### 5.1.4 Wavelength Engineering

| We will now try to find some answers to our fifth question: How can we change the wavelength of the light produced by radiative recombination?
|  | The recipe coming to mind is: Mix two similar (direct) compound semiconductors with different bandgaps.
|  | Luckily, most III-V compounds are completely miscible in ternary or even quaternary crystals.
|  | In other words: From the 2 compounds GaAs and AlAs we can make ternary GaAl1-xAsx for o<= x<=1, from GaAs and InP we can produce quaternary Ga1-xInxAs1-yPy.
| This gives a lot of options. What happens upon mixing, which changes of properties are useful and which are not? Are there guidelines or do we have to try it out?
|  | Generally, all properties of interest as given in a table in subchapter 5.1.1 will change while x and y run through the accessible range, but not necessarily smoothly or monotonously with the composition.
|  | Here we focus on just a few of the especially important properties: Bandgap Band type (direct or indirect) Lattice constant Thermal expansion coefficient
|  | The two last properties will be of overriding technical importance as soon as we learn how to make heterostructures, i.e. combinations of two different semiconductors.
| There are some standard diagrams plotting properties the most important combinations.
|  | The first and most important one shows the bandgap vs. the lattice constant plus information about the band type. It is shown below, with the II-VI compounds included for good measure:

| There is a tremendous amount of information in this diagram (note that "X-gap" and L-gap" both denote indirect band gaps a the respective positions in the band diagram):
|  | Most III-V compounds radiate at wavelength above the visible region. However, adding some Al to GaAs producing AlxGa1-xAs, will shift the wavelength into the red region of the spectrum - here are our red luminescence diodes and Lasers!
|  | Very fortunate: GaAs and AlAs have almost the same lattice constant; we can thus combine any combinations of these materials without encountering mechanical stress.
|  | Very unfortunate: There are no III-V compounds in the diagram that emit blue light - this is a severe problem for many potential applications. While SiC (not contained in the diagram) could be used to some extent, it was only with the recent advent of GaN that this problem was solved. SiC and GaN crystals, however, are not of the "zinc-blende" type common to all the III-Vs in the diagram but have a hexagonal unit cell. They therefore do not easily mix with the others!
|  | If we want to radiate at 1.3 µm or 1,5 µm - infrared wavelength of prime importance for optical communications - we should work with combinations of InAs, GaAs, and AlSb
|  | Most interesting: The II-VI compounds are all direct semiconductors and span a much larger range of wavelengths than the III-V's. The fact that they are not much used for products tells us that there must be big problems in utilizing these compounds for mass products.
| Let us now look a bit more closely at some other properties for the more important systems.
|  | The following diagrams show the direct and indirect bandgap and the refractive index for Ga1-xAlxAs as a function of x.
| Mixing does not only affect the band gap and the lattice constant, but also the quantum efficiency of light production. The next graphic shows the system GaAs - GaP.
|  | The quantum efficiency decreases rapidly as the systems approaches the indirect bandgap region.
|  | If an isoelectronic center - N in this case - is added, the GaP side obtains a strong radiative recombination channel via bound excitons and the quantum efficiency is two orders of magnitude larger.
| Next the lattice parameters of various mixtures as a function of x are shown.
|  | This is easy to calculate, for complete mixing it simply changes linearly with the composition index x between the values for x = 0 and x = 1.
|  | Finally, the technically most important systems are listed together with some key properties
|  | We see that all kinds of ternary and quaternary compounds are used, and that the external or total efficiency - the relation of light out to total power in - is relatively small in most cases. The external efficiency should not be confused with the quantum efficiency (relation of light produced to total power minus ohmic losses), since some of the light produced may never leave the device - remember the fourth question!
|  | Also remember that the total efficiency of a light bulb is just a few percent. The semiconductor values don't look so bad in this context, and that we can get up to 30 % in extreme cases is encouraging. Note that the somewhat exotic exciton process can account for an efficiency of 15 %!!
Material(Doping) | Wavelength [nm] | Transition | External efficiency [% of power] | color
SiC (Al, N) | 480 | ??? | 0.01 - 0,05 | blue
GaP (N) | 565 | Exciton | 0,1 - 0,7 | green - yellow
GaAs0,15P0,85 (N) | 590 | Exciton | 0,1 - 0,3 | yellow-orange
GaAs0,3P0,7 (N) | 630 | Exciton | 0,4 - 0,6 | orange-red
GaAs0,35P0,65 (N) | 640 | Exciton | 0,2 - 0,5 | red
GaAs0,6P0,4 | 650 | Band-band | 0,2 - 0,5 | Infrared
Ga0,6Al0,4P (N) | 650 | Band-band | 1 - 3
GaP (ZnO) | 690 | Exciton | 4 - 15
GaAs | 870 | Band-band | 0,1
GaAs (Zn) | 900 | Band-acceptor | 0,5 - 2
GaAs (Si) | 940 | Deep level | 12 - 30
In0,73Ga0,27As0,58P0,42 | 1310 | Band-band | 1 - 2
In0,58Ga0,42As0,9P0,1 | 1550 | Band-band |