# In as number of photons incident on

In this subtask, the EQE of 3 a-Si solar cells was measured using 7 different light sources in the visible range of the spectrum. The short circuit current density is measured and thereby the EQE of the cell is measured.
The correction factor can be associated with the relative special response taking the spectrum of colored LED as a single Gaussian and the relative spectral response fitted curve given in the previous task with the formula 3.11 can give correction factor for 7 different colored LED lights.
Table 2:Correction factor of colored LED
LED Wavelength(nm) Correlation factor (k)
Royal Blue 447.5 0.13
Blue 470 0.18
Cyan 505 0.26
Green 530 0.32
Amber 590 0.45
Red-orange 617 0.51
Deep Purple 655 0.60

As the LED is p-n junction semiconductor material that emits light when current is passed through it. The Table 3 shows the Bias voltage across each colored LED lights.
Table 3: Colored LED’s Bias Voltages
S. No LED Colour Voltage (V)
1 Royal Blue 3.07
2 Blue 3.04
3 Cyan 2.98
4 Green 2.95
5 Amber 3
6 Red-Orange 2.39
7 Deep Red 2.16

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It can be inferred that all the colored LED has different bias voltages. The energy required to emit a photon from the blue spectrum is much more than the energy required to emit a photon in red spectrum. By applying a constant current of 0.4A blue led requires more voltage to reach the required energy than a red led. The trend in decreasing voltage as we move along the spectrum from blue to red is clearly seen in Table 3.
The spectral irradiance and photon flux are the important properties of any light source. Spectral irradiance I_(e,?) is the power received by a given surface for a wavelength of light 2. Whereas the photon flux is defined as number of photons incident on the surface per unit time 2.

I_pd=k×S(?_0 )×A×I_(e,?) 3.13
Here k is correlation factor, S(?_0 ) is the spectral sensitivity at peak wavelength, I_pdis photodiode current, A is the photodiode area and I_(e,?) is the spectral power density. Spectral power density and photon flux is related by the below equation.
I_(e,?)= ?_(ph,?)×hc/? 3.14
Equation 3.13 and 3.14 can be rearranged to form the below relation.
?_(ph,?)=(I_pd×?)/(k×S(?_0 )×A×h×c) 3.15
The External quantum efficiency (EQE) is defined as the ratio of number of electron hole pair created to the number incident photons. The EQE is dependent on wavelength so, it is computed over a certain range of wavelength as given in equation.

EQE(?)= ((dn_e (?))/dt)/(A_cell×?_ph (?)) 3.16
Here (dn_e (?))/dt is the number of electrons exiting the solar cell, A_cell (16 ??2) is the area of the solar cell and ???(?) is the incident photon flux at certain wavelength.
The rate of change of electron movement gives rise to the short circuit current I_sc.

(dn_e (?))/dt =I_sc/e 3.17

Here, e is elementary charge. The EQE in terms of photocurrent, correlation factor, and spectral sensitivity can be expressed by using equation

EQE(?)= (k×S(?_0 )×A×h×c×I_sc)/(I_pd×? ×e × A_cell ) 3.18
Electron flux (?e) can be obtained from short circuit current as follows,

?_e=Jsc/e 3.19
The nominal wavelength of LED, photodiode current, and photon flux is shown in Table 4.

Table 4: Electron flux of different LED sources
LED Colour Wave
length nm Photodiode Current uA ??? Photon flux ?10?^20 ph/(m^2.nm)

Royal Blue 447.5 63.5 1.57
Blue 470 43.1 0.81
Cyan 505 72.1 1.01
Green 530 77 0.92
Amber 590 195.1 1.84
Red-Orange 617 322 2.81
Deep Red 655 213.8 1.68

The electron flux generated in each of the cell is tabulated in Table 5.

Table 5 : Electron flux generated in a-Si cell for different light sources.
LED Colour Short-circuit Current uA Electron flux
?10?^20 elec/(m^2.nm)
Cell A Cell B Cell C Cell A Cell B Cell C
Royal Blue 250 241 223.4 0.98 0.94 0.87
Blue 179.9 168 180.5 0.70 0.66 0.70
Cyan 204 188.5 248.2 0.80 0.74 0.97
Green 211.5 196.1 229.6 0.83 0.77 0.90
Amber 452 382.6 332.5 1.76 1.49 1.30
Red-Orange 580 390.5 605 2.26 1.52 2.36
Deep Red 391.2 335.4 296 1.53 1.31 1.15

The calculated EQE for all the three cells for different color LEDs are tabulated in Table 6.

Table 6: EQE of a-Si solar cells for different light sources
LED Colour Cell A Cell B Cell C
Royal Blue 0.62 0.60 0.56
Blue 0.86 0.81 0.87
Cyan 0.79 0.73 0.96
Green 0.90 0.83 0.97
Amber 0.96 0.81 0.71
Red-Orange 0.81 0.54 0.84
Deep Red 0.91 0.78 0.69
The Figure 7 shows EQE of the solar cell A, B and C. We can notice that EQE for all the solar cell show similar trend are close to 1. This shows that the optical and electrical losses in the solar cell is very minimal. Losses might be due to the surface reflection and surface recombination. Even though the top surface is hydrogen passivated, surface recombination might increase due to the scratches in the solar cell surface.

Figure 7: EQE of a-Si solar cells
Short circuit current density can be obtained using photon flux and EQE of the cell using the below formula.
J_sc=e?_?1^?2??EQE(?)?_ph d?? 3.20
The short circuit current density calculated through this method is tabulated in the Table 7.
Table 7: Short circuit current density
Solar Cell Jsc A/m^2
White LED Jsc A/m^2
Colored LED
Cell A 180.6 141.78
Cell B 159.3 118.10
Cell C 168.1 132.2
The short circuit current density is different measured through the colored LEDs are lower because the of the difference in the spectrum.

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