CdS based photovoltaic cell: A numerical simulation approach

Accepted Manuscript Analysis of Cu2ZnSnS4/CdS based photovoltaic cell: A numerical simulation approach S.R. Meher, L. Balakrishnan, Z.C. Alex PII:

S0749-6036(16)30482-7

DOI:

10.1016/j.spmi.2016.10.028

Reference:

YSPMI 4573

To appear in:

Superlattices and Microstructures

Received Date: 15 July 2016 Revised Date:

11 October 2016

Accepted Date: 12 October 2016

Please cite this article as: S.R. Meher, L. Balakrishnan, Z.C. Alex, Analysis of Cu2ZnSnS4/CdS based photovoltaic cell: A numerical simulation approach, Superlattices and Microstructures (2016), doi: 10.1016/j.spmi.2016.10.028. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Analysis of Cu2ZnSnS4/CdS Based Photovoltaic Cell: A Numerical Simulation Approach

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S. R. Meher1,*, L. Balakrishnan1 and Z. C. Alex2 Department of Physics, School of Advanced Sciences, VIT University, Vellore-632014,

India

MEMS and Sensor Division, School of Electronics Engineering, VIT University, Vellore-

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632014, India

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Corresponding author:- Tel: +91 416 2202717

E-mail address: [email protected] (S. R. Meher) Abstract

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In the present work, p-Cu2ZnSnS4 / n-CdS heterojunction solar cells have been analysed through Solar Cell Capacitance Simulator (SCAPS). The effects of various layer parameters like thickness, carrier concentration, defect density, mobility, conduction band off-set, etc. on

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the cell performance have been studied in detail. The different reasons for current-voltage

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distortions (cross-over and red-kink) have been investigated. The optimized cell shows 14.57% efficiency with an open circuit voltage of 1.009 V. The photovoltaic cell has been studied further through capacitance-voltage simulations to obtain the net built-in potential and the apparent doping profile. Thermal admittance spectra have been simulated for defect characterization of the Cu2ZnSnS4 absorber layer and to isolate the effect of back contact barrier. The impedance plot at 300 K has been fitted to an equivalent circuit to get an insight into the secondary barriers of the complete device and also to estimate the carrier lifetime for the trap level. In order to have an idea regarding the effect of inhomogeneity in Cu2ZnSnS4 1

ACCEPTED MANUSCRIPT layer on the device performance, further simulations have been carried out for a randomly graded absorber layer.

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Keywords: Thin film photovoltaics, CZTS, SCAPS, Cross-over, Admittance spectroscopy

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ACCEPTED MANUSCRIPT 1. Introduction The widespread application of photovoltaics (PV) requires a significant drop in cost factor. Together with this, environment friendly and earth abundant materials are highly desirable

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for PV applications. At present, CdTe and Cu(In, Ga)S/Se2 (CIGS) based thin film PV cells provide very good efficiencies of ~21% [1] which is not far behind the crystalline Si

technology. But, Cd is known to be one of the most toxic metals whereas In’s availability is limited due to its widespread use in the form of transparent conducting oxide (Sn:In2O3).

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Owing to these reasons, Cu2ZnSnS4 (CZTS) based thin film PV [2 – 4] has gained significant

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attention in the present decade. This quaternary semiconductor is considered to be non-toxic and its constituents are abundant in nature. The abundance of Zn and Sn in earth’s crust are 1500 and 45 times than that of In, respectively [5]. Again, the price of Zn and Sn is almost two orders of magnitude lower than that of In. CZTS thin films have direct optical band gap of 1.4 – 1.6 eV and large optical absorption coefficient (~ 104/cm). The intrinsic defects in

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CZTS material are mainly p-type: CuZn antisite (Cu at Zn antisite) and Cu vacancies [6 – 8]. In CZTS, CuZn antisite defects are easily formed (formation energy ~ -0.32 – 0.01 eV) as

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compared to Cu vacancies (formation energy ~ 0.21 – 0.77 eV). But CuZn antisites form deep level defects and are not desirable for PV applications. Instead Cu vacancies are preferred for

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high efficiency PV devices. Hence, Cu poor and Zn rich conditions are required for high efficiency CZTS based devices. Together with these p-type defects, electrically neutral selfcompensated defect complexes such as [CuZn- + ZnCu+] and [VCu- + ZnCu+] are also present in CZTS films. These defect complexes passivate the deep levels in band gap to a great extent and help in reducing the recombination rate in PV device. The defect formation energy calculation shows that n-type doping for CZTS is impossible in thermal equilibrium because

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ACCEPTED MANUSCRIPT of the exceedingly stable CuZn antisite defects. Taking all these parameters into account, CZTS should be an ideal choice for replacing CIGS and CdTe based thin film PV devices. A variety of techniques like co-evaporation [9], pulsed laser deposition [10],

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sputtering [11, 12], screen printing [13], sol-gel [14], chemical bath deposition [15] etc. has been reported for the growth of CZTS absorber layers. The major problem in growing CZTS thin film absorber layers is its multiphasic nature [16]. The window for a stable CZTS phase is very narrow and many a times it contains secondary phases of ZnS, Cu2S and Cu2SnS3.

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Under Cu poor and Zn rich conditions, ZnS is the prominent secondary phase. There exists a

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definite mismatch between the valence or conduction band of these secondary phases with that of CZTS which creates additional potential barrier [17]. This also results in a decrease in the lifetime of photogenerated carriers by carrier traps or recombination centers at the interface and thereby reduces the overall cell efficiency. The current record efficiency of pCZTS/n-CdS heterojunction PV cell is ~9.1% [18, 1] which is far below that of CIGS or

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CdTe based cells. Keeping in mind the ideal material properties of CZTS as solar cell absorber layer, there is a considerable scope for improvement in its conversion efficiencies.

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Numerical simulation for PV device helps researchers for a thorough understanding of the device processes. This results in optimization of the device parameters for better

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conversion efficiencies. The basic governing equations for electrons and holes i.e. Poisson’s equation and continuity equations are used for the numerical simulation of PV devices. In the literature, several solar cell simulators like AMPS-1D [19], SCAPS-1D [20], PC-1D [21], Sentaurus etc. have been used for modelling thin film PV devices. There are few reports on the numerical studies of CZTS based solar cells using SCAPS and AMPS simulation software. Patel et al. [22] have discussed the enhancement in output performance of CZTS thin film solar cells in terms of back contact metal work function, absorber thickness and 4

ACCEPTED MANUSCRIPT acceptor concentration. Simya et al. [23] have performed a comparative study on the performance of different kesterite based thin film solar cells by optimizing them in terms of layer thicknesses, back contact work function, series resistance and different kinds of band to band recombination mechanisms (radiative and Auger). Frisk et al. [4] have suggested a

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device model for CZTS solar cells using SCAPS based on a standard reference device. They have incorporated band gap narrowing, short minority carrier diffusion length and interface recombination into this model. Zhao et al. [24] have optimized the cell parameters like CZTS

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layer thickness, carrier density, defect density etc. using AMPS-1D simulator. In the present investigation, we have used SCAPS-1D simulation software to study the CZTS based thin

