The Effect of Bandgap Graded Absorber on the Performance of a-Si 1 – x Ge x : H Single-Junction Cells with μ cSiO x : H N-Type Layer

We reported the effect of bandgap grading of absorbers on the performance of a-Si 1−xGex:H cells employing μc-SiOx:H n-layer.The influence of bandgap grading widths extended from the p-layer (the p/i grading) and the n-layer (the i/n grading) to the absorber on the cell performance which were systematically studied. The p/i grading reduced the interface defects and thus improved the VOC. The reduced JSC and FF were presumably due to the degraded hole transport by the potential gradient of p/i grading. Increasing the i/n grading width improved the carrier collection significantly. The EQE, the JSC, and the FF were improved substantially. Bias-dependent EQE revealed that the carrier collection is efficient in the cell employing optimal i/n grading. On the other hand, increasing the i/n grading width was accompanied by the decrease in long-wavelength response which potentially constrained the i/n grading width. Compared to the cell without grading, the a-Si 1−xGex:H cells with optimal p/i and i/n grading width improved the efficiency from 5.5 to 7.5%.


Introduction
Hydrogenated amorphous silicon germanium (a-Si 1−x Ge x :H) has been shown to be a promising material for low-bandgap absorber in the multijunction structure [1].Yan et al. reported that an initial efficiency over 16% was achieved by using a-Si:H/a-Si 1−x Ge x :H/nc-Si:H triple-stacked structure and by employing n-type microcrystalline silicon oxide (c-SiO x :H(n)) as the n-layer for each subcell [2].The c-SiO x :H(n) has larger bandgap and lower refractive index compared to conventional amorphous or microcrystalline silicon n-layer, which reduced the parasitic absorption loss and increased the current density of component cell due to internal reflection, respectively [3,4].Moreover, the c-SiO x :H(n) has been intensively studied for the application as the intermediate reflecting layer between component cells [5,6], as the window layer in the n-side illuminated c-Si:H singlejunction cells [7], and as the back reflector in a-Si:H singlejunction cells [8].We also found that the c-SiO x :H(n) functioned well as back reflector in a-Si 1−x Ge x :H single-junction cells in our previous work [9].This functional c-SiO x :H n-layer can significantly improve the performance of singleand multijunction cells.
On the other hand, one of the major challenges in developing a-Si 1−x Ge x :H solar cells is the defective interfaces between the low-bandgap a-Si 1−x Ge x :H absorber and the doped layers, which deteriorated, cell performance significantly.The p/i and the i/n interfaces contained considerable defects due to sharp changes in material composition [4].The situation is even worse at the interface between the undoped a-Si 1−x Ge x :H and n-type c-SiO x :H.High defect density at the interfaces increases the carrier recombination loss and weakened the built-in electric field in the absorber, which leads to the decrease in  OC ,  SC , and FF.Guha et al. have reported that the employment of bandgap graded layers in the absorber can facilitate carrier collection, strengthen the built-in electric field, and thus improve the cell efficiency [10].Several groups have reported the optimized bandgap grading structure in a-Si 1−x Ge x :H absorber with a-Si:H n-layer through numerical simulation approaches [11][12][13][14][15][16].However, there are still possibilities in designing the graded bandgap structure.
In this work, we systematically investigated the effect of bandgap grading widths on the performance and spectral responses of a-Si 1−x Ge x :H cells with c-SiO x :H(n) as n-layer.

International Journal of Photoenergy
The biased quantum efficiency serves as an important tool in the investigation of carrier collection losses in a-Si 1−x Ge x :H single-junction cells [15].This approach would give us physical insight into the correlation among carrier collection, carrier generation, and bandgap grading width in the absorber.

