Double-group diffusion composite model applied to perovskite carrier kinetic analysis

Abstract

The invention belongs to the technical field of solar photovoltaics, and particularly provides a double-group diffusion composite model applied to perovskite carrier dynamics analysis, which is used for solving the problem that an existing model cannot accurately describe behaviors of electrons and holes in a complex device structure. The invention provides a double-group diffusion recombination model based on a PN junction and a built-in electric field theory, which is used for accurately describing the dynamics of photon-generated carriers in a perovskite solar cell comprising an electron transport layer (ETL) and a hole transport layer (HTL), can accurately describe the diffusion, recombination and migration processes of electrons and holes in different layers, and can accurately describe the dynamics of the photon-generated carriers in the perovskite solar cell. The model considers the separation and acceleration effects of a built-in electric field on carriers, so that the carrier separation efficiency is improved, and a new theoretical basis is provided for design and optimization of a perovskite photovoltaic device.

Description

Technical Field

[0001] The present invention belongs to the field of solar photovoltaic technology and relates to a kinetic modeling method for photogenerated carriers in a perovskite solar cell. The present invention specifically provides a double-group diffusion composite model applied to the kinetic analysis of perovskite carriers to solve the problem that the existing model cannot accurately describe the behavior of electrons and holes in a complex device structure. Background Art

[0002] As an emerging type of high-efficiency solar cell, perovskite photovoltaic devices have made significant progress in the photovoltaic field in recent years. Due to their excellent photoelectric performance, low cost and simple preparation process, perovskite photovoltaic devices have become a research hotspot. However, although perovskite photovoltaic devices have made great breakthroughs in efficiency, their carrier dynamics behavior still needs in-depth research, especially for complete devices considering the transport layer (electron transport layer (ETL) and hole transport layer (HTL)).

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

[0004] For the dynamic modeling of photogenerated carriers in perovskite solar cells, the existing single-group diffusion recombination model can better describe the carrier behavior in the perovskite layer, but it has certain limitations when dealing with photovoltaic devices with multilayer structures. In particular, when considering the influence of the built-in electric field, the single diffusion recombination model often cannot fully capture the different diffusion behaviors of electrons and holes under the influence of different electric fields; in addition, most existing models ignore the influence of the electron transport layer (ETL) and the hole transport layer (HTL) on the carrier dynamics, which makes it difficult for researchers to fully understand the role of the transport layer when optimizing the device structure. Further research found that the existence of the PN junction and the interface characteristics between the perovskite layer and the transport layer determine the separation and migration mechanism of carriers in the device. The built-in electric field plays a key role in this process, which not only affects the distribution of electrons and holes, but also determines the diffusion rate and recombination rate of electrons and holes; therefore, for complete perovskite photovoltaic devices considering the electron transport layer (ETL) and the hole transport layer (HTL), accurate carrier dynamics modeling has become an important way to improve device efficiency and stability.

[0005] At present, although some researchers have tried to combine PN junction theory and built-in electric field effect for more sophisticated modeling, there is a lack of systematic models to describe the carrier behavior of the complete device structure including the electron transport layer (ETL) and the hole transport layer (HTL). Most existing studies only focus on the carrier dynamics of the perovskite absorption layer itself or the local structure, and have not fully considered the synergistic effect of each functional layer in the device; therefore, how to use the built-in electric field theory and PN junction theory on the basis of considering the complete device structure to more accurately describe the behavior of electrons and holes is still a major challenge in the current research of photovoltaic devices. Summary of the invention

[0006] The purpose of the present invention is to provide a double-group diffusion composite model for perovskite carrier dynamics analysis, so as to solve the problem that the existing model cannot accurately describe the behavior of electrons and holes in complex device structures. The present invention proposes a double-group diffusion composite model based on PN junction and built-in electric field theory, which is used to accurately describe the dynamics of photogenerated carriers in perovskite solar cells containing electron transport layers (ETL) and hole transport layers (HTL), and the model can accurately describe the diffusion, recombination and migration processes of electrons and holes at different levels. At the same time, the model takes into account the separation and acceleration effects of the built-in electric field on carriers, thereby improving the carrier separation efficiency, thereby providing a new theoretical basis for the design and optimization of perovskite photovoltaic devices.

