Organic semiconductor carrier mobility optimization model establishment method, application, device and medium

Abstract

The invention discloses an organic semiconductor carrier mobility optimization model establishment method, application, a device and a medium, and relates to the technical field of electron mobility. The establishing method comprises the following steps: establishing an Arwnus type analytical model for the temperature dependence of the zero field mobility; replacing the actual temperature in the Arwnus type analytical model with an effective temperature, and adding a dimensionless energy scale factor and a temperature item into the Arwnus type analytical model to obtain a simulated expansion model; and introducing a weak density dependency function into the simulation expansion model to obtain an organic semiconductor carrier mobility optimization model. The model established by the above method reconciles long-term opposition between Arligans and non-Arligans temperature dependence through a self-consistent framework, and the prediction precision of the carrier mobility in the disordered organic semiconductor is significantly improved.

Description

Technical Field

[0001] The present invention relates to the field of electron mobility technology, and more specifically, to a method for establishing an organic semiconductor carrier mobility optimization model, its application, device and medium. Background Art

[0002] Organic disordered semiconductors (ODSs) hold great potential for fabricating economical optoelectronic devices, including organic photovoltaics (OPVs), efficient organic light-emitting diodes (OLEDs), and field-effect transistors. The performance of electronic devices based on ODSs depends crucially on the transport properties of charge carriers within the semiconductor. Mobility is crucial for charge transport, raising a fundamental question regarding its temperature dependence. In organic semiconductor devices, charge carrier transport is thermally activated, with characteristic activation energies ranging from 0.2 to 0.6 eV, leading to strongly temperature-dependent behavior. Currently, there is no consensus physical model to describe hopping mobility in realistic OPV systems.

[0003] One view is that the mobility is determined by the activation energy of polarons jumping between nearly identical "transport sites," which may be related to the molecular structure and morphology of the material. A notable feature of this jumping process is the observation that the logarithm of the mobility μ exhibits a 1 / T dependence, and that the carrier mobility, although initially low, increases with increasing temperature. In contrast, another view is that the carrier transport mechanism is a jumping process between highly localized electronic states with energy disorder. Within the Gaussian density of states (DOS), and colleagues found through kinetic Monte Carlo (kMC) simulations that the Gaussian disorder model (GDM) predicts that at low carrier concentrations, carriers behave as independent particles (Boltzmann limit) and the logarithm of the mobility decreases with 1 / T. 2 In addition to temperature, mobility is also affected by the electric field and carrier concentration, and these dependencies become more pronounced at lower temperatures.

[0004] Research on inorganic semiconductors has long established that under conditions of low carrier density and small energy disorder, the temperature dependence of mobility is lnμ∝T -2, while under conditions of high carrier density and large energy disorder, the Arrhenius temperature dependence dominates. For disordered organic materials, in space-charge limited diodes, the effective low-field mobility in various disordered organic semiconductors generally follows the Arrhenius temperature dependence. This dependence has an almost constant activation energy, indicating that the Fermi level position is independent of temperature. However, the extended Gaussian disorder model (eGDM) proposed by Pasveer et al. can accurately explain the experimental results of the polymer poly(p-phenylene ethylene). The model proves that the non-Arrhenius GDM formula can better describe the charge mobility under transient conditions. In addition to these two mainstream models, there are other temperature dependencies of mobility. For example, the competitive hopping model shows that the temperature dependence of mobility follows the power law lnμ∝T -n (where n is between 1 and 2), which successfully explains the trap energy dependence of carrier mobility in deep trap systems. Over the years, many studies have explored variable range hopping (VRH). At low temperatures, VRH dominates the transport mechanism near the Fermi level, as described in organic thin film transistors, which exhibit unique temperature characteristics lnμ∝T. -1 / 4 The temperature dependence of mobility, as a function of temperature, is a function of the material properties and measurement conditions. Therefore, the effect of temperature on mobility exhibits diverse dependencies across different materials and conditions, reflecting distinct mechanisms of carrier transport. In organic semiconductors, the temperature dependence of mobility is even more complex, strongly influenced by material properties and measurement conditions. These diverse dependencies reveal the complexity of carrier transport and the diverse physical processes that must be considered when designing and optimizing organic electronic devices.

[0005] Theoretically, the Fermi level (E f ) and the equilibrium energy level (E eq ) is crucial to explain various temperature-dependent charge transport. eq It can be precisely described by the product of the Gaussian density of states (DOS) and the Fermi-Dirac distribution as lnμ∝T -2 .like Figure 1 As shown, at low carrier density, E f Located in E eq Here, E eq can be considered as transferring energy level E t The average starting point of the jump process, at which the jump rate is the highest, resulting in the non-Arrhenius temperature dependence expressed as lnμ∝T -2 However, as the carrier density increases, E f More than E eq , closer to E t . E f Then it becomes a new starting point of the hopping transport process. When the carrier concentration is high enough and E f >Eeq For a system with a Gaussian DOS, the logarithm of the mobility follows the Arrhenius behavior lnμ∝T -1 , which is effective over a relatively wide temperature range.

