有機發光二極體以及鈣鈦礦太陽能電池的電性以及光學元件模擬

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國立臺灣大學電機資訊學院光電工程學研究所博士論文

Graduate Institute of Photonics and Optoelectronics College of Electrical Engineering and Computer Science

National Taiwan University Doctoral Dissertation

Device Modeling of Organic Light-Emitting Diodes and Perovskite Solar Cell including Electrical and Optical

Properties

黃雋宇 Jun-Yu Huang

指導教授: 吳育任博士 Advisor: Yuh-Renn Wu Ph.D.

中華民國 112 年 1 月 January, 2023

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Acknowledgements

I appreciate Profs. Jiun-Haw Lee, Tien-Lung Chiu, and Mei-Hsin Chen for providing experimental data to help me verify and complete my modeling work, and my advisor, Prof. Yuh-Renn Wu, for training and providing kind suggestions during my Ph.D.

career. Also, I appreciate Richard H. Friend giving me a chance to be a visiting student at Cavendish Laboratory, University of Cambridge. And thank the people who helped me when I struggled and my parents.

This thesis was supported by Ministry of Science and Technology (MOST) during my Ph.D. career. The grant numbers are Nos. 106-2221-E-002-164-MY3, 108-2628- E-002-010-MY3, 108-2627-H-028-002, MOST-109-2221-E-011-150, 109-2622-E-155- 014, 109-2221-E-002-196-MY2.

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摘要

本論文使用了實驗室自主開發的 Poisson& drift-diffusion 軟體 (DDCC) 來探討有機發光二極體以及鈣鈦礦太陽能電池的元件表現，並且針對元件的特性進行模擬上的優化。例如，在有機發光二極體以及鈣鈦礦太陽能電池中使用了高斯態密度以及 Poole-Frenkel 場效載子遷移率模型來模擬載子在有機主動層以及傳輸層的傳輸情形、透過求解激子擴散模型來探討激子在有機發光二極體中對於效率的影響以及優化以及透過 time-dependent 離子擴散模型探討鈣鈦礦太陽能電池中由移動離子造成的遲滯效應的影響。各章節的細節如下：(1) 以及探討在有機主客混合系統中的載子遷移率變化模型，電子電洞在發光層中平衡分佈是各種有機發光二極體中的重要課題，然而目前大部分高效的有機發光二極體需要藉由摻雜主客體有機材料來增加發光效率，許多研究指出有機系統摻雜後的載子遷移率變化是非線性的變化，因此這讓載子平衡在設計上變成一件困難的事情。我們利用上述提到的求解器並且配合易辛模型來展示主客體材料中載子遷移的變化，為了驗證求解器的正確性，我們分別製備了不同濃度的單一電子/電洞元件以及參考文獻中三種不同的有機主客體混合系統的量測資料來確認求解器的正確性和可靠度。驗證過後則透過模擬結果可以發現產生這種非線性變化的原因為在客體材料濃度較低時，客體材料在系統中扮演了類似缺陷陷阱的角色，由於濃度太低以及主客材料能量差過大，因此將會導致系統大部分載子被局域化至客體材料且系統整體的移動性載子數量大量下降，而造成載子遷移率的大幅下降。而在摻雜濃度漸漸上

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升的過程中，對於載子而言，客體材料會漸漸形成通道的角色因而使載子能夠在這些低能態的通道上傳輸，因此載子遷移率會漸漸上升至接近客體材料本身的載子遷移率。(2) 探討 TTF-OLEDs 的電性模擬，在這此工作中，該求解器用於探討 TTF 和 hyper-TTF-OLEDs 的電性差異。並且能夠用於解釋 hyper-TTF-OLEDs 的機制並且分析不同激子機制造成效率的耗損。透過模擬結果可以將內量子效率由 23% 提升至 35%。(3) 並且透過時變離子遷移模型，能夠探討由離子引起的鈣鈦礦太陽能電池中的電流電壓遲滯效應，並且透過模擬結果可以發現造成遲滯效應最關鍵的因素為鈣鈦礦材料中的內建電場，並且透過模擬以及實驗對比展示了在不同電壓掃描速率下的非線性遲滯曲線。此外，透過模擬可以發現影響遲滯程度的關鍵在於鈣鈦礦材料的解離程度、鈣鈦礦晶體的品質以及載子傳輸層的材料。其中載子傳輸層的影響來自於所選材料的介電常數，選擇介電常數較低的材料作為載子傳輸層，由於能夠將整體的電壓較大程度的分壓至傳輸層，進而讓鈣鈦礦材料層的分壓較低而降低離子帶來的遲滯效應。