Materials and Methods
Silicon-based thin films were prepared in a 27.12 MHz singlechamber PECVD system with a load-lock and a transfer chamber.Gas mixture of SiH 4 , GeH 4 , CO 2 , B 2 H 6 , PH 3 , and H 2 was used as source gases.N-type c-SiO x :H layer was prepared under power of 30 W and CO 2 -to-SiH 4 flow ratio of 0.54.The resulting refractive index (at wavelength of 650 nm) and the optical bandgap,  04 (photon energy where the absorption coefficient is 10 4 cm −1 ), were 3.2 and 2.2 eV, respectively.The a-Si 1−x Ge x :H single-junction solar cells were deposited on the SnO 2 :F coated glass substrates in a p-i-n superstrate configuration.The bandgap graded absorber was prepared by continuously varying the germane-to-silane flow rate ratio during the deposition process while maintaining the total thickness of the absorber at 230 nm.The bandgap graded layers were extended from the p/i and i/n interfaces toward the middle of the absorber with the bandgap changed from 1.75 to 1.53 eV.Photoconductivities of the bandgap graded layers decreased from 1.2 × 10 −5 to 3.1 × 10 −6 S/cm while the dark conductivities are quite similar (∼4 × 10 −10 S/cm) with decreasing the bandgap from 1.75 to 1.53 eV.After the deposition, the cells were transferred to a sputter chamber to deposit the ITO/Ag back contacts.
The bandgaps were obtained by analyzing the transmittance and reflection spectra of a-Si 1−x Ge x :H films using Tauc's method [17].The optical reflection of cells was measured by UV/VIS spectroscopy.The external quantum efficiency (EQE) was characterized under both short-circuit and voltage-biased conditions.The - characteristics of a-Si 1−x Ge x :H single-junction solar cells were obtained from the - measurement under illumination of AM1.5G light source with the electrode area of 0.25 cm 2 .

Inefficient Carrier Collection in a-Si 1−x Ge x :H Single-Junction Cells with
Single-Bandgap Absorber.Figure 1 shows the external quantum efficiency (EQE) of a-Si 1−x Ge x :H single-junction cells measured under different reverse biases.Bandgap graded layers were not employed in this cell.As the bias voltage increased from 0 to −0.5 V, the EQE increased significantly in longer wavelength region (>450 nm).Further increase in bias voltage from −1.0 to −1.5 V had only marginal enhancement in EQE which indicated that most carriers were extracted from the device.The difference in EQE between 0 and −1.5 V revealed that the carrier collection is inefficient in a-Si 1−x Ge x :H cells using single-bandgap absorber.We believed that the asymmetric EQE enhancement is due to the inefficient hole collection coming from the low drift mobility of holes in amorphous material.Both the bulk defects and interface defects can trap carriers and hinder photogenerated carriers from being collected.Moreover, trapped carriers can  weaken the built-in electric field in the middle of the absorber which worsened the carrier collection efficiency.To mitigate the detrimental effect of the inefficient carrier collection in the single-bandgap absorber, we employ the bandgap graded layers extended from the p/i and the i/n interfaces toward the middle of the absorber.The effect of p/i and i/n grading widths on cell performance was systematically studied.
The schematic band structures of a-Si 1−x Ge x :H singlejunction solar cells without and with bandgap grading at the p/i and the i/n interfaces were illustrated in Figures 2(a) and 2(b).The valence and the conduction band were assumed to shift equally as the film Ge content varied in the bandgap graded layer.The lowest bandgap of a-Si 1−x Ge x :H undopedlayer was 1.53 eV, while the a-Si:H p-layer and c-SiO x :H n-layer had bandgaps of 1.75 eV and 1.1 eV, respectively.The bandgap of c-SiO x :H n-layer was approximately 1.1 eV because of its microcrystalline nature and the low oxygen (∼4 at.%) we used.The bandgaps of the bandgap graded layers were changed from 1.75 to 1.53 eV.To investigate the appropriate bandgap grading structure, the p/i grading width was varied from 0 to 70 nm and the i/n grading width was varied from 0 to 180 nm.The total thickness of a-Si 1−x Ge x :H was fixed at 230 nm for every cell presented.