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

[0008] A double-group diffusion composite model applied to perovskite carrier dynamics analysis, characterized in that the equation expression of the double-group diffusion composite model is:

[0009]

[0010] Where n(x, t) and p(x, t) represent the temporal and spatial distribution of electrons and holes, respectively, x represents the spatial variable, and t represents the temporal variable; D n With D p are the diffusion coefficients of electrons and holes, μ n With μ p They represent the mobility of electrons and holes respectively, E(t) represents the total built-in electric field strength, k 1 represents the first-order compound probability (defect compound), k 2 is the second-order recombination probability (radiative recombination); E 0 represents the built-in electric field of the PIN junction (hole transport layer / perovskite / electron transport layer), and C represents 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 absorption layer, S 0 represents the surface recombination velocity at x = 0, S l represents the surface recombination velocity at x=l.

[0014] Furthermore, in the dual-group diffusion composite model, n(x,0)=N 0 e -αx , p(x,0)=N 0 e -αx , N 0 represents the initial concentration of carriers, and α represents the absorption coefficient of the medium to monochromatic light.

[0015] Furthermore, in the dual-group diffusion composite 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 compound probability k 1 , second-order compound probability k 2 , surface recombination velocity S 0 With S l , the built-in electric field E of the PIN junction 0 And the built-in electric field attenuation coefficient C is the model parameter, and all model parameters are obtained by data fitting.

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

[0017] The present invention provides a dual-group diffusion composite model for perovskite carrier dynamics analysis, which is used to describe the photogenerated carrier dynamics process in perovskite photovoltaic devices (perovskite solar cells), including the diffusion and recombination process of electron groups and hole groups, and combines the influence of built-in electric fields on carrier migration; firstly, electrons and holes are regarded as independent groups and described by equations and boundary conditions respectively, then the effect of the built-in electric field is considered to simulate the directional motion and acceleration effect of the built-in electric field on the carriers, and finally the key parameters are fitted in combination with experimental data to improve the accuracy and prediction ability of the model; and the diffusion coefficients of the electron group and the hole group in the dual-group diffusion composite model are The recombination rate can be adjusted according to the actual situation, thereby accurately simulating the movement of photogenerated carriers in the perovskite absorption layer; in addition, the drift term generated by the built-in electric field in the double-group diffusion recombination model exists in both sets of equations, indicating the different effects of the built-in electric field on the electron group and the hole group; in the double-group diffusion recombination model, at the corresponding carrier transport layer position, the boundary conditions of the equations have drift terms affected by the built-in electric field, indicating the different effects of the extraction layer on the electron group and the hole group; the initial conditions of the equations in the double-group diffusion recombination model depend on the actual situation, indicating the different carrier distribution effects under different light excitation conditions; the second-order recombination probability k in the double-group diffusion recombination model 2 The radiation recombination term represented by the latter is the product of the concentrations of electron and hole populations, indicating a process that conforms to the physical substance;

[0018] In summary, the dual-group diffusion recombination model of the present invention takes into account the changes in carrier dynamics caused by the device structure, and can provide theoretical support for the optimal design of perovskite photovoltaic devices (perovskite solar cells), thereby improving the photoelectric conversion efficiency of photovoltaic devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the structure of the perovskite photovoltaic device used in Example 1 of the present invention and Comparative Example 1.

