# 5. Fundamentals of Optoelectronics

## 5.1 Materials and Radiant Recombination

### 5.1.1 Basic Questions and Material Issues

Basic Questions

| With "optoelectronics" in the context of this lecture we mean only electronic devices based on semiconductors where recombination processes emit light. We call this radiation process spontaneous emission of light, because it just happens statistically without any other ingredients but electrons and holes.
|  | We thus do not (yet) look at the opposite process - the absorption of light important in photo-diodes (or solar cells already discussed before).
|  | Transmission of light in waveguides (which might be integrated on a chip) is also not considered here.
| We have seen that Silicon is an indirect semiconductor and recombination proceeds via deep levels. The energy released does not produce photons in an appreciable amount and Si is therefore not useful for optoelectronic applications.
|  | This is, however, not a general truth. While recombination via deep levels indeed does not produce light, recombination requiring some third partner may, and we will see that there are indirect semiconductors that emit enough light to be useful for practical applications.
|  | But generally, we are looking for direct semiconductors where it can be expects that recombination does result in light production.
| This leads us to some general questions which can be translated to requests for material properties. Let us consider the more fundamental ones:
| The first question is: What is the wavelength of the light produced?
|  | If the light is produced by direct band-to-band recombination, we have of course h n = EC - EV, or, with cmat = n l, and cmat = velocity of light in the material = c0 /n with c0 = velocity of light in vacuum, and n = refractive index of the material, we obtain
|  | l = hc0 /n
|  | If the radiant recombination proceeds from some other energy states we simply replace EC - EV by D E, the relevant energy difference.
| This leaves us with two material questions:
|  | First, we are asking for the value of D E or in most cases EC - EV for optoelectronic materials. The answer comes from the band diagram and from finer details, still to be considered.
|  | Second, we now must know the (dynamic) refractive index of the material. This is not only important for the value of the wave length in the material, but especially for the transmission of light out of the material - where the difference in the refractive indices between two materials is a prime property of interest. This is a new property that we did not address before.
| The second question coming to mind is: How much light is produced by recombination, or more precisely, what is the quantum efficiency hqu, defined as the fraction of recombination events that produces light?
|  | For this we have to look at the various pathways open for recombination. In the preceding chapters we have discussed recombination in general and for one particular mechanism in detail.
|  | However, there might be several mechanisms for recombination open to minority carriers, and only one might produce light. We thus must consider recombination in optoelectronic materials in more detail.
| Third, we may wonder about the absolute intensity or even more specific, the intensity density we can produce.
|  | In other words, how many light-producing recombination events per second are attainable in a given volume of material? What is the limit and which factors determine it?
|  | Or, reformulated in technical terms. How do we produce a large non-equilibrium density of minorities (and majorities, too)? How do we inject electronically (by currents driven by external voltages) high densities of carriers in small volumes with no way out but recombination?
|  | This question leads to the overwhelmingly complex issue of hetero junctions, quantum wells, and the like.
| Now that we produced light, we must ask our fourth question: How do we get it out of the semiconductor? Which percentage of the light produces will actually escape - some, for sure, will be absorbed in the material.
|  | Will it come out in all directions, with a preferred direction, or even as a LASER beam?
|  | What do we have to do to optimize whatever we want?
|  | How do we meet the two basic requirements for Laser activity - inversion and feed-back? (what ever that means; we will come back to it).
| Finally, we ask the fifth question: What can we do to modify the wavelength of the emitted light?.
|  | Can we "tune" a given semiconductor, or mix different ones? What are the criteria for success?
| And finally, we must consider the technology: How do we make the needed materials and devices. What technologies exist, what are the pro and cons?
| All these questions are interrelated; very often we can not deal with just one at a time. In other words, if you optimize one property, you will change most of the others, too.
|  | Selecting materials and processes for an optimized device is a complex process and still a topic of front-end research.
|  | While much progress has been made during the last 20 years or so, there is still no cheap and reliable blue semiconductor Laser also first prototypes based on the fairly new technical semiconductor GaN have been introduced around 1998. It is a safe bet that we will see a lot more progress for the next 20 years and that it will come from rather involved physics and materials research employing quite a bit of quantum theory, new concepts like "photonic crystals" and "spintronics" - buzz words that you, the student, may not have heard yet but that may well become part of your professional career.

