Theoretical Study of Quantum Efficiency and Spectral Response of Solar Cells

A theoretical study of Quantum Efficiency (QE) and Spectral Response (SR) of solar cells was done in order to suggest ways in which related parameters could be optimized for maximum conversion efficiency of solar cells. Secondary data for the base, emitter and total parameters of QE and SR were obtained. MATLAB was employed in plotting and analysing these data across different diffusion lengths. From the results obtained, it was observed that when the value of the Emitter Diffusion Length (EDL) was varied from 0.3μm to 0.5μm, the emitter and total values of QE increased by about 700% at wavelength 300nm – 400nm. In the case of SR, it was observed that when there was an increase in the Base Diffusion Length (BDL) from 20μm to 50μm, there was an increase of about 26% at wavelength 800nm – 900nm. A rise in the diffusion length was seen to increase both the QE and SR of the cell. Thus, it can be suggested that an increase in the emitter and base diffusion length of a solar cell leads to a decrease in the recombination charges in the cell, giving more time for the charge carriers to exit the cell.


Background
A solar cell's quality is reflected in its conversion efficiency [1].Therefore, for the conversion efficiency of the cell to improve, the Quantum Efficiency (QE) measurement needs to be performed.The QE of a solar cell is the ratio of the number of electrons that contribute to the photogenerated electricity to the incident photon at a specified wavelength [2].The QE can be given either as a wavelength function or as energy.QE provides additional knowledge on the cell, as such, improving the QE, thereby improving and enhancing the solar cell and its IOP Publishing doi:10.1088/1755-1315/1342/1/012043 2 conversion efficiency.The amount of current a solar cell can produce when irradiated by photons of a given wavelength determines the QE value.Thus, if photons of a specific wavelength are absorbed then the QE at that particular wavelength is 100%.However, QE is at one or unity at a particular wavelength if all the photons at said wavelength are assimilated and are zero if the energy of the photon is less than that of the bandgap.QE is zero if the photon's energy is less than that of the bandgap.Spectral Response is the ratio of the solar cellgenerated current to the incident power of the solar cells [3].This is also the ratio of the photocurrent produced by a solar cell to the spectral irradiance value at the same wavelength under monochromatic illumination at a given wavelength.It has S.I. unit of Amperes per watt (A/W).The QE correlates to the Spectral Response (SR), which dictates the spectral distribution of the current in the short circuit or ISC.By measuring the QE, it is possible to know both the SR and ISC contributions of different wavelengths [4], leading to the analysis of the quantum yields from the different cell regions, thus improving cell performance.
Different parameters were considered when discussing the optimization of solar cells, some include a) front and rear surface recombination velocity, b) diffusion length at the emitter and base, c) the width of the depletion region, and d) light trapping [5].QE is used for testing new cell structures as well as for verifying the reproducible output of PV cells [6].Unfortunately, the QE for most solar cells is limited due to the consequences of recombination where carriers in the cell cannot move into an external circuit.Hence, this paper will study and analyse the overall QE and SR of a cell, the QE and SR of different parts of the cell and the QE and SR at different wavelengths to identify the trend and suggest ways recombination can be reduced.

Quantum Efficiency (QE)
Quantum Efficiency of solar cells is of two types.
External Quantum Efficiency (EQE) refers to the difference in the number of charge carriers by the solar cell and the number of incident photons of the given energy irradiated on the solar cell from outside.The effect of optical loss, such as transmission and reflection, shall also be considered when EQE is measured for silicon solar cells.Internal Quantum Efficiency (IQE) is the difference in the number of charge carriers received by a solar cell and the number of photons of the obtained energy irradiated and absorbed from the outside of the solar cell.IQE is the efficiency with which photons are absorbed to produce collectable carriers [7].The IQE is notably higher than the EQE [8].A low IQE means that the photons are unable to make sufficient use of the active layer of the solar cell.To measure the IQE, the cell's EQE is measured first, then its transmission and reflection are measured, and these data are combined to determine IQE.The EQE curve may be modified by measuring a device's reflection and transmission to obtain the IQE curve.EQE is dependent on light absorption and charge collection.The recombination of charges causes the EQE to decrease as charge carriers cannot move into an external circuit.Other mechanisms which affect quantity efficiency are those that also affect collection probability [8].
EQE and IQE differ in the treatment of photons reflected from the cell.The EQE value considers all photons impacting the cell surface directly, while the IQE value considers all other photons that are not reflected [9].IQE and EQE values are frequently measured with the use of interference filters or monochromators to determine the competence of a solar cell.Chander et al. studied the SR and EQE of monocrystalline silicon solar cells at wavelengths between 350 to 1100 nm.At 350nm, the EQE increased until a peak value of 590 nm, then a gradual decrease from 970 to 1100 nm [10].

