A two-group diffusion recombination model for perovskite carrier dynamics analysis

Abstract

This invention belongs to the field of solar photovoltaic technology, specifically providing a two-group diffusion-recombination model for perovskite carrier dynamics analysis, addressing the problem that existing models cannot accurately describe the behavior of electrons and holes in complex device structures. This invention proposes a two-group diffusion-recombination model based on PN junction and built-in electric field theory to accurately describe the dynamics of photogenerated carriers in perovskite solar cells containing an electron transport layer (ETL) and a hole transport layer (HTL). Furthermore, the model can accurately describe the diffusion, recombination, and migration processes of electrons and holes at different levels. Simultaneously, the model considers the separation and acceleration effects of the built-in electric field on carriers, thereby improving carrier separation efficiency and providing a new theoretical basis for the design and optimization of perovskite photovoltaic devices.

Description

Technical Field

[0001] This invention belongs to the field of solar photovoltaic technology and relates to a dynamic modeling method for photogenerated carriers in perovskite solar cells. Specifically, it provides a dual-group diffusion recombination model for perovskite carrier dynamics analysis to solve the problem that existing models cannot accurately describe the behavior of electrons and holes in complex device structures. Background Technology

[0002] Perovskite photovoltaic devices, as a new type of high-efficiency solar cell, have made significant progress in the photovoltaic field in recent years. Due to their excellent photoelectric performance, low cost, and simple fabrication process, perovskite photovoltaic devices have become a research hotspot. However, although perovskite photovoltaic devices have made great breakthroughs in efficiency, their carrier dynamics still need in-depth research, especially for complete devices that consider the transport layers (electron transport layer (ETL) and hole transport layer (HTL)).

[0003] In perovskite photovoltaic devices, the diffusion, recombination, and migration processes of charge carriers determine the photoelectric conversion efficiency. Traditional studies on charge carrier dynamics have focused on the characteristics of the perovskite absorber layer (PER). However, perovskite photovoltaic devices are not simply a single absorber layer structure. Modern perovskite photovoltaic devices are usually composed of multiple functional layers, such as the electron transport layer (ETL) and hole transport layer (HTL). The transport layer not only affects the efficiency of photon absorption and charge carrier separation, but also plays a key role in the process of charge carrier migration and recombination.

[0004] For the dynamic modeling of photogenerated carriers in perovskite solar cells, while existing single-group diffusion-recombination models can describe carrier behavior within the perovskite layer relatively well, they have certain limitations when dealing with photovoltaic devices with multilayer structures. Particularly when considering the influence of the built-in electric field, single diffusion-recombination models often fail to fully capture the different diffusion behaviors of electrons and holes under different electric fields. Furthermore, most existing models neglect the influence of the electron transport layer (ETL) and hole transport layer (HTL) on carrier dynamics, making it difficult for researchers to fully understand the role of the transport layer when optimizing device structures. Further research has revealed that the presence of the PN junction and the interface characteristics between the perovskite layer and the transport layer determine the separation and migration mechanisms of carriers in the device. The built-in electric field plays a crucial role in this process, affecting not only the distribution of electrons and holes but also determining their diffusion and recombination rates. Therefore, for complete perovskite photovoltaic devices considering both the electron transport layer (ETL) and hole transport layer (HTL), accurate carrier dynamics modeling has become an important approach to improving device efficiency and stability.

[0005] Currently, although some researchers have attempted to combine PN junction theory and built-in electric field effects for more refined modeling, a systematic model is lacking to describe the carrier behavior of the complete device structure, including the electron transport layer (ETL) and hole transport layer (HTL). Existing research mostly focuses only on the carrier dynamics of the perovskite absorber layer itself or local structures, without fully considering the synergistic effects of the various functional layers in the device. Therefore, how to more accurately describe the behavior of electrons and holes using built-in electric field theory and PN junction theory, while considering the complete device structure, remains a major challenge in current photovoltaic device research. Summary of the Invention

[0006] The purpose of this invention is to provide a two-group diffusion-recombination model for perovskite carrier dynamics analysis, addressing the problem that existing models cannot accurately describe the behavior of electrons and holes in complex device structures. This invention proposes a two-group diffusion-recombination model based on PN junction and built-in electric field theory to accurately describe the dynamics of photogenerated carriers in perovskite solar cells containing an electron transport layer (ETL) and a hole transport layer (HTL). Furthermore, the model can accurately describe the diffusion, recombination, and migration processes of electrons and holes at different layers. Simultaneously, the model considers the separation and acceleration effects of the built-in electric field on carriers, thereby improving carrier separation efficiency and providing a new theoretical basis for the design and optimization of perovskite photovoltaic devices.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A two-group diffusion-recombination model for perovskite carrier dynamics analysis, characterized in that the equation expression of the two-group diffusion-recombination model is as follows:

[0009]

[0010] Where n(x,t) and p(x,t) represent the spatiotemporal distributions of electrons and holes, respectively, x represents the spatial variable, and t represents the time variable; D n With D p Let μ represent the diffusion coefficients of electrons and holes, respectively. n With μ p Let E(t) represent the mobility of electrons and holes respectively, E(t) represent the total built-in electric field strength, k1 represent the first-order recombination probability (defect recombination), k2 represent the second-order recombination probability (radiative recombination), E0 represent the built-in electric field of the PIN junction (hole transport layer / perovskite / electron transport layer), and C represent the built-in electric field attenuation coefficient.