[0006] Many experimental findings confirm the above theory. In time-of-flight (TOF) experiments involving many small-molecule organic semiconductors, carrier injection is prevented, resulting in relatively low carrier density. Therefore, the non-Arrhenius relation lnμ∝T -2 This provides a more consistent explanation of the transport mechanism. In contrast, in steady-state experiments such as the space charge limited current (SCLC) method or field effect transistor (FET) measurements, efficient carrier injection leads to a higher carrier density. Here, the Arrhenius relation lnμ∝T -1 The carrier transport process is described more accurately.

[0007] Although based on 1 / T 2 The extended Gaussian disorder model (eGDM) with field-dependent charge transport is widely used and conveniently implemented in drift-diffusion solvers, but it faces significant criticism and several shortcomings. (i) Its unique non-Arrhenius temperature dependence fails to accurately describe charge transport at high carrier densities. (ii) Computer simulations show that the inter-site distance represented by the lattice constant b in the model is independent of the field-dependent mobility. (iii) It lacks a complementary variable-range hopping component, which is particularly critical for fullerene-containing layers, where electron hopping to non-nearest neighbors cannot be neglected, leading to an underestimate of the energetic disorder in the lowest unoccupied molecular orbital (LUMO). Summary of the Invention

[0008] In order to solve the above technical problems, the present invention provides a method, application, device and medium for establishing an organic semiconductor carrier mobility optimization model, aiming to construct an organic semiconductor carrier mobility optimization model based on dual temperature dependence and effective temperature regulation, which combines Arrhenius and non-Arrhenius temperature dependence. This model expands the scope of application of the original model and provides a more accurate description of carrier mobility. By using effective temperature instead of actual temperature, the weakening effect of the electric field is reduced. In the temperature dependence of mobility, 1 / T and 1 / T 2The apparent paradox between the dependences can be explained within the framework of the improved model. Compared with the temperature dependence of the mobility predicted by eGDM for the conjugated polymer poly[2,3-bis-(3-octyloxyphenyl)quinoline-5,8-diacyl-alt-thiophene-2,5-diacyl]:[6,6]-phenylC71 methyl butyrate (TQ1:PC71BM), the improved model provides a deeper understanding of charge transport and electrical properties in organic electronic materials and devices.

[0009] In a first aspect, the present invention provides a method for establishing an optimization model for carrier mobility of an organic semiconductor, the method comprising:

[0010] An Arrhenius-type analytical model for the temperature dependence of zero-field mobility is developed;

[0011] Replacing the actual temperature in the Arrhenius type analytical model with the effective temperature, and adding a dimensionless energy scaling factor and a temperature term to the Arrhenius type analytical model to obtain a pseudo-expanded model;

[0012] A weak density-dependent function is introduced into the pseudo-extended model to obtain an optimized model for carrier mobility of organic semiconductors.

[0013] Furthermore, the Arrhenius analytical model is expressed as:

[0014]

[0015] Where μ0(T) represents the zero-field mobility corresponding to the actual temperature, μ * represents infinite high temperature mobility, T represents actual temperature, exp represents natural exponential function, Δ represents activation energy, k B represents the Boltzmann constant.

[0016] Furthermore, the pseudo-expansion model is expressed as:

[0017]

[0018] Where, μ0(T eff ) represents the zero-field mobility corresponding to the effective temperature, represents the dimensionless energy scaling factor, represents the temperature-normalized energy disorder; λ quantifies the scaling dependence of the correlation length of the carrier transition path on the energy disorder; c0 represents the energy disorder suppression coefficient, E crit represents the critical energy, k B represents the Boltzmann constant, T eff represents the effective temperature, p represents the carrier concentration, μ(Teff ,p) represents the mobility that depends on the effective temperature and carrier concentration, b represents the lattice constant, δ represents the exponential adjustment factor of the influence of carrier density on mobility, which quantifies the nonlinear enhancement effect on mobility when carriers fill localized states, c1 represents the pre-correction coefficient in the mobility formula, which is used to quantify the implicit dependence of the nearest neighbor tunneling probability on the hopping rate; e represents the element charge, v0 represents the attempted hopping frequency, and σ represents the static Gaussian energy disorder.

[0019] Furthermore, the weak density dependent function is expressed as:

[0020]

[0021] In the formula, g(T eff ,F) represents the weak density dependence function, F represents the electric field, α represents the local length, and c2 represents the first weak density dependence parameter.

[0022] Furthermore, the organic semiconductor carrier mobility optimization model is expressed as:

[0023]

[0024] Where c3 represents the second weak density-dependent parameter.

[0025] Furthermore, in the organic semiconductor carrier mobility optimization model, c2 and c3 are determined by the following formula:

[0026] c2=116.2+8.96ln(pb 3 )

[0027] c3=d1+d2 ln(pb 3 )

[0028]

[0029] Where d1 and d2 are empirical correction coefficients used to adjust the combined effects of temperature and carrier concentration on the mobility model.

[0030] In a second aspect, the present invention provides an application method of the organic semiconductor carrier mobility optimization model established by the above method, the application method comprising:

[0031] Based on the organic semiconductor carrier mobility optimization model, the drift and Poisson equations are solved simultaneously to simulate the space charge limited current and voltage characteristics of organic electronic devices with single carrier transport.

