Modeling and Design of Graphene GaAs Junction Solar Cell

Graphene based GaAs junction solar cell is modeled and investigated by Silvaco TCAD tools. The photovoltaic behaviors have been investigated considering structure and process parameters such as substrate thickness, dependence between graphene work function and transmittance, and n-type doping concentration in GaAs. The results show that the most effective region for photo photogenerated carriers locates very close to the interface under light illumination. Comprehensive technological design for junction yields a significant improvement of power conversion efficiency from0.772% to 2.218%.These results are in good agreement with the reported experimental work.


Introduction
Graphene, a single atom layer of carbon hexagons, has attracted much attention owing to its unique structure and fascination, such as low resistivity, ultra-high mobility, and near-zero band gap [1].Graphene has been produced in the form of ultrathin sheets consisting of one or a few atomic layers by chemical vapor deposition or mechanical exfoliation and can be transferred to various substrates, which open a wide field of potential applications such as high performance electronic devices, photosensors, and smart composite [2,3].In particular the graphene film has a unique combination of high electrical conductivity and optical transparency in visible and near-infrared regions, which gives it the ability to serve as an active layer for metal-semiconductor (M/S) junction solar cells [4].Recently, graphene based solar cells had been fabricated on various substrates such as Si [5], CdS [6], and GaAs [7]; much process has been achieved in the past several years.Moreover graphene/semiconductor nanowires heterojunction photoelectric devices have also been achieved [8], which is combined with the unique one-dimensional (1D) structural characteristics and versatile physical properties of 1D nanowires [9][10][11][12].
Graphene based junction solar cell could be fabricated at room temperature which shows great potential in light harvesting and conversion application with the advantage of low cost, facile processibility, and environmental amity.Li et al. reported the first graphene based silicon solar cell with the average power conversion efficiency of about 1.65% [13].After this work, many effects have been exerted to improve the performance of solar cell by using silicon nanowire array [14], modifying the work function of graphene [15], chemical doping to graphene [16], and so forth.In comparison with currently widely used silicon substrate, GaAs has direct band gap and is highly resistant to radiation which makes it suitable for high efficiency solar cell design and space application.The present technique can also provide the possibility to combine large area graphene with GaAs [17,18].Jie group transferred single and bilayer graphene sheets onto n-type GaAs substrates and got a power conversion efficiency of 1.95% [19].Behura et al. calculated the photovoltaic response of graphene junction using the fundamental models for voltage and current; they pointed out that graphene GaAs heterojunction has a superior photovoltaic behavior to graphene silicon junctions [20].
However, the device based graphene GaAs junction is still far lower in efficiency.The application of graphene in solar cell requires much more investigation on devices especially in structure and technical parameter optimizing.In this work, simulation of graphene GaAs solar cells is carried out with the effect of substrate thickness, graphene transmittance and resistance, and n-type doping concentration.The graphene GaAs solar cell was modeled using Silvaco TCAD tools while the performance of solar cell was improved by parameter optimization.

Structure and Modeling
As mentioned above, Figure 1 shows the cross section of the graphene GaAs solar cell simulated using TCAD tools.The device consists of three regions which are Gallium arsenide (GaAs) substrate, SiO 2 window layer, and graphene layer from bottom to the top area, respectively.Here the graphene layer with a thickness of 10 nm was coated onto the silicon substrate with 1 m × 12 m oxide window which could decrease the surface recombination.
Basically, any semiconductor can form a Schottky junction with a certain metal if their work function difference is big enough and the carrier density of the semiconductor is moderate [21].GaAs, with a direct band gap of 1.42 ev, is a promising material for optoelectronic device application.Calculations' results indicate that graphene films form a Schottky junction with GaAs, which is favorable for producing a relatively large built-in field [22].
The nonlinear I-V characteristic of the Schottky junction can be expressed by the thermionic emission model: where  is the contact area,  * is the effective Richardson constant,  is the absolute temperature,  is Boltzmann constant, and C  is the barrier height for n-type semiconductor where C  is the work function of graphene and  is the electron affinity of semiconductor.Under illumination, the photoexcited electrons and holes are generated in the GaAs substrate and then separated by the built-in electric field at the Schottky junction.Electrons and holes are collected by bottom electrodes and graphene film which form a photovoltaic action for n-type GaAs as shown in Figure 2. No doping: 8000 cm 2 /Vs N-type doping 1 × 10 14 cm −3 : 7300 cm 2 /Vs N-type doping 1 × 10 15 cm −3 : 5900 cm 2 /Vs N-type doping 1 × 10 16 cm −3 : 4600 cm 2 /Vs