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film PV cells in more detail. At first, the CZTS cell have been optimized by taking into account the layer parameters like thickness, carrier concentration, carrier mobility, neutral and interface defect density, series and shunt resistances and CZTS/CdS conduction band offset (CBO). These optimizations are performed on the basis of higher cell efficiency and

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reduced cost. For this optimized cell, cross-over and red-kink effects in the current-voltage (J-V) characteristics have been studied in terms of the back contact barrier and charged midgap defect density of the CdS buffer layer. The capacitance-voltage (C-V) simulations have

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been analysed to obtain the built-in potential of the junction and apparent doping profile of

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the CZTS absorber layer. Further, thermal admittance spectra (TAS) in different temperature and frequency regimes have been analysed for defect characterization and to isolate the effect of back contact barrier. Finally, to account for the difficulties in growing homogeneous quaternary CZTS layers, a randomly graded absorber layer in terms of band gap, optical absorption coefficient, carrier concentration, defect density and carrier mobility has been simulated. 2. Device Modelling and Material Parameters 5

ACCEPTED MANUSCRIPT The numerical simulation programme called SCAPS (Solar Cell Capacitance Simulator, Version 3.1.02) has been used in the present study to model the J-V, C-V and capacitancefrequency (C-f) characteristics of CZTS based thin film PV cell. The device properties of many crystalline and thin film based photovoltaic cells (Si, CdTe, CIGS, CZTS, CZTSSe)

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have been successfully simulated using SCAPS [25 – 29]. SCAPS estimates the steady state band diagram, recombination profile and carrier transport in 1-dimension using the Poisson’s equation and continuity equations for electrons and holes. The vertical cross-section of the

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device structure proposed in this work is shown in Fig.1. Here p-CZTS acts as the absorber layer, n-CdS as the buffer layer, i-ZnO as the high resistance (HR) layer and Al:ZnO which is

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a transparent conducting oxide (TCO) as the front contact. Transport of majority charge carriers at the back metal-semiconductor interface is described by thermionic emission. Transport of minority carriers is described by their surface recombination velocities (SRVs). The back metal contact is chosen to have a work function of 5.5 eV with SRVs of 107 cm/s

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and 105 cm/s for electrons and holes respectively. The front metal contact is treated under flat band approximation with same SRVs as that of the back metal contact. The recombination at the deep bulk levels and their occupation is treated under Shockley-Read-Hall (SRH)

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mechanism. To start with, an ideal single neutral defect level at 0.6 eV above the valence

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band with a capture cross-section of 10-15 cm2 is considered for all the layers. In the later part of optimization, a more realistic scenario involving charged mid-gap defects with asymmetric capture cross-section has been taken into consideration. Since CZTS is a direct band gap semiconductor, the radiative recombination coefficient is chosen to be 10-10 cm3/s for band to band recombination. Auger non-radiative recombination is assumed to be very small as it prevails only at high carrier concentrations. The corresponding electron and hole capture coefficient was chosen to be 10-29 cm6/sec. The band gap of CZTS thin films grown by different methods has been reported to vary from 1.4 – 1.6 eV [30, 31]. This variation mainly 6

ACCEPTED MANUSCRIPT depends on the Cu/Zn and Sn/Cu stoichiometry [32]. In the present simulation, a realistic band gap of 1.5 eV is considered by taking into account the Cu poor conditions which is necessary to avoid Cu rich defects. The light illumination is from the top using the standard AM1.5 global spectrum (1000 Watt/m2). The series and shunt resistances for the cell are

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taken to be 3 and 400 Ω.cm2 respectively. The frequency for AC characteristics of the device is chosen to be 1 MHz. The default operation temperature is set at 300 K. For temperature dependent studies, the carrier mobility is assumed to be constant. Other basic input

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parameters for different layers are based on the literature and are given in Table 1.

3.1 Absorber layer (CZTS) thickness

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3. Device Optimization

Absorber layer is the most important component of the solar cell where the incident photons are absorbed and excess carriers are generated. The absorption of photons in a

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semiconducting material follows Beer-Lambert law. Hence, more photons with higher wavelengths are absorbed with increase in absorber layer thickness generating more number of excess carriers. This leads to higher quantum efficiency (QE) and hence the cell efficiency

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increases. In the present study, the effect of absorber layer thickness on the cell efficiency is

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simulated by changing the thickness of CZTS from 0.5 – 3 µm (Fig. 2). The solar cell efficiency increases initially with increase in CZTS layer thickness and nearly saturates at higher values. This saturation in efficiency is because of increased probability of SRH recombination (due to finite carrier diffusion length) with increase in absorber thickness. Moreover, thicker absorber layer means higher material cost and fabrication cost. Hence, for the present investigation, the optimized thickness for CZTS absorber layer is taken to be 1.0 µm. The corresponding cell efficiency and fill factor are 9.54% and 65% respectively.

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conductivity in CZTS. For PV application, Cu vacancies are preferred over CuZn antisite defects because the former constitutes shallow level acceptors [33]. Therefore, Cu/Zn and Cu/Sn stoichiometry decides the majority hole concentration in CZTS. In the present

investigation, the hole concentration in CZTS absorber layer is varied from 1013 – 1017 /cm3.

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The efficiency as well as FF is found to be maximum at a hole concentration of 1016 /cm3

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(Fig. 3a,b). The difference in quasi-Fermi levels corresponding to minority carriers in both the sides of the junction becomes large with increased carrier density. This leads to an enhancement in VOC up to a certain critical concentration after which the semiconductor attains degeneracy. In degenerate state, the carrier diffusion length is very small which leads to a drastic reduction in open-circuit voltage and hence the efficiency. On the other hand JSC

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decreases continuously with increase in carrier density because of recombination. The quantum efficiency is also observed to be reduced for higher acceptor densities due to enhanced recombination process (Fig. 3c). Therefore, the optimized hole density for CZTS

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to a FF of 68.6%.

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absorber layer is chosen to be 1016 /cm3 for which the cell efficiency is 11.77% corresponding

3.3 Absorber layer (CZTS) neutral defect density and interface defect density CZTS routinely contains large concentration of neutral and charged point defects. The neutral point defects include the vacancies (VCu, VZn, VS), antisites (CuZn, ZnSn, ZnCu) and interstitials (Cui, Zni) in their unionized state. Chen et al. [6] have calculated the corresponding formation energies and their relative positions in the forbidden gap. In addition to this, neutral defects are also present at the interfaces of several secondary phases formed during the growth of 8

ACCEPTED MANUSCRIPT CZTS. These neutral point defects can act as centers for SRH recombination which is one of the major causes for low conversion efficiency in CZTS based solar cell. The defects which lie very close to any of the band edges are less likely to contribute to SRH recombination. This is because, for shallow levels the probability for the carrier to go back to their respective

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bands is very high.