Material Issues

| Pondering the questions from above, it becomes clear very quickly that we need several suitable semiconductors to cover all aspects of optoelectronics.
|  | It also becomes clear that we have to look at more properties than we did for Si - the dielectric constant, e.g. is a prime parameter now.
|  | The value if the band gap, too, is now of prime importance (We wouldn't have cared much if it would have been somewhat different in Si!).
|  | The precise mechanisms of recombination are a matter of interest. In Si, all that counted was that you had some, but not too many deep level around midgap - now we may have to do part of the engineering with some levels in the bad gap if they influence in a major way the light emission.
|  | Lets start with looking at major semiconductors and their properties in detail

Properties | Si | GaAs | InP | In0,53Ga0,47As | GaP | GaN
Crystal
Unit weight [mol] | 29,09 | 144,63 | 145,79 | 168,545 |  |
Density [g/cm3] | 2,33 | 5,32 | 5,49 | 5,49 |  |
Crystal structure | Diamond | sphalerite | sphalerite | sphalerite |  |
Lattice constant [nm] | 0,5431 | 0,56533 | 0,5867 | 0,5867 |  |
Transport properties
Band gap [eV] | 1,12 | 1,42 | 0,078 | 0,75 | 2,26 |
Type | Indirect | Direct | direct | direct | indirect |
Effective e- mass [m*/m0] | 0,98 |  |  |  |  |
Effective h+ mass [m*/m0 light heavy | 0,16 0,49 | 0,082 0,45 | 0,12 0,56 | 0,051 0,50 |  |
Neff in C [1018cm-3] | 28 | 0,47 | 0,54 | 0,21 |  |
Neff in V [018cm-3] | 10 | 7 | 2,9 | 7,4 |  |
ni [106cm-3] | 6 600 | 2,2 | 5,7 | 63 000 |  |
Mobility (undoped) [cm2/Vs] µn µh | 1 500 450 | 8500 450 | 5 000 200 | 14 000 400 | 300 150 |
Lifetime (general) [µs] | 2500 | 0,01 | 0,005 | 0,02 |  |
Mechanism of luminescence | None | band-band | band-band | band-band | exciton-band if doped |
Dielectric properties
Dielectric constant | 11,9 | 13,1 | 12,4 | 13,7 | 11,1 |
Break through field strength [kV/cm] | 300 | 350 | 400 | 100 |  |
Specific intrinsic resistance [MWcm] | 0,2 | 310 | 11 | 0,0008 |  |
Electron affinity [eV] | 4,05 | 4,07 | 4,4 | 4,63 | 4,3 |
Thermal Properties
Expansion coefficient [10-6 oC-1 | 2,6 | 6,86 | 4,75 | 5,66 | 5,3 |
Therm. conductivity [W/cmK] | 1,5 | 0,45 | 0,68 | 0,05 |  |
Specific heat [J/goC] | 0,7 | 0,35 | 0,31 | 0,29 |  |
Melting point [oC] | 1 412 | 1 238 | 1,062 | 970 |  |

| Silicon is included as a reference. We find expected properties, but also some perhaps unexpected ones
|  | Dielectric constants are relatively large even at the very high optical frequencies. This is not necessarily self-evident since at least for Si the only polarization mechanism accountable is atomic polarization, i.e. the shift of electrons relative to the atom core.
|  | There is at least one recombination mechanism not mentioned before: Exciton - band recombination.
| Lets then by with looking at recombination mechanisms in more detail.