關鍵字： Poisson and Drift-Diffusion Solver、元件模擬、激子擴散、鈣鈦礦太陽能電池、有機發光二極體、TCAD

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Abstract

In this thesis, an in-house Poisson & drift-diffusion solver (DDCC) is implemented to

calculate the performances of organic light-emitting diodes (OLEDs) and perovskite solar

cells (PSCs) and optimize the characteristics of the device. The multi-Gaussian shape den-

sity of state and Poole-Frenkel field-dependent mobility model are introduced to describe

the carrier distribution and transport mechanism in organic materials. Moreover, an ad-

vanced exciton diffusion model considering most exciton behavior and the interaction of

singlet and triplet exciton is developed to demonstrate the radiative recombination mech-

anism. This exciton model can be utilized for fluorescent, phosphorescent (Ph), TADF,

and TTF-OLEDs. Also, this solver can couple with optical modeling program to cal-

culate the optical field of PSCs to demonstrate the performance of PSCs and utilize the

time-dependent ion migration model to discuss the effect of mobile ions on the hysteresis

phenomenon. The details of all work are shown in the following: (1) Discussing the carrier

mobility change in the organic-based host-guest system. The balance of electron and hole

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distribution in EML is a crucial issue in optimizing the performance of OLEDs. Doping

is a standard method to achieve the high performance of OLEDs. However, many stud-

ies have shown that the carrier change is non-linear and unpredictable for the host-guest

system, making the design of carrier balance tough to achieve. We applied this solver,

Ising model, and SCLC model to demonstrate the carrier mobility under different doping

concentrations. Also, this model is verified by different electron- and hole-only devices

prepared by ourselves and other measurement data from previous studies. Modeling re-

sults show that the reason for this non-linear change is that the guest materials act as a trap

state when the doping concentration is low. Due to the difference in host-guest energy

being too high, most carriers would be localized in the guest materials, resulting in the

number of mobile carriers decreasing significantly and the mobility declines simultane-

ously. However, the number of mobile carriers would grow when the doping concentration

increases. The guest materials would cluster together gradually and form the channel in

the system, which causes the mobility increases smoothly to approach the mobility of pure

guest material. (2) Discussing on modeling of TTF-OLEDs. In this work, this solver is ap-

plied to demonstrate the characteristics of TTF- and hyper-TTF-OLEDs. Also, This solver

can be used to explain the mechanism of hyper-TTF-OLEDs and analysis the loss from

different exciton mechanisms. Furthermore, we can do further optimization for hyper-

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TTF-OLEDs to achieve an internal quantum efficiency increase of 23% (from 29% to

35%). (3) Moreover, a time-dependent ion migration model coupled with a Poisson-DD

solver is presented in this thesis to demonstrate the hysteresis of PSCs. Modeling results

show that the crucial issue in hysteresis is the built-in electric field. Also, three different

factors of PSCs (carrier lifetime, scan rates, and dielectric constant of transport layer) were

demonstrated to understand hysteresis. Finally, we found that choosing a transport layer

with a lower dielectric constant can decline the hysteresis of PSCs.

Keywords: Poisson and Drift-Diffusion Solver, Device Modeling, Exciton Diffusion, Per- ovksite, Organic Light-Emitting Diodes, TCAD

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List of Figures

1.1 The modelled electron and hole mobilities for different blended host–guest system by our simulation [1]. . . 4 1.2 The schematic illustration of mechanism of TTF-OLEDs emission process

from the initial stage to the final stage [2]. . . 5 1.3 The working principal of hyper-TTF-OLEDs [2]. . . 7 1.4 The schematic diagram of hysteresis phenomenon in current-voltage char-

acteristic in PSCs [3]. . . 9

2.1 (a)and (b) The absorption spectrum for traditional semiconductor and organic materials, respectively. . . 14 2.2 The schematic illustration of Gaussian density of state. . . 14 2.3 (a) The schematic illustration of carrier hopping process in organic ma-

terials. (b) The carrier mobility change with different electric fields in organic materials [1]. . . 16 2.4 Schematic illustration of triplet exciton density flow at the interface be-

tween two different materials [4]. . . 19

3.1 A typical experimental J-V curve which shows Ohmic and SCLC regimes [5]. . . 24 3.2 The simulation flowchart of Ising model [1]. . . 24 3.3 The crystal structure of iridium compound. And the cif file of FIrpic and

Ir(ppy)₃ refer to these studies [6, 7]. And it’s based on the Cambridge Crystallographic Data Centre (CCDC) database [1]. . . 25

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3.4 (a) The map is generated by randomly assigning in which one and zero corresponding host and guest material, respectively. (b) The map is re- distributed by 2D Ising model which corresponds the influence of interaction energy between host and guest materials. (c) The map is assigned by Gaussian-averaging method, a number from 0 and 1 means the carrier (electron and hole) can transport in a sub-state of guest material, and DOS is modified by this number. Furthermore, the doping concentration is fixed in these figures (20%) [1]. . . 26

3.5 The schematic diagram of Gaussian-averaging method. The distribution of host (blue) and guest (red) materials are decided by a randomly assigning and 2D Ising model [1]. . . 27

3.6 The figures are the current density at 5.0 V and 10.0 V and the doping concentration is 20% with a variety of seeding numbers. The result shows 100 a variety of seeding maps can achieve convergence of current density [1]. . . 28

