values |  |
Transport properties
Band gap [eV] | 1,12 | 0,66 | 1,42 | 1,35 | 0,17 | 0,75 | 2,26 |  | 2.39 - 3.26 | 5.47 |
Type | Indirect | Indirect | Direct | direct |  | direct | indirect |  | indirect |  |
Effective e- mass [m*/m0] | 0,98 |  |  |  |  |  |  |  | 0,24 - 0,7 |  |
Effective h+ mass [m*/m0] light heavy | 0,16 0,49 |  | 0,082 0,45 | 0,12 0,56 | 7,3 | 0,051 0,50 |  |  | 0.9 |  |
Neff in C [1018cm–3] | 28 (32) | 10,4 | 0,47 | 0,54 | 0,042 | 0,21 |  |  |  |  |
Neff in V [1018cm-3] | 10 (18) | 6 | 7 | 2,9 |  | 7,4 |  |  |  |  |
ni [106cm–3] | 6 600 13.000 |  | 2,2 | 5,7 |  | 63 000 |  |  |  |  |
Mobility (undoped) [cm2/Vs] µn µh | 1 500 450 | 1 900 3 900 | 8500 450 | 5 000 200 | 80 000 1 250 | 14 000 400 | 300 150 |  | 500 - 1 000 20 - 50 | 200 - 2 200 1.800 - 2 100 |
Lifetime (general) [µs] | 2500 |  | 0,01 | 0,005 |  | 0,02 |  |  |  |  |
Mecha- nism of lumines- cence | None |  | band-band | band-band |  | band-band | exciton -band if doped |  |  |  |
Dielectric properties
Dielectric constant | 11,9 | 16 | 13,1 | 12,4 | 17,7 | 13,7 | 11,1 |  | 9.7 - 10 | 5.5 |
Break through field strength [kV/cm] | 300 |  | 350 | 400 |  | 100 |  |  |  |  |
Specific intrinsic resistance [MWcm] | 0,2 |  | 310 | 11 |  | 0,0008 |  |  |  |  |
Electron affinity [eV] | 4,0 | 4,05 | 4,07 | 4,4 | 4,59 | 4,63 | 4,3 |  |  |  |
Thermal Properties
Expansion coefficient [10–6 oC–1] | 2,6 |  | 6,86 | 4,75 |  | 5,66 | 5,3 |  |  | 1 |
Therm. conductivity [W/cmK] | 1,5 |  | 0,45 | 0,68 |  | 0,05 |  |  | 5.0 | 22 | Cu: 4.01
Specific heat [J/goC] | 0,7 |  | 0,35 | 0,31 |  | 0,29 |  |  | 0.671 | 0.428 | Cu: 0.38
Melting point [oC] | 1 412 | 937 | 1 238 | 1 062 | 527 | 970 |  |  |  |  |

| Si, Ge and diamond are included as references; if there are several numbers, they are from different sources. We find expected properties, but also, perhaps, some unexpected ones:
|  | Dielectric constants are relatively large even at the very high optical frequencies. That means we have also large indexes of refraction n=(e)½.
|  | Thermal conductivity can be rather large (SiC and diamond!). That's good because we have to get a lot of heat out of our optoelectronic "power" devices.
|  | There is at least one recombination mechanism not mentioned before: Exciton - band recombination.
| This tells us that we now need to look a bit more closely at radiant recombination, the key to light generation.

Radiant and Non-radiant Recombination

| Let's start from the typical situation of a working LED or Laser. A large number of electrons and holes finds themselves in some volume of a semiconductor at concentrations far above equilibrium. They are running around in a random matter and every now and then a hole and an electron get real close on their perambulations.
|  | What they want to do is to recombine because that would be the right step towards equilibrium.
|  | What they are going to do depends on the conditions. They must be "just right" otherwise recombination will not take place. Essentially three conditions must be met:
|  | The electron and the hole must be in the same place at the same time. The probability for that happening is certainly proportional to the respective concentrations ne and nh. We must preserve energy. The energy released by the recombination (=Eg) must appear somewhere else; in the world of quantum mechanics always in some particle like a freshly generated photon. We must conserve (crystal) momentum.
|  | In direct semiconductors we know we don't have to worry about point 2 and 3. Whenever boy meets girl in this case, things can happen and they can recombine, emitting a photon. We have what we now will call direct recombination.
| This is still true and will remain true. But now we have to look a bit more closely and realize that other things beside the direct recombination might happen too.
|  | For instance, an electron on its random migration might encounter a defect, e.g. an impurity atom with an energy level somewhere in the bandgap which it occupies and now is trapped and mellow (low in energy, at least for some time). A hole, somewhat later, also finds the impurity atom plus the electron unable to run away, and happily recombines with the electron. In other words: a girl, wandering around at random finds an irresistible café and sits down for a while. A boy, coming accidentally by the café, seeing the girl trapped there and in a mellow mood, knows what to do...
|  | This is exactly how recombination happens with the help of defects in indirect semiconductors. There is no reason in the world why this must not happen in direct semiconductors, too. It does, and the problem is that you can meet conditions 2. and 3. from above without emitting a photon, The third partner to the process - the defect - takes care of energy and momentum conservation.
| We thus have recombination via defects as a second recombination channel, to use the proper term. We don't like this recombination channel because it takes electrons and holes out of circulation without producing light, and therefore decreases the efficiency of our LED.
| Now we must make a leap in imagination. Third partners to the recombination process, that much is clear, may somehow influence what happens. The question is thus: What kind of third partners besides defects do we find in semiconductors and what, exactly, are they doing to recombination?
|  | A simple first answer is: Electrons in the conduction band. What happens is that an electron meets an attractive hole, recombines, and the energy released goes right to a second electron that happens to be close by. This process is called "Auger recombination" and we don't like it because it does not produce light.
|  | A not-so-simple-answer is: Bound excitons! So an electron gets very close to nice hole, but can't recombine because they are in an indirect semiconductor, and their momentums just don't fit. However, there is still some attraction (Coulomb attraction) as long as they stay real close because they have opposite charges. So they form a bound electron-hole pair, encircling each other (always exactly opposite momentum!), and run about as a pair called "exciton" that would like to do it but can't quite without a little help from a friend. Then they encounter a friend in the form of a special defect (N atoms in GaP, for example) that traps the couple, i.e. localizes it in space. Great - because now Heisenbergs uncertainty relation kicks in: D x · D p > h. If D x is small, D p, the uncertainty of the momentum p, is large. If your momentum is uncertain, what exactly needs to be preserved? Right - happy recombination, you have made it now. And don't forget to use a condom emit a photon while you're doing it because we still must have energy conservation!
|  | Wow! We now have a somewhat strange recombination channel that produces radiation, which is good!. It is actually the only reason why the indirect semiconductor GaP, if "doped" with N to catch the excitons (in addition to the doping that produces the electrons and holes), will be a quite efficient material for green LED's.
|  | This little excursion into more advanced semiconductor technology just serves to demonstrate that there are indeed more recombination channels than we might have thought of. Moreover, the "blabla-ons", they many so-called "quasi-particles" of solid state physics, often considered to be exotic curiosities with no conceivable uses, are quite useful, after all. At least some of them, including the exciton. The link will go somewhat deeper into these subjects.
| We aren't even done yet. There are even more recombination channels but what we have learned so far suffice to make the point:
|  | If you want a high-efficiency LEDs and Lasers, you must optimize your recombination channels - and this may not be easy.

© H. Föll (Semiconductor Technology - Script)