[0011] Furthermore, the boundary conditions of the dual-group diffusion composite model are:

[0012]

[0013] Where l represents the thickness of the perovskite absorber layer, S0 represents the surface recombination velocity at x = 0, and S l This represents the surface recombination velocity at x = l.

[0014] Furthermore, in the aforementioned dual-group diffusion recombination model, n(x,0)=N0e -αx p(x,0)=N0e -αx N0 represents the initial concentration of charge carriers, and α represents the absorption coefficient of the medium for monochromatic light.

[0015] Furthermore, in the aforementioned dual-group diffusion recombination model, the spatial variable x and the time variable t are independent variables, the spatiotemporal distribution of electrons n(x,t) and the spatiotemporal distribution of holes p(x,t) are the results to be solved, and the carrier diffusion coefficient D... n With D p First-order recombination probability k1, second-order recombination probability k2, surface recombination velocities S0 and S l The built-in electric field E0 and the built-in electric field attenuation coefficient C of the PIN junction are model parameters, and all model parameters are obtained through data fitting.

[0016] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0017] This invention provides a two-group diffusion-recombination model for perovskite carrier dynamics analysis, used to describe the photogenerated carrier dynamics in perovskite photovoltaic devices (perovskite solar cells), including the diffusion and recombination processes of electron and hole groups, and incorporating the influence of the built-in electric field on carrier migration. First, electrons and holes are treated as independent groups and described separately using equations and boundary conditions. Then, the effect of the built-in electric field is considered to simulate its directional motion and acceleration effect on carriers. Finally, key parameters are fitted using experimental data to improve the model's accuracy and predictive ability. Furthermore, the diffusion coefficients and recombination rates of the electron and hole groups in the two-group diffusion-recombination model can be adjusted according to actual conditions. The model accurately simulates the movement of photogenerated carriers in the perovskite absorption layer. Furthermore, in the two-group diffusion recombination model, drift terms caused by the built-in electric field exist simultaneously in both sets of equations, representing the different effects of the built-in electric field on the electron and hole swarms. At the corresponding carrier transport layer positions, the boundary conditions of the equations in the two-group diffusion recombination model exhibit drift terms influenced by the built-in electric field, representing the different effects of the extraction layer on the electron and hole swarms. The initial conditions of the equations in the two-group diffusion recombination model vary depending on the actual situation, representing the different carrier distribution effects under different photoexcitation conditions. In the two-group diffusion recombination model, the radiative recombination term represented by the second-order recombination probability k2 is the product of the electron and hole swarm concentrations, representing a physically consistent process.

[0018] In summary, the dual-group diffusion recombination model of this invention considers the carrier dynamics changes caused by the device structure, and can provide theoretical support for the optimized design of perovskite photovoltaic devices (perovskite solar cells), thereby improving the photoelectric conversion efficiency of photovoltaic devices. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the perovskite photovoltaic device used in Embodiment 1 and Comparative Example 1 of the present invention.

[0020] Figure 2 The results are the test and fitting curves of the transient fluorescence curve of the perovskite photovoltaic device in Example 1 of the present invention.

[0021] Figure 3 The results show the test and fitting curves of the transient fluorescence curve of the perovskite photovoltaic device in Comparative Example 1 of this invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0023] This invention provides a two-group diffusion recombination model for perovskite carrier dynamics analysis, primarily simulating photogenerated carrier dynamics through numerical calculations; specifically:

[0024] First, diffusion-recombination equations for electrons and holes are established to describe their movement in the absorption layer of a complete perovskite photovoltaic device structure.

[0025] The basic single-group diffusion recombination model has the following equation form:

[0026]

[0027] n(x,0)=N0e -αx

[0028] Where n(x,t) represents the spatiotemporal distribution of electrons and holes, x represents the spatial variable, t represents the time variable; D represents the diffusion coefficient, k1 represents the first-order recombination probability (defect recombination), k2 represents the second-order recombination probability (radiative recombination); N0 represents the initial concentration of charge carriers, and α represents the absorption coefficient of the medium for monochromatic light.

