Alloy broadening

The alloy widening ( English alloy broadening ) denotes a caused by the random distribution of the alloying partners broadening of luminescence lines of alloys .

The alloy broadening is one of the line broadening . The statistical distribution of the alloy partners locally leads to a different material composition, which results in a local variation of the band gap in semiconductor materials and insulators . For this reason, the exciton recombination leads , depending on the material environment in which it takes place, to the emission of photons with different energies. The alloy broadening therefore belongs to the inhomogeneous line broadening, which means that the line broadening is Gaussian . The broadening is independent of the excitation mechanism.

This line broadening occurs only with alloys and is of the order of a few meV . A large number of line broadening occurs in solids. At high temperatures, which can be temperatures of around 20 K depending on the material, the alloy broadening is covered by other line broadening and does not play a role at room temperature.

Mathematical description

The alloy broadening has been proven experimentally in the diatomic alloy, for example . In a diatomic alloy of the type , there are Ge atoms and Si atoms in the section in the volume . Here is the particle density, i.e. the number of atoms per volume. The probability of counting Ge atoms exactly in the volume is given by the binomial distribution . The standard deviation of the binomial distribution is ${\displaystyle {\ce {Si_{1-x}Ge_{x}}}}$ ${\displaystyle {\ce {Si_{1-x}Ge_{x}}}}$ ${\displaystyle V}$ ${\displaystyle x\cdot V\cdot n}$ ${\displaystyle (1-x)\cdot V\cdot n}$ ${\displaystyle n}$ ${\displaystyle V}$ ${\displaystyle k}$

${\displaystyle \sigma _{x}=\Delta k={\sqrt {N\cdot x\cdot (1-x)}}}$,

where is the total number of atoms in the volume . In order to calculate the change in the band gap energy one is interested in. It applies ${\displaystyle N}$ ${\displaystyle V}$ ${\displaystyle \Delta x}$

${\displaystyle \Delta x={\frac {\Delta k}{N}}.}$

It follows that

${\displaystyle \Delta x={\sqrt {x\cdot {\frac {1-x}{N}}}}}$

is. The following applies to the variation of the band gap energy:

${\displaystyle \Delta E={\frac {\mathrm {d} E_{g}}{\mathrm {d} x}}\cdot {\sqrt {x\cdot {\frac {1-x}{N}}}}}$

Since the luminescence occurs in the exciton recombination, the volume of an exciton must be used. ${\displaystyle V}$

The alloy broadening follows a Gaussian distribution, that is, by means of

${\displaystyle I(E)\sim \exp \left(-{\frac {(E-E_{0})^{2}}{2\cdot \Delta E^{2}}}\right)}$

are described, the luminescence intensity broadened purely by the alloy broadening being as a function of the light energy . In order to examine the alloy broadening, the examined material system must be examined at low temperatures (around 4 K) and low charge carrier densities. ${\displaystyle I(E)}$ ${\displaystyle E}$

Individual evidence

1. ^ Bahaa EA Saleh, Malvin Carl Teich: Fundamentals of Photonics. Wiley-VCH, ISBN 978-3-527-40677-7 , page 825 ( limited preview in Google book search).
2. ↑ J. Weber, MI Alonso: Near-band-gap photoluminescence of Si-Ge alloys . In: Phys. Rev. B . tape 40 , 1989, pp. 5683 , doi : 10.1103 / PhysRevB.40.5683 ( full text [PDF; 2.1 MB ; accessed on June 15, 2018]).