In SCAPS simulation, the neutral point defects are used only to specify the lifetimes of certain carriers in terms of SRH recombination. They do not contribute to the space

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charge. In the present investigation at the initial stage for simplicity, only one kind of ideal

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neutral point defects with energy 0.6 eV above the valence band edge of CZTS were chosen. In the later part of optimization, donor and acceptor type mid-gap charged defects will be taken into consideration. The average carrier capture cross-section for these defects was taken to be 10-15 cm2. The defect density was varied from 108 – 1018 /cm3. From Fig. 4a, it is observed that the cell efficiency is severely affected for defect densities higher than 1014

chosen to be 1012 /cm3.

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/cm3. For the optimized cell, the neutral defect density in the CZTS absorber layer was

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Similarly, the neutral defects in CZTS/CdS interface are also primary centers for carrier recombination. They are mainly formed due to the lattice mismatch between the two

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layers and are a major source of SRH recombination in thin film PV cell. It is found that the interface defect density should be less than 1015 /cm2, beyond which the cell efficiency reduces considerably (Fig. 4b). In the present study, a realistic interface defect density of 5 × 1014 /cm2 was chosen for the final structure. 3.4 Absorber layer (CZTS) hole mobility

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ACCEPTED MANUSCRIPT The hole mobility of CZTS thin films are reported to have a wide range (0.1 – 30 cm2/V.s) of values depending on the growth conditions [34, 35]. The major cause for low mobility in CZTS quaternary films are grain boundary scattering and existence of secondary phases. Lower carrier mobility hinders effective charge separation and leads to recombination. In the

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present investigation, the hole mobility was varied from 5 – 100 cm2/V.s and its effect on the device performance was studied (Fig. 5). The cell efficiency is found to be affected severely if the hole mobility is less than 30 cm2/V.s. Therefore, for better device performance at the

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optimized thickness, it is very important to minimize the grain boundary scattering and

suppress the secondary phases. In the present study, the optimized mobility for CZTS is

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chosen to be 30 cm2/V.s corresponding to a cell efficiency of 11.49%. 3.5 CdS buffer layer and HR ZnO layer thickness

The primary role of n-CdS buffer layer is to form a p-n junction with the p-CZTS absorber

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layer. The optical band gap of CdS is ~2.4 eV which allows maximum amount of light to the junction region. Moreover, the conduction band offset between the absorber and buffer layer plays a major role in minority carrier transport in the junction region (discussed in more

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detail in Section 3.7). Ideally, the thickness of buffer layer should be as small as possible to reduce the series resistance of the PV device. But, very thin buffer layer results in a poor

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collection of the photogenerated carriers due to reduction in the space charge width of the junction. Moreover, thin buffer layer may also lead to higher leakage current. On the other hand, thicker buffer layer will absorb more number of photons and they cannot reach the CZTS absorber layer. This will decrease the quantum efficiency of the device. In the present study, the device is simulated by varying the CdS-buffer layer thickness from 20 – 100 nm (Fig. 6). At first, the cell efficiency improves with increase in CdS layer thickness up to ~80 nm. With further increase in buffer layer thickness, the efficiency remains nearly constant. 10

ACCEPTED MANUSCRIPT Hence, for the present study we have chosen the optimal thickness of CdS-buffer layer to be 80 nm. This corresponds to a cell efficiency of 11.58%. The main role of high resistance ZnO layer is to minimize the forward current through

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pin-holes present in the chemical bath deposited (CBD) CdS buffer layer [36]. This layer also allows to minimize the CdS buffer layer thickness and helps in improving the blue response of the device. In the present simulation, the cell efficiency is found to be nearly independent of HR-ZnO layer thickness (Fig. 6). The optimal thickness for this layer is chosen to be 50

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nm to mimic the actual device structure.

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3.6 Impact of Series and Shunt Resistance

The presence of parasitic resistances influences the FF of the solar cell. These parasitic effects include the series (RS) and shunt (RSh) resistances which are unavoidable for all practical cells. An ideal PV cell should have zero series resistance and infinite shunt

PV cell is given by,

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resistance. In the presence of these parasitic resistances, the current-voltage relation for the

(1)

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 e(V − IRS )  V − IRS I = I 0 exp   − IL − RSh  nkbT 

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where, IL is the light generated current, n is the ideality factor and kb is the Boltzmann constant. The resistance at the front (Al:ZnO) and back electrodes are the primary sources for series resistance. The interfacial resistance between different layers also contribute to the series resistance. The formation of sulphide (e.g. MoS2 for Mo/CZTS) at absorber/back contact interface is responsible for high series resistance of the CZTS based devices. High series resistance leads to a decrease in FF and as a result, the efficiency of the device is affected. In the present simulation (Fig. 7), the efficiency of CZTS solar cell is found to 11

ACCEPTED MANUSCRIPT decrease from 12% to 9% for an increase in series resistance from 1 Ω.cm2 to 10 Ω.cm2. On the other hand, a finite shunt resistance leads to leakage current in the device. In thin film solar cells, the grain boundaries act as the major shunting path. In CZTS/CdS heterojunction, the leakage current is conventionally reduced by the insertion of a HR-ZnO layer on top of

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CBD deposited CdS. In the present study the CZTS cell was simulated for shunt resistance varying from 102 – 108 Ω.cm2. The VOC and JSC values together with FF decrease for low values of RSh (≤ 103 Ω.cm2). This leads to a reduction in the cell efficiency (Fig. 7). Hence,

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for the optimized practical cell, the values of RS and RSh are chosen to be 1 and 104 Ω.cm2

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respectively.

With the above optimized parameters, the efficiency and FF for the CZTS/CdS solar cell was found to be 11.97% and 78.12% respectively.

3.7 Introduction of charged mid-gap defects, Final Optimization and J-V distortion

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In order to simulate the real CZTS/CdS heterojunction solar cells, the deep level charged defects in these semiconductors need to be taken into consideration. It is well known that

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CZTS as well as CdS are naturally compensated defect semiconductors. The acceptor like point defects in CZTS are vacancies: VCu, VZn, VSn and antisites: CuZn, CuSn, ZnSn whereas

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donor like defects include vacancy: VS, interstitials: Cui, Zni and antisites: ZnCu, SnCu, SnZn. The formation energy of the donor like defects are higher compared to that of the acceptors. The CuSn and CuZn deep level acceptors are considered to be one of the most active SRH recombination center for CZTS based device [8]. Together with this, the deep level donor like defects (VS and SnZn) also contribute significantly to SRH recombination [37]. On the other hand, the self-compensated neutral defect complexes like [CuZn- + ZnCu+] and [VCu- + ZnCu+] act as passivation centers for these kinds of deep level defects. Similarly, cadmium vacancies 12

ACCEPTED MANUSCRIPT (VCd) act as deep level acceptors in self-compensated CdS [38, 39]. To account for these charged carrier traps, Gaussian mid-gap donor and acceptor type defects with total densities of 1 × 1015 cm-3 each were introduced in CZTS. Similarly, Gaussian mid-gap acceptor type defects with density 1 × 1016 cm-3 were also introduced in CdS. The characteristic energy of

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these defects were taken to be 100 meV. The carrier capture cross-section of charged defects is influenced by the Coulombic interaction. Hence, for Coulombic attraction, the cross-

section was assumed to be one order of magnitude higher (10-14 cm2) compared to that of the

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neutral centers. Similarly, for Coulombic repulsion, capture cross-section was considered to be one order of magnitude lower (10-16 cm2). After introduction of these charged mid-gap

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defects with asymmetric capture cross-section, the efficiency and FF of the optimized solar cell is reduced to 11.18% and 73.86% respectively.

