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 as 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 as the required third partner does not produce light, indeed, recombination proceeding via some other third partner may. 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 expected 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 = E_C – E_V

With c_mat = n · l, and c_mat = 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	=	h · c₀ n

If the radiant recombination proceeds from some other energy states we simply replace E_C – E_V by DE, the relevant energy difference.

This leaves us with two material questions:

First, we are asking for the value of DE, or in most cases E_C – E_V, for optoelectronic materials. The answer comes from the band diagram and from finer details, still to be considered.

Second, we now must know the (complex) 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. The refractive index of a semiconductor 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 h_qu, 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 heterojunctions, 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 produced will actually escape - some light, 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).

We now 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, for question number six, we must consider the technology: How do we make the needed materials and devices ?

What technologies exist, what are the pro and cons?

What can we use from Si technology? What kind of technologies do we need that are specific to optoelectronics ?

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 although first prototypes based on the fairly new technical semiconductor GaN (Gallium nitride) 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 of 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 for recombination are a prime matter of interest. In Si, all that counted was that you had some, but not too many deep level around midgap, giving a large recombination life time. With optoelectronics we may have to make sure that recombination proceeds exactly as needed.

Let's start with looking at major semiconductors and their properties in detail

Properties	Si	Ge	GaAs	InP	InSb	In_0,53Ga_0,47As	GaP	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
N_eff in C [10¹⁸cm^–3]	28 (32)	10,4	0,47	0,54	0,042	0,21
N_eff in V [10¹⁸cm^-3]	10 (18)	6	7	2,9		7,4
n_i [10⁶cm^–3]	6 600 13.000		2,2	5,7		63 000
Mobility (undoped) [cm²/Vs] µ_n µ_h	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
Mechanism of luminescence	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/g^oC]	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


	Silicon is included as a reference (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. This is not necessarily self-evident since at least for Si the only polarization mechanism operational 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 continue by looking at recombination mechanisms in more detail.