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

[0021] Figure 3 These are the test and fitting curve results of the transient fluorescence curve of the perovskite photovoltaic device in Comparative Example 1 of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and beneficial effects of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0023] The present invention provides a dual-group diffusion composite model for perovskite carrier dynamics analysis, which mainly simulates the photogenerated carrier dynamics through numerical calculation; specifically:

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

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

[0026]

[0027] n(x,0)=N 0 e -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, k 1 represents the first-order compound probability (defect compound), k 2 is the second-order recombination probability (radiative recombination); N 0 represents the initial concentration of carriers, and α represents the absorption coefficient of the medium to monochromatic light;

[0029] Its boundary conditions are:

[0030]

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

[0032] The single-group diffusion composite model is very effective in describing perovskite films with balanced electron and hole diffusion coefficients because electrons and holes behave in the same way; however, in Figure 1 In the complete perovskite photovoltaic device structure shown, according to the PN junction theory, the charge migration and rebalancing between the transport layer and the perovskite layer will generate a built-in electric field in the perovskite to promote the migration and extraction of photogenerated carriers. This process alienates the behavior of electrons and holes, and it is necessary to consider the diffusion of electrons and holes independently; therefore, the present invention proposes to obtain a double-group diffusion composite model, and its equation form is:

[0033]

[0034] n(x,0)=N 0 e -αx

[0035] p(x,0)=N 0 e -αx

[0036] Where n(x, t) and p(x, t) represent the temporal and spatial distribution of electrons and holes, respectively, x represents the spatial variable, and t represents the temporal variable; D n With D p are the diffusion coefficients of electrons and holes, μ n With μ p They represent the mobility of electrons and holes respectively, E represents the total built-in electric field strength, k 1 represents the first-order compound probability (defect compound), k 2 is the second-order recombination probability (radiative recombination); N 0 represents the initial concentration of carriers, and α represents the absorption coefficient of the medium to monochromatic light;

[0037] Based on the accumulation effect of carriers in the transport layer, the derivation process of the total built-in electric field strength E is:

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

[0039] I(t)=J(t)S=(E 0 -E 1 (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; E 0 represents the built-in electric field of the PIN junction (hole transport layer / perovskite / electron transport layer), E 1 (t) represents the electric field generated by carrier accumulation, and σ represents the conductivity of the perovskite absorption layer;

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

[0042] However, the charge accumulation is derived from capacitor theory, and the derived charge accumulation is expressed as: Q(t) = BE 1 (t), where Q(t) represents the accumulated charge of the equivalent capacitance of the perovskite photovoltaic device, and B represents a constant term;

[0043] According to the above two expressions of charge accumulation, the equation is obtained: Where C represents a constant term, which is defined as the built-in electric field attenuation coefficient. The solution is: E 1 (t) = E 0 -E 0 e -Ct ;

[0044] Therefore, the total built-in electric field strength E is expressed as: E = E0 -E 1 (t) = E 0 e -Ct ;It should be noted that the constant terms A, B, and C in the above derivation represent the positive correlation of the equation;

[0045] From this deduction, it can be concluded that the built-in electric field in the cumulative case is in the form of exponential decay. After introducing the equation, the following form is obtained:

[0046]

[0047] Then update the boundary conditions of the equation to the following form:

[0048]

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

[0050] Combined with the boundary conditions, the equation expression of the dual-group diffusion composite model is obtained, where the independent variables are x and t, the solutions are n(x, t) and p(x, t), and the parameter is D n , D p , k 1 , k 2 , S 0 , S l 、E 0 , C;

[0051] Then, the parameters of the above two-group diffusion composite model are fitted, and the key parameters in the model are fitted by experimental data: carrier diffusion coefficient D n With D p , first-order compound probability k 1 , second-order compound probability k 2 , surface recombination velocity S 0 With S l , the built-in electric field E of the PIN junction 0 As well as the built-in electric field attenuation coefficient C, a complete dual-group diffusion recombination model is obtained to achieve an accurate description of carrier behavior.

