Team:USTC/Model/4
Abstract
CdS is a kind of Ⅱ-Ⅵ type semiconductor which is well studied previously, that can guide our experiment to optimize the system efficient by modeling .In this part, we'll show some factors affecting the electron flux transformed into E.coli. and come up with some practical strategies to improve the efficiency of our system.
Basic theory
Carriers density:
According to quantum theory, states of electrons could be described by energy band:
Fig. 1 | The distribution of energy level and the process of creating free electrons
Ef is Fermi energy,which gives the average level of electrons' energy.
Ec is the minimum energy of conduction band.
Ev is the maximum energy of valence band.
Generally speaking, Ef and Ec,Ev have no direct relationship because Ec,Ev are derived from Schrodinger equation and Ef is determined by the real circumstances of electrons.
And the density of carriers is:
Among them, E represents the energy of each electron. g(E) represents the density of state(one energy line in the energy band image). f(E,Ef) shows the possibility whether the states will be occupied by one electron(Pauli exclusion principle tells that one state can only be occupied by one electron at most).
The concrete form of f(E,Ef) and g(E) is:
Expression of f(E,Ef) is called Fermi-Dirac distribution,which is derived from statistical mechanics,and g(E) is from the periodical boundary condition because we regard the CdS as the ideal crystal, that means, no dislocation, no impurity.
ε:difference of E and Ec,represent the electrons' kinetic energy.
m:valid mass of electron.
h:Plank constant
Fig. 2 | A demonstrate of f(ε),g(ε) and f(ε)g(ε)
Substitute the expression in the integral ,we have:
That is the density of electrons in standard crystal.
Similarly, we can derive the concentration of holes in valence band as a function of Ef:
Let's consider about the situation that the semiconductor material keep electrical neutrality ,so we have :n=p
Substitute the expression for Nc and Nv ,we have:
Now Ef is called intrinsic Fermi level, it is proportion to the temperature where the semiconductor locates.
So we can derive the intrinsic carrier density：
We have to notice that the function is very simplified because we consider the CdS as the ideal crystal, neglect impurity and flaws, though inevitable in fact.
Band Gap:
Band Gap in quantum mechanics plays an important role to describe the circumstance when quantum leaping. Larger the gap is, harder the electron transit to the high energy band, making it be a carrier of electricity .It can be tested indirectly with Absorption spectrum.
Absorption spectrum can be measured in experiment and we can derive absorbance index α by:
T : material transmission of light with different wave length
d : the thickness of sample.
Thus we can get a curve of α as a function of wave length λ. To calculate the band gap of CdS we use, we can use the relationship between absorbance index and band gap:
We can get a diagram with axes (αhν)2 and hν from the experiment, deriving intercept on x axis by plotting a straight line that is tangent to the raising part of the curve[2]:
Fig. 3 | The curve of (αhν)2 and hν
Now we know the band gap in CdS attached to Shewanella is 2.51eV
(Relation of α and hν are not sufficient consistently because under 2.51eV, electrons don't have enough energy to transit .Beyond 2.84eV, situation become more intrinsic because we have to consider about both direct absorption and indirect absorption.)
Practice and Improvement:
According to the literature, CdS Nc is 0.224e+19/cm3 and Nv is 2.5e+19/cm3,[1] which is all measured under room temperature. The final intrinsic electron density of CdS on the surface of cell membrane is 5.6e-3/cm3, which is too small when compared to other semiconductor material (in room temperature, 1 atm):
We hope for more free intrinsic electrons in our material because that'll largely increase the electrons transferring into E.coli. We could replace CdS with CdTe for better efficiency.
CdTe is another kind of nanoparticle which is fully researched both in semiconductor physics and biology due to lower energy gap(1.5eV, compared to CdS 2.51eV),which result in more intrinsic free electrons activated. In the mean while, it is a very popular material as Quantum dots (QDs) which is supposed to attach to living cells for the sake of application of colorful lighting. Though CdTe has toxicity to E.coli but according to Fang TT1 et al, scale of CdTe has reverse ratio to the toxicity adhering on the cell. So we can control the reaction condition to minimize the toxicity to E.coli.
Reference
- Sez S M. *Physics of Semiconductor Devices*.New York:John Wiley and Sons,1981:19.
- Kelsey K. Sakimoto, Andrew B W, Peidong Y *Self-photosensitization of nonphotosynthetic bacteria for solar-to-chemical production*. Science 2016,vol 351,issue 6268.
- Fang TT1, Li X, Wang QS, Zhang ZJ, Liu P, Zhang CC. *Toxicity evaluation of CdTe quantum dots with different size on Escherichia coli*NCBI 2012:1233-9.