[0032] Furthermore, the application method further includes:

[0033] Based on the organic semiconductor carrier mobility optimization model, the behavior of organic electronic devices is calculated as follows:

[0034] J=P(x)eμ(T,P(x),F(x))F(x)

[0035]

[0036] Where J represents the hole current density, x represents the position coordinate along the electrode injection direction, P(x) represents the carrier concentration at position x, ε0 represents the vacuum dielectric constant, and ε r represents the relative dielectric constant of the organic layer, L is the thickness of the organic layer, e is the amount of elementary charge, μ(T, P(x), F(x)) represents the mobility that depends on temperature, concentration, and electric field, V is the voltage between the two electrodes, and F(x) is the electric field strength at position x.

[0037] In a third aspect, the present invention provides a device for establishing an optimization model for carrier mobility of an organic semiconductor, for implementing the method for establishing an optimization model for carrier mobility of an organic semiconductor as described above, the device comprising:

[0038] a first model building module configured to build an Arrhenius-type analytical model for the temperature dependence of zero-field mobility;

[0039] a second model building module configured to replace the actual temperature in the Arrhenius type analytical model with the effective temperature, and add a dimensionless energy scaling factor and a temperature term to the Arrhenius type analytical model to obtain a pseudo-expanded model;

[0040] The final model building module is configured to introduce a weak density-dependent function into the pseudo-extended model to obtain an optimized model for carrier mobility of organic semiconductors.

[0041] In a fourth aspect, the present invention provides a readable storage medium, wherein the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0042] The present invention has at least the following beneficial effects:

[0043] The present invention designs an improved model by conducting a detailed investigation of the temperature-dependent characteristics of hole and electron carrier mobility in the conjugated polymer [2,3-bis(3-octyloxyphenyl)quinoline-5,8-diacyl-alt-thiophene-2,5-diacyl]:[6,6]-phenyl C71 methyl butyrate (TQ1:PC71BM) system. The improved model combines the Arrhenius and non-Arrhenius temperature dependence to describe the carrier mobility under zero electric field conditions. The Arrhenius-type analytical model can more accurately reflect the temperature dependence of charge carrier mobility as the carrier concentration changes, and fits the low-temperature experimental data more effectively than the previous model. In order to further clarify the effect of temperature on the current-voltage characteristics under low electric field conditions, the effective temperature T is introduced. eff and weak density-dependent functions to obtain an optimized model for organic semiconductor carrier mobility. The effective temperature comprehensively considers the local length α, the electric field strength F, and the actual temperature T, replacing the absolute temperature in the experiment. Under the conditions of zero electric field and carrier density, the mobility observed using this organic semiconductor carrier mobility optimization model is approximately 10 cm 2 / Vs, with disorder energies of 85 meV for holes and 76 meV for electrons. Using an optimized model for organic semiconductor carrier mobility, the density of states (DOS) width was evaluated and found to be reduced in both electron and hole devices, indicating a more pronounced dependence of mobility on electric field. Furthermore, this optimized model for organic semiconductor carrier mobility successfully explains experimental results from other studies on charge mobility in organic semiconductors under temperature variations. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The transport energy (E t ), equilibrium energy level (E eq ) and the Fermi level (E f ) schematic diagram of the positional relationship; wherein, (a), low carrier density; (b), high carrier density;

[0045] Figure 2 A flow chart of a method for establishing an optimization model for carrier mobility of an organic semiconductor according to an embodiment of the present invention is shown;

[0046] Figure 3 shows a schematic diagram of the mobility of a hole-only device under zero field according to an embodiment of the present invention;

[0047] Figure 4 Schematic diagram showing the temperature dependence of low-field mobility of pure TQ1, PC71BM, and TQ1:PC71BM (1:n, n=1, 2.5) compound devices according to an embodiment of the present invention;

[0048] Figure 5 Schematic diagram showing the temperature-dependent JV characteristics of a pure TQ1 hole-only device (layer thickness of 160 nm) according to an embodiment of the present invention;

[0049] Figure 6 JV curves for TQ1:PC71BM devices containing only holes and only electrons according to an embodiment of the present invention, as well as numerical drift model fitting based on the mobility derived from the eGDM (dashed line) and the improved model (solid line) are shown; (a) TQ1:PC71BM device containing only holes; (b) TQ1:PC71BM device containing only electrons;

[0050] Figure 7 The figure shows a structural diagram of an organic semiconductor carrier mobility optimization model establishment device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below with reference to the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a contextual relationship between each other, the order in which they are described as examples herein should not be regarded as limiting, and those skilled in the art should know that they can be adjusted in order as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0052] Example 1:

[0053] The embodiment of the present invention provides a method for establishing an optimization model of organic semiconductor carrier mobility, such as Figure 2 As shown, the method for establishing an optimization model for carrier mobility of organic semiconductors can be implemented through the following steps S10-S30.

[0054] S10: Develop an Arrhenius-type analytical model for the temperature dependence of the zero-field mobility.

