Variation in efficiency with change in band gap and thickness in thin film amorphous silicon tandem heterojunction solar cells with AFORS-HET

Muhammad Riaz; Ahmed C. Kadhim; Susan K. Earles; Ahmad Azzahrani

doi:10.1364/OE.26.00A626

1. Introduction

In recent years, the hydrogenated amorphous silicon (a-SiH) thin film solar cell has attracted lots of attention due to its low cost [1]. Today, the most economical technology is Si based technology. However, it undergoes a serious light-induced degradation effect, the (S-W) effect [2], which becomes a bottleneck for the application of a-SiH thin film solar cell. Despite its limitations, including the degradation effect (S-W), and its low efficiency [3], silicon is still a promising cost-effective source due to its abundance [1]. Some methods that can resolve these limitations are the following. (a) Using tandem technology, the S-W effect in a-SiH thin film can be improved with amorphous hydrogenated silicon germanium (a-SiGeH) [1]. The S-W effect is not obvious in a-SiGeH. An alloy of s-SiH with Ge reduces the optical gap and allows band gap tuning by varying Ge content. (b) Inserting a-SiC as a window layer [4, 5] helps to improve the efficiency of a-SiH thin film solar cell. Amorphous hydrogenated silicon carbide (a-SiC) thin layer has been widely used as a window layer in tandem technology to achieve better optical transparency [4]. It does so by widening the band gap of material [6, 7]. (c) Inserting a thin buffer layer or back surface layer of intrinsic amorphous silicon a-Si(i) at the interface helps to reduce recombination of carriers. Thus, the tandem thin film solar cell, a-SiH/a-SiGeH, is fabricated by stacking sub-cells within the band gaps of 1.75eV to 1.55eV respectively. The top, middle, and bottom of a tandem cell is designed to absorb blue, green, and red photons [5, 8].

The technique of tandem design is used to minimize the contact recombination, by different semiconductors with different band gaps, which are used to form solar absorbing layers for a collection of photons. The generated excess carriers are separated by an electric field, and attracted towards the outer contact. These selective contacts are designed by adjusting the doping concentrations at the edges of the solar cell. As a result, it creates an internal electric field by which the excess carriers are separated and collected at different contacts.

Amorphous silicon is considered the cheapest source in photovoltaic (PV) design giving researchers a wide range of options to improve its efficiency using a-Si alloys. The potential of this technology has been demonstrated by Sanyo by reaching 22.80% cell efficiency in lab [9] and 15.00% in a commercial module [10]. Recently, The Advance Institute of Industrial Science and Technology (AIST) designed high efficiency (11.00%) microcrystalline silicon thin film solar cells using superior light trapping capabilities (honeycomb textured substrates) [11]. Some other groups also have demonstrated efficiencies close to 20% [12–16].

The main objective of this study is to use simulation to simply show the improvement in efficiency when using double absorbing layers versus single absorbing layers and suggest optimal device layer thickness to reduce recombination losses in the bulk as well as the interfaces. To address these objectives, first, numerical simulations of both single and double absorbing layers of amorphous silicon thin film solar cell are performed. Single absorbing layer solar cells with a-SiH and a-SiGeH are designed and compared with a tandem heterojunction solar cell comprised of both a-SiH and a-SiGeH absorbing layers. Then, the design parameters are investigated, compared and optimized to predict the maximum efficiency. The simulation is performed using AFORS-HET (simulation program for hetero-junction solar cells) [17]. Moreover, the effect of back surface field (BSF) on the parameters of a-Si solar cell was also investigated. Results are validated using two different analysis methods.

2. Theoretical model

The incoming spectral photon flux Ф₀(λ, t), is measured with respect to the front contact absorption and reflectance. The photon flux incoming through the first semiconductor layer is calculated by all three terms as Ф₀(λ, t) R(λ) A(λ). The theoretical model uses AFORS-HET for the tracing of light extended path caused by textured surface, is needed to be adjust the incident angle δ of incoming light. For a silicon textured wafer with <111> direction the angle is δ = 54.74°, and for normal plane δ = 0°. The angle γ by which the light travels through the layer stack depends on the wavelength of the incoming light and is calculated by Snell’s law.