3.7 The diagrams of LUMO and HOMO for these materials which is used in this chapter (DPPS, CBP, mCP, o-DiCbzBz, btp₂Ir(acac), FIrpic, Ir(ppy)₃, and TCTA) and molecular structures of these materials [1]. . . 29

3.8 The experimental and modeling characteristics of J-V curve for DPPS- based EOD and HOD [1]. . . 29

3.9 (a) and (b) device structures of the o-DiCbzBz:FIrpic-based EOD and HOD [1]. . . 31

3.10 The characteristics of the J-V curve of simulation and experiment results for the EOD and HOD with a variety of doping concentrations [1]. . . 31

3.11 (a)-(d) The current density under specific voltages of 3V, 6V, 9V, and 11V, respectively for electron- and hole-only devices. The blue and red data corresponds to electron and hole current density, respectively [1]. . . 32

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3.12 (a) and (b) The simulated carrier mobility for electron and hole versus electric field with a variety of doping concentrations. The symbols represent simulated results, and solid-lines represent experimental results extracted by the SCLC model [1]. . . 33 3.13 The simulated zero-field mobility and field activation parameters under a

variety of doping concentration for electron and hole carrier in the blended organic system of o-DiCbzBz and FIrpic [1]. . . 34 3.14 (a) The experimental data of TCTA:Ir(ppy)₃ by TOF measurement [8].

(b) The experimental data of CBP:FIrpic and CBP:btp₂Ir(acac) by TOF measurement [1, 9]. . . 35 3.15 The simulated and experimental carrier mobility for a variety of blended

organic system: CBP:FIrpic, TCTA:Ir(ppy)₃, and CBP:btp₂Ir(acac), which corresponds shallow electron trapping system, hole trapping system, and severe electron trapping system, respectively [1]. . . 36 3.16 The simulated zero-field mobility and field-activation parameters under

a variety of doping concentrations of hole carriers in the blended system of CBP:FIrpic. These symbols represent simulated results, and solid lines are experimental results extracted by the SCLC model [1]. . . 37 3.17 The simulated zero-field mobility and field-activation parameters under

a variety of doping concentrations of hole carriers in the blended system of TCTA:Ir(ppy)3. These symbols represent simulated results, and solid lines are experimental results extracted by the SCLC model [1]. . . 38 3.18 The simulated zero-field mobility and field-activation parameters under a

variety of doping concentrations of hole carriers in the blended system of CBP:btp₂Ir(acac). These symbols represent simulated results, and solid lines are experimental results extracted by the SCLC model [1]. . . 38 3.19 The simulated carrier mobility for case with no difference between host

and guest materials for a variety of guest mobility: 10⁻⁴cm²/V s, 10⁻⁵cm²/V s, and 10⁻⁶ cm²/V s, respectively. The host mobility is fixed 10⁻⁴cm²/V s [1]. . . 39

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3.20 (a) and (b) The simulated carrier density for the cases of electron mobility being 10⁻⁵cm²/Vs and 10⁻⁶cm²/Vs for guest material, respectively. The applied bias is fixed to 4 V and corresponding electric field is 4× 10⁵ V/

cm [1]. . . 40 3.21 The simulated electron carrier mobility with a variety of energy difference

between host and guest materials from 0.0 eV to 0.8 eV [1]. . . 41 3.22 (a) and (b) The simulated carrier density and the distribution of host and

guest materials for the energy difference between host and guest materials being 0.2 eV and 0.8 eV, respectively. The applied bias is under 4.0 V and the corresponding electric field is 4× 10⁵ V/cm [1]. . . 42 3.23 (a) and (b) The simulated carrier density and the distribution of host and

guest materials for the energy difference between host and guest materials being 0.2 eV and 0.8 eV, respectively. Deep blue region represents guest material and pale blue region represents host material. The applied bias is under 4.0 V and the corresponding electric field is 4× 10⁵ V/cm [1]. . . . 42 3.24 The simulated carrier density and the distribution of host and guest ma-

terials for the energy difference between host and guest materials being 0.8 eV and doping concentration is fixed to 25%. The applied bias is under 4.0 V and the corresponding electric field is 4× 10⁵V/cm [1]. . . 43 3.25 The schematic illustration of cases under low and high doping concentra-

tions [1]. . . 44

4.1 (a)–(c) Energy levels and structures of devices A, B, and C, respectively [2]. . . 50 4.2 (a) J-V characteristic curves for devices A, B, and C. (b) Simulated IQE

curves for devices A, B, and C [2]. . . 50 4.3 (a) Recombination rate, singlet excitons, triplet excitons, electron density,

and hole density for device A. (b) Loss results from radiative singlet ex- citon, electron-induced TPQ, hole-induced TPQ, and TSA for device A [2]. . . 51

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4.4 (a)–(c) TREL spectra for devices A, B, and C, respectively. The solid and dashed lines show the experimental and simulated results, respectively [2]. 51 4.5 (a), (b) Recombination rate, singlet excitons, triplet excitons, electron

density, and hole density for devices B and C, respectively [2]. . . 54 4.6 (a)–(b) Loss resulting from radiative singlet excitons, electron-induced