[0029] Its boundary conditions are:

[0030]

[0031] Where l represents the thickness of the perovskite absorber layer, S0 represents the surface recombination velocity at x = 0, and S l This represents the surface recombination velocity at x = l;

[0032] The single-group diffuse recombination model is very effective in describing perovskite thin films where the electron and hole diffusion coefficients are balanced, because electrons and holes behave similarly; however, in... Figure 1 In the complete perovskite photovoltaic device structure shown, according to PN junction theory, charge migration and rebalancing between the transport layer and the perovskite layer will generate a built-in electric field in the perovskite, promoting the migration and extraction of photogenerated carriers. This process causes the behavior of electrons and holes to become dissimilar, necessitating independent consideration of the diffusion of electrons and holes. Therefore, this invention proposes a two-group diffusion recombination model, whose equation form is:

[0033]

[0034] n(x,0)=N0e -αx

[0035] p(x,0)=N0e -αx

[0036] Where n(x,t) and p(x,t) represent the spatiotemporal distributions of electrons and holes, respectively, x represents the spatial variable, and t represents the time variable; D n With D p Let μ represent the diffusion coefficients of electrons and holes, respectively. n With μ p Let N and K represent the mobility of electrons and holes, respectively; E represents the total built-in electric field strength; k1 represents the first-order recombination probability (defect recombination); k2 represents the second-order recombination probability (radiative recombination); N0 represents the initial concentration of charge carriers; and α represents the absorption coefficient of the medium for monochromatic light.

[0037] Based on the cumulative effect of charge carriers in the transport layer, the derivation process of the total built-in electric field intensity E is as follows:

[0038] Charge accumulation is derived from the short-circuit equivalent current of perovskite photovoltaic devices. The short-circuit equivalent current of perovskite photovoltaic devices is expressed as:

[0039] I(t)=J(t)S=(E0-E1(t))σS

[0040] Where I(t) represents the short-circuit equivalent current of the perovskite photovoltaic device, J(t) represents the short-circuit equivalent current density of the perovskite photovoltaic device, S represents the effective area of ​​the capacitor; E0 represents the built-in electric field of the PIN junction (hole transport layer / perovskite / electron transport layer), E1(t) represents the electric field generated by carrier accumulation, and σ represents the conductivity of the perovskite absorber layer.

[0041] The accumulation of charge is then expressed as: Where Q(t) represents the cumulative charge of the equivalent capacitance of the perovskite photovoltaic device, and A represents a constant term;

[0042] However, based on capacitor theory, the charge accumulation is derived as follows: Q(t) = BE1(t), where Q(t) represents the accumulated charge of the equivalent capacitance of the perovskite photovoltaic device, and B represents a constant term.

[0043] Based on the two expressions for charge accumulation above, we obtain the equation: Where C represents a constant term, defined as the built-in electric field attenuation coefficient, and is obtained by solving for: E1(t)=E0-E0e -Ct ;

[0044] Therefore, the total built-in electric field strength E is expressed as: E = E0 - E1(t) = E0e -Ct It should be noted that the constant terms A, B, and C in the above derivation represent the positive correlation of the equations.

[0045] Therefore, we can deduce that the built-in electric field in the cumulative case exhibits exponential decay, which, after introducing the equation, becomes the following form:

[0046]

[0047] The boundary conditions of the equation are then updated to the following form:

[0048]

[0049] Where l represents the thickness of the perovskite absorber layer, S0 represents the surface recombination velocity at x = 0, and S l This represents the surface recombination velocity at x = l;

[0050] The equation expression for the two-group diffusion composite model is obtained by combining the boundary conditions, where the independent variables are x and t, and the solutions are n(x,t) and p(x,t), with parameter D. n D p k1, k2, S0, S l E0, C;

[0051] Then, the parameters of the above two-group diffusion recombination model were fitted, and the key parameter in the model, carrier diffusion coefficient D, was fitted using experimental data. n With D p First-order recombination probability k1, second-order recombination probability k2, surface recombination velocities S0 and S l The built-in electric field E0 and the built-in electric field attenuation coefficient C of the PIN junction are used to obtain a complete double-group diffusion recombination model, which enables an accurate description of carrier behavior.

[0052] Furthermore, by using numerical methods to solve the above model equations, the distribution, migration, and recombination processes of charge carriers (n(x,t)\p(x,t)) can be obtained.

[0053] In addition, by comparing the simulation results of different design schemes, the influence of built-in electric field and material hierarchy on photogenerated carriers can be analyzed, providing a basis for the structural optimization of perovskite photovoltaic devices.

[0054] In summary, this invention provides a dual-group diffusion recombination model that, through a combination of numerical calculations and experimental data, can not only describe the behavior of photogenerated carriers at different levels, but also predict the performance improvement potential of perovskite photovoltaic devices.

