Hi dear friends of steemit, in this first part I talk about the coefficient of optical absorption. In other publications I will talk about reflectivity.
When a monochromatic beam of light passes through a substance, its intensity decreases due to reflection and absorption. Suppose that the fraction of energy reflected in the interface is R, magnitude with the name of reflection coefficient. If the intensity of the incident light is I0 and that of the reflected light is IR, then:
The dependence of the reflection coefficient on energy is called the reflection spectrum.
Let us denote by I the intensity of the light incident on the layer dx. Due to the absorption of light in this layer the intensity of the radiation suffers a decrease dI. The amount of energy absorbed dI is proportional to the amount of energy incident in the layer and the thickness of the absorbent layer:
Where alpha is a factor of proportionality that expresses the amount of energy of the intensity beam absorbed by the unit thickness sample, and is called the absorption coefficient.
By integrating the previous equation, considering that I decreases with increasing x we obtain:
leading up to
Known as Buger-Lambert's law. The alpha magnitude is characteristic of the absorbing medium and depends on the energy of the radiation. The dependence of the absorption coefficient on energy is called the absorption spectrum.
Suppose that the material has N absorption centers, we designate by alpha the probability of absorption of a photon by an absorption center. That is, alpha is the effective absorption section of a photon in the unit of time. The alpha cross section depends on the energy of the photon and the nature of the absorbent centers. The free path of a photon is:
While the absorption factor is:
It is the probability of absorption of the photon in the unit of length.
Suppose that in the material there are absorption centers of different nature. If Ni absorption centers are characterized by an alpha cross section, then:
The total absorption coefficient of the substance is the sum of the partial absorption coefficients:
Therefore, the total absorption spectrum is composed of the absorption spectra of the different absorption centers.
When interacting the electrons of the material with the electromagnetic radiation, two laws must be fulfilled: the law of conservation of energy and the law of conservation of the moment. Therefore, it must be fulfilled:
Where E and E 'are the energy of the electron before and after interacting with a photon of energy hν. p and p 'its moment before and after interacting with a photon at the moment k.
The absorption of radiation in semiconductors can be linked to the variation of the energy state of free electrons, of electrons linked to "own" atoms or to impurities, as well as to the variation of the vibratory energy of the atoms of the net. Due to this, five fundamental types of optical absorption are distinguished in semiconductors: intrinsic, excitonic, free charge carriers, extrinsic and absorption of light by the crystalline lattice.
If, when absorbing a photon, the electrons of the valence band of a semiconductor acquire an additional energy equal to or greater than the width of the band gap or energy gap (Eg), transiting the conduction band, it is said that a intrinsic or fundamental absorption. When studying the fundamental absorption of a semiconductor, the structure of its energy bands must be taken into account.
SOURCES
Pankove J, (1971),Optical Processes in Semiconductors, New York,Dover Publications.
Hecht E, Zajac A, (1977),Óptica, Fondo Educativo Interamericano.
Díaz R, Merino J. M., Martín T, Rueda F, León M,(1998),An approach to the energygap determination from the reflectance measurements.
D.B Gadkari, K. B Lal y B M Arora. (1999). Growth of undoped and Te doped InSb crystals by vertical directional solidification technique, Indian Academy of Sciences.