[0055] Specifically, for low mobility (μ<0.01cm 2 / Vs) materials, such as conjugated polymers, polaron transport is characterized by hopping processes between adjacent localized states. Static energy disorder can be estimated by analyzing the temperature-dependent mobility. According to the Gaussian disorder model (GDM), the mobility at zero electric field follows 1 / T 2 relation:

[0056]

[0057] In the Gaussian disorder model (GDM), μ* is a field-independent prefactor representing the mobility at infinitely high temperatures, while σ represents the static Gaussian energy disorder. Although the GDM is only applicable to the Boltzmann limit (low carrier density), under space-charge-limited current (SCLC) conditions, such as high charge density near ohmic contacts, density and field dependence need to be considered to accurately describe SCLC transport. Therefore, it is necessary to develop an extended Gaussian disorder model (eGDM) within the GDM framework to better simulate carrier mobility under different carrier concentrations.

[0058] Based on the above requirements, this embodiment first constructs an Arrhenius-type analytical model for the temperature dependence of zero-field mobility in step S10. In contrast to the GDM model described previously, the Arrhenius-type analytical model describes the temperature dependence of zero-field mobility as follows:

[0059]

[0060] Where μ0(T) represents the zero-field mobility corresponding to the actual temperature, μ * represents infinite high temperature mobility, T represents actual temperature, exp represents natural exponential function, Δ represents activation energy, k B represents the Boltzmann constant.

[0061] In this Arrhenius-type analytical model, Δ represents the activation energy and no specific assumptions are made about the shape of the density of states (DOS). For a series of pristine, pure hole materials, this example proposes a model called the infinite high-temperature mobility μ * This mobility model implies that, in theory, a single measurement is sufficient to capture the dependence of a material's mobility at all temperatures. This example further extends the scope of this concept to include a wider range of material systems, such as pristine, binary, and ternary materials. The results show that μ * Significant variations are shown in these different material systems, indicating that there is no simple, universal law that can describe the temperature dependence of mobility for all materials.

[0062] This finding emphasizes that, although a universal infinite high-temperature mobility can be defined in theory, in practice this mobility is strongly influenced by the specific material properties. The electronic structure and disorder of the material, as well as other environmental factors, can lead to significant differences in mobility. Therefore, in order to more accurately evaluate and understand these effects, this example will apply a unified mobility model to explore the relationship between mobility and temperature, 1 / T and 1 / T. 2 This method can provide a deeper understanding of the charge transport properties of different materials over a wide temperature range. Based on the above ideas, step S20 is further designed.

[0063] S20: The actual temperature in the Arrhenius analytical model is replaced by the effective temperature, and the dimensionless energy scaling factor and temperature term are added to the Arrhenius analytical model to obtain the pseudo-extended model.

[0064] Specifically, in order to consider the influence of the finite electric field, this embodiment adopts the concept of effective temperature. In this embodiment, the actual temperature T is replaced by the effective temperature T. eff , which combines the effects of electric field and temperature. The dimensionless disorder parameter is expressed as Under the conditions of F = 0 and zero carrier density, the temperature-dependent mobility expression is expressed by adding an additional dimensionless energy scaling factor in front and two temperature terms on the right side. The resulting pseudo-expanded model is expressed as:

[0065]

[0066] Where, μ0(T eff ) represents the zero-field mobility corresponding to the effective temperature, represents the dimensionless energy scaling factor, represents the temperature-normalized energy disorder; λ quantifies the scaling dependence of the correlation length of the carrier transition path on the energy disorder; c0 represents the energy disorder suppression coefficient, E crit represents the critical energy, k B represents the Boltzmann constant, T eff represents the effective temperature, p represents the carrier concentration, μ(T eff ,p) represents the mobility that depends on the effective temperature and carrier concentration, b represents the lattice constant, δ represents the exponential adjustment factor of the influence of carrier density on mobility, which quantifies the nonlinear enhancement effect on mobility when carriers fill localized states, c1 represents the pre-correction coefficient in the mobility formula, which is used to quantify the implicit dependence of the nearest neighbor tunneling probability on the hopping rate; e represents the element charge, v0 represents the attempted hopping frequency, and σ represents the static Gaussian energy disorder.

[0067] For example, c1=0.7×10 -9 and λ = 0.4. Taking into account the carrier concentration dependence in the extended Gaussian disorder model (eGDM), it is found that in the density vanishing limit p→0, the general expression of the mobility is Critical energy E crit =-0.491σ represents the energy of the key bond position involved in Miller-Abrahams (MA) hopping. λ and E critcan be used to distinguish between various hopping mechanisms. The above expression is consistent with the nearest neighbor hopping result c0=1 / 2. In technical terms, the variable range hopping (VRH) model describes the temperature dependence of the transport energy, where the transport or critical energy represents the highest energy involved in a characteristic hop within the percolation network.

[0068] S30: A weak density-dependent function is introduced into the pseudo-extended model to obtain an optimized model for carrier mobility in organic semiconductors.

