1 THE GEORGE WASHINGTON UNIVERSITY Department of Electrical and Computer Engineering Device Electronics ECE 6030 spring xxx Final Project MoS2 Based Photovoltaics xxx 2 1. INTRODUCTION Solar energy represents one of the most abundant and yet least harnessed sources of renewable energy. Solar constant, which is the total energy flux incident on a unit area perpendicular to a beam outside the Earth's atmosphere, is about 1367[W/m2]. That corresponds to an annual average of $ 3000 [KW hr/m2 year] if we consider the distribution over the total surface area of earth. In recent years, great progress has been made in developing photovoltaics that have the potential to be deployed on a massive scale. Novel device structures and materials allow for cost- effective and efficient solar cells. [3] Films of semiconductor transition metal dichalcogenide (TMD) have long been considered for photovoltaic devices, due to their large optical absorption, which is greater than 107−1across the visible range, meaning that 95% of the light can be absorbed by a 300-nm film [1]. Two dimensional materials, such as graphene and TMD, represent the ultimate scaling of material thickness. They are of great interest for applications in atomically thin, flexible and transparent optoelectronics for few known reasons. First, unlike traditional semiconductors, layered semiconductors show thickness dependent optical properties. For instance: bulk semiconductor TMD has indirect band-gap, but it shows direct band-gap when exfoliated to few layers (3 to 5 layers) or monolayer. Value of the band-gap also increases as number of layers decrease. Second, 2D materials are free of dangling bond and do not show degrading of performance due to Fermi level pinning. Third, strong absorption in monolayer TMDs is due to the dipole transition between localized d orbital contributing to visible absorbance and excitonic coupling of such transitions 3 [4]. Fourth, presence of critical points called Van Hove singularities that generate in 2D or 1D leads to strong light-matter interaction [1]. MULTIPHYSIC SIMULATION Defining solar cell efficiency requires a multi physics approach combining optical and electrical study. At first we have optical efficiency; it is something that we can calculate with FDTD. An incident light come into material and we assume every photon that is absorbed by material is generating electron-hole pairs; also assuming that each of these electron hole pairs can find their ways to the contacts. This is the upper limit efficiency. We then proceed to electrical simulation with DEVICE software and investigate the process by which these pairs are separated and collected in contacts and some the loss effects that can consume those charges before they can actually reach the contact reducing the efficiency of the device. WHY SIMULATION? Semiconductor electronics is widely dominated by Si at present. The choice of a semiconductor material with optimal properties for a specific application, the complexity of the required fabrication technology, reliability of its performance, all together determine the final cost of the technology development. High costs and investment reliability has prevented any alternative semiconductor material from entering the commercial market for decades except for high- frequency GaAs and very specific optical applications. Silicon had significantly less development complexity compared to other materials in the first place. Furthermore, each new semiconductor material has now to compete with a well established silicon technology. However, any 4 breakthrough in development of these materials can improve the device performance in the field of high-temperature, high-power, high-frequency, and optical applications. Device simulations can be thought of as virtual measurement of the electrical behavior of a semiconductor device, such as a transistor or diode. The device is represented as a meshed finite- element structure. Each node of the device has properties associated with it, such as material type, doping concentration. For each node, the carrier concentration, current densities, electric field, generation, recombination and so on are computed. SOLAR SPECTRUM Solar spectrum is very broadband. We calculate absorption rate as a function of wavelength for a flat spectrum. Later we renormalize the data to the solar spectrum as a post processing step. Sunlight is unpolarized. We model sun light with a plane wave source. Sunlight is unpolarized with two orthogonal polarization simulations. 2. OPTICAL SIMULATION Finite-difference time-domain (FDTD) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to the associated system of differential equations). Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way. To implement an FDTD solution of Maxwell's equations, a computational domain must first be established. The computational domain is simply the physical region over which the simulation 5 will be performed. The E and H fields are determined at every point in space within that computational domain. The material of each cell within the computational domain must be specified. Typically, the material is either free-space (air), metal, or dielectric. Any material can be used as long as the permeability, permittivity, and conductivity are specified. [14] BOUNDARY CONDITION Perfectly matched layer (PML) boundaries absorb electromagnetic energy incident upon them. PML is most effective when absorbing radiation at normal incidence, but can have significant reflection at grazing incidence. Periodic boundary condition should be used when both the structures and EM fields are periodic. Periodic boundary conditions can be used in one or more directions. PML boundary condition was applied for top and bottom and periodic boundary condition for the sides. REFRACTIVE INDEX Refractive index of a substrate is a dimensionless number that describes how light propagates through the medium: = Where c is the speed of light in vacuum and v is the speed of light in medium. The refractive index also determines how much light is bent when entering a material. The refractive index varies with the wavelength of light. This is called dispersion and causes the splitting of white light. 6 Light propagation in absorbing materials can be described using a complex valued refractive index: � = + The real part of the refractive index indicates the phase velocity, while the imaginary part indicates the amount of absorption loss when the electromagnetic wave propagates through the material. is often called the extinction coefficient; and the absorption coefficient becomes: = 4 0 The measured intensity of transmitted wave through a layer of material with thickness and attenuation coefficient is related to the incident intensity 0 according to Beer-Lambert law. = 0− 0 is the incident intensity and is is intensity of wave after travelling distance x in the material. 7 Figure 1 the refractive index n and extinction coefficient k values of the MoS2 layers for the five different thicknesses. Samples A to E are in order 2, 3, 5.5, 10, and 20 nm. [2] An important parameter is the extrinsic quantum efficiency (EQE), defined as the ration of the number of charge carriers generated to the number of incident photons. This can be expressed in terms of the photocurrent , incident power per unit area , and excitation wavelength by: = ℎ Where ℎ is the Planck constant, the speed of light in vaccum, and the electron charge. [1] 8 Figure 2 Fitting FDTD model to data for refractive index from literature. RESULTS I have run FDTD simulation from Lumerical to calculate power absorption, electron-hole pair generation and short circuit current for many different structures, 3 of which are listed in Figure 3. As we can see in these figures, 2 nm of a trilayer MoS2 can absorb up to 20 percent of in blue light wavelength. And the band gap of a trilayer MoS2 is 1.6, less than 1.9 for a monolayer MoS2 but still it is a direct bandgap material according to [4]. 9 Figure 3 absorption of light by 2 nm thin MoS2, 10 nm thin MoS2 and five of 2 nm thin MoS2 layers. We have refractive index and extinction coefficient for 15 layer bulk MoS2 as well which is an indirect bandgap material with bandgap of 1.35 [eV]. Since 15 layer bulk MoS2 has 5 times the thickness of the 3 layer MoS2, the pick absorption has increased to about 50 percent for short wavelengths. In third case I stacked 5 of 3 layer MoS2 10 and investigated its absorption which shows two picks similar to 3 layer case and up to 45 percent absorption. By these data, we can use an integral to calculate the ideal short-circuit current density: = � ()ℎ()∞ where is the band gap of the absorber, ℎ() is the incident photon flux in AM1.5 (units of photons/cm2.s.eV), and E is the photon energy. In this ideal case, every photon absorbed by the absorber is converted to a carrier extracted in a PV device, so =89.46 and 79.16 A/m2 for 15 layer and five 3 layer MoS2 structures, sets the upper limit of the 1nm thickness solar cell short- circuit current density. Back Reflector Metallic back reflector is one of methods to increase light matter interaction. A plain metallic reflector behind the cell will make light to bounce back and double pass the photoactive material. The metallic reflector can come in different shapes, plain, triangle, rectangular grading, or a rough surface. I have studied some of these structures which naturally demonstrate a superior absorption. However for a metallic reflector to bounce back light; it requires to have certain thickness which is not advised to be less than 100 nm. 100 nm thickness for our ultrathin device is considered very thick which stands against the Selling point of these materials (ultrathin flexible PV cells). I have listed some of the simulation results to show why metallic reflector needs to be 11 more than 100 nm. Figure 4 Investigation of thickness of metallic back reflector for purpose of increasing interaction of light with photoactive material. 3. ELECTRICAL SIMULATION Light (electromagnetic radiation) is typically absorbed in a photosensitive device through the excitation of charge, where the energy of the photon is transferred to an electron in the solid. In a semiconductor, electrons in the valence band are excited to the conduction band when a photon whose energy exceeds the band gap is absorbed. The excited electron leaves behind a positive, mobile vacancy, known as a hole. The process is commonly referred to as electron-hole pair generation. [13] 12 To start electrical simulation one need to define MoS2 for the simulator. Since this is a not a widely used material we need to go through exploring every property of material and specifying it for simulator. WORK FUNCTION The first step in this calculation is determining the work function, Φ, of MoS2. This value has been measured in experimental observations