Spectral Response (SR)
Spectral Response was given in relation to quantum efficiency as there is a similarity in the number of photons as well as in solar insolation.
(  ⁄ ) =  ℎ () () (5) where λ=micrometre (μm); JPh (λ)= total photogenerated short circuit density; I(λ)=Spectral Irradiance of the incident light.The spectral response can be internal or external depending on the value of quantum efficiency used to obtain it [11].Ideally, spectral response is limited due to the semiconductor's inability to absorb photons below certain bandgap energies at long wavelengths.This limit is the same as detected in the quantum efficiency curve.In contrast, spectral response decreases at lower photon wavelengths.Each photon has huge energy at these wavelengths, and therefore the ratio of photons to power is reduced.The solar cell does not use any energy above the bandgap energy; instead, it goes to heating the solar cell.A significant power loss in solar cells controlled by a single p-n junction is the failure to completely use the incident energy at high energies and the failure to absorb low luminous energy.

Material and Methods
Matrix Laboratory, MATLAB, is a high-level matrix/array language with control flow statements, a digital computation environment and a proprietary programming language developed by MathWorks [12].MATLAB helps in manipulating matrices, mapping out functions and results, implementing algorithms, and communicating with programs written in other computer languages [12].The version of choice is R2023a.MATLAB and Simulink are used in the automobile, aerospace, communications, telecommunications and industrial automation sectors as basic methods for research and development.Likewise, they are used for simulation and modelling in technical fields like mathematics, economics, engineering, finance, computational biology, image processing, and medical research [13].The data obtained for spectral response and quantum efficiency were processed using MATLAB to obtain a plot.The data comprised of Emitter (N-type semiconductor) values, Base (P-type semiconductor) values and the total of these values for both spectral response and quantum efficiency.

Comparison Analysis for Emitter and Base
In Fig. 5, when analysing the Quantum Efficiency and Spectral Response for the base (the bulk material) of a solar cell, the QE is seen to have its peak at 800nm while SR has its peak at 850nm.The peak values for QE and SR lie within the 750-950 nm range.This implies that in order to obtain high values of QE and SR, light photons within the near-infrared region of the electromagnetic spectrum are required.Also, radiation from the UV-A region (300-400nm) does not show any Spectral Response or Quantum Efficiency.In Fig. 6, SR and QE peak at 450nm.This implies that in order to obtain high QE and SR values for the emitter, the light photons from the visible and near-ultraviolet regions of the EM spectrum will be required.Light photons from the near-infrared region would give very low to no values for both SR and QE.Just like the base, Fig. 6 validates Eqn. 3 due to the direct proportionality nature between SR and QE.Thus, as SR increases, QE increases and vice versa.Likewise, because QE is a function of SR, QE will always be higher than SR.This is verified with the presence of the SR curve within the QE curve.
Thus, in Fig. 5, it can be observed that photons with lower energy (longer wavelength) contribute more to the QE of the base, compared to photons with higher energy.Whereas, in Fig. 6, it can be observed that photons with higher energy (shorter wavelength) contribute more to the QE of the emitter, compared to photons with lower energy and longer wavelength.Hence, the high QE values in the emitter are due to the absorption of the photons in the UV region (180 nm -400 nm) of the solar spectrum, and the high QE values in the base are due to the absorption of photons in the visible region (700 nm -900 nm) of the solar spectrum, all leading to a higher generation of carriers in the emitter and base respectively.