[0052] Furthermore, by solving the above model equations using numerical methods, the distribution, migration and recombination processes of 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, the present invention provides a dual-group diffusion recombination model, which, by combining numerical calculations with 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 adopts Figure 1 The perovskite photovoltaic device shown in the figure is used to verify the validity of the double-group diffusion composite model in the present invention. The perovskite photovoltaic device is a three-layer photovoltaic device structure including a perovskite absorption layer (PER), an electron transport layer (ETL) and a hole transport layer (HT), wherein the absorption layer is a perovskite material (CH 3 NH 3 PbI 3 ), the electron transport layer uses tin dioxide film, and the hole transport layer uses Spiro; the specific process of verification is:

[0057] First, the perovskite photovoltaic device is manufactured in a laboratory environment, and the sample is excited by laser to generate photogenerated carriers to obtain a transient fluorescence test curve;

[0058] Then, the double-group diffusion composite model proposed in the present invention is used to numerically simulate the behavior of electrons and holes in the perovskite photovoltaic device, including the following steps:

[0059] Step 1: Collect transient fluorescence test data, including intensity and time step vector; collect device response function IRF, including intensity and time step vector, and convert it into an EXCEL table file;

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

[0061] Step 3: Use Matlab to load the dual-group diffusion composite model for later use;

[0062] Step 4: Use Matlab to load the transient fluorescence decay curve simulation script for use, which needs to call the model in step 3 to calculate the carrier concentration and then simulate the transient fluorescence decay curve using the traditional composite luminescence model;

[0063] Step 5: Use Matlab to run the particle swarm algorithm (PSO) and set reasonable initial parameter values ​​(D n , D p , k 1 , k 2 , S 0 , S l 、E 0, C) start iteration, wherein it is necessary to repeatedly call step 4 to obtain the simulated transient fluorescence decay curve and compare it with the test curve data, iterate the initial parameters in the direction of the smallest difference between the two, and obtain the fitting parameters (the values ​​of the initial parameters after iterative changes) and the corresponding fitting curve data after a certain number of iterations;

[0064] Step 6: Use Matlab to run the drawing script, and the fitting curve, i.e. the final simulated fluorescence decay curve and the test curve, will appear at the same time, as shown in the figure below: Figure 2 shown.

[0065] At the same time, the present invention also provides a comparative example 1, which is different from the embodiment 1 in that: in step 3, the single-group diffusion composite model is loaded, and the final simulated fluorescence decay curve is as follows: Figure 3 shown.

[0066] Depend on Figure 2 and Figure 3 It can be seen from the fitting results that compared with the traditional single-group diffusion recombination model, the double-group diffusion recombination model considering the built-in electric field in the present invention can more accurately predict the migration process of carriers between the absorption layer and the transmission layer, and is more consistent with the experimental data.

[0067] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A dual-group diffusion composite model for perovskite carrier dynamics analysis, characterized in that: The equation expression of the dual-group diffusion composite model is: Where n(x, t) and p(x, t) represent the spatiotemporal distribution of electrons and holes, respectively, x represents the spatial variable, and t represents the temporal variable; D n With D p are the diffusion coefficients of electrons and holes, μ n With μ p They represent the mobility of electrons and holes respectively, E(t) 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); E0 represents the built-in electric field of the PIN junction (hole transport layer / perovskite / electron transport layer), and C represents the built-in electric field attenuation coefficient.

2. The dual-group diffusion composite model for perovskite carrier dynamics analysis according to claim 1, characterized in that: The boundary conditions of the dual-group diffusion composite model are: Where l represents the thickness of the perovskite absorption layer, S0 represents the surface recombination velocity at x = 0, and S l represents the surface recombination velocity at x=l.

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

4. The dual-group diffusion composite model for perovskite carrier dynamics analysis according to claim 1, characterized in that: In the dual-group diffusion composite 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 velocity S0 and S l , the built-in electric field E0 of the PIN junction and the built-in electric field attenuation coefficient C are model parameters, and all model parameters are obtained by data fitting.

Images