TPQ, hole-induced TPQ, and TSA for devices B and C, respectively [2]. . 55 4.7 (a) Optimized structure of hyper-TTF-OLEDs. (b) IQE versus current

density for cases with different LUMO in the DMPPP layer [2]. . . 56 4.8 (a) Losses resulting from radiative singlet excitons, TPQ, and TSA in dif-

ferent layers for the device with a DMPPP layer LUMO of 2.7 eV. (b) Re- combination rate, singlet excitons, triplet excitons, electron density, and hole density for the device with a DMPPP layer LUMO of 2.7 eV [2]. . . 57 4.9 (a) Characteristics of J-V curve for cases with different electron mobilities

in the NPAN layer. (b) Losses resulting from radiative singlet excitons, TPQ, and TSA for an electron mobility of 5× 10⁻⁸ cm²/Vs in the NPAN layer. (c) Recombination rate, singlet excitons, triplet excitons, electron density, and hole density for an electron mobility of 5× 10⁻⁸ cm²/Vs in the NPAN layer [2]. . . 59 4.10 (a) IQE versus current density for cases with different diffusion coeffi-

cients of triplet excitons. (b) IQE of delayed emission versus current den- sity for cases with different diffusion coefficient of triplet excitons [2]. . . 59 4.11 (a), (b) Recombination rate, singlet excitons, triplet excitons, electron

density, and hole density and the losses resulting from radiative singlet excitons, electron-induced TPQ, hole-induced TPQ, and TSA for a triplet exciton diffusion coefficient of 1× 10⁻⁶ cm²/s in the DMPPP layer. (c) Losses resulting from radiative singlet excitons, TPQ, and TSA in the optimized case [2]. . . 61 5.1 The simulated generation rate in this chapter [3]. . . 65 5.2 The simulated absorption of wavelengths from 300 nm to 800 nm for PSCs

in this chapter [3]. . . 65

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5.3 The extinction coefficient and refractive index of materials, ITO, MAPbI₃, Spiro-OMeTAD and SnO₂, used in this chapter [3]. . . 66 5.4 (a) The schematic diagram of energy for PSCs device. (b) The schematic

diagrams of anion (Iodide, I⁻) and cation (MA⁺), and the net ion density [3]. . . 66 5.5 The simulation flowchart in this chapter, include Poisson-DD solver, time-

dependent ion migration model, and FD-TD optical modeling [3]. . . 68 5.6 The simulated conduction and valence bands and net ion distribution in

the device at (a) 0.0 V and (b) V_oc [3]. . . 70 5.7 The changes of conduction band with a variety of applied bias for (a) for-

ward scanning and (b) reverse scanning [3]. . . 70 5.8 (a) The characteristics of current-voltage curve under both forward and

reverse scanning. (b) The simulated conduction band and non-radiative recombination rate for forward (solid line) and reverse (dash line) scanning under applied voltage of 0.8 V [3]. . . 71 5.9 (a) The schematic diagram of current-voltage hysteresis index. (b) The

change of hysteresis index with a variety of scan rate, the dash and solid lines represent simulated and experimental results ,respectively [3]. . . . 72 5.10 The experimental characteristics of current-voltage curve with a variety

of scan rates: (a) 10 mV/s, (b) 100 mV/s, (c) 700 mV/s, and (d) 1200 mV/

s [3]. . . 73 5.11 The band diagrams and ion distribution under 0.6 V with a variety of scan

rates: (a) 10 mV/s, (b) 10⁴ mV/s, and (c) 700 mV/s [3]. . . 74 5.12 The central electric field and change of central electric field versus applied

bias for a variety of scan rates: (a) 10 mV/s, (b) 10⁴mV/s,and (c) 700 mV/

s [3]. . . 75 5.13 The values of Hysteresis index with a variety of scan rates with a variety

of ETL (SnO₂and TiO₂). (a) Experimental results. (b) Simulated results [3]. . . 77

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5.14 The simulated values of hysteresis index with a variety of dielectric constants and the scan rate is fixed to 700 mV/s [3]. . . 78 5.15 The band diagram and net ion distribution under an applied bias of 0.6 V

for cases of dielectric constants being (a) 3ϵ₀, and (b) 31ϵ₀ [3]. . . 79 5.16 The central electric field versus applied voltage under both forward and

reverse scanning [3]. . . 80 5.17 The values of hysteresis index versus scan rates with a variety of N_ion:

1× 10¹⁶cm⁻³, 1× 10¹⁷cm⁻³, 1× 10¹⁸cm⁻³and 1× 10¹⁹cm⁻³[3]. . . 81 5.18 The current-voltage curves with (a) lower net ion density. (b) higher net

ion density [3]. . . 82 5.19 The band diagram and net ion distribution under voltage of 0.6 V for both

forward and reverse scanning with a variety of N_ion: (a) 1× 10¹⁶ cm⁻³, and (b) 1× 10¹⁷cm⁻³[3]. . . 83 5.20 The band diagrams and ion density of interfaces between perovskite and

transporting layers under voltage of 0.6 V for a variety of N_ion: 1 × 10¹⁷cm⁻³, 1× 10¹⁸cm⁻³and 1× 10¹⁹cm⁻³[3]. . . 84 5.21 (a) The values of hysteresis index versus scan rates with a variety of carrier

lifetimes: 1 ns, 5 ns, and 10 ns. (b) The current-voltage curves with a variety of carrier lifetimes: 20 ns, 70 ns, and 200 ns [3]. . . 85 5.22 The band diagram and electron/hole density with lifetimes of 20 ns and

200 ns under voltage of 0.6 V for (a) forward scanning, and (b) reverse scanning [3]. . . 85 5.23 (a) The net ion density versus position under voltage of 0.6 V for both

forward and reverse scanning. (b) The non-radiative recombination rate versus position under voltage of 0.6 V for both forward and reverse scanning [3]. . . 86

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List of Tables

3.1 The parameters of Gaussian DOS which is used in this chapter. . . 30 3.2 The parameters of mobility which is used in this chapter. . . 30 4.1 Parameters of the density of states and mobility used in this work. . . 48 4.2 The parameters of Gaussian DOS and mobility which is used in this chapter. 48 4.3 Singlet exciton’s parameters of exciton diffusion model used in this chapter. 52 4.4 Triplet exciton’s parameters of exciton diffusion model used in this chapter. 52 5.1 Parameters used in the modeling in this study . . . 69 5.2 Non-radiative recombination rates at 0.6 V . . . 86

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Chapter 1 Introduction

1.1 Background

1.1.1 Organic Light-Emitting Diodes

Our previous study has mentioned before: 『Since the first organic light-emitting diodes (OLEDs) were fabricated by Prof. Tang [10], they have attracted the attention of re- searchers and consumers because of their ability to emit light that is very similar to natural light. Recently, several OLED-based devices (e.g., TVs, smartphones, wearable devices) have been developed as consumer electronics [11–13]』[1]. However, the efficiency of OLEDs is still lower than that of traditional solid-state lighting devices, especially blue OLEDs [14–16]. The reason is that the emitting mechanism of solid-state light devices is different from that of OLEDs. For solid-state lighting devices, the electron and hole directly recombine as a photon through fluorescent processes, whereas the electron and hole form as singlet and triplet excitons before emitting a photon in OLEDs. The long lifetime of triplet photons means that excitons might experience several decay processes before the exciton transforms into a photon. First-generation OLED devices (fluorescent OLEDs) had a disadvantage in terms of a lower external quantum efficiency (EQE) because they only used a singlet exciton to generate fluorescence. However, according to

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the spin selection rule, 25% singlet and 75% triplet excitons are generated from electron and hole recombination [17–19], so the theoretical maximum internal quantum efficiency (IQE) is only 25%. Second-generation phosphorescent (Ph) OLED devices implement a triplet exciton mechanism to generate phosphorescence [20]. Although PhOLED devices achieve higher performance, they contain heavy metal compounds (iridium-based organic compounds), which increases costs [20–22].』[1]

1.1.2 Perovskite Solar Cells

Our previous study has mentioned before: 『Perovskite solar cells have attracted re- searcher’s attentions and are considered as the most potential candidate of next generation solar cells since the first perovskite solar cells were prepared by Prof. Miyasaka [23]. Per- ovskite solar cells have excellent optical and electrical properties. For optical property, most perovskite material has strong absorption in visible wavelength (300 to 800 nm), so perovskite can be fabricated as thin-film solar cells. A typical thickness of perovskite layer is merely around 300 to 1000 nm, so the ability of electron and hole extraction is better than other solar cells [24]. Hence, many groups are working on improvement of the performance of perovskite solar cells recently. As a result, the PCE of perovskite solar cells has be improved to 25% and 28% for single junction solar cells and hybrid perovksite/

silicon trandem solar cells, respectively within a decade [24].』[3]

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1.2 Motivation

1.2.1 Organic Light-Emitting Diodes

1.2.1.1 Carrier Transport in Host-Guest system for Phosphorescent OLEDs

Our previous study has mentioned before:『Many reports indicate that the position of excitons should be located at the center of the EML as much as possible because excitons may diffuse to other layers to cause additional non-radiative recombination loss. Further- more, the position of exciton would be determined by the mobility of both electrons and holes [25–27]. Therefore, the carrier balance (electron and hole) is one of the most critical issues in achieving high-performance organic light-emitting diodes. To achieve carrier balance, mobility matching is necessary. The EML of OLEDs, including Ph-, TADF-, and TTF-OLEDs, is usually composed of two different organic materials, or more than two [28]. Therefore, PhOLEDs, TTF-OLEDs, and TADF-OLEDs can be defined as a blended host-guest system. Many studies have shown that the carrier mobility of the host-guest system shows a non-linear behavior with different doping concentrations [29–32]. However, the physical mechanisms behind this non-linear behavior are still ambiguous. Typically mobility parameters are usually measured by time of flight (TOF) method for organic ma- terials. However, this method requires a thicker sample, typically more than 1 µm, and the cost is high, especially for dopant materials [33–35]. Another concern is that there are still debates if the properties of mobility are similar between thin film (below 100 nm) and thick film (1 µm) for organic materials.