The next step of optimization was carried out with respect to the conduction band offset (CBO) of CZTS/CdS heterojunction interface. The interface is strongly dependent on

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the respective electron affinities (χ) which can be varied by changing the deposition conditions. The deposition methods and post-deposition conditions can have important

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impact on the nature of CZTS/CdS heterojunction and hence the band alignment. The heterojunction interface can give rise to “spike” (type-I) or “cliff” (type-II) like CBO

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depending upon the difference in the electron affinities of the absorber and buffer layer. The band alignment of CZTS/CdS heterojunction is highly debatable in the literature. Haight et al. [40] have measured a spike-like CBO of 0.41 eV via pump/probe photovoltage shifts of the photoelectron spectra. Kato et al. [41] have measured 0.1 eV spike-like CBO in CZTS/CdS interface using ultraviolet photoelectron spectroscopy. Nagoya et al. [42] have reported a CBO of 0.2 eV (spike) using first principle calculations. In contrary, there are also some reports which support the cliff-like CBO of CZTS/CdS heterojunction [43 – 45]. Tajima et al. 13

ACCEPTED MANUSCRIPT [46] have measured a flat CBO for CZTS/CdS interface using hard X-ray photoelectron spectroscopy. The cliff-like band offset increases the probability of interface recombination of the majority carriers. This leads to flat band condition for bias smaller than the band gap voltage of the absorber layer. As a result of this, the VOC of the cell is limited. On the other

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hand, larger spike limits the flow of the minority carriers which reduces the conversion

efficiency. Therefore, an optimal spike of 0.1 – 0.4 eV has been prescribed in the literature. In the present simulation, the electron affinity of CZTS which is dependent on its growth

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conditions has been varied from 4.1 – 4.7 eV and its effect on the J-V characteristics of the PV cell has been studied. We can observe the transition from cliff to spike like behaviour in

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CB edge (under AM1.5G) with increase in χCZTS (Fig. 8a). The efficiency is found to be the highest (~14.57%) for χCZTS = 4.3 eV corresponding to a small spike of 0.1 eV (Fig. 8e). Moreover, the Schottky barrier height for the majority carriers ( ϕ BS ) between the back

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contact and p-CZTS is given by,

ϕ BS = Eg − (ϕm − χ CZTS )

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Here ϕm is the work function of the back contact (5.5 eV) and Eg is the band gap of p-CZTS

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(1.5 eV). With increase in χCZTS from 4.1 – 4.7 eV, the back contact barrier also rises from

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0.1 – 0.7 eV. This also affects the collection efficiency and the overall cell efficiency drops. Hence for the optimized cell, χCZTS was chosen to be 4.3 eV (CBO = 0.1 eV; ϕ BS = 0.3 eV). The current-voltage (J-V) crossover between the dark, AM1.5G and long wavelength

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approximately equal to VOC of the cell. The reduction in dark current for large values of χCZTS is ascribed to the development of a large back-contact Schottky barrier ( ϕ BS ) which impedes the hole transport. In the presence of illumination, the net electric field to separate the

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photogenerated carriers vanishes when the cell is biased to its built-in potential (Vbi,t). Here Vbi,t corresponds to the net built-in potential between the front and back contact which is

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affected by ϕ BS to a great extent. As a result, the net photocurrent becomes zero when the cell is biased to Vbi,t. This leads to a crossover between the dark and illuminated J-V curves. The roll-over process observed at higher voltages for larger spike like CBO (large χCZTS) at the heterojunction interface can be rather linked to the Schottky barrier height between the CZTS

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absorber and back contact. This roll-over phenomenon effects the cell efficiency by reducing the FF and is commonly observed in CdTe based solar cells [48]. The fully optimized final

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cell parameters for the CZTS/CdS PV cell is given in Table 2. Fig. 9 shows the PV characteristics of the fully optimized device. The conversion

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efficiency is found to be 14.57% with a quantum efficiency of more than 75% in the visible region. The FF of the final optimized cell is 77.29%. The band diagram shows an optimal spike of 0.1 eV for the CZTS/CdS interface. The spike between the buffer layer and HR ZnO layer is ~0.35 eV. No J-V cross-over between the dark and illuminated curves is observed. The back contact Schottky barrier height for the optimized cell is 0.3 eV which is not sufficient enough to exhibit the roll-over phenomenon. The open circuit voltage of the optimized device which is proportional to the difference in the quasi-Fermi levels (Efn and 15

ACCEPTED MANUSCRIPT Efp) is 300 – 400 meV higher than the experimental values reported in the literature [49, 50]. The depth profile for carrier generation and recombination rates in the optimized device (at V = VOC) is shown in Fig. 10a. The carrier generation rate follows Beer-Lambert law across the depth of the absorber layer. The absorption in the CdS buffer layer is one order of magnitude

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less than that of the absorber layer. In dark condition, the carriers mostly recombine in the space charge region. But under illumination, interface recombination dominates in the

junction region. In the bulk quasi-neutral region, for compensated semiconductors like CZTS

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and CdS, SRH recombination through the various kinds of defects (neutral/acceptor/donor) is dominant. The electron occupation probability at the open-circuit voltage in various defect

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levels (ft (electrons)) for different layers is shown in Fig. 10b. The SRH recombination rate is two and five orders of magnitude higher compared to radiative and Auger recombination rates respectively.

The effect of various layer parameters (thickness, carrier concentration, mobility and

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defect density) on the efficiency of the completely optimized CZTS/CdS device is shown in Fig. 11. The cell efficiency saturates at ~15.8% for CZTS thickness values of around 2.5 – 3

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µm (Fig. 11a). But, the growth of thicker absorber layers is not cost-effective. In addition to this, for thicker CZTS films the secondary phases (e.g. ZnS, Cu2S and Cu2SnS3) are expected

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to be more and are very hard to detect experimentally. These secondary phases deteriorate the overall efficiency by forming additional secondary barriers. Therefore, CZTS absorber layer thickness is recommended to be in 1.0 – 1.5 µm range. For CdS thickness variation from 20 – 100 nm, the device efficiency lies in the range of 12.3 – 14.5%. There is negligible change in the efficiency for CZTS hole mobility variation from 5 – 100 cm2/V.s (Fig. 11c). For the optimized cell, the device efficiency is found to be maximum for the acceptor concentration

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ACCEPTED MANUSCRIPT of 5 × 1015 cm-3 (Fig. 11b). The efficiency is simulated to be reduced to 8.61% for a donor trap density of 1017 cm-3. 4. Cross-over and Red-kink

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In the present simulation, J-V crossover or red-kink is not observed for the fully optimized cell. But, in the conventional CIGS/CdS or CZTSSe/CdS heterojunction solar cell, the

crossover and red-kink effects are reported and are related to the photo-doping of CdS buffer

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layer [51, 28]. The photo-doping in heavily compensated CdS occurs mainly because of

asymmetry in carrier capture cross-section of the charged mid-gap acceptors for electrons and

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holes. In the present study, the above mentioned J-V distortions are suppressed when the midgap acceptor density in CdS buffer layer is less than 1017/cm3. For higher densities, the conventional J-V crossover and red-kink effects are observed as shown in Fig. 12. The energy band diagram for different illuminations is shown in the inset. For low energy photons (600

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nm) or in the dark, the e-h pairs are not generated in the CdS buffer layer and hence the corresponding conduction band is far from the electron quasi-Fermi level. The secondary barrier is lowered at the CZTS/CdS as well as CdS/ZnO interface for high energy photons.

