When a beam of monochromatic light passes through a substance its intensity decreases due to reflection and absorption. Let us suppose that the energy faction reflected in the interface is R, magnitude with the name of reflection coefficient. If the intensity of the incident light is I_o and that of the reflected light is I_R, then:
The dependence of the reflection coefficient on the energy, R (hν), is called the reflection spectrum.
To demonstrate the veracity of this equation (1), physicists must scientifically demonstrate the relationships that appear in that relationship. For this we must represent an experiment, which meets the requirements of the equation. Said formula will be demonstrated from the image (1), in which we can see, that the absorption of light in this layer the intensity of the radiation suffers a decrease in the amount dI. This amount of energy absorbed dI must be proportional to the amount of energy incident in the layer and the thickness of the absorbent layer:
In equation (2), the proportionality factor α, which expresses the amount of energy absorbed by the unit intensity beam by the unit thickness sample, or absorption coefficient.
Absorption of light by a material
To find the equation that gives us the total incidence (I) we must integrate the (2). Considering that the incidence (I) decreases with increasing x, we obtain:
Resolving we get:
The relation (4) is known as the Buger-Lampert law. Where the magnitude α is characteristic of the absorbing medium and depends on the radiation energy. The dependence of the absorption coefficient on the energy, α (hν) is called the absorption spectrum.
The task that we scientists love, is to find creative solutions to each of the various problems that we find in our work, and that we achieve using the most important muscle of our body, the brain. With it we can imagine simple solutions, under extremely stable conditions, which later will not allow extrapolation to real conditions. For them suppose that certain material has N absorption centers, we designate by σ the probability of absorption of different nature. That is, σ is the effective absorption section of a photon in the unit of time. The effective section σ depends on the energy of the photon and on the nature of the absorbent centers. The free path of the photon l_f is:
While the absorption factor is:
This is the probability of absorption of the photon in the unit of length. If we assume that in the material there are absorption centers of different nature. If N_i absorption centers are characterized by an effective section σ_i, 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 the energy and the law of the conservation of the moment. If before interacting with a photon of energy hν and a moment hk the electron has energy E and m moment p, after interacting it will have E 'and p' and these laws are written as:
The absorption of radiation in semiconductors can be linked to the variation of the energy state of free electrons or electrons linked to the "own" atoms or to the impurities, as well as to the variation of the vibratory energy of the atoms of network. 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 gap of supplementary energy equal to or greater than the width of the band gap or energy gap ( E_g), transiting the conduction band, such absorption is called intrinsic or fundamental. When studying the fundamental absorption of a semiconductor, the structure of its energy bands must be taken into account. Currently known semiconductors are divided into two fundamental types according to the configuration of the energy bands. In the first type the minimum energy of the conduction band characterized by the wave vector k_min, and the maximum energy of the valence band, determined by the wave vector k_max, are arranged at the same point in the Brillouin zone ( generally at the point k = 0).
That is, in these semiconductors k_min = k_max and are called direct gap.
In a second group of materials the ends of the valence band and conduction are in different k, k_min ≠ k_max, being called indirect gap
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