The Effect of p/i Grading Width on the Performance of a-Si 1−x Ge
x :H Single-Junction Cells. Figure 3 illustrates the absorptance () and EQE of a-Si 1−x Ge x :H single-junction cells as a function of the p/i grading width.The EQEs were measured under 0 and −0.5 V bias voltages.For EQEs measured under short-circuit condition (0 V), increasing the p/i grading width from 0 to 20 nm reduced the EQE at wavelength from 700 to 800 nm.Since the absorptance of cells had no noticeable change in this region, the decrease in EQE can be attributed to the degradation of carrier collection.Presumably, the degraded hole collection was responsible for the reduced EQE [10][11][12].Holes generated by long-wavelength Wavelength (nm) Figure 3: Absorptance () and EQE of a-Si 1−x Ge x :H single-junction cells measured with 0 V and −0.5 V biases as a function of the p/i grading width.The p/i grading width was changed from 0 to 70 nm meanwhile keeping the total thickness of the absorber as 230 nm for all the cells.photons near back contact would travel longer distance before being collected than the generated electrons.The potential gradient created by the p/i grading would hinder the hole transport which made the hole collection more difficult.Further increase in the p/i grading width to 70 nm reduced the EQE from 550 to 900 nm, which revealed that the hole collection was further degraded.
Table 1 summarizes the difference of current densities (Δ) measured with bias voltages of 0 and −0.5 V in EQE as a function of the p/i grading width.The Δ increased from 1.07 to 1.40 mA/cm 2 as the p/i grading width increased from 0 to 70 nm.The increased Δ manifested that the p/i grading degraded the carrier collection.
The performance of a-Si 1−x Ge x :H single-junction cells with different p/i grading width was demonstrated in Figure 4.The short-circuit current ( SC ) and FF were slightly decreased as the p/i grading width increased from 0 to 20 nm.Further increase in the grading width to 70 nm reduced the  SC and the FF to 14.6 mA/cm 2 and 0.50, respectively.The reduction in the  SC and the FF as the grading width increased from 0 to 70 nm was due to the degraded hole transport arising from the reduced potential gradient created by the p/i grading.
On the other hand, as the p/i grading width increased from 0 to 20 nm, the open-circuit voltage ( OC ) increased from 0.63 to 0.67 V. Further increase in the grading width to 70 nm increased the  OC to 0.69 V.The improvement in  OC may be due to the reduced defects at interfaces by bandgap graded layers [11,12,14].Table 1 summarizes the reverse saturation current ( 0 ) of cells with different p/i grading width.As the grading width increased from 0 to 20 nm, the  0 decreased approximately one order in magnitude from 2.8 × 10 −8 to 1.3 × 10 −9 A. The reduction in  0 revealed that the defect density at the p/i interface was reduced by the bandgap graded layers, which improved the  OC .In consequence, the thickness of the p/i grading width should be 10 to 20 nm to reduce the interface defects meanwhile minimizing the loss in  SC and FF.