[0069] Specifically, the local length α is often used to describe the spatial scale of carrier mobility in organic semiconductors. It is a parameter related to the electronic properties of the material and is used to characterize the distance that carriers can effectively transmit before being scattered. This is different from the concept of lattice constant, which is more related to the internal arrangement of the crystal structure. The internal irregularities of organic semiconductors and the weak interactions between molecules lead to the complexity of their crystal structure. Although in some cases, organic semiconductors can form long-range ordered crystal structures, there are often many grain boundaries and defects. These irregularities and defects can cause carriers to scatter during transmission, thereby affecting their mobility. In this case, the local length α, as a parameter that characterizes the distance that carriers can effectively transmit before being scattered, can more accurately describe the carrier mobility properties in organic semiconductors.

[0070] Considering the importance of local length α in describing the carrier transport properties in organic semiconductors, we further explored how to incorporate this concept into the study of electric field dependence, especially when using the effective temperature T eff (T,F) framework. In this improved method, the effective temperature T eff (T, F) not only includes the effects of the actual temperature T and the electric field F, but also potentially involves the influence of the local length α on the carrier transport path and scattering process. This example uses a density-independent prefactor f(T, F) to account for the electric field dependence and explores how the local length α can adjust carrier migration behavior within this framework.

[0071] In the eGDM model, f(T,F) is a function related to temperature T and electric field F, which is used to adjust the temperature and electric field dependence of mobility. These models usually do not directly involve the concept of local length, but focus on how to describe the transport characteristics of carriers by changes in temperature and electric field. However, by implicitly including the influence of local length α in the effective temperature T eff By analyzing the dependence of the charge carriers on the charge carriers in organic semiconductors, we can more comprehensively understand and simulate the carrier migration behavior in organic semiconductors, especially under different electric field conditions. This approach not only improves the accuracy of theoretical models, but also provides new perspectives for interpreting experimental data, helping to better understand the behavior of organic semiconductor materials in practical applications.

[0072] Although the eGDM model has made significant progress in describing carrier mobility in organic semiconductors, under certain specific conditions, such as when σ>1.7 / k B The validity of the eGDM model is challenged when T and Feb > σ. Under these conditions, the exponent predicted by the model becomes positive, leading to the incorrect prediction of an exponential increase in mobility with increasing electric field and an unrealistic infinite limit. This problem points to the limitations of the eGDM model under high electric field and specific temperature conditions and highlights the need for further research to develop more accurate and widely applicable models.

[0073] To address these problems, this embodiment introduces a weak density-dependent function g(T eff ,F), is designed to better explain the electric field effect. The weak density-dependent function g(T eff ,F) is based on the effective temperature T eff The mobility calculation is adjusted by adjusting the electric field F to ensure that the mobility growth at high electric fields does not show an exponential growth, but is more consistent with reality. This adjustment enables the model to more accurately describe the behavior of carriers under the influence of electric fields, thereby improving the model's predictive power and applicability. This improvement not only resolves issues existing in the original model but also improves the accuracy of the model's predictions of the field dependence of carrier mobility. This improvement enables the model to more accurately reflect the migration behavior of carriers under different electric field strengths, providing more reliable theoretical support for the understanding and design of electronic devices.

[0074] Based on the above theory, the weak density dependence function and the organic semiconductor carrier mobility optimization model finally determined in this embodiment are shown in equations (4) and (5), respectively.

[0075]

[0076] In the formula, g(T eff ,F) represents the weak density dependence function, F represents the electric field, α represents the local length, c2 represents the first weak density dependence parameter, and c3 represents the second weak density dependence parameter.

[0077] Determine c2 and c3 using the following formula:

[0078] c2=116.2+8.96ln(pb 3 )(6a)

[0079] c3=d1+d2 ln(pb 3 )(6b)

[0080]

[0081] Where d1 and d2 are empirical correction coefficients used to adjust the combined effects of temperature and carrier concentration on the mobility model.

[0082] Example 2:

[0083] This embodiment of the present invention provides an application method for the organic semiconductor carrier mobility optimization model established by the method described in Example 1. Based on this established organic semiconductor carrier mobility optimization model and by simultaneously solving the drift and Poisson equations, the space-charge-limited current-voltage characteristics of organic electronic devices with single carrier transport are simulated. For example, a specific nonuniform discretization method can be employed to achieve an accurate numerical solution, thereby calculating the behavior of organic electronic devices based on the following equation.

[0084] J=P(x)eμ(T,P(x),F(x))F(x)(8a)

[0085]

[0086] Where J represents the hole current density, x represents the position coordinate along the electrode injection direction, P(x) represents the carrier concentration at position x, ε0 represents the vacuum dielectric constant, and ε r represents the relative dielectric constant of the organic layer, L is the thickness of the organic layer, e is the amount of elementary charge, μ(T, P(x), F(x)) represents the mobility that depends on temperature, concentration, and electric field, V is the voltage between the two electrodes, and F(x) is the electric field strength at position x.

[0087] Example 3:

[0088] This embodiment of the present invention provides an example of experimental SCLC data analysis based on the organic semiconductor carrier mobility optimization model established in Example 1.

[0089] Specifically, the carrier mobility decreases with increasing reciprocal temperature, reflecting the typical temperature dependence observed in hopping transport. As mentioned earlier, the 1 / T dependence of the mobility is usually reported and interpreted as a sign that the activation energy of hopping transport is linked to the polaron formation energy. However, this 1 / T dependence can be more accurately explained by considering the energy disorder described by the Gaussian density of states (DOS).