and Density Function Theory (DFT) calculations to about 5.1 [eV]. The work function of graphene is commonly measured in the 4.3 to 4.6 [eV] range. The work function for other important semiconducting TMDs was also studied. The work functions vary considerably depending on the transition metal used and their thickness. A summary of their work functions is listed in Table 1. Notice that as the work function of graphene is comparable in magnitude, it has been shown that it has a very minimal effect on the band structure of TMD, and the Dirac point of graphene stays within the gap, facilitating efficient extraction of both electrons and holes from TMD. DIELECTRIC CONSTANT Relative dielectric permittivity for monolayer MoS2 was achieved by abinit to 6.8-7.3 which is close to the relative dielectric constant for bulk MoS2. [5] 13 BANDGAP Bulk semiconducting TMDCs have indirect band-gap, but the show direct band-gap when exfoliated to few layers (3 to 5 layers) or monolayer. Value of the band-gap also increases as number of layers decrease. This can be seen both in Figure 5 and Figure 6. Figure 5. Band structures calculated from first-principles density functional theory (DFT) for bulk and monolayer MoS2 and WS2. The horizontal dashed lines indicate the Fermi level. The arrows indicate the fundamental bandgap (direct or indirect). The top of the valence band (blue) and bottom of the conduction band (green) are highlighted.[12] Figure 6. Plot of bandgap versus MoS2 thickness for five different samples of Figure 1. [2] 14 EFFECTIVE MASS Hybrid density functional theory and Bethe-Salpeter equation were used to calculate electron and hole effective mass in MoS2. The values for hole effective mass and electron effective mass are 0.46 and 0.43, respectively. For bulk MoS2 the values are 0.9 and 0.7 in the same order. [6][7] CARRIER LIFETIME AND DIFFUSION LENGTH Reference [8] develops a relatively complete description of charge carrier transport characteristics in the FET, the minority carrier (hole) diffusion length was extracted from line profiles of the zero bias photocurrent. They convolved an exponential decay with the experimentally measured Gaussian beam width. The best fit yields = 0.22 . The results of this direct transport measurement agree with previously reported measurements. The field effect mobility extracted from the transconductance, together with diffusion length, can be used to estimate the minority carrier lifetime: = 2 Calculated carrier lifetime = 2.4 also agrees with literature values. The same analysis applied to a single layer device yields a diffusion length of about 0.4 and a lifetime of about 60 ns.[8] 15 MOBILITY AND STAURATION VELOCITY There are various reports on electron effective mobility ranging from 1 to 480 2−1−1 depending on the device structure, dielectric environment and processing [9]. Here I have considered mobility to be 470 2−1−1 for electrons and 480 2−1−1 for holes. Velocity saturation was also found in literature [10] to be 0.28 × 107/ and the critical electric field to be 1.15 × 105 /. DEVICE SIMULATION RESULTS List of input parameters for device simulation is brought in Table 2: Table 1 Input parameters for device simulation 10 L MoS2 3 layer MoS2 Work function 4.5 eV 5.1 eV Effective mass 0.7 e, 0.9 h 0.43 e, 0.46 h Bandgap 1.35 eV; indirect 1.6 eV; direct Diffusion Length 0.22 um 0.4 um Life Time 2.4 ns 60 ns Mobility 480 cm2/vs for hole 470 for electron Saturation Velocity 0.28 e7 cm/s 16 Next the 15 layer MoS2 device was simulated with a graphene transparent contact on top of the MoS2 making a completely flat structure. Some of the results are listed in Figure 7. The short circuit current for this photovoltaic cell was 89.46 A/m2. Figure 7. The device simulation results (Electric Potential, Electric Fied, Charge density, Current density, External optical generation and meshing triangle area) using DEVICE after importing generation from FDTD. Both these software are from Lumerical. Reference [1] Britnell, “Strong light-matter interactions in heterostructures of atomically thin films”, 2013, Science. [2]Chanyoung Yim, “Investigation of the optical properties of Mos2 thin films using spectroscopic ellipsometry”, 2014, Applied Physics Letters. 17 [3] Three-dimensional nanopillar-array photovoltaics on low-cost and flexible substrates. Nature Materials 2009. [4] Bernardi M, Palummo M, Grossman JC. Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials. Nano Letters 2013. [5] Mehdi Salmani-Jelodar, “Single Layer MoS2 Band Structure and Transport”, 2011. [6] Eugene Kadantsev, “Electronic structure of a single MoS2 monolayer”, Solid State Communications, 2012. [7] Ferdows Zahid, “A generic tight-binding model for monolayer, bilayer and bulk MoS2”, 2013. [8] Chung-Chiang Wu, “Elucidating the photoresponse of ultrathin MoS2 field effect transistor by scanning photocurrent microscopy”. [9] Wenzhong Bao, “High mobility ambipolar MoS2 field effective transistors: substarte and dielectric effects”. [10] Gianluca Fiori, “Velocity saturation in few-layer MoS2 transistor” 2013, Applied physics letters. [11] Mohammad Tahersima, Zhizhen Ma, Yijing Tong , “Solar Cells Based on Layered Semiconductor”, Energy and Society. [12] Qing Hua Wang, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides”, Nature nanotechnology, 2013. [13] lumerical [14] Wikipedia; complex refractive index
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