Three-dimensional master equation simulations of charge-carrier transport and recombination in organic semiconductor materials and devices
Three-dimensional master equation modeling for disordered semiconductor devices is provided. Charge transport is modeled as incoherent hopping between localized molecular states, and recombination is modeled as a nearest-neighbor process where an electron at a first location and a hole at a second location can recombine at either the first location or the second location. Here the first and second locations are any pair of nearest neighbor locations. We have found that this nearest neighbor recombination model performs substantially better than the conventional local recombination model where an electron and a hole must be at the same location to recombine. The recombination rate is modeled as a product of a prefactor γ, hopping rates and state occupancies. Importantly, we have found that sufficient simulation accuracy can be obtained by taking γ to be given by an empirically derived analytic expression.
1. A computer implemented method of simulating operation of a semiconductor, the method comprising:
(a) receiving an input specification of composition and geometry of the semiconductor;
(b) performing a master equation simulation of and/or charge recombination based on the input specification;
(c) wherein charge transport is modeled as transport of charged species between states within the semiconductor;
(d) wherein recombination is modeled as a non-local process where a charge at a first location and a charge at a second location can recombine;
(e) wherein a rate of the recombination is modeled as a product of a prefactor γ, hopping rates and state occupancies;
(f) wherein the prefactor γ is calculated using parameters of the semiconductor including one or more of the following: a temperature, a relative dielectric permittivity, and a disorder energy; and
(g) providing simulated transport results of the semiconductor as an output.
2. The method of claim 1 , wherein the master equation simulation is performed for one or more applied voltages less than or equal to a built-in voltage of the semiconductor.
3. The method of claim 1 , wherein the semiconductor is an organic semiconductor.
4. The method of claim 1 , wherein the semiconductor is configured as a device is selected from the group consisting of: light emitting diodes, solar cells, photodetectors, photovoltaic energy conversion devices, and light emitting field effect transistors.
5. The method of claim 1 , wherein a geometry of the input specification is selected from the group consisting of: single layer structures, two layer structures, three layer structures, multi-layer structures, 1D device geometries, 2D device geometries, and 3D device geometries.
6. The method of claim 1 , wherein composition parameters of the input specification are selected from the group consisting of: mean energy of a density of states and energy width of a density of states.
7. The method of claim 1 , wherein the simulated transport results are selected from the group consisting of: current density, position-dependent current density, electron concentration, hole concentration, current-voltage relations, position-dependent recombination rate, light emission(voltage) relations, voltage(light absorption) relations, light emission(current density) relations and current density(light absorption) relations.
8. The method of claim 1 , wherein the input specification is a multi-layer structure, wherein the semiconductor is an organic light emitting diode, wherein a first layer is a metal cathode, wherein a second layer is an organic semiconductor electron transport layer (ETL), wherein a third layer is an organic semiconductor emissive layer (EML), wherein a fourth layer is an organic semiconductor hole transport layer (HTL), wherein a fifth layer is an indium tin oxide layer and wherein a sixth layer is a glass substrate.
9. The method of claim 8 , further comprising automatic optimization of at least thicknesses of the ETL, EML and HTL to maximize light output.
10. A method of automatic and systematic design of a semiconductor, the method comprising:
(a) receiving a partial input specification of composition and geometry of the semiconductor;
(b) defining a simulation space of device parameters and corresponding parameter ranges of the semiconductor;
(c) automatically performing the method of claim 1 for two or more different cases, wherein the input specification is determined for each case by selecting values for each of the device parameters within the corresponding parameter ranges; and
(d) providing an optimized device configuration as an output.
11. The method of claim 1 , wherein the charged species are electrons and holes.
12. The method of claim 1 , wherein the master equation simulation is a 3D master equation simulation.
13. The method of claim 1 , wherein the semiconductor is a disordered semiconductor and wherein the charge transport is modeled as incoherent hopping between localized molecular states.
14. The method of claim 13 , wherein the first location and the second location are nearest neighbors in a set of the localized molecular states.
15. The method of claim 1 , wherein the prefactor γ is given by an empirically derived analytic expression.
16. The method of claim 15 , wherein e is electron charge, wherein ε 0 is the dielectric permittivity of free space, wherein ε r is the relative dielectric permittivity of the organic semiconductor, wherein a is a lattice constant of the semiconductor, wherein k B is Boltzmann's constant, wherein T is temperature, and wherein σ is an energy width of a Gaussian density of states of the semiconductor; and wherein the empirically derived analytic expression is given by
γ
≅
A
e
2
ε
r
ε
0
ak
B
T
exp
[
-
B
(
σ
k
B
T
)
2
]
wherein coefficient A and coefficient B are independent of a charge carrier concentration c and independent of σ/k B T.
17. The method of claim 16 , wherein the coefficient A is in a range from about 0.019 to about 0.029 and the coefficient B is about 0.154.
18. The method of claim 17 , wherein the coefficient A is 0.024.