International Journal on Advanced Electrical and Electronics Engineering, (IJAEEE), ISSN (Print): 2278-8948, Volume-1, Issue-1, 2012
89
Modelling of Solar Cell Using Odd Size Quantum Dots
P. Balaji 1, B. Murali Babu2, A. Shafarna3
1,3Paavai Engineering College, 2 Paavai Engineering College, TamilNadu
1[email protected], 2[email protected], 3[email protected]
Abstract - — Photovoltaic conversion of solar energy from the sun is becoming the primary source of energy replacing the depleting fossil fuel. The 3 dimensional numerical model for GaAs Quantum Dot solar cell has been developed and presented. This work proposes a better way to improve the efficiency of the solar cell by implementing different size (odd) quantum dots. The QD Model utilizes the Schrödinger Equation and the same is validated using simulator tool, Quantum Dot Lab, and the band gap energy of QD is calculated at different temperatures. The results obtained shows good improvement of the efficiency of the solar cell at different wavelengths of solar spectrum.
Keywords - Quantum Dot, Schrodinger Equation, Solar Cell.
I. INTRODUCTION
One of the largest challenges, the mankind faces in the twenty-first century is how to meet the increasing energy demand. Recent energy production versus energy consumption comparison shows that alternative energy source to fossil fuels will be required by the end of this century [1]. Photovoltaic power is becoming increasingly important and widespread as an alternative energy source because of environmental concerns resulting from fossil fuels. Efficiency on the order of 25% is now achievable on silicon crystalline solar cells [2].The operation of conventional PN solar cells is explained and modeled in essence through drift- diffusion models [3]. Single crystal silicon solar cells generally achieve power conversion efficiency values of
~15%-19.3% commercially with experimental cells developed in lab environments capable of 24.7% to 25%
efficiency [1]. Recent advances are primarily attributed to improvements in light in-coupling by optimizing the silicon surface geometry and have allowed the cells to near the ~31% efficiency upper limit. Alternative polycrystalline CdTe-based solar modules have also proven to be reasonably successful, with panel conversion efficiencies of 11.1% [4].
S.N. Mohammad et al presented solutions for the continuity equation for excess carrier density in polycrystalline cells using a two-dimensional model [5],[ 6]. A. Fickou et al presented a three-dimensional model [7], but all of them considered a cubic geometry for the grain.
The primary reason why solar cells are not 100%
efficient is because the semiconductors do not respond to the entire spectrum of sunlight. Photons with energy less than silicon's band gap pass through the cell and are not absorbed, which wastes about 18% of incoming energy. The energy content of photons above the band gap will be wasted as heat or re-emitted. This accounts for an additional loss of about 49%. Thus about 67% of the energy from the original sunlight is lost, or only 33%
is usable for electricity in an ideal solar cell. In a solar cell, photons are absorbed mainly in the p-layer. Thus it is important to tune this layer to the properties of incoming photons to absorb as many as possible, and therefore to free up as many electrons as possible.
The first advantage of the QDs over dyes is the ability to tune the absorption threshold simply by choice of dot diameter. For example, colloidal InP QDs, separated by dot size, have thresholds which span the optical spectrum. Secondly, high luminescence quantum efficiency has been observed. CdSe/CdS heterostructure dots have demonstrated luminescence quantum yields above 80% at room temperature [8].
From the above discussion, it is clear that quantum dot solar cells have the potential to address many of the issues present in current technology of photovoltaics.
The carrier confinement property of quantum dots leads to additional desirable properties such as extended hot carrier lifetimes and multiple exciton generation. A hot carrier is generated when a quantum dot absorbs light with energy greater than its band gap.
International Journal on Advanced Electrical and Electronics Engineering, (IJAEEE), ISSN (Print): 2278-8948, Volume-1, Issue-1, 2012
90 This work proposes a better solar cell model with higher cell efficiency and spectral response than conventional solar cell by using quantum dots. Since these exhibit a tuneable spectrum response and large short circuit photo electric current (>25mA/cm2). The quantum confinement characteristics of a quantum dot enable us to decide the band gap energy of the semiconductor material which is very essential parameter which decides the efficiency of a cell.
II. MATHEMATICAL MODELING A. Device Structure
In this the solar cell structure is fabricated as shown in Figure (1) with two layers of quantum dots which are of different diameter as different size dots have different band gap energy. This ensures harvesting of wide spectrum of light and also lattice mismatching loss is reduced since both layers of quantum dots are made of same materials. The modelling of the cell is done by solving Schrodinger equation
Figure No 1. Proposed model of Quantum Dot Solar Cell
B. Equations
Quantum dot solar cell is governed by the Schrödinger Equation (1). The kinetic and potential energies are transformed into the Hamiltonian which acts upon the wave function to generate the evolution of the wave function in time and space. The Schrodinger equation gives the quantized energies of the system and gives the form of the wave function so that other properties may be calculated. Integrating the equation with boundary condition Where V(x) = {0 0 < x < Lx; ∞ elsewhere
1)
2)
Considering the wave function to find the area of the first energy state curve, the limits are taken as below and
integrated and substituting the values and considering the potential to be zero within the quantum well, in the Schrodinger Equation (2) we get,
The Equation (4) shows the same in 3 Dimensional axis representing the physical dimension of the Quantum Dot, where ―n‖ is the excited state level, ―L‖
is the physical dimension of the quantum dot in nm.
