3. Methodology
3.3 Research methods
When semiconductor films interact with electromagnetic radiation, they exhibit certain properties which are referred to as optical properties. These optical properties when studied carefully help to reveal the industrial importance of semiconductor materials. Some of these optical properties include absorbance (A), transmittance (T), reflectance (R), absorption coefficient (α), refractive index (n), optical conductivity (ζ), extinction coefficient (k), dielectric function (ε) and band gap energy (Eg).
2.9.1. Absorbance (A).
When a sample interacts with light, part of the incident light on the surface of the sample is absorbed. This process is known as absorption and the mathematical quantity of the light absorbed is termed “absorbance.”
The absorbance of a sample can also be defined as the ratio of the absorbed beam of light to the incident beam of light. If the incident beam of the sample is Io and the absorbed beam is IA, then the absorbance of the sample is expressed by equation 2.3:
A = Absorbed beam (IA)
Incident beam (I0) (2.3)
Absorbance is measured in arbitrary unit (a.u).
2.9.2. Transmittance (T)
The transmittance of a sample is defined as the quantity of light at a particular wavelength which passes through the sample when light or electromagnetic radiation is incident on the sample. It can also be defined as the ratio of the transmitted light to the incident radiation. If
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the transmitted light is designated by IT and the incident radiation is given by Io, then the transmittance can be expressed mathematically by the relation:
Tλ = IT
Io (2.4).
where Tλ = Transmittance of the sample at a particular wavelength, IT = Intensity of the transmitted light,
Io = Intensity of the incident radiation.
However, it is pertinent to state that the term “transmission” is used to refer to the physical process of radiation which passes through a sample while “transmittance” refers to the mathematical quantity.
2.9.3. Reflectance (R)
When electromagnetic radiation strikes a sample at a particular wavelength, the portion of reflected light is called reflection and the quantity of the incident radiation at a given wavelength that is reflected back when it strikes a surface is referred to as the reflectance.
Reflectance can also be defined as the ratio of the reflected light to the incident radiation. If the reflected light is designated by IR and the incident radiation is given by Io, then the reflectance can be expressed mathematically by the relation:
R = Reflected Light (IR)
Incident Radiation (I0) (2.5)
The spectral absorbance (A), transmittance (T) and reflectance (R) are related by a single equation as shown in equation 2.6.
A + T + R = 1 (2.6)
The value of reflectance (R) of a given sample can be calculated from equation 2.6 when the values of absorbance (A) and transmittance (T) are known.
33 2.9.4. Absorption coefficient (α)
The amount of light absorbed by a material is defined by its absorption coefficient. It can be seen as the decrease in the intensity of a beam of photons or particles when they pass through a particular sample or medium (Jeroh, 2012).
Consider an incident radiation Io on a material having thickness t, then the transmitted intensity IT can be expressed as:
IT = Io exp (- α t) (2.7)
IT / Io = exp (- α t) (2.8)
But, T = IT / Io
Therefore, T = e–αt (2.9)
Where α = absorption coefficient.
Equation 2.9 can be re-written in the form:
In T = - αt (2.10)
α = − [In T]
t (2.11)
2.9.5 Refractive index
The refractive index of a material is defined as a measure of the speed of light in that material.
It can be expressed as a ratio of the speed of light in vacuum relative to that in the considered medium. The refractive index of a material can be calculated as expressed in equation 2.12.
n = Speed of light in vacuum
Speed of light in medium (2.12)
The refractive index can also be expressed as shown in equation 2.13.
n = 1+ R
1/2
1− R1/2 (2.13)
where R = reflectance of the film.
34 2.9.6. Optical conductivity
The frequency response of a material when it is irradiated by light is referred to as the optical conductivity of the material. The optical conductivity of a material directly depends on the absorption coefficient and is found to increase sharply for higher energy values due to large absorption coefficient for the values.
2.9.7 Extinction coefficient
The extinction coefficient of a sample is defined as a measure of the rate of diminution of transmitted light via scattering and absorption for the sample. The absorption and refraction of a medium can be described by a single quantity called the refractive index. This is usually given by the symbol; ñ and is defined through the equation:
ñ = n + ik. (2.14)
The real part of ñ, namely n, is the normal refractive index while the imaginary part of ñ, namely k, is called the extinction coefficient.
2.9.8. Dielectric function
The dielectric function of a thin film is a complex quantity which consists of both the real and imaginary parts. It is a fundamental intrinsic property of a material. The real part indicates how the speed of light in the material can be slowed down while the imaginary part deals with the absorption of energy by a dielectric from electric field due to dipole motion.
2.9.9 Band gap energy
Band gap is defined as the distance between the upper valence band and the lower conduction band. The energy associated with band gap energy and transition type can be defined from
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mathematical treatment of data obtained from optical absorbance versus wavelength with the following relationship for near edge absorption (Anuar et al., 2010).
The band gap energy of semiconductor thin/nanofilms can be calculated from the expression (Anuar et al., 2010):
α = [k(hν−Eg)n /2
hν (2.15)
where α is absorption coefficient, υ is the frequency, h is Planck‟s constant, k is a constant and n= 1 or 4.
For a direct transition, n is equal to 1, while n is equal to 4 for an indirect transition.
Hence, the intercept of the plot of (αhv)2 versus the photon energy, hυ, gives the value of the band gap for a direct transition while the band gap energy for an indirect transition is obtained from the intercept of the plot of (αhv)1/2 versus the photon energy, hυ.