[0090] Figure 3The mobility of hole-only devices at zero field is shown, fitted using the Arrhenius temperature-dependent model with the activation energy Δ as a free parameter. The experimental data are from Reference 1: "N. Felekidis, A. Melianas, M. Kemerink. Automated open-source software for charge transport analysis in single-carrier organic semiconductor diodes [J]. Organic Electronics, 2018, 61: 318-328.", represented by symbols (triangles, circles, and squares). The universal mobility μ* does not provide an accurate fit for hole-only devices (including pristine TQ1, TQ1:PC71BM 1:1, and TQ1:PC71BM 1:2.5).

[0091] In the analysis Figure 3 When the temperature dependence of the low-field mobility μ0 is shown, it is observed that the carrier mobility in polymer and fullerene derivative devices decreases with increasing reciprocal temperature, which is a characteristic of hopping transport. This temperature dependence can be well described by the Arrhenius form, i.e., lnμ∝T -1 , which reflects the fundamental properties of transport along the polymer chain. Although there are variations between different material systems, the results of the analysis are similar to those of Craciun et al., revealing an approximate 1 / T dependence over a wide temperature range below room temperature. Craciun et al. extrapolated the mobility at infinite temperature to a single value μ * =30-40cm 2 / Vs, which is independent of the material thickness. In contrast, the results of this study show that lnμ∝T -1 The curve converges to a single value of about μ as 1 / T→0 * =10cm 2 / Vs, which is one-third of the value reported by Craciun et al. This general value generally applies to most material systems studied, but some deviations exist that do not alter the overall conclusions. These differences can be attributed to variations in disorder type, internal coupling, and alternating potential effects.

[0092] Although the Arrhenius model is effective in describing the temperature dependence of carrier mobility in polymer and fullerene derivative devices, it primarily focuses on thermally activated processes and may overlook important non-thermal activation mechanisms at low temperatures. The model's simplified transport mechanisms and exponential relationships may not accurately reflect the complexity of actual transport processes. Furthermore, due to the diversity of material properties, a single model is difficult to fully describe diverse material systems. The limited temperature range and unclear physical meaning of the activation energy parameter also limit the model's general applicability and the depth of understanding of material properties. Therefore, more complex models and additional physical processes need to be considered when understanding and designing charge transport mechanisms.

[0093] Figure 4 The temperature dependence of the low-field mobility of devices made with pure TQ1, PC71BM, and a TQ1:PC71BM (1:n, n = 1, 2.5) compound is shown. The experimental data are represented by symbols and are from Reference 1. The dashed line represents the fit using equation (1) as described in Example 1, which only considers the non-Arrhenius temperature dependence; the solid line shows the fit based on equation (3a), which includes both Arrhenius and non-Arrhenius effects.

[0094] In the analysis Figure 4 When comparing the experimental data shown, the temperature dependence of the low-field mobility μ0(T) of devices made of pure TQ1, PC71BM, and TQ1:PC71BM (1:n, n=1, 2.5) compounds can be observed. The dashed lines represent the fit results using equation (1), which only considers the non-Arrhenius temperature dependence; while the solid lines show the fit based on equation (3a), which combines the Arrhenius and non-Arrhenius effects. The results show that equation (1), which only considers the non-Arrhenius temperature dependence, is insufficient in describing the mobility-temperature relationship of these materials, especially at low temperatures. This suggests that there are other factors at work in addition to the non-Arrhenius mechanism. In contrast, equation (3a) provides a significantly better fit to the experimental data by integrating the Arrhenius and non-Arrhenius effects. This improvement highlights the important influence of the Arrhenius temperature dependence on charge transport in disordered organic field-effect transistors.

[0095] This comparison not only validates the model in Equation (3a) but also reveals that carrier transport in organic semiconductor materials is significantly affected by thermal excitation, and that the presence of activation energy significantly influences mobility. Therefore, the comprehensive model in Equation (3a) more accurately describes the charge transport characteristics of materials at different temperatures, which is of great significance for understanding and designing charge transport mechanisms in organic electronic devices, helping to optimize device performance and stability.

[0096] Figure 5The temperature-dependent JV characteristics of a pure TQ1 hole-only device (layer thickness 160 nm) are shown. The experimental data are represented by symbols and are taken from Reference 1. The solid line represents the numerical results based on the improved model, while the dashed line shows the results of the eGDM.

[0097] Figure 5 The temperature-dependent JV characteristics are clearly demonstrated and are valid for all layer thicknesses studied. The temperature-dependent hole current can be accurately described using a single parameter set, highlighting the consistency and applicability of the model in describing the current behavior at different layer thicknesses. However, the observation that the mobility predicted by eGDM is lower than the experimentally observed mobility reveals the limitations of the model in predicting carrier mobility. Although the eGDM provides a good fit at most temperatures, its accuracy is insufficient at very low temperatures. This is probably because at very low temperatures, the behavior of the carriers is affected by more complex factors that are not fully accounted for in the eGDM model. For example, the carriers may be affected by more scattering mechanisms, or the electronic properties of the material may behave differently at low temperatures.