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The reduction in the barrier height between CdS buffer layer and ZnO window layer for high energy photons leads to J-V crossover with the dark or low energy photons. The red kink is

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due to the increased barrier height at the CZTS/CdS interface for low energy photons. Hence, we can infer that the carrier compensation can be minimized if the mid-gap acceptor density in CdS is below 1017/cm3 for which no J-V distortions are observed. Moreover, poor compensation results in decreased secondary barrier irrespective of the illumination leading to higher device efficiency. The elimination of crossover and red-kink by the suppression of deep level VCd acceptors has been observed by Neuschitzer et al. [39] for CZTSe/CdS heterojunction based solar cells. 17

ACCEPTED MANUSCRIPT 5. Capacitance-Voltage studies The capacitance-voltage (C-V) characteristics of PV cell provides an estimation of the apparent doping profile of the absorber layer, junction built-in voltage and width of the space

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charge region (SCR). In C-V measurement, the effect of an AC signal on the DC biased p-n junction is studied. The capacitance at different applied bias is calculated from the measured complex admittance (Y) by considering the cell to be a parallel combination of the shunt

resistance and the junction capacitance. This is a fairly valid approximation for small series

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resistance. Under this consideration, the capacitance is approximately equal to Im(Y)/ω,

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where ω is the applied AC frequency. But, in practice this kind of simple diode model for a PV device may not be feasible. This is because, the thin film PV device contains many layers and more than one junction. Experimentally, the capacitance of the entire cell is measured and it is a complex task to isolate the response of a defect level from that of a secondary

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diode or to get the apparent doping profile. Therefore, one needs to substantiate the experimental C-V results with that of the numerical simulations. In the present investigation, C-V simulation was performed for the complete device as

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well as for the one diode model p-CZTS/n-CdS junction. For the model p-n junction, the iZnO and Al:ZnO layers were not considered and the back contact was treated under flat band

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approximation to remove any kind of secondary diode effects. In order to remove the contributions of deep level defects from the apparent doping profile, the C-V simulations were performed at high frequency (1 MHz). The deep level traps can modify the space charge density as well as the depletion width. At high frequencies, the deep level defects cannot follow the AC-voltage. Therefore, an accurate carrier concentration profile is obtained only at high frequencies and low temperatures for which the deep levels traps are frozen out.

18

ACCEPTED MANUSCRIPT The simulated C-V plots at 300 K for the complete device and the model p-n junction are shown in Fig. 13a. For an abrupt one-sided p-n+ junction under depletion approximation, the capacitance per unit area (C) and the doping (NA) at the edge of the p-side space charge

1 2(Vbi − Va ) = C2 eε N A

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region are related through the Mott-Schottky equation:

(3)

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Here, ε is the dielectric permittivity for p-CZTS, Vbi is the built-in potential and Va is the applied DC bias. The built-in potential can be obtained from the x-axis intercept of Mott-

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Schottky plot. For the model p-n junction, Mott-Schottky plot is found to be linear with a built-in potential of 1.04 V (Fig. 13b). But for the complete device, the plot is slightly nonlinear which may be due to the presence of more than one junction. Due to this, the built-in potential for the complete device is reduced to ~1.00 V. The apparent doping (Napp) profiles

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as a function of depletion width for both the configurations are shown in Fig. 14a. The doping profile as a function of depletion width is obtained from the parallel plate capacitance

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relation:

C=

ε

(4)

W

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where, C is the capacitance per unit area and W is the depletion width. For the complete device, a U-shaped carrier concentration profile is observed. The U-shaped profile for apparent carrier concentration from C-V measurements is common in CIGS based cells [52]. In the literature, this kind of non-uniform carrier concentration is attributed to the dependence of charge state of the deep level defects on the applied DC bias. The accumulated charge in the deep level defect follows the voltage sweep of the C-V simulations. In few reports, the non-uniform apparent carrier concentration has also been attributed to the presence of 19

ACCEPTED MANUSCRIPT secondary diodes [53]. In the present simulation for the complete cell, there is only little increase (decrease) in the dopant concentration when only acceptors (donors) are considered as deep level defects in CZTS absorber layer. Moreover, the change in the apparent doping profile is negligible in the complete absence of deep traps. On the other hand, for the model

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p-n junction, the U-shaped profile is almost absent. The increase in Napp towards the back contact is very small and the profile is nearly flat with a sharp increase towards the

heterointerface (Fig. 14a). Hence for the complete cell, it can be concluded that the apparent

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increase in doping at the CZTS/CdS heterojunction interface is a combined effect of the

formation of a secondary barrier at the back contact and charging of deep level defects. The

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increase in Napp towards the back contact is because of the formation of secondary diode at the front due to the presence of i-ZnO and Al:ZnO layers. The average apparent carrier concentration obtained from the C-V simulations is ~8 × 1015 cm-3. The dashed line in the graph shows the input shallow acceptor density (1 × 1016 cm-3). The small deviation can be

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attributed to the depletion approximation and consideration of one-sided p-n+ junction to obtain the doping profile from eqn. (2). The simulated carrier concentration profile at different temperatures are shown in Fig.14b. No marked changes in the dopant concentration

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as well as in the profile is observed at lower temperatures for which the deep level defects are

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partially ionized. Fig.14c illustrates the change in apparent doping profile with change in the input shallow level acceptor density (NA). The apparent doping concentration decreases systematically with decrease in input shallow doping concentration. The profile has higher curvature for higher doping concentrations which is mainly due to the decrease in depletion width with increasing NA. 6. Admittance Spectroscopy

20

ACCEPTED MANUSCRIPT Thermal admittance spectroscopy (TAS) is primarily meant for studying the position and concentration of deep traps in the absorber layer of a PV device. The other techniques like photoluminescence can be used to study the radiative recombination centres. But in thin film solar cells (e.g. CZTS/CdS), the non-radiative processes leading to SRH recombination is of

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particular interest. In TAS, the CZTS/CdS junction is modulated by applying sinusoidal voltages of different frequencies (ω). The sinusoidal voltage induces charging and

discharging of the defect around the point where the Fermi level intersects the defect level.