[0055] Example 1

[0056] This embodiment uses, as follows: Figure 1 The perovskite photovoltaic device shown is used to verify the effectiveness of the two-group diffusion recombination model in this invention. The perovskite photovoltaic device is a three-layer photovoltaic device structure comprising a perovskite absorber layer (PER), an electron transport layer (ETL), and a hole transport layer (HT). The absorber layer is made of perovskite material (CH3NH3PbI3), the electron transport layer uses a tin dioxide thin film, and the hole transport layer uses Spiro. The specific verification process is as follows:

[0057] First, the perovskite photovoltaic device was fabricated in a laboratory environment, and the sample was excited by laser to generate photogenerated carriers, and transient fluorescence test curves were obtained.

[0058] Then, the electron and hole behavior in perovskite photovoltaic devices is numerically simulated using the dual-group diffusion recombination model proposed in this invention, including the following steps:

[0059] Step 1: Collect transient fluorescence test data, including intensity and time step vectors; collect the device's corresponding IRF function, including intensity and time step vectors, and convert it into an EXCEL spreadsheet file;

[0060] Step 2: Use Matlab to load the data from the Excel spreadsheet file as a vector for later use;

[0061] Step 3: Load the two-group diffusion composite model into Matlab for later use;

[0062] Step 4: Load the transient fluorescence decay curve simulation script into Matlab for later use. This script requires calling the model from Step 3 to calculate the carrier concentration and then simulating the transient fluorescence decay curve using the traditional recombination luminescence model.

[0063] Step 5: Run the Particle Swarm Optimization (PSO) algorithm using Matlab, and set appropriate initial parameter values ​​(D). n D p k1, k2, S0, S lThe iteration begins with E0 and C, during which step 4 is repeatedly called to obtain the simulated transient fluorescence decay curve and the test curve data for comparison. The initial parameters are iterated in the direction with the smallest difference between the two. After a certain number of iterations, the fitting parameters (the values ​​of the initial parameters after iteration) and the corresponding fitting curve data are obtained.

[0064] Step 6: Run the plotting script using Matlab. The fitted curve (the final simulated fluorescence decay curve) and the test curve will appear simultaneously. Figure 2 As shown.

[0065] Meanwhile, this invention also provides a comparative example 1, the only difference from example 1 being that: in step 3, a single-group diffusion recombination model is loaded, and the final simulated fluorescence decay curve and the test curve are as follows. Figure 3 As shown.

[0066] Depend on Figure 2 and Figure 3 As can be seen from the fitting results, compared with the traditional single-group diffusion recombination model, the double-group diffusion recombination model considering the built-in electric field in this invention can more accurately predict the migration process of charge carriers between the absorption layer and the transport layer, and has a higher degree of agreement with the experimental data.

[0067] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A two-group diffusion recombination model for perovskite carrier dynamics analysis, characterized in that, The equation for the two-group diffusion recombination model is as follows: Where n(x,t) and p(x,t) represent the spatiotemporal distributions of electrons and holes, respectively, x represents the spatial variable, and t represents the time variable; D n With D p Let μ represent the diffusion coefficients of electrons and holes, respectively. n With μ p Let E(t) represent the mobility of electrons and holes respectively, E(t) represent the total built-in electric field strength, k1 represent the first-order recombination probability, k2 represent the second-order recombination probability, the first-order recombination probability is the defect recombination probability, and the second-order recombination probability is the radiative recombination probability; E0 represents the built-in electric field of the PIN junction of the hole transport layer / perovskite / electron transport layer, and C represents the built-in electric field attenuation coefficient. The boundary conditions for the dual-group diffusion recombination model are: Where l represents the thickness of the perovskite absorber layer, S0 represents the surface recombination velocity at x = 0, and S l This represents the surface recombination velocity at x = l.

2. The two-group diffusion recombination model for perovskite carrier dynamics analysis according to claim 1, characterized in that, In the aforementioned dual-group diffusion recombination model, n(x,0)=N0e -αx p(x,0)=N0e -αx N0 represents the initial concentration of charge carriers, and α represents the absorption coefficient.

3. The two-group diffusion recombination model for perovskite carrier dynamics analysis according to claim 1, characterized in that, In the dual-group diffusion recombination model, the spatial variable x and the time variable t are the independent variables, the spatiotemporal distribution of electrons n(x,t) and the spatiotemporal distribution of holes p(x,t) are the results to be solved, and the carrier diffusion coefficient D is... n With D p First-order recombination probability k1, second-order recombination probability k2, surface recombination velocities S0 and S l The built-in electric field E0 and the built-in electric field attenuation coefficient C of the PIN junction are model parameters, and all model parameters are obtained through data fitting.

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