Effect of i/n Grading Width on the Performance of a-Si 1−x Ge
x :H Single-Junction Cells. Figure 5 illustrates the absorptance () and EQE of a-Si 1−x Ge x :H cells with different i/n grading width.The p/i grading width and the total thickness of absorber were 15 and 230 nm, respectively, for all the cells.As the i/n grading width increased from 0 to 100 nm, the EQE at wavelength from 400 to 720 nm improved significantly.Since the absorptance had no obvious change from 400 to 720 nm, the increased EQE in this region can be attributed to the improved hole collection.Presumably, the potential gradient established by i/n grading facilitated International Journal of Photoenergy Figure 4: The performance of a-Si 1−x Ge x :H single-junction cells as a function of the p/i grading width under illumination of AM1.5G light source.The p/i grading width was changed from 0 to 70 nm meanwhile keeping the total thickness of the absorber at 230 nm for all the cells.The lines were drawn to guide the eye.Wavelength (nm) i/n grading width 0 nm 40 nm 100 nm 160 nm 180 nm the hole transport.Also, the i/n grading modified the distribution of defects in the absorber which strengthened the built-in electric field that improved the carrier collection [11,12,14].The reduction at the wavelength approximately 750 nm as the i/n grading width increased from 0 to 100 nm coincided with the decrease in absorptance in the same region, which was due to the reduction in carrier generation by the wider-bandgap graded layers.
As the i/n grading width increased from 100 to 160 nm, the EQE was further improved at wavelength from 650 to 750 nm while the EQE from 750 to 900 nm decreased noticeably.The former was due to the improved carrier collection while the latter, which coincided with the reduction in absorptance, revealed that the carrier generation was further reduced by wider bandgap graded absorbers.Further increase of i/n grading width to 180 nm reduced the EQE at the wavelength from 680 to 900 nm, which implied that the carrier generation was further suppressed.
The effect of the i/n grading width on the performance of a-Si 1−x Ge x :H cells was demonstrated in Figure 6.As the i/n grading width increased from 0 to 180 nm, the  OC increased monotonically from 0.66 to 0.69 V.The improvement in  OC was due to the reduced defect density at the interfaces and the redistribution of defects in the absorber which strengthened the built-in electric field [11,12,14].Since the p/i interface is the dominant junction for high  OC , the modification of the i/n grading width had relatively smaller improvement on  OC than the p/i grading presented in Figure 4.
In addition, when the i/n grading width increased from 0 to 100 nm, the  SC increased significantly from approximately 15 to 16 mA/cm 2 and the FF increased from 0.56 to 0.61 accordingly.The increase in  SC and FF suggested that the i/n grading enhanced the carrier collection in the absorber.Presumably, the potential gradient created by the i/n grading Figure 6: The performance of a-Si 1−x Ge x :H single-junction cells as a function of the i/n grading width under illumination of AM1.5G light source.The p/i grading width and the total thickness of absorber were 15 and 230 nm, respectively, for all the cells.The lines were drawn to guide the eye.
facilitated the hole transport and also strengthened the builtin electric field in the absorber [12,14].As the i/n grading width increased from 100 to 160 nm, the  SC seemed saturated at approximately 16.5 mA/cm 2 while the FF increased from 0.61 to 0.65 monotonically.The increased FF suggested that the carrier collection was further improved by the i/n grading.The saturated  SC was due to the cancellation of improved EQE at wavelength from 650 to 750 nm and the reduced EQE from 750 to 900 nm as shown in Figure 5.Further increase in the i/n grading width to 180 nm improved the FF to 0.66 while reducing  SC to 16.1 mA/cm 2 due to the reduced longerwavelength response.The cell efficiency improved significantly from 5.5% to 7.5% as the i/n grading width increased from 0 to 180 nm.However, since a-Si 1−x Ge x :H cells were generally used as bottom cells, thicker i/n grading width would lead to substantial reduction in long-wavelength response which may be potentially unfavorable in the tandem cell design.As a result, the i/n grading should be as thick as 100 to 160 nm to take advantage of the improved carrier collection meanwhile minimizing the reduction in longer-wavelength response.
Figure 7 compares the EQEs of a-Si 1−x Ge x :H cells with and without bandgap graded layers measured under different bias voltages.The cell without bandgap grading exhibited substantially larger increase at wavelength from 400 to 900 nm under −0.5 V bias.In contrast, the cell employing bandgap graded layers showed only marginal increase in EQE under −0.5 V at wavelength from 450 to 700 nm, which suggested that most carriers were extracted under short-circuit condition.This result suggested that the bandgap graded layers improved the carrier collection significantly and thus can make a more efficient light management in a-Si 1−x Ge x :H w/o E g grading (−0.5 V) / w o E g grading (0 V) Figure 7: Comparison between EQEs of a-Si 1−x Ge x :H singlejunction cells with and without bandgap graded layers at the p/i and the i/n regions.The circle and square symbols denote the cell with and without bandgap grading, respectively.The p/i and i/n grading widths and the total thickness of absorber were 15, 160, and 230 nm, respectively.The EQEs measured under reverse bias of −0.5 V were represented by the dash lines.cells.On the other hand, the reduction in the EQE at wavelength below 400 nm with reverse bias was probably due to the electron collection issues or the signal instability of the EQE system under biased condition.Further exploration on the nonlinear bandgap grading profiles shall lead to enhanced longer-wavelength response.

Figure 1 :
Figure 1: External quantum efficiency (EQE) of a-Si 1−x Ge x :H singlejunction cells with different reverse biases.The bias voltage was changed from 0 to −1.5 V.

Figure 2 :
Figure 2: The schematic band structure of a-Si 1−x Ge x :H single-junction cell (a) without bandgap grading and (b) with bandgap grading at both the p/i and the i/n interfaces.

Figure 5 :
Figure 5: Absorptance () and EQE of a-Si 1−x Ge x :H single-junction cells as a function of the i/n grading width.The i/n grading width was changed from 0 to 180 nm meanwhile keeping the p/i grading width and the total thickness of the absorber at 15 and 230 nm, respectively.
1−x Ge x :H single-junction cells E g grading grading E g grading (0 V) EQE (%) w/o E g E g grading (−0.5 V)

Table 1 :
The reverse saturation current ( 0 ) and the difference of current densities (Δ) measured with bias voltages of 0 and −0.5 V in EQE as a function of the p/i grading width.