γ (λ) = δ - {\sin s (δ) \frac{1}{n (λ)}}

where, the

n (λ)

depends on refractive index of the first semiconductor layer on the front side.

The doping densities N_D and N_A at position x of fixed donor or acceptor state within any cell is supposed to always be completely ionized and defects N_trap at any position with specific energy E within the band gap of the semiconductor can be locally charged or uncharged within the system. These defects can be defined like acceptor-like Shockley-Read-Hall defects, donor-like Shockley-Read-Hall defects or dangling bond defects. The Poisson equation, which is to be solved within each layer as given

\frac{ε_{0} ε_{r}}{q} \frac{\partial^{2} φ (x, t)}{\partial x^{2}} = p (x, t) - n (x, t) + N D (x) - N A (x) + \sum_{t r a p} ρ_{t r a p} (x, t)

where, q is electron charge,

ε_{0} ε_{r}

are absolute and relative dielectric constant.

ρ_{t r a p}

will depend on the defect type of the defect under consideration and on local particle densities n and p. Further it is defined by the trap density distribution function N_trap(E) of the defect, specifying the number of traps at any energy position E within the band gap. Also by some corresponding defect occupation function, defining the probability that a trap with an energy E within band gap are empty or occupied with a single or double electron. The defect-type chosen, can be empty, singly occupied with electrons, or even doubly occupied with electrons (in case of the dangling band defect).

The one-dimensional equations of continuity and transport for electron and holes, which have to be solved with in each layer,

- \frac{1}{q} \frac{\partial J_{n} (x, t)}{\partial x} = G_{n} (x, t) - R_{n} (x, t) - \frac{\partial}{\partial t} n (x, t)

+ \frac{1}{q} \frac{\partial J_{p} (x, t)}{\partial x} = G_{p} (x, t) - R_{p} (x, t) - \frac{\partial}{\partial t} p (x, t)

The super band gap generation rates G_n and G_p are determined by optical modeling and the recombination rates R_n or R_p. The electron and hole currents J_n and J_p are derived by the gradient of the corresponding quasi Fermi energy E_Fn and E_F. The position dependent Fermi energies and the corresponding local electron and hole current are defined with the help of Maxwell Boltzmann approximation for Fermi-Dirac distribution function.

J_{n} (x, t) = q μ_{n} n (x, t) \frac{\partial E_{F n} (x, t)}{\partial x}

J_{p} (x, t) = q μ_{p} n (x, t) \frac{\partial E_{F p} (x, t)}{\partial x}

E_{F n} (x, t) = E_{C} (x) + k T l n {\frac{n (x, t)}{N_{C} (x)}} = - q χ (x) + q φ (x, t) + k T l n {\frac{n (x, t)}{N_{C} (x)}}

E_{F p} (x, t) = E_{V} (x) - k T l n {\frac{p (x, t)}{N_{V} (x)}} = - q χ (x) + q φ (x, t) - E_{g} (x) + k T l n {\frac{p (x, t)}{N_{V} (x)}}

where, μ_n and μ_P are the electron and hole motilities,

χ

is the electron affinity, E_c, and E_v are conduction and valance band energies, the E_g is the band gap, and the effective conduction and valance band density of states N_C and N_V of the semiconductor.

The radiative band to band rate constant r has to be defined in order to balance the radiative band to band recombination rates R_n,p; as the result the electrons and holes are always equal.

R_{n, p} (x, t) = r {n (x, t) p (x, t) - N_{C} N_{V} e^{\frac{- E_{g}}{k T}}}

According to Krichen, and Arab [19], the effect of back surface field (BSF) in terms of surface recombination velocity ERV (S_bsf) in the vicinity of back surface junction is defined as:

S_{b s f} = \frac{N_{d} D_{n} \frac{S_{n} L_{n}}{D_{n}} \cos h (\frac{W_{B S F}}{L_{n}}) + \sin h (\frac{W_{B S F}}{L_{n}})}{N_{d} L_{n} \cos h (\frac{W_{B S F}}{L_{n}}) + \frac{S_{n} L_{n}}{D_{n}} \sin h (\frac{W_{B S F}}{L_{n}})} F_{n} a n d F_{n} = \frac{N_{}_{c}^{a - Si} N_{v}^{a - Si}}{N_{c} N_{v}} esp (- \frac{E_{}_{g}^{a - Si} - E_{g}^{n}}{k_{B} T})

where,

E_{}_{g}^{a - S i}

and

E_{g}^{n}

refers to the band gap of amorphous back surface layer and highly doped n⁺ layer. The

D_{n}

refers to electron diffusion coefficient in the n⁺ region,

L_{n}

refers the thickness n⁺ region, and

W_{B S F}

refer to the thickness of back surface layer. The increase in the open circuit V_oc and efficiency

η

due to the BSF is expressed by the following equations.

Δ V_{o c} = V_{o c} (S_{b s f}) - V_{o c} (S_{n})

Δ η = η (S_{b s f}) - η (S_{n}) = (Δ P / P_{i n}) x 100

3. Computer model

Figure 1 shows the schematics diagram for the solar cells simulated using AFORS–HET. For all cells, the top p⁺ layer (Layer 2) and the bottom n⁺ layer (Layer 6 and 8) have a 5nm thickness with doping concentrations of $N_{A} = 3 \times 10^{18} c m^{- 2}$ and $N_{D} = 8 \times 10^{18} c m^{- 2}$ , respectively. The band gap of the top p⁺ layer (layer 2) is 2eV, and the bottom, n⁺ layer is 1.8eV.

Fig. 1 Schematic diagram of individual absorbing layers (a) a-Si:H and a-SiGe:H; (b) Schematic Layout double layer, tandem heterojunction solar cell.

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The single absorbing layer cells: both a–SiH and a-SiGeH are shown in Fig. 1(a). In both cells, layer 4 is the absorbing layer, and layer 5 is the mid intrinsic absorbing region. The tandem heterojunction (with double absorbing layers) solar cell is designed using 100nm a-SiH absorbing layer and 80nm a-SiGeH absorbing layer separated by 10nm mid intrinsic absorbing region, layer 5. The schematics of the tandem heterojunction solar cell is shown in Fig. 1(b). For the simulations, the a-SiH absorbing layer has a graded band gap varying from 1.75eV to 1.65eV. The a-SiGeH absorbing layer has a fixed band gap of 1.55eV. The band gap diagram for double layer tandem heterojunction solar cell is shown in Fig. 2.

Fig. 2 Band gap for double layer, tandem solar cell.

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An n-type 80nm indium doped tin oxide (ITO) layer is used at the top surface. A 200nm thick region of Ag is used as a bottom contact. For the ITO and Ag regions, the default optical constant models for n(E) and k(E) available in the database of AFORS-HET software are used. A 10nm intrinsic a-SiC with 1.85eV band gap is used as window layer. The a-Si(i) buffer layer, layer 7, acts as back surface field (BSF) layer. A band gap of 1.7eV is used for all of the intrinsic silicon layers.

Cells are illuminated with AM 1.5 radiation. For front and back contacts, MS Shockley model is applied. The Drift –diffusion model and thermionic emission model are used for the interfaces. The Beer-Lambert absorption model is applied for the optical bulk layer.

4. Result and discussion

The width of the intrinsic region and diffusion length of both electrons and holes determine the short circuit current (Jsc) of the cell. To reduce the probability of recombination of excess carriers, simulations show the highly doped p⁺ and n⁺ regions need to have a width less than five percent of the total intrinsic layer.

Amorphous silicon materials such as a-SiH, a-SiGeH and a-SiCH contain a large number of defect states within the band gap. To accurately model the device, the continuous density of defect states in a-Si and in all of its alloys is considered. The density of states (DOS) is described as a combination of exponential decaying band tail states (for both donor like states and acceptors like states) and Gaussian distribution of mid gap states as shown in Fig. 3. The a-Si characteristics energies of the conduction band and valence band tails are 0.06eV and 0.03eV. Similarly, the peak energy distributions of acceptor and donor type Gaussian states are 1.2eV and 0.56eV with a deviation of 0.08eV. The concept of Gaussian distribution of defect states in amorphous silicon material reflects its disordered structure and disorder of states at a particular energy level. This distribution of density of defect states is defined for all layers including a-SiC and a-Si(i) layers using conduction and valence tail states and two Gaussian states [3] as shown in Fig. 3.