The Equation (4) shows the same in 3 Dimensional axis representing the physical dimension of the Quantum Dot, where ―n‖ is the excited state level, ―L‖
is the physical dimension of the quantum dot in nm.
(4)
(5)
(6) Considering for a Quantum Dot where all dimension are equal (Lx=Ly=Lz=L), given by the Equation (5), (6) shows that energy is inversely proportion to dimension of the Quantum Dot and the band gap energy for different temperature can be found using the Equation.
(7)
The power output that can be obtained from the cell is given by the Equation (8)
P = J×V (8)
At power maximum, dP
dV = 0= and V = Vm; Jm is determined from the Equation (9) [12]
(9) 2nm
4 nm
Substrate
International Journal on Advanced Electrical and Electronics Engineering, (IJAEEE), ISSN (Print): 2278-8948, Volume-1, Issue-1, 2012
91 Solar cells may also be described in terms of several key parameters, including the open circuit voltage (Voc), short circuit current (Isc) and Fill Factor (FF). While under illumination, the open circuit voltage is the voltage across the cell when the cell current is zero and the short circuit current is the current across the cell when the cell voltage is zero. The fill factor may then be defined the following Equation (10)
(10) Where Vm, is the maximum power point voltage and Im is the maximum power point current. As such, the fill factor is a measure of the closeness to an ideal solar cell, which would have a rectangular shape in the fourth quadrant of an I-V output graph for a given light exposure. The power conversion efficiency may then be determined as below.
(11)
Where Pin is the incident light source power measured in Watts AM1 (Pin = 0.1 W.cm-2).
III. COMPUTATIONAL ANALYSIS
This Equation is numerically solved and also correlated with online simulator ―Quantum Dot Lab‖
[9]. The Table (1) shows the band gap energy for different size quantum dots of GaAs material with Effective Mass 0.067, along with results of the numerical calculation solved using Schrodinger equation.
Dimension in nm
Eg in ev (nanohub)
Eg in ev (calculated)
2 3.5669 4.203
3 2.5182 1.872
4 1.3029 1.051
5 0.7718 0.673
6 0.5059 0.4675
7 0.4211 0.3435
8 0.3046 0.2629
9 0.2301 0.2078
10 0.18 0.1683
Table No 1. Simulated and Calculated Band Gap Energy of GaAs Quantum Dot
And similarly the Table (2) shows the band gap energy of the GaAs quantum dot at various temperature levels which is derived from the Equation (7).
Temperature in K
Eg of GaAs
50 1.514
100 1.501
200 1.465
300 1.422
400 1.376
500 1.327
600 1.277
700 1.226
Table No 2. Energy of Band gap at various Temperatures
The fitting constants for the equation are provided in the table (3)
S.No Parameter value
1. Eg of GaAs at 300k 1.43ev 2. Eg of GaAs at 0k 1.52ev 3. Effective mass of
GaAs 0.067 kg
4. Electron rest mass 9.11×10-31Kg 5. Planks constant (h) 4.135×10-15 ev 6. Reduced planks
constant 6.582×10-16 ev 7. Speed of light 3×108 m/s
8. Angle theta 45°
9. Fitting parameter 𝛼 = 0.541 mev 𝛽 = 204k Table No 3. Values of Constants IV. RESULT AND DISCUSSION
The Figure (2) shows the simulated Quantum Dot structure of GaAs with dimension 5nm, Discretization 0.565nm and Energy Gap 1.43ev for the first energy state. The simulator also provides the value of energy level of ground, first excited states and band gap energy.
Simulation and numerical calculation is done for QD with size ranging from 2nm to 10 nm.
International Journal on Advanced Electrical and Electronics Engineering, (IJAEEE), ISSN (Print): 2278-8948, Volume-1, Issue-1, 2012
92
0 1 2 3 4 5
0 1 2 3 4 5 6 7 8 9 10 11 12
Energy Gap in ev
Dimension in nm
Size Vs Bandgap Energy
Eg (simulator)
Eg (calculated )
Figure No.2. Simulated GaAs Quantum Dot structure using Quantum Dot Lab Simulator
The Figure (3) shows the comparative energy gap between numerical solution and simulator results. The results show that the band gap energy of the GaAs
quantum dot increases as its size decrease. The
numerically obtained graph is very close to the simulator result.
Figure No. 3. Comparison of Band Gap Energy of GaAs Quantum Dot using Simulator and Numerically
Calculated values
The Figure (4) shows the characteristic of GaAs Quantum Dots Eg at different temperature levels, obtained from Equation (7). This shows an inverse characteristic.
Figure No 4. Band Gap Energy of GaAs Quantum Dot for different Temperature
With these results, it is clear that when implemented in the solar cell the 2nm and 4 nm quantum dots will produce excitons for violet and red spectrum with wavelength 400um and 600um respectively.
IV. CONCLUSION AND FUTURE WORK
The proposed solar cell model he cell is capable of harvesting photon energy from a wide wavelength. With different size quantum dot providing excitons of different energy level the overall efficiency of the cell increase considerably.
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International Journal on Advanced Electrical and Electronics Engineering, (IJAEEE), ISSN (Print): 2278-8948, Volume-1, Issue-1, 2012
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