Line broadening

A line broadening (as broadening mechanism hereinafter) is in the physics the most undesirable increase in the line width of a spectral line of the radiation - emitting systems (eg. Laser ) relative to the natural line width . The natural line width as a basis of comparison follows as the minimum width from the energy-time uncertainty relation .

Overview

A distinction is made between the following dissemination mechanisms:

In the case of homogeneous broadening, the emission probability for a certain frequency is the same for all particles; ${\ displaystyle \ omega}$
in the case of inhomogeneous broadening, the emission probability for a certain frequency is not the same for all particles. ${\ displaystyle \ omega}$

Broadening	Explanation
Homogeneous Mechanisms
Print broadening (also butt broadening )	Occurs when there are collisions (elastic and inelastic) between the particles.
Saturation broadening	Depends on the irradiated laser intensity.
Inhomogeneous mechanisms
Doppler broadening	Follows from the optical Doppler effect with particles moving relative to the laser.
Flight time broadening	Occurs with interaction times that are shorter than the natural lifespan (e.g. when the particles to be measured cross the laser beam at high speed).

Line broadening on X-ray , electron and neutron diffraction recordings can also be caused by internal stresses in the sample or by the fact that only a very small area (<10 ⁻⁵ cm ) scatters coherently . This is used in the radiographic tension measurement .

The line width to be expected even with an almost fault-free crystal can be broadened by such effects. Also, stacking faults and other deviations from the ideal crystal structure have an impact on the line profile. The amount of broadening is obtained by

carries out a comparative measurement with a sample which does not show this effect;
the width caused by the test arrangement is mathematically taken into account.

The line broadening can be evaluated using various methods. Special functions are required for the line profile, e.g. B. a Gaussian distribution or the Cauchy distribution . With the help of such methods it is possible to break down the line broadening into a lattice distortion and a particle size component.

In the mathematically more complex Warren-Averbach method , a Fourier analysis of the line profile is carried out, which leads to a distribution function for the lattice distortion and the particle sizes.

Doppler broadening

If all possible directions of movement relative to the receiver occur in the velocity distribution of the emitting particles, positive and negative Doppler shifts of different sizes result. This makes the spectral line wider. This effect increases with increasing temperature.

Alloy broadening

In alloys in which no clusters are formed, but the alloy partners are arranged purely statistically, such as at , the alloy broadening occurs. As a rule, it is only a few meV and therefore only plays a role at low temperatures, since it is covered by other line broadening at high temperatures. It is an inhomogeneous line broadening. ${\ displaystyle {\ ce {Si_ {1-x} Ge_ {x}}}}$

Phonon broadening

In solids in which phonons are also involved in luminescence , the phonon lifetime also has an influence on the luminescence line width. Phonons are involved in the luminescence of indirect semiconductors such as silicon. The phonon broadening is a homogeneous line broadening and therefore has the shape of a Lorentz curve . The phonon broadening increases with temperature, but does not go to 0 for temperatures around absolute zero. The reason is that phonons are also scattered at defects. In silicon, the half-width of the phonon broadening is well below 1 meV even at room temperature . In the case of alloys in which the phonons have many scattering centers, the half-width can, however, take on significantly larger values.

Butt or pressure broadening

Radiation from hot gases or plasmas shows a line broadening that increases with the pressure . The cause lies in the collisions between the emitters, in which the electron shells deform. On the one hand, this shifts the energy levels of the issuer's initial and final state. On the other hand, the life of the excited state is often prematurely terminated by the impact. Both lead to a shift in frequency or energy of the emitted photon .

Temperature broadening

The population distribution of the bands of a semiconductor or insulator follows a Fermi-Dirac statistic . At higher temperatures, therefore, statistically higher energies are also occupied. The special thing about this line broadening is that it cannot be classified in the scheme of homogeneous or inhomogeneous line broadening. At sufficiently high temperatures it can be described using Boltzmann statistics , i.e. a decreasing exponential function. In solids, at high temperatures, it is the determining line broadening that hides other effects.

Further information

Overview and explanation of the line widening (PDF; 725 kB)
Wolfgang Demtröder: Laser Spectroscopy . 5th edition. Springer, Berlin / Heidelberg / New York 2007, ISBN 978-3-540-33792-8 .

Individual evidence

↑ T .R. Hart, RL Aggarwal, B. Lax: Temperature Dependence of Raman Scattering in Silicon . In: Phys. Rev. B . tape 1 , 1970, p. 638 .

[1] T .R. Hart, RL Aggarwal, B. Lax: Temperature Dependence of Raman Scattering in Silicon . In: Phys. Rev. B . tape 1 , 1970, p. 638 .