Fig. 3 Defect density distribution of conduction and valence band tail states and two Gaussian states for hydrogenated (a) a-SiGe:H and (b) .a-Si:H.

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The efficiency of a-SiH is 9.64% with FF = 83.07%, V_oc = 1069 mV, and Jsc = 10.86 mA/cm². The V_oc is highest as compare to the other designs due to thickness of the layer. The short circuit current is nearly comparable to the tandem design. It is because of the high band gap of a-Si as compare to a-SiGeH. The a-Si layer is sensitive to thermal generation, there is more generation rate as compare to other layers but it has high recombination. The Fig. 4 shows the efficiencies of a-SiH cell.

Fig. 4 Efficiency of a-SiH versus thickness.

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The efficiency of a-SiGeH is 5.40% with FF = 81.85%, V_oc = 1026 mV, and J_sc = 6.43 mA/cm². The short circuit current and efficiency of a-SiGeH is lower because of lower band gap and thickness. The a-SiGeH is supposed to have high reliability as compared to a-SiH by having less defect density. The Fig. 5 shows the efficiencies of a-SiGeH cell. The efficiency of a-SiGeH is lower than the efficacy of a-Si, obviously, the short circuit current is lower because of lower band gap and thickness of the layer but it has high reliability as compared to a-SiH by having less defect density.

Fig. 5 (a) Efficiency of a-SiGeH versus thickness.

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The IV characteristics for tandem solar cell is shown in Fig. 6. The short circuit current (J_sc), open circuit voltage (V_oc), fill factor (FF), and efficiencies (η) of the single absorbing layer solar cells and tandem heterojunction solar cell are shown in Table 1.

Fig. 6 IV curve of tandem heterojunction solar cell.

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Table 1. Efficiencies of All Designs

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The buffer layer, layer (5), helps to reduce the interface recombination and improves the interface quality with better surface passivation [18]. The thicknesses of buffer layers a-Si(i) are varied from 5nm to 20nm. By increasing thinness of mid a-Si(i) buffer layer, layer 5, Voc decreases, Joc increases, and FF and efficiency also increase. The 10nm thinness is considered the optimum thickness for layer 5 after investigating the thickness versus efficiency contributed by this layer with overall efficiency for tandem heterojunction solar cell is 9.46%.

The layer 7 acts as back surface field layer. The effect of varying the band gap of amorphous silicon layer, after removing the BSF (layer 7), on its efficacy (η), is shown in Fig. 7(c). Overall, 7.17% increase in efficiency with addition of BSF, which is contributed by back surface layer (layer 7).

Fig. 7 Tandem heterojunction solar cell characteristics after eliminating the BSF layer (layer 7): (a) change in Voc, (b) change in Jsc, and (c) change in efficiency, with respect to change in band gap of the absorbing layer (layer 4).

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The Figs. 7(a)-7(c) show the variation in open circuit voltages, short circuit current, and efficiency as a function of layer thickness and band gap of absorbing layer (layer 4), calculated for the tandem heterojunction solar cell after removing BSF layer (layer 7) from the design. However, after inserting the BSF layer (layer 7) the efficiency increases with increasing the thickness and band gap of the same layer. The improvement in open circuit voltage can be noted decreasing with increase band gap and with decrease of thickness. It can also be noted that the improvement in open circuit voltage is particularly important when the surface recombination velocity (S_bsf) reduces. However, when back surface recombination declines, the reverse saturation current density in the layer decreases. Consequently, the improvement observed in open circuit voltage, when S_bsf decreases can be attributed to reverse saturated current density in the base region, coupled with an increase in short circuit current. Back surface field layer band gap varied from 1.20 to 1.80eV. The increase in band gap causes increase in Jsc. As the band gap broadens, it interferes as a barrier for the majority carriers. The optimum band gap selected for the BSF layer is 1.5-1.7 eV. Similarly, eliminating both buffer layers (layer 5 and 7), but keeping the same design and all parameters of the solar cell, the efficiency reduces to 9.71% with Voc = 1049mA, Joc = 10.83mA/cm².