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The capture or emission of carriers by the trap, which is strongly dependent on temperature and frequency leads to an additional trap capacitance (Ct). This charging and discharging of

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defect has certain characteristic angular frequency (ω0) which is dependent on temperature. At a particular temperature, a decay from low frequency capacitance (CLF) to high frequency capacitance (CHF) occurs around ω0 which can be observed in the C-f spectrum. This is because, at higher frequencies the defect no longer contributes to the capacitance. The

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characteristic frequency of a defect level can be expressed as [54]:



EA    kbT 

(5)

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ω0 = 2ξ 0T 2 exp  −

Here, ξ0 is called as the attempt to escape frequency and EA is the energetic distance of the

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trap level from the band extrema. But in thin film solar cells together with trap levels, other processes like presence of secondary diodes, interface states and dielectric relaxation in bulk layer can also lead to a capacitance step in the observed C-f spectrum [55]. The proper mechanism can be interpreted only when each phenomenon dominates in a well-defined range of frequency and temperature. The numerical simulation plays a vital role in the interpretation of C-f spectrum when an interplay among these phenomena exists.

21

ACCEPTED MANUSCRIPT In the present analysis, the C-f spectra for completely optimized CZTS based PV cell were simulated under dark conditions and at zero bias. In Fig. 15a, the spectrum is shown for the temperature range 120 – 300 K. Depending upon the temperature, the C-f spectra have different features at different frequency ranges. At low temperatures, the back contact barrier

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( ϕ BS ) contributes significantly to the capacitance step. On the other hand, the mid-gap defect levels of CZTS lead to a gradually decreasing capacitance at relatively higher temperatures and lower frequencies. Fig. 15b show the effect of different back contact barriers on the C-f

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curves at 300 K. With increase in ϕ BS , the capacitance step shifts towards lower frequencies.

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The effect of increase in the mid-gap defect (donor) concentration on the simulated C-f curves at 350 K is shown in Fig. 15c. Because of the Gaussian distribution of defect concentration, there is a gradual change instead of a sharp decay in the capacitance spectra. The capacitance difference (CLF to CHF) becomes larger with increase in the defect

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concentration.

In the present investigation to simplify the TAS analysis, only one kind of single midgap defect (donors) was considered for the CZTS absorber layer. The other optimized

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parameters were kept the same. The C-f spectra at two different temperature ranges (350 – 450 K and 120 – 220 K) are shown in Fig. 16. For higher temperatures and lower frequencies

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(Fig. 16a), the contribution from mid-gap trap is evident in the form of a decay in the capacitance. High temperature admittance spectroscopy is needed to characterize the mid-gap defects by reducing other secondary barrier effects. Similarly for lower temperatures and higher frequencies (Fig. 16b), the back contact barrier results in a sharp decrease in the capacitance. The scaled derivatives for each temperature is shown in Fig. 16c and 16d. The maxima corresponds to the characteristic frequency ω0 for the defect or for the barrier. The asymmetric nature of the scaled derivatives at lower temperatures (~350 K) in Fig. 16c is due 22

ACCEPTED MANUSCRIPT to the band offset existing between CdS buffer layer and HR-ZnO layer. This band offset results in a secondary diode. The energetic distance of the defect level from the band extremum (EA) can be obtained from the Arrhenius plot of ln(ω0/T2) vs. 1/T [56]. This is shown in the inset of Fig. 16c. The value of EA obtained from the slope of Arrhenius plot is

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0.773 eV which is close to the input value of 0.7 eV. The slight mismatch can be attributed to fitting error because of the asymmetric nature of the peaks. Similarly, the characteristic

frequencies for the back contact barrier is shown in terms of the scaled derivatives in Fig.

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16d. The defect density of states at a certain energetic position Eω for a PV cell is given by

N t ( Eω ) =

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(assuming parabolic band) [54],

ω dC W e eVbi − ( E f ∞ − Eω ) kbT d ω 2Vbi3/ 2

(6)

n

Here, Efn∞ is the quasi electron Fermi level and Eω is given by,

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 2ξ T 2  Eω = kbT ln  0   ω 

(7)

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The density of states spectra for the defect and the back contact barrier Nt (Eω) are shown in the insets. The peak for the mid-gap donor defect lies at ~0.7 eV with a density of states

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~1015 /cm3/eV. For the back contact, the density of states peaks at ~0.25 eV which is close to the input value of 0.3 eV. To further analyse the defects and the effect of secondary diodes, the simulated Cole-Cole plot [57] for impedance at 300 K is shown in Fig. 17. The higher intercept of the X-axis corresponds to the shunt resistance which is equal to the input value (104 Ω.cm2). The corresponding equivalent circuit consists of a series resistance Rs and three pairs of parallel resistance and capacitance corresponding to the three junctions (back contact, CZTS/CdS and CdS-ZnO). The capacitor-resistor pair (Ct and Rt) accounts for the SRH 23

ACCEPTED MANUSCRIPT recombination in CZTS. The fitting is satisfactory with less than 3% deviations in the entire frequency range. The extracted value of RS is found to be 1.0472 Ω.cm2 which matches closely with the input value (1 Ω.cm2). The resistance and capacitance value for the back contact barrier is extracted to be 2821.4 Ω.cm2 and 6.73 × 10-8 F/cm2 respectively. For the

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CZTS/CdS junction the corresponding values are found to be 3716.8 Ω.cm2 and 4.5 × 10-8 F/cm2 respectively. For CdS/ZnO band offset, the junction resistance and capacitance values are extracted to be 3461.8 Ω.cm2 and 5.49 × 10-8 F/cm2 respectively. The resistance and

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capacitance values for the trap level are found to be 2.368 Ω.cm2 and 6.13 × 10-9 F/cm2

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respectively. The corresponding time constant (RtCt) is 14.5 ns which is the carrier lifetime for the particular trap level. One major disadvantage of TAS is that it cannot distinguish between majority and minority carrier traps. For this the deep level transient spectroscopy (DLTS) is generally prescribed.

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7. Effect of illumination intensity and temperature

In order to evaluate the efficiency of the fully optimized CZTS/CdS PV cells during cloudy conditions and in different parts of the world, the effect of the variation in the illumination

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intensity was studied (Fig. 18). At lower intensity, less number of carriers are generated and

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thereby the overall efficiency reduces. The illumination intensity was varied from standard AM1.5 (1000 Watt/m2) to 1 Watt/m2. The conversion efficiency is found to be decreased to 0.86% for 1 Watt/m2 intensity. Further, the effect of operating temperature on the cell efficiency is shown in Fig. 18. There is no drastic change in the efficiency over the ambient temperature range on the earth surface (270 – 330 K). At higher temperatures, the slight decrease in efficiency is due to the increase in SRH recombination rate. 8. Inhomogeneity in CZTS absorber layer 24

ACCEPTED MANUSCRIPT One of the major problems in the fabrication of cost-effective thin film solar cells is to maintain the compositional homogeneity of the absorber layer. This is even more challenging for the growth of quaternary films like CZTS. In order to include this compositional inhomogeneity in the present study, a randomly graded CZTS absorber layer was considered.