Quantum Efficiency Analysis Graphs
The trends and patterns of the graphs were discussed and analysed at various wavelengths.All QE graphs have their Emitter Diffusion Length (EDL) and Base Diffusion Length (BDL).For Fig. 7 and 9, the values of the emitter and total QE at wavelength were observed to increase as the EDL was increased gradually from 0.3 µm -1.5 µm.This implies that as the EDL increases, the peak QE increases.Nevertheless, the wavelength bearing the peak QE decreases slightly.The total QE is the sum of the emitter's QE and the base's QE.From Fig 8, the peak value for base QE was constant, at a value of about 0.72.The QE curve lies and remains within 400 to 1140 nm.These observations were made at a wavelength of about 700 nm.The emitter and total QE were observed to tend to zero at this wavelength and above.In summarizing Fig. 7 to 9, it can be observed from Fig. 7 that the emitter diffusion length was varied as follows: 0.3μm, 0.5μm, 0.7μm, 1.0μm and 1.5μm.The quantum efficiency at wavelength 300 nm -400 nm yielded the following values, 0.03, 0.25, 0.42, 0.68 and 0.82.This gave a percentage increase of about 700 % for the first step increase, while the next three steps increased respectively as follows: 68 %, 62 % and 20 %.A sample of approximate percentage increase calculation is as shown: 0.42 − 0.25 0.25 × 100% = 68% (7) Variation of EDL from 0.3μm to 0.5μm recorded the maximum increase while that of 1.0μm to 1.5μm had the least.

Spectral Response Analysis Graphs
The trends and patterns of the graphs were discussed and analyzed at various wavelengths.All SR graphs have their emitter diffusion length (EDL) and base diffusion length (BDL).For Fig. 10 and 12, the values of the total SR at wavelength were observed to increase as the BDL was increased gradually from 20 µm -200 µm while the value of base remained zero.This implies that as the BDL increases, the peak SR increases.Nevertheless, the wavelength bearing the peak SR decreases slightly.The total SR is the sum of the emitter's SR and the base's SR.From Fig. 11, the peak value for emitter SR was constant, at a value of about 0.23.The SR curve lies and remains within 300 to 1050 nm.These observations were made at a wavelength of about 800 nm.The base and total SR were observed to tend to zero at this wavelength and above.In summarizing Fig. 10 to 12, it can be observed from Fig. 10 that the base diffusion length was varied as follows: 20μm, 50μm, 70μm, 100μm and 200μm.The spectral response at wavelength 300 nm -400 nm yielded no change as it was zero.However, Variation of BDL from 20μm to 50μm recorded the maximum increase while that of 70μm to 100μm was the least.

Conclusion and Recommendation
This paper has been able to analyse, interpret and identify the different trends that exist in Quantum Efficiency and Spectral Response.Across SR and QE, there has been a consistent trend that has been identified.The QE and SR values were always seen to increase whenever the diffusion lengths increased regardless of whether it was the emitter or base.This is because the charge carriers in the solar cells (either emitter or base) are less susceptible to recombination due to the increase in their diffusion lengths.The increment in the length allows the carrier more space to diffuse, thereby reducing their chances of recombination and increasing the chances of current generation across the cell.Therefore, in order to improve the photoelectric conversion efficiency of solar cells, recombination in solar cells that limits their efficiency and lifetime can be reduced.Based on this research, it can be achieved by increasing the diffusion length of the cells, thereby yielding greater quantum efficiency that optimizes the overall efficiency of the cell.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :
Figure 1: MATLAB Code for the combined base values of QE and SR

Figure 5 :
Figure 5: Graph showing the Base values of Quantum Efficiency and Spectral Response against Wavelength

Figure 6 :
Figure 6: Graph showing the Emitter values of Quantum Efficiency and Spectral Response against Wavelength

Figure 7 :
Figure 7: Graph of the Emitter values of Quantum Efficiency against Wavelength

Figure 8 :Figure 9 :
Figure 8: Graph of the Base values of Quantum Efficiency against Wavelength

Figure 10 :
Figure 10: Graph of the Base values of Spectral Response against Wavelength

Figure 11 :Figure 12 :
Figure 11: Graph of the Emitter values of Spectral Response against Wavelength of about 700 nm -900 nm yielded the following values, 0.38, 0.48, 0.52, 0.55 and 0.61.This gave a percentage increase of about 26% for the first step increase, while the next three steps increased respectively as follows: 8.3%, 5.8% and 10.9%.A sample of approximate percentage increase calculation is as shown: 9at a wavelength