𝜇 ℎ
GaAs hole mobility, 300 K No doping: 400 cm 2 /Vs N-type doping 1 × 10 14 cm −3 : 340 cm 2 /Vs N-type doping 1 × 10 15 cm −3 : 302 cm 2 /Vs N-type doping 1 × 10 16 cm −3 : 240 cm 2 /Vs To investigate the performance of graphene based solar cell, simulations were carried out using TCAD, which divides into two steps since there is not graphene default involved in the material declination.Firstly, we deposit 10 nm aluminum film as anode electrode instead of graphene film using ATHENA tool to generate the device structure.Secondly, we redefine the anode electrode material as graphene layer using ATLAS tool.
Graphene is modeled as a semimetal, a carrier mobility of 15,000 cm 2 /Vs.The carrier densities were calculated by Fermi distribution and by adjusting the values of effective masses, a thickness of 10 nm, and band gap such that the cattier densities agree with experimental results.It is important to point out that, for multilayer graphene film, the - dispersion relationship is weakly parabolic rather than linear as in the case of monolayer graphene.Simulation parameters used in Atlas tool for this device are listed in Table 1.

GaAs Substrate Thickness Effect.
GaAs crystal is chosen as absorption area.Graphene layer acts as a transparent electrode, that is, for the intensity of photogenerated carriers.A Schottky junction is built in for the difference between their work functions.Figures 3(a)-3(d) show the photogeneration rates of GaAs solar cell under AM1.5 illumination with depth for absorption layer were maintained at 1 m, 2 m, 5 m, and 10 m, respectively.The light could be absorbed in barrier layer and inside the semiconductor.Both results show the most effective absorption area located in the surface attachment about 0.1 m.Meanwhile, Figure 3(d) shows that 10 m thickness is enough for full spectrum absorption since the intensity of the photogenerated carriers dramatically reduces in the deep area of GaAs substrate.
To investigate the effect of GaAs thickness on the performance of solar cell, we calculate the current-voltage curves and internal quantum efficiency (IQE) shown in Figures 4  and 5, respectively.Most carriers are generated around the surface for GaAs under light illumination.At the condition of the thickness below 5 m, the absorption of long wavelength photo is strengthened with the increase of thickness.In comparison the absorption of long wavelength photo decreases when the thickness at 5 m and 10 m expects the absorption peak at 870 nm which is according to the band energy level of GaAs.As a result, the light current gets a peak value versus different substrate thickness which leads to the biggest power conversion efficiency at 1.392% (listed in Table 2).

Graphene Work Function and Transmittance Effect.
According to the theory model described in Figure 2, the battier height C  is related to the difference between graphene work function C  and electron affinity  of GaAs.Consequently, higher work function increases C  and further enhances the built-in potential  bi via the equation   = C  −   , where   means the distance between   and   in GaAs.
Therefore, the increase of graphene work function implies the increase of  bi corresponding to the upper limitation of  oc .
Lancellotti et al. reported the dependence of graphene work function and transmittance on the number of layers [21].We calculated the current-voltage curves and IQE of graphene GaAs solar cells versus different graphene work function considering the dependence of transmittance.We noticed that the IQE of three kinds of graphene layer have almost the same absorption spectrum zone as shown in Figure 7.However, the higher transmittance means the lower work function which leads to the balance between short circuit current and open-circuit voltage as shown in Figure 6.Accordingly, higher barrier also leads to a bigger fill factor.As a result, we got the biggest power conversion efficiency at 1.481% (listed in Table 2).the short-circuit current and open-circuit voltage are both increased due to higher barrier height as shown in Figure 8.The variation of  oc is much more significant than that of  sc which has great consistency with the IQE results shown in Figure 9.In other words, n-type doping for GaAs mainly affects the height of barrier which leads to the enhancement of open-circuit voltage while the current generated by photos does not show great shifts.It may be due to the movement of depletion boundary in the region close to the interface of graphene and GaAs with increasing doping density.

Figure 4 :
Figure 4: Current-voltage curves of graphene solar cells versus different GaAs thickness.

Figure 7 :
Figure 7: IQE of graphene solar cells versus different graphene work function.

Table 1 :
Simulation parameters for graphene GaAs solar cell.

Table 2 :
Efficiency versus GaAs thickness, graphene work function and transmittance, and n-type doping concentration under AM1.5 illumination.
Doping Effect.It is well known that the n-type doping in GaAs can increase the Fermi energy level and intensity of photogeneration carriers.For doping concentration at 1 × 10 14 cm −3 , 1 × 10 15 cm −3 , and 1 × 10 16 cm −3 ,