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The CZTS composition across its thickness was varied by using a random number generating function (Fig. 19a). The CZTS layer was divided randomly into 20 domains with slightly varying material properties to account for the inhomogeneity. The band gap as a function of

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composition was chosen to be parabolic with variation in the range of 1.41 – 1.52 eV (Fig. 19b). The shallow acceptor concentration was assumed to be varying logarithmically with the

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composition in 1014 – 1017 cm-3 range (Fig. 19c). The mid-gap donor (Fig. 19c) and acceptor density was chosen to be in the range of 1014 – 1016 cm-3 and 1016 – 1014 cm-3 respectively with parabolic variation with respect to composition. Logarithmic variation was assumed for the electron and hole mobility in the range 10 -50 cm2/V.s and 30 – 10 cm2/V.s respectively.

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The optical absorption constant ‘A’ in SCAPS simulation was varied from 3 × 104 – 1.0 × 105 cm-1 eV-1/2. Since, the CBO depends only on the electron affinity at the heterojunction interface, it was not considered for inhomogeneous grading. The CZTS/CdS interface defect

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density was assumed to be of Gaussian distribution. The J-V curve for this inhomogeneous

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CZTS absorber is shown in Fig. 20. The J-V curve is slightly distorted compared to that of the homogeneous absorber layer resulting in a reduction in the FF. The cell efficiency for the inhomogeneous absorber layer is found to be 12.04% with VOC of 0.8884 V. The QE is observed to be slightly improved because of the inclusion of lower band gap domains. 9. Conclusion In conclusion, cost-effective and earth abundant p-CZTS/n-CdS solar cells are analysed using the solar cell simulator, SCAPS. The solar cell is optimized for different controllable 25

ACCEPTED MANUSCRIPT parameters like thickness, carrier concentration, defect density, carrier mobility, parasitic resistance, etc. within the experimentally permissible ranges. In addition to these layer parameters, the CBO (between the CZTS absorber layer and CdS buffer layer) and the presence of back contact barrier are also found to influence the cell efficiency and J-V

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distortions. The J-V distortions observed for larger χCZTS is linked to the Schottky barrier developed between the CZTS absorber and back contact. An optimal χCZTS of 4.3 eV

corresponding to a CBO of 0.1 eV and a back contact barrier of 0.3 eV gives rise to the

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highest cell efficiency. At higher level of mid-gap acceptor density (> 1017 /cm3) in CdS, the J-V cross-over can be linked to its photodoping. This photodoping is associated with a red-

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kink in the J-V curve for long wavelength illuminations. The overall optimized cell is found to have an efficiency of 14.57% with more than 75% QE in the visible region. The built-in potential for the complete device as obtained from Mott-Schottky plot is ~1.04 V. The C-V studies yield a U-shaped apparent doping profile for p-CZTS layer which can be due to the

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combined effect of the formation of a secondary barrier and charging of deep level defects. The C-f spectra show the capacitance steps at different frequency and temperature regimes corresponding to deep level traps responsible for SRH recombination or to the presence of

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secondary diodes. The activation energy for the model mid-gap donor level obtained from

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TAS, agrees well with the input value. The carrier lifetime for the CZTS donor trap obtained by fitting the impedance plot at 300 K with the corresponding equivalent circuit is 14.5 ns. The compositional inhomogeneity in CZTS is simulated for which there is a reduction in VOC. The device with the inhomogeneous absorber layer is found to have a cell efficiency of 12.04% with a FF of 66.89%. Acknowledgement

26

ACCEPTED MANUSCRIPT The authors would like to acknowledge Marc Burgelman, University of Gent, Belgium for providing the SCAPS solar cell simulator. Funding

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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D: Appl. Phys. 46 (2013) 175101-1 – 175101-5. [45] Z.Y. Dong, Y.F. Li, B. Yao, Z.H. Ding, G. Yang, R. Deng, X. Fang, Z.P. Wei, L. Liu, An experimental and first-principle study on band alignments at interfaces of Cu2ZnSnS4/CdS/ZnO heterojunctions, J. Phys. D: Appl. Phys. 47 (2014) 075304-1 – 0753046. [46] S. Tajima, K. Kataoka, N. Takahashi, Y. Kimoto, T. Fukano, M. Hasegawa, H. Hazama, Direct measurement of band offset at the interface between CdS and Cu2ZnSnS4 using hard X-ray photoelectron spectroscopy, Appl. Phys. Lett. 103 (2013) 243906-1 – 243906-4. 31

ACCEPTED MANUSCRIPT [47] J.E. Moore, S. Dongaonkar, R.V.K. Chavali, M.A. Alam, M.S. Lundstrom, Correlation of built-in potential and I-V crossover in thin film solar cells, IEEE J. Photovolt. 4 (2014) 1138 – 1148. [48] B.L. Williams, J.D. Major, L. Bowen, L. Phillips, G. Zoppi, I. Forbes, K. Durose, Challenges and prospects for developing CdS/CdTe substrate solar cells on Mo foils, Sol.

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Energ. Mat. Sol. Cells 124 (2014) 31 – 38.

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082302-1 – 082302-4.

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capacitance profiling in Cu(In,Ga)Se2 solar cells, J. Appl. Phys., 103 (2008) 063701-1 –

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admittance, capacitance-voltage, and current-voltage signatures in Cu(In,Ga)Se2 thin film solar cells, J. Appl. Phys. 107 (2010) 034509-1 – 034509-12.

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[54] T. Walter, R. Herberholz, C. Muller, H.W. Schock, Determination of defect distributions from admittance measurements and application to Cu(In,Ga)Se2 based heterojunctions, J. Appl. Phys. 80 (1996) 4411 – 4420. [55] M. Burgelman, P. Nollet, Admittance spectroscopy of thin film solar cells, Solid State Ionics 176 (2005) 2171 – 2175. [56] Y. Kim, I.H. Choi, Defect characterization in co-evaporated Cu2ZnSnSe4 thin film solar cells, Curr. Appl. Phys. 16 (2016) 944 – 948.

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ACCEPTED MANUSCRIPT [57] P.A. Fernandes, A.F. Sartori, P.M.P. Salome, J. Malaquias, A.F. da Cunha, Admittance spectroscopy of Cu2ZnSnS4 based thin film solar cells, Appl. Phys. Lett. 100 (2012) 2335041 – 233504-4. Figure Captions

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Fig. 1. (Colour online) Schematic of CZTS based solar cell used for simulation.

Fig. 2. (Colour online) Solar cell efficiency as a function of CZTS absorber layer thickness.

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The inset shows the change in the external QE.

Fig. 3. (Colour online) Output performance of the solar cell as a function of CZTS shallow

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acceptor density. (a) Fill factor (b) Efficiency (c) External QE.

Fig. 4. Efficiency as a function of the (a) CZTS neutral defect density and (b) CZTS/CdS interface defect density.

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Fig. 5. Efficiency as a function of the CZTS hole mobility.

Fig. 6. (Colour online) Efficiency as a function of CdS and HR-ZnO layer thickness. Fig. 7. (Colour online) Efficiency as a function of the series and shunt resistance. The inset

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shows the corresponding J-V characteristics.