The spectral response for the tandem heterojunction solar cell is shown in Fig. 8. The internal quantum efficiency (IQE) proceeds to zero when the incident photon has less energy than the band gap. This was observed at a wavelength of 766 nm for a-SiH solar cell and at 700 nm for a-SiGeH. The internal quantum efficiency for the tandem heterojunction solar cell proceeds to zero at 820 nm. The least absorbing layer is a-SiGeH, whereas the combination ofboth individual absorbing layers (a-SiH and a-SiGeH) results in an increase in the internal quantum efficiency (IQE) and external quantum efficiency (EQE) of the tandem heterojunction solar cell. The internal quantum efficiency should be always greater than the external quantum efficiency since the IQE governs the generation of electrons via absorption of each photon. The external efficiency depends on both the absorption and collection of charges (Table 2).

Fig. 8 The IQE and EQE of tandem heterojunction solar cell.

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Table 2. Parameters and Structural Dimensions used in this Simulation

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The AFORS-HET analysis model is based on the density of states; therefore, the same design of the a-Si tandem heterojunction solar cell with the Lumerical FDTD/Device 4.6 [20] was investigated in order to confirm the findings. With the use of the Lumarical FDTD/Device 4.6, similar results were observed for all three designs as when had been done using AFORS-HET. Results with Lumerical FDTD/Device 4.6 indicated the fill factor and the efficiency for a-SiGeH (FF = 78.98% and η = 6.03%), a-SiH (FF = 84.27% and η = 7.06%), and Tendon design (FF = 81.90% and η = 9.84%) respectively. These findings are recorded in Table 1.

5. Conclusion

The numerical analysis of amorphous silicon thin film solar cell was investigated with the use of AFORS-HET. The efficiencies of both single absorbing layers a-SiH and a-SiGeH were compared with tandem heterojunction thin film solar cell (a-SiH + a-SiGeH). The efficiencies for single absorbing layers were observed to be 9.64% for a-SiH and 5.40% for a-SiGeH respectively. The overall efficiency of the tandem heterojunction cell was recorded as 10.46%. The buffer layers contributed to a 7.17% increase in efficiency of the tandem solar cell. In order to validate these findings, the results were compared using the Lumerical FDTD/Device 4.6. Similar results were observed by both models of analysis as seen in Table 1.

References and links

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Parameter Name	a-SiC layer	a-Si(i) layer	a-Si:H layer	a-SiGe:H layer
Layer thickness (nm)	10.00	10.00	100.00	80.00
Band gap, Eg (eV)	1.85	1.7	1.75 - 1.65	1.55
Electron affinity (eV)	4.03	3.9	3.95	4.17
Effective conduction band density (cm⁻³)	$2.84 \times 10^{19}$	$1 \times 10^{20}$	$2.5 \times 10^{20}$	$2.84 \times 10^{19}$
Effective valence band density (cm⁻³)	$2.84 \times 10^{19}$	$1 \times 10^{20}$	$2.5 \times 10^{20}$	$2.84 \times 10^{19}$
Electron mobility (cm⁻²V⁻¹s⁻¹)	20.00	20.00	20.00	20.00
hole mobility (cm⁻²V⁻¹s⁻¹)	2.00	5.00	2.00	2.00
Total DOS in accepter like Gaussian (cm⁻³)	$7 \times 10^{15}$ - $5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$	$5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$
Total DOS in donor like Gaussian (cm⁻³)	$7 \times 10^{15}$ - $5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$	$5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$
Gaussian donor like peak energy (eV) from Ec	1.2	1.12	1.2	1.12
Gaussian accepter like peak energy (eV) from	0.7	0.56	0.56	0.6
Standard deviation (eV)	0.08	0.08	0.08	0.08
Capture cross-section for donor states e, h (cm⁻³)	$1 \times 10^{- 15}$ $1 \times 10^{16}$	$1 \times 10^{- 15}$ $1 \times 10^{- 15}$	$1 \times 10^{- 15}$ $1 \times 10^{16}$	$1 \times 10^{- 15}$ $1 \times 10^{16}$
Capture cross-section for accepter states e, h (cm⁻³)	$1 \times 10^{- 17}$ $1 \times 10^{15}$	$1 \times 10^{- 17},$ $1 \times 10^{15}$	$1 \times 10^{- 17}$ $1 \times 10^{15}$	$1 \times 10^{- 17}$ $1 \times 10^{15}$
Characteristic energy for donor and acceptor (eV)	0.06, 0.3	0.055, 0.03	0.06, 0.3	0.06, 0.03
Thermal velocity (cm/s)	$1 \times 10^{7}$	$1 \times 10^{7}$	$1 \times 10^{7}$	$1 \times 10^{7}$
Layer density(g/cm³)	2.33	2.32	2.32	2.32