[0098] Compared to the eGDM, the improved model shows a better fit to the experimental data over the entire temperature range. This indicates that the improved model is able to more accurately capture the behavior of carriers at different temperatures, especially at low temperatures. The improved model incorporates the Arrhenius temperature effect, a law that describes the effect of temperature on chemical reaction rates and is also applicable to describing the effect of temperature on carrier mobility. In this way, the improved model is able to correct the inaccuracies of the eGDM at low temperatures and more accurately reflect the experimental data. The eGDM equation shows that a decrease in temperature increases The value of , thereby enhancing the influence of carrier concentration on mobility. This means that at lower temperatures, carrier mobility is more dependent on its concentration, which can cause the difference between experimental results and conventional model predictions to become more significant. However, by considering additional temperature-dependent factors, such as the Arrhenius effect, the improved model is able to more comprehensively explain and predict carrier behavior, especially under extreme temperature conditions.

[0099] Figure 6 Shown are the experimental J-V curves (symbols from Ref. 1) and the numerical drift model fits based on the mobilities derived from the eGDM (dashed line) and the improved model (solid line) for TQ1:PC71BM devices with only holes (a) and only electrons (b).

[0100] Considering the enhanced hole properties in fullerene donor materials and the progress in conversion efficiency in the field of organic photovoltaics (OPVs), the proposed improved model must effectively describe the charge transfer in these systems. Figure 6An analysis of hole-only and electron-only devices in the amorphous polymer:fullerene system TQ1:PC71BM is presented, using mobilities derived from eGDM and a modified model.

[0101] For devices containing only holes, although the fit quality of the two models is comparable, the disorder values obtained are different. The eGDM gives 102meV, while the improved model gives 85meV. In addition, the lattice constant of the improved model is smaller, at 1.1nm, compared to 1.6nm for the eGDM. This shows that the improved model can more accurately reflect the intrinsic disorder and structural properties of the material when describing the hole transport properties. In contrast, for devices containing only electrons, the performance difference is significant. At the lowest temperature, the eGDM (dashed line) cannot adequately fit the data, while the improved model (solid line) provides a good fit. This further shows that the improved model can more comprehensively consider the effect of temperature when describing the electron transport properties and accurately predict the behavior of carriers.

[0102] In addition to the difference in the mobility fits between the two models for TQ1:PC71BM devices, the disorder values obtained by the eGDM and improved models are also different, being 80 meV and 76 meV, respectively. As observed in other studies, σ LUMO Usually slightly smaller than σ HOMO . The inter-site distance is consistently measured to be approximately 1.5 nm. It is noteworthy that at room temperature, the charge carrier concentration mainly affects the JV characteristics of the space charge limited current. However, at low temperatures and high field conditions, the effect of the electric field strength becomes more significant. Compared with the eGDM, the improved model incorporating the effective temperature is more sensitive to the electric field strength and less dependent on the carrier concentration, which explains the observed differences. These differences are not only reflected in the predictive ability of the model, but also reflect the in-depth understanding of the intrinsic mechanism of the material.

[0103] These results not only confirm the effectiveness of the improved model in describing different types of devices but also highlight its potential for understanding material properties and optimizing device performance. By accurately simulating the charge transfer process, the improved model provides strong theoretical support for the design of more efficient organic electronic devices. In summary, the improved model not only improves the accuracy of predictions but also provides a new perspective for understanding the charge transfer mechanism in complex material systems. This has important scientific and technological significance for the field of organic electronics, especially in the design and optimization of new organic photovoltaic devices.

[0104] In summary, the organic semiconductor carrier mobility optimization model (improved model) established by the present invention reconciles the long-standing opposition between Arrhenius and non-Arrhenius temperature dependence through a self-consistent framework, significantly improving the prediction accuracy of carrier mobility in disordered organic semiconductors. This dual-mechanism model reveals two completely different transport mechanisms: under low carrier density and weak energy disorder conditions, non-Arrhenius behavior dominates; while in high carrier density and strong disorder environment, the Arrhenius relationship becomes the main mechanism. Systematic energy landscape analysis shows that this transition mechanism is fundamentally determined by the relative position of the Fermi level and the equilibrium energy level. The breakthrough of this model lies in the multi-dimensional parameter expression it constructs, which can simultaneously handle the coupling effects of temperature, electric field and carrier concentration. In particular, by synergistically considering the reduction of thermal effects and carrier density regulation, the model successfully solves the abnormal data deviation in low-temperature experiments. Comparative studies with the extended Gaussian disorder model (eGDM) show that the new model exhibits better consistency in the prediction of current-voltage characteristics over a wide temperature range, especially in electron-dominated transport systems, while the traditional model has significant deviations.

[0105] Example 4:

[0106] The embodiment of the present invention also provides a device for establishing an optimization model of organic semiconductor carrier mobility, such as Figure 7 As shown, the device includes:

[0107] A first model building module 701 is configured to build an Arrhenius-type analytical model for the temperature dependence of zero-field mobility;

[0108] A second model building module 702 is configured to replace the actual temperature in the Arrhenius type analytical model with the effective temperature, and add a dimensionless energy scaling factor and a temperature term to the Arrhenius type analytical model to obtain a pseudo-expanded model;

[0109] The final model building module 703 is configured to introduce a weak density-dependent function into the pseudo-extended model to obtain an optimized model for carrier mobility of organic semiconductors.

