Graphene is a 2-D atomic layer of carbon atoms with unique electronic properties like outstanding carrier mobility, high carrier saturation velocity, excellent thermal conductivity, high mechanical strength, transparency, thinness, and flexibility which make graphene an excellent choice of material for advanced applications in future solar cell design. We modeled a solar cell using graphene as the front electrode to study its performance and compare the performance with that of other possible contenders- indium tin oxide (ITO), widely used material at present and carbon nanotube (CNT), another promising material in this regard. Numerical solutions of the electrostatic and transport equations were obtained using the finite-element method. It was found that solar cell with graphene electrode can outperform the others. We also studied its performance as a function of various parameters. The developed model and obtained results are important for the design of solar cell with graphene as electrode.

1. BY
Mohammad Wahiduzzaman Khan
Tanmoy Das Gupta
And
Samia Subrina
p-i-n Solar Cell
Modeling with
Graphene as
Electrode

2. OUTLINE
• Theory of Solar Cell
• Graphene
• Graphene as Electrode
• Model of Solar Cell with
Graphene as Electrode
• J-V Characteristics
• Comparative Study
2

3. Theory of Solar Cell
• Converts the incident solar
radiation energy into electrical
energy
• Incident photons are absorbed to
photo-generate charge carriers
• Illumination is given through the
thin n-side
• The built-in field separates EHPs
photo-generated in the depletion
region
• EHPs further away from depletion
region by minority carrier diffusion
length are lost by recombination
3

4. Theory of Solar Cell
PN Semiconductor Solar Cell PIN Semiconductor Solar Cell
PIN Solar Cell is more efficient as the
depletion region here is wider and more
carriers are generated and drifted
4

5. Theory of Solar Cell
J = −𝐽𝑝ℎ + 𝐽𝑜[𝑒𝑥𝑝(
𝑒𝑉
𝑛𝑘𝑇
) − 1
Jph= Photo-current Density
Jo= Reverse Saturation Current
Density
V= Bias Voltage
n= Ideality factor
k= Boltzman Constant
T= Absolute Temperate
𝐽𝑝ℎ =
𝑞𝐺𝑜
𝛼
1 − exp[−𝛼(ℓ𝑛 + 𝑊 + ℓ𝑝)
J-V Characteristic of Solar Cell
5
ln & lp are minority carrier diffusion
length for electrons and holes
Go= Carrier generation at the top
surface
𝛼= Absorption Coefficient
q= Charge of Electron

6. Solar Cell Electrode
• The back electrode can be metallic
(opaque)
• But the front electrode must be transparent
in order to let the incident photons pass
through it
• Electrodes must present with minimum
series resistance
• Previously metallic finger electrodes were
used
• Now Indium-Tin-Oxide (ITO) is used widely
as transparent electrode
• Graphene is a material with the potential to
replace ITO as the solar front electrode
6

7. Graphene
 2D Carbon Sheet (only one atom thick = 0.35nm)
 Hexagonal Crystal Structure
 Zero bandgap Semiconductor or zero overlap Metal (tunable 0-
0.25eV)
 High metallic strength (few hundred times stronger than steel)
 Flexible
 High Thermal Conductivity (K= 5,000 W / m.K )
 Excellent Electron Mobility (as high as 20,000 sq cm / V.s)
 High Intrinsic Carrier Concentration (1012 cm-2 sheet density)
 High Transparency (upto 98%)
7

8. Graphene vs ITO
• ITO is more costly and the
world supply is expected
to be depleted by 2017
• The production process of
Graphene has been
improving and becoming
cheaper
• ITO is rigid and fragile
• Graphene is flexible and
mechanically strong. So it can
be incorporated with flexible
solar cell
• Transparency of ITO is
around 85%
• Graphene shows more
transparency than ITO
• ITO has a mobility of upto 70
cm2/V.s
• Graphene has a mobility of
upto 20,000 cm2/V.s
8

9. • Another material with the potential of being used as
the electrode of solar cell is Carbon Nanotube (CNT)
• It is a one dimensional (1D) material ;
Graphene can be rolled in to make CNT
• It has a transparency of around 90%
• Its mobility is also very high (as high as 79,000cm2/V.s)
9
CNT

10. Graphene as Electrode
All the properties of Graphene makes it
extremely suitable for its use as the front
electrode of solar cell.
10

11. Physics
. v D
n nD n n
q
   

nJ
E
p pD p p
q
   
pJ
E
Drift-Diffusion EquationPoisson’s Equation
11
Where,
D = Electrical Displacement Field
 = Free Charge Density
Where,
n & p are concentration
𝐉𝐩 are current density𝐉𝐧 &
Dn and Dp are diffusion coefficient,
µn and µp are mobility
of electrons and holes respectively

12. Geometry
(47nm)p-Si
(30nm)n-Si
i-Si (250nm)
Contact
Graphene
(1nm)
12

13. Sample Doping Profile
13

14. 0.0 0.1 0.2 0.3 0.4 0.5
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
100
CurrentDensity(A/m
2
)
Voltage (V)
J-V Characteristic of PIN Solar Cell with
Graphene
Jph 378.5 A/m^2
Voc 0.4147 V
FF 76.45%
Eff 12 %
0.00 0.25 0.50
-400
-300
-200
-100
0
100 cSi
aSi
14

15. J-V Characteristic with Intrinsic Layer Variation
0.0 0.1 0.2 0.3 0.4 0.5
-500
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
CurrentDensity(A/m
2
)
Voltage (V)
0.25m
0.19m
0.09m
PN
15

16. J-V Characteristic with Intensity Variation
0.0 0.1 0.2 0.3 0.4 0.5
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000CurrentDensity(A/m
2
)
Voltage (V)
100 W/m
2
1,000 W/m
2
10,000 W/m
2
16

17. J-V Characteristic with Wavelength Variation
0.0 0.1 0.2 0.3 0.4 0.5
-500
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
CurrentDensity(A/m
2
)
Voltage (V)
400nm
470nm
530nm
600nm
17
Ref: Reporting solar cell efficiencies in Solar Energy Materials
and Solar Cells; Solar Energy Materials & Solar Cells 92 (2008) 371–373

18. Theoretical Measurement
In our base design:
• The incident optical power, Pin = 1000 W/m2
• Wavelength of photon, 𝜆 = 530nm
• Absorption Coefficient, 𝛼 = 1.58x 107m-1
• Generation, G = )Goexp(−𝛼𝑦 :: Beer-Lambart Equation
• Photo-current density, 𝐽𝑝ℎ =
𝑞𝐺𝑜
𝛼
1 − exp[−𝛼(ℓ𝑛 + 𝑊 + ℓ𝑝) = 415
A/m2
18

19. Graphene vs ITO vs CNT
0.0 0.1 0.2 0.3 0.4 0.5
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
50
CurrentDensity(A/m
2
)
Voltage (V)
ITO
CNT
Graphene
19

20. Graphene vs ITO vs CNT
Performance
indices
Graphene CNT ITO
Jph (A/m2) 378.5 349.5 339.3
Voc (V) 0.4147 0.4135 0.4076
FF 76.45% 75.72% 68.23%
Eff 12% 10.9% 9.4%
20

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