Parameter Name	a-SiC layer	a-Si(i) layer	a-Si:H layer	a-SiGe:H layer
Layer thickness (nm)	10.00	10.00	100.00	80.00
Band gap, Eg (eV)	1.85	1.7	1.75 - 1.65	1.55
Electron affinity (eV)	4.03	3.9	3.95	4.17
Effective conduction band density (cm⁻³)	$2.84 \times 10^{19}$	$1 \times 10^{20}$	$2.5 \times 10^{20}$	$2.84 \times 10^{19}$
Effective valence band density (cm⁻³)	$2.84 \times 10^{19}$	$1 \times 10^{20}$	$2.5 \times 10^{20}$	$2.84 \times 10^{19}$
Electron mobility (cm⁻²V⁻¹s⁻¹)	20.00	20.00	20.00	20.00
hole mobility (cm⁻²V⁻¹s⁻¹)	2.00	5.00	2.00	2.00
Total DOS in accepter like Gaussian (cm⁻³)	$7 \times 10^{15}$ - $5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$	$5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$
Total DOS in donor like Gaussian (cm⁻³)	$7 \times 10^{15}$ - $5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$	$5 \times 10^{17}$	$7 \times 10^{15}$ - $5 \times 10^{17}$
Gaussian donor like peak energy (eV) from Ec	1.2	1.12	1.2	1.12
Gaussian accepter like peak energy (eV) from	0.7	0.56	0.56	0.6
Standard deviation (eV)	0.08	0.08	0.08	0.08
Capture cross-section for donor states e, h (cm⁻³)	$1 \times 10^{- 15}$ $1 \times 10^{16}$	$1 \times 10^{- 15}$ $1 \times 10^{- 15}$	$1 \times 10^{- 15}$ $1 \times 10^{16}$	$1 \times 10^{- 15}$ $1 \times 10^{16}$
Capture cross-section for accepter states e, h (cm⁻³)	$1 \times 10^{- 17}$ $1 \times 10^{15}$	$1 \times 10^{- 17},$ $1 \times 10^{15}$	$1 \times 10^{- 17}$ $1 \times 10^{15}$	$1 \times 10^{- 17}$ $1 \times 10^{15}$
Characteristic energy for donor and acceptor (eV)	0.06, 0.3	0.055, 0.03	0.06, 0.3	0.06, 0.03
Thermal velocity (cm/s)	$1 \times 10^{7}$	$1 \times 10^{7}$	$1 \times 10^{7}$	$1 \times 10^{7}$
Layer density(g/cm³)	2.33	2.32	2.32	2.32

Variation in efficiency with change in band gap and thickness in thin film amorphous silicon tandem heterojunction solar cells with AFORS-HET

Abstract

1. Introduction

2. Theoretical model

3. Computer model

4. Result and discussion

5. Conclusion

References and links

Cited By

Figures (8)

Tables (2)

Equations (12)

Optics Express

Method Analysis
Layer	Jsc (mA/cm²)	Voc (mV)	FF (%)	η (%)	FF (%)	η (%)
a-SiH	10.86	1069	83.07	9.64	84.27	7.06
a-SiGeH	6.43	1026	81.85	5.40	78.98	6.03
Tendon design (a-SiH + a-SiGeH)	11.66	1045	85.85	10.46	81.90	9.84