Many numerical methods have been utilized to calculate the carrier transport (both electron and hole) in the organic host-guest systems [36–40]. The primary method is the

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kinetic Monte Carlo (kMC) method. This method has been utilized to estimate the carrier transport in the organic photovoltaics (OPV) devices [41–43]. However, the drawback of this method is higher time and resource costs because kMC is a statistical method to calculate the current density and potential of the system. Poisson-DD solver is often used to calculate current density and potential in the device as well, which provides an efficient model for simulating current flow and potential changes in devices under bias operation than kMC method. Although the simulated parameters in kMC and Poisson-DD are different, they have similar physical meanings. Poisson-DD solver can also demonstrate ETL, HTL, and EML to model OLED behavior. However, only some studies based on the Poisson-DD solver have been implemented to demonstrate the carrier transport in blended host-guest systems with different doping concentrations [44, 45]. Therefore, in the following chapter, an improved Poisson-DD solver is developed to demonstrate the properties of organic host-guest systems, including Gaussian density of states (DOS), Poole-Frenkel field-dependent mobility model, random doping models, 2D Ising model, and coupled with Space Charge Limited Current (SCLC) model to extract the mobility at different doping concentrations.』[1]

Figure 1.1: The modelled electron and hole mobilities for different blended host–guest system by our simulation [1].

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1.2.1.2 Triplet-Triplet Fusion OLEDs

Our previous study has mentioned before: 『The next-generation OLED candidates have in common utilizing both singlet and triplet exciton as much as possible. Two potential candidates are thermally activated delayed fluorescence (TADF) and triplet–triplet fusion (TTF) OLEDs. The former can achieve a theoretical IQE of 100% (25% + 75%), whereas the latter has a theoretical IQE of 62.5% (25% + 75%/2) if higher triplet and quin- tet states are inaccessible [46–52]. However, PhOLEDs and TADF-OLEDs suffer from the same issues as blue-OLEDs, which have worse EQE. The device lifetime of blue-OLEDs is shorter than that of red- and green-OLEDs, because they rely on high-energy and longer- lifetime triplet excitons to achieve emission, resulting in material degradation [53]. Hence, TTF-OLEDs are regarded as having the most significant potential as next-generation com- mercialized blue-OLEDs [53]. Figure 1.2 shows the process of TTF-OLEDs. This kind of OLED utilizes a singlet exciton to emit prompt fluorescence (PF) in the first stage. The next stage involves the singlet undergoing the triplet–triplet annihilation-upconversion (TTA-UC) process, which generates delayed fluorescence (DF).

Figure 1.2: The schematic illustration of mechanism of TTF-OLEDs emission process from the initial stage to the final stage [2].

However, there is still a concern about TTF-OLEDs. The main reason is the dif- ficulty of utilizing both singlet and triplet excitons to generate light because the triplet

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exciton (which has a longer lifetime) is likely to be annihilated or quenched by polaron and singlet excitons in the emitting layer (EML). Hence, the reported performance of TTF- OLEDs is lower than the theoretical EQE of 12.5% (assuming a light extraction efficiency of 20%), while the delay ratio (the ratio of PF to DF) is usually less than 25%. Hence, TTF- OLEDs cannot achieve efficient usage of the triplet excitons. To overcome this problem, many groups have proposed a new hyper-structure for TTF-OLEDs [54,55]. The primary concept is the implementation of a triplet tank layer (TTL) to separate the recombination zone, singlet excitons, and triplet excitons, thus avoiding triplet–polaron quenching (TPQ) and triplet–singlet annihilation (TSA) [56,57]. Using hyper-TTF-OLEDs, Lee et al. achieved a recorded high EQE of 15.4% for blue TTF-OLEDs and a high delay ratio of 33% [54]. To clarify the mechanism of hyper-TTF-OLEDs, quantitative numerical modeling is needed. However, current commercial TCAD software only supports singlet or triplet exciton behavior. Next-generation OLED devices cannot be simulated because it is impossible to handle the exciton coupling between singlets and triplets. Hence, in this study, we develop a complete exciton diffusion model considering both singlet and triplet excitons and their interactions (TSA, TTA, and TTF) to demonstrate the performance of TTF-OLEDs.』[2]

1.2.2 Perovskite Solar Cells

.

1.2.2.1 Hysteresis effect on Perovskite Solar Cells

Our previous study has mentioned before: 『Nowadays, most numerical simulation approaches have been developed for Silicon-based solar cells [58–60]. Hence, there are

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e e Te T

T T T

h h

h

S S

h h

h T T T T

TT e T T T

e^T ^S

e e e e e

S

TTL TPQ

TPQ TTF TPQ

TSA TTF

S DET S

S!

T T

S!