[0110] It should be noted that the structures of the various organic semiconductor carrier mobility optimization model establishment devices described in this embodiment and the previously described organic semiconductor carrier mobility optimization model establishment methods belong to the same technical concept, and achieve the same beneficial effects through the same principles, which will not be repeated here.

[0111] An embodiment of the present invention further provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0112] The above is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, which should be covered by the scope of protection of the present invention.

Claims

1. A method for establishing an optimization model for carrier mobility of an organic semiconductor, characterized in that: The method comprises: An Arrhenius-type analytical model for the temperature dependence of zero-field mobility is developed; Replacing the actual temperature in the Arrhenius type analytical model with the effective temperature, and adding a dimensionless energy scaling factor and a temperature term to the Arrhenius type analytical model to obtain a pseudo-expanded model; A weak density-dependent function is introduced into the pseudo-extended model to obtain an optimized model for carrier mobility of organic semiconductors.

2. The method for establishing an optimization model for carrier mobility of an organic semiconductor according to claim 1, wherein: The Arrhenius type analytical model is expressed as: Where μ0(T) represents the zero-field mobility corresponding to the actual temperature, μ * represents infinite high temperature mobility, T represents actual temperature, exp represents natural exponential function, Δ represents activation energy, k B represents the Boltzmann constant.

3. The method for establishing an optimization model for carrier mobility of organic semiconductors according to claim 2, wherein: The pseudo-expansion model is expressed as: Where, μ0(T eff ) represents the zero-field mobility corresponding to the effective temperature, represents the dimensionless energy scaling factor, Characterizes the temperature-normalized energy disorder; λ quantifies the scaling dependence of the correlation length of the carrier transition path on the energy disorder; c0 represents the energy disorder suppression coefficient, E crit represents the critical energy, k B represents the Boltzmann constant, T eff represents the effective temperature, p represents the carrier concentration, μ(T eff ,p) represents the mobility that depends on the effective temperature and carrier concentration, b represents the lattice constant, δ represents the exponential adjustment factor of the influence of carrier density on mobility, c1 represents the pre-correction coefficient in the mobility formula, which is used to quantify the implicit dependence of the nearest neighbor tunneling probability on the hopping rate; e represents the element charge, v0 represents the attempted hopping frequency, and σ represents the static Gaussian energy disorder.

4. The method for establishing an optimization model for carrier mobility of an organic semiconductor according to claim 3, wherein: The weak density dependent function is expressed as: In the formula, g(T eff ,F) represents the weak density dependence function, F represents the electric field, α represents the local length, and c2 represents the first weak density dependence parameter.

5. The method for establishing an optimization model for carrier mobility of organic semiconductors according to claim 4, characterized in that: The organic semiconductor carrier mobility optimization model is expressed as: Where c3 represents the second weak density-dependent parameter.

6. The method for establishing an optimization model for carrier mobility of an organic semiconductor according to claim 5, wherein: In the organic semiconductor carrier mobility optimization model, c2 and c3 are determined by the following formula: c2=116.2+8.96ln(pb 3 ) c3=d1+d2 ln(pb 3 ) Where d1 and d2 are empirical correction coefficients used to adjust the combined effects of temperature and carrier concentration on the mobility model.

7. A method for applying the organic semiconductor carrier mobility optimization model established by the method according to any one of claims 1 to 6, characterized in that: The application method comprises: Based on the organic semiconductor carrier mobility optimization model, the drift and Poisson equations are solved simultaneously to simulate the space charge limited current and voltage characteristics of organic electronic devices with single carrier transport.

8. The application method according to claim 7, characterized in that: The application method further comprises: Based on the organic semiconductor carrier mobility optimization model, the behavior of organic electronic devices is calculated as follows: J=P(x)eμ(T,P(x),F(x))F(x) Where J represents the hole current density, x represents the position coordinate along the electrode injection direction, P(x) represents the carrier concentration at position x, ε0 represents the vacuum dielectric constant, and ε r represents the relative dielectric constant of the organic layer, L is the thickness of the organic layer, e is the amount of elementary charge, μ(T, P(x), F(x)) represents the mobility that depends on temperature, concentration, and electric field, V is the voltage between the two electrodes, and F(x) is the electric field strength at position x.

9. An organic semiconductor carrier mobility optimization model establishment device, used to implement the method according to any one of claims 1 to 6, characterized in that: The device comprises: a first model building module configured to build an Arrhenius-type analytical model for the temperature dependence of zero-field mobility; a second model building module configured to replace the actual temperature in the Arrhenius type analytical model with the effective temperature, and add a dimensionless energy scaling factor and a temperature term to the Arrhenius type analytical model to obtain a pseudo-expanded model; The final model building module is configured to introduce a weak density-dependent function into the pseudo-extended model to obtain an optimized model for carrier mobility of organic semiconductors.

10. A non-transitory computer-readable storage medium storing instructions, characterized in that: When the instructions are executed by a processor, the establishment method according to any one of claims 1 to 6 or the application method according to any one of claims 7 to 8 is performed.

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