I need to calculate the conductivity of the my material. From the previous reported articles i got these formulas
1. σ ∝ exp(-Eg/2*Kb*T)
Kb - Boltzmann constant
T - Temperature (in kelvin)
Eg - Energy gap (in eV)
2. σ = A*T^3/2 exp(-Eg/2*Kb*T)
Kb - Boltzmann constant
T - Temperature (in kelvin)
Eg - Energy gap (in eV)
A - constant ( in some article it is mentioned as Richardson Constant = 6 * 10^5 A/m^2)
3. σ = A*T^3/2 exp(-Eg/Kb*T)
Kb - Boltzmann constant
T - Temperature (in kelvin)
Eg - Energy gap (in eV)
A - constant
among the above formulas which one is correct to calculate conductivity?
Ref:
1. Article Adsorption of Rare Base-pairs on Surface of B/N Atom Doped γ...
2.Article A quantum mechanical prediction of C24 fullerene as a DNA nu...
@Akielesh, None of the formulas you give can be considered correct for calculating the connectivity of a new material.
In general you have that the connectivity is given by the carrier concentration and the carrier mobility.( 1/sigma = n*my ; n=carrier concentration, my=mobility)
Both carrier concentration and mobility has a temperature dependence which is different, and for a given material the dominating temperature dependence varies with temperature. For many technological important semiconductors, the conductivity is following the temperature dependence of the carrier concentration at high temperature. The carrier concentrating temperature dependence will in simple models have the temperature dependence of equation at high temperatures. It means that the energy gap can be determined experimentally by plotting the log of sigma vs 1/T , and from the slope of the straight line fit get Eg/2. It is a common way to check that the material behaves like a semiconductor. You see that this temperature dependence is in your given equation 2. In equation the exponential term has a dominating temperature dependence over the term T^(3/2). The latter comes from the temperature dependence of the effective density of states in, and reflects that the energy distribution of carriers will vary with temperature.
The high temperature region where the temperature dependence follows equation 2 is usually called the “intrinsic “ region.
Your eq1 and eq2 gives the correct temperature dependence for the intrinsic region.Your equation 3 could be a print error. a factor 2 missing. The exponent. does not describe that region.
One can have a situation where you don’t have free carriers for conduction, but the movement of a carrier requires an activated jump over a barrier. (Some might call the energy barrier a gap) and you would have a exp(-E/kT)
The first and second formulas are the same, but the first is a proportion and the second is an equality. To get an equality from a proportion, you need to introduce a proportionality factor. It is АТ3/2. The coefficient A is a value that depends on the effective masses and mobilities of electrons and holes, so to calculate the conductivity, you need to know these values. In practice, they do the opposite - they measure the conductivity and calculate the effective masses and mobilities. Also keep in mind that this formula 2 is correct at intrinsic conduction temperatures. If the temperature is in the region of impurity conduction, the formula is the same, but instead of Eg, the activation energy of the impurity Ea is used.
The third formula is wrong.
As for the Richardson constant А=6*105А/(m2K2) it appears in a similar formula describing the saturation current density at thermoelectronic emission js=AT2exp(-w/kbT), where w is the work of electron yield.
Thank you so much professors for sharing your knowledge Terje Finstad and Yuriy Uhryn
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