Recombination Zone

Prompt Emission

Delayed Emission

TTL TTF-EML

T

T T

S

TTF Single EML TTF-OLEDs

Double EML TTF-OLEDs

Figure 1.3: The working principal of hyper-TTF-OLEDs [2].

few TCAD software designed for PSCs devices, including electric and optical properties.

Because the transport layer (electron or hole) of PSCs usually includes organic material and the carrier transport is super different from inorganic material. Thus, a complete numerical simulation approach for PSCs devices must include optical and electrical simulation techniques. We need to analyze the impact of different geometric designs (textured surfaces) and device configurations by optical simulation. However, only a few works are done with a complete numerical model to investigate electrical and optical properties si- multaneously for PSCs devices. The bottleneck is mainly divided into two parts. (1) PSCs are usually fabricated as hybrid structures combined with organic materials. (2) Properties of organic materials are pretty different from inorganic materials, such as transportation properties and the distribution of density of states that would impact the carrier injection mechanism. Thus, a complete numerical simulation approach for PSCs devices must include optical and electrical simulation techniques. For the simulation of electric property, the effects of different carrier lifetimes and material’s intrinsic properties on the efficiency of PSCs should be considered. Also, the Gaussian DOS model is implemented in the simulation progress to demonstrate the carrier transport in the organic materials [61]. In the

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following chapter, we will present a solver including the functions we have mentioned before to demonstrate and optimize the performance of PSCs.

Furthermore, PSCs still have a challenging problem of instability. Typically, perovskite materials hydrolyze within a few hours as they are exposed to the air, which causes a lower device lifetime. Hence, encapsulation is a critical technology for com- mercialized PSCs devices [62, 63]. Another problem with stability for PSCs devices is the hysteresis phenomenon in current-voltage characteristics. Generally, the origin of the hysteresis phenomenon is complicated and is influenced by many factors, the structure of the PSCs device, the voltage scan direction, the voltage scan rate, measurement conditions, and other aspects. The hysteresis phenomenon demands re-producing and correctly measuring the characteristics of PSCs devices. The first report mentioning the hysteresis phenomenon of current-voltage characteristics of PSCs is proposed by Prof. Henry Snaith et al. [64]. The main reason for the hysteresis in PSCs devices is mainly attributed to ion migration in perovskite materials in previous studies, even though the origin of the hysteresis phenomenon remains debated [65–71]. Therefore, ion migration might be the main index resulting in the hysteresis in current-voltage characteristics. This influence can be explained as the following. Both cation and anion are mobile ions in the perovskite, and the built-in electric field determines the ion’s distribution, and mobile ions do accumulate at the interfacial layer between the transport layer and perovskite. Therefore, various characteristics of current density are measured as the applied bias is the same under different operation conditions (forward and reverse scanning). Recent simulation works of the hysteresis phenomenon of PSCs devices focused on (1) the influence of the ion accumulation at the interface, (2) the influences of ion accumulation on the hysteresis phenomenon, and (3) the influences of various parameters of PSCs on hysteresis phenomenon [72,72–76].

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Furthermore, heavily doping in electron/hole transport layers are implemented in previous works to simplify the carrier transport in the simulation [77–82]. However, heavily doping would affect the band bending influences, which can not demonstrate a correct ion distribution in the devices. To evaluate carrier transportation characteristics in the organic materials, we utilized a Gaussian density of state coupled with our Poisson-DD solver recently [1,4,83].

Figure 1.4: The schematic diagram of hysteresis phenomenon in current-voltage characteristic in PSCs [3].

In the following chapter, experiments and modeling will be demonstrated to understand the hysteresis mechanism clearly. In the experimental part, we fabricated a series of devices with different transporting layer materials and measured under different voltage scan rates to figure out the hysteresis phenomenon under different conditions. In the modeling part, our program implements Gaussian density of states to demonstrate the carrier transport in the transport layers in order to model various influences of transport layers correctly, including metal oxides, organic materials, and perovskite, instead of utilizing heavily doped transport layers [84]. Furthermore, this work presents an in-house Poisson- DD solver (ddcc) coupled with a time-dependent ion model to demonstrate the influence of mobile ions in the PSCs. The simulation results of the hysteresis phenomenon are super

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similar to the experimental results. Then, we implemented this simulation program to explain and analyze the physical mechanism behind the hysteresis phenomenon. Therefore, the program utilizes Gaussian density of states to correctly model various effects of transport layers, including organic materials, metal oxides, and perovskites, rather than heavily doped transport layers [84]. Furthermore, this paper presents a fully time-dependent ion mobility model combined with an improved Poisson-DD solver. With these methods, our simulation results of hysteresis characteristics are similar to the experimental results, which can be used to analyze and explain the mechanism of voltage sweep rate-dependent hysteresis in the current-voltage characteristics.』[3]

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Chapter 2 Methodology

2.1 Simulation of Electrical Property

In order to demonstrate the electrical characteristics of organic-based devices (OLEDs and PSCs), this solver has been modified according to some unique behavior of organic material. As we have mentioned before, the distribution of density of states, mobility model, and recombination mechanism should be modified.