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Fig. 8. (Colour online) (a) CBE for different values of χCZTS showing the cliff to spike like transition of CBO between CZTS/CdS junction, (b) J-V crossover for χCZTS = 4.1 eV under different kinds of illuminations, (c) J-V crossover for χCZTS = 4.2 eV under different kinds of illuminations, (d) J-V crossover for χCZTS = 4.6 eV under different kinds of illuminations showing a strong cross-over and roll-over, (e) Solar cell efficiency as a function of χCZTS and CBO.

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ACCEPTED MANUSCRIPT Fig. 9. (Colour online) J-V characteristics for the completely optimized cell under AM1.5 and dark conditions. The insets show the energy band diagram and external QE of the completely optimized cell.

Electron occupation probability of the defects.

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Fig. 10. (Colour online) (a) Generation-Recombination rate for the optimized cell. (b)

Fig. 11. (Colour online) PV efficiency of the completely optimized CZTS/CdS solar cell as a

gap (donor) defect density (c) CZTS hole mobility.

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function of (a) CZTS and CdS thickness (b) CZTS shallow acceptor concentration and mid-

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Fig. 12. (Colour online) J-V characteristics of the CZTS solar cell for CdS mid-gap acceptor concentration = 1017 /cm3 under different kinds of illumination showing cross-over and redkink effects. The inset shows the CBE of the complete device under different illuminations. Fig. 13. (Colour online) (a) C-V profile for the complete cell and for the model p-CZTS/n-

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CdS junction. (b) Corresponding Mott-Schottky plots for extraction of the built-in potential. Fig. 14. (Colour online) (a) Apparent doping profile for the complete device and the model p-

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CZTS/n-CdS junction. (b) Apparent doping profile for the complete device at different temperatures. (c) Apparent doping profile for the complete device at different shallow level

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acceptor concentrations.

Fig. 15. (Colour online) (a) C-f spectra for the complete device at different temperatures (120 – 300 K). (b) C-f spectra at 300 K for different values of back contact Schottky barrier height. (c) C-f spectra at 350 K for different concentrations of donor level traps in CZTS. Fig. 16. (Colour online) (a) C-f spectra at high temperature range (350 – 450 K) for the CZTS based device containing only single donor level. (b) C-f spectra at low temperature range 34

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barrier (inset shows the corresponding density of states).

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activation energy). (d) Scaled derivatives at low temperature regime due to the back contact

Fig. 17. (Colour online) Cole-Cole plot for the completely optimized device at 350 K with

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corresponding equivalent circuit and fitting.

Fig. 18. (Colour online) Effect of operating temperature and illumination intensity on the

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efficiency of the optimized cell.

Fig. 19. (Colour online) (a) Random composition as a function of CZTS thickness. (b) Parabolic variation of CZTS band gap as a function of composition. (c) Logarithmic variation of hole density as a function of composition. (d) Parabolic variation of mid-gap donor density

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Fig. 20. (Colour online) J-V curve for the inhomogeneous CZTS absorber layer. The inset

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shows the corresponding external QE. The dashed lines are for comparison with the homogeneous absorber layer.

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Table Captions

Table 1. Summary of initial parameters set for the simulation of CZTS solar cells. Table 2. Summary of layer parameters for CZTS solar cells after complete optimization.

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ACCEPTED MANUSCRIPT Table 1. Summary of initial parameters set for the simulation of CZTS solar cells

CZTS

CdS

i-ZnO

Al:ZnO

Thickness (µm)

2

0.05

0.05

0.2

Bandgap (eV)

1.5

2.45

3.3

3.3

Electron affinity (eV)

4.58

4.2

4.55

4.55

Dielectric permittivity

9.5

8.9

8.12

8.12

NC (/cm3)

1.91 × 1018

2.52 × 1018

4.1 × 1018

4.1 × 1018

NV (/cm3)

2.58 × 1018

2.01 × 1018

8.2 × 1018

8.2 × 1018

vth (electrons, cm/s)

2.75 × 107

2.12 × 107

1.73 × 107

1.73 × 107

vth (holes, cm/s)

2.12 × 107

Shallow NA (/cm3)

2 × 1015

Shallow ND (/cm3)

0

µn (cm2/V.s)

50

µh (cm2/V.s)

10

A (cm-1 eV1/2)

5 × 104

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(relative)

1.03 × 107

1.03 × 107

0

0

0

1 × 1017

1 × 1010

1 × 1020

50

100

100

20

20

20

5 × 104

5 × 104

5 × 104

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1.18 × 107

CZTS/CdS interface defect density: 1 × 1010 cm-2 (single; neutral)

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NC – Conduction band effective density of states, NV – Valence band effective density of states, vth – Thermal speed, NA/ND – Acceptor/Donor density, µn/µh – Electron/Hole mobility,

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ACCEPTED MANUSCRIPT Table 2. Summary of layer parameters for CZTS solar cells after realistic optimization

CZTS

CdS

i-ZnO

Al:ZnO

Thickness (µm)

1.0

0.08

0.05

0.2

Bandgap (eV)

1.5

2.45

3.3

3.3

Electron affinity (eV)

4.3

4.2

4.55

4.55

Dielectric permittivity

9.5

8.9

8.12

8.12

NC (/cm3)

1.91 × 1018

2.52 × 1018

4.1 × 1018

4.1 × 1018

NV (/cm3)

2.58 × 1018

2.01 × 1018

8.2 × 1018

8.2 × 1018

vth (electrons, cm/s)

2.75 × 107

2.12 × 107

1.73 × 107

1.73 × 107

vth (holes, cm/s)

2.12 × 107

Shallow NA (/cm3)

1 × 1016

Shallow ND (/cm3)

0

µn (cm2/V.s)

50

µh (cm2/V.s)

30

A (cm-1 eV1/2)

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Parameter

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(relative)

1.03 × 107

1.03 × 107

0

0

0

1 × 1017

1 × 1010

1 × 1020

50

100

100

20

20

20

5 × 104

5 × 104

5 × 104

5 × 104

Defect type

a/d/n

a/n

n

n

Defect distribution

Gaussian

Gaussian

Single

Single

Total Defect density

1015/1015/1012

1016/1014

1012

1014

10-16/10-14/10-15

10-16/10-15

10-15

10-15

10-14/10-15

10-15

10-15

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σn (cm2)

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(/cm3)

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1.18 × 107

σh (cm2)

10-14/10-16/10-15

CZTS/CdS interface defect density: 5 × 1014 cm-2 (single; neutral) a - Acceptor, d – donor, n – neutral, RS – 1 Ω cm2, RSh – 104 Ω cm2

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ACCEPTED MANUSCRIPT Highlights
Different reasons for J-V distortions in CZTS/CdS photovoltaic device is investigated
C-V simulation is used to obtain net built-in potential and apparent doping profile
Thermal admittance spectra are simulated to isolate the effects of deep defects and

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secondary diodes

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Optimized CZTS/CdS cell shows an efficiency of 14.57% with VOC of 1.009 V