2.1.1 Poisson and Dirft-Diffusion Equation

In this thesis, we applied 1D and 2D Poisson-DD solver, drift-diffusion charge con- trol (ddcc) solver, which is an in-house numerical solver developed by our laboratory, to demonstrate the electrical characteristics of devices. More details can be found on our website [85]. This solver includes the following equations: Poisson, drift-diffusion, and continuity equations. (2.1)–(2.4):

∇r· (ε∇rV (r)) = q(n_{f ree}− pf ree+ N_a⁻− N_d⁺+· · · ); (2.1)

J_n =−qµnn_{f ree}(r)∇rV (r) + qD_n∇rn_{f ree}(r); (2.2)

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J_p =−qµpp_{f ree}(r)∇rV (r)− qDp∇rp_{f ree}(r); (2.3)

∇r(J_n,p) = q(R− G), (2.4)

Equations [(2.1)-2.3) are Poisson and drift-diffusion equations, respectively. For Poisson equation, V is the energy, ε is dielectric constant, n_{f ree} is the electron carrier density, and p_{f ree} is the hole carrier density. For the drift-diffusion equation, J_nis elec- tron current density, J_pis hole current density, µ_nis electron mobility, µ_pis hole mobility, D_nis electron diffusion coefficient, D_p is hole diffusion coefficient, and R is the recombination rate shown in the following:

R = SRH + Bnp + C₀(n²p + p²n), (2.5)

where B is the radiative-recombination rate, and C₀is the coefficient of Auger recombination. However, generally, there is merely no Auger recombination in OLEDs. Moreover, SRH is Shockley-Read-Hall recombination, which is shown in the following:

SRH = np− n²i

τ_n0(p + n_i) + τ_p0(n + n_i), (2.6)

where n and p are electron and hole, respectively; τnis electron carrier lifetime, and τp is hole carrier lifetime, and ni is intrinsic carrier density.

Moreover, G is the generation rate, and this term is zero if this solver is applied to calculate the characteristic of OLEDs. For modeling of PSCs device, the generation can be calculated by light absorption obtained by FD-TD solver, and it can be expressed as

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the following:

G_opt = 1

¯

hωRe(∇ · P ) = nk

¯

h ε₀| ⃗E|², (2.7) Where ¯hω is the photon energy, P is the Poynting vector, n is the refractive index, k is the extinction coefficient, and ⃗E is the stable electric field.

2.1.1.1 Gaussian Density of State

The energy bands in organic materials are called the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO). Although the bands are similar to the valance and conduction bands of traditional semiconductors, there are still some differences from semiconductors. The main difference is

The distribution of energy states in organic materials is not similar to the conventional semiconductor. Figures 2.1(a) and (b) show that the absorption spectrum of most traditional semiconductors is abrupt at around bandgap. However, there are still many states in the bandgap for organic materials. This shallow state is called the tail state. Many studies have shown that the carrier transportation depends on these tail states [86,87]. Previous studies have shown that this kind of disordered density of state can be regarded as a Gaus- sian density of state [88–90], which can be utilized to describe carrier transport in organic material. Figure 2.2(a) shows that implemented Gaussian density of state in this work.

Hence, Gaussian density of state [Eq. (2.8)] is utilized to describe these tail states in organic materials in this thesis:

N_tail(E) = N_t 1 σ√

2πexp [

−(E− Et)² 2σ²

]

, (2.8)

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Figure 2.1: (a)and (b) The absorption spectrum for traditional semiconductor and organic materials, respectively.

Figure 2.2: The schematic illustration of Gaussian density of state.

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where N_t is the summation of the density of state, σ is the broadening factor of the Gaussian, and E_t is the difference between the center of the Gaussian and HOMO (for holes) or LUMO (for electrons).

As the Gaussian density of state is implemented, the electron and hole carrier densities are modified as the following:

n, p =

∫ _∞

−∞

N_tail(E)f_e,h(E) dE; (2.9)

else, the electron and hole carrier densities are described as

n =

∫ _∞

−∞

1 2π²

(2m^∗_e

¯ h²

)³

2√

E− Ec f_e(E) dE, (2.10)

and

p =

∫ _∞

−∞

1 2π²

(2m^∗_h

¯ h²

)³₂√

E_v − E fh(E) dE, (2.11)

where m_eis electron effective mass, m_h is electron effective mass, E_c is the conduc- tion band, E_v is the valance band, f_e is electron’s Fermi–Dirac function, and f_h is hole’s Fermi–Dirac function.

2.1.1.2 Poole-Frenkel Field-Dependent Mobility Model

As we have mentioned before, many studies have shown that carrier transportation in organic materials differs from that in traditional semiconductors. The carrier transport in organic materials is by hopping process in tail states. Hence, the mobility would be

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accelerated by applied electric fields, shown in figure 2.3. Therefore, in this thesis, the mobility function is expressed as Poole-Frenkel field-dependent mobility model [91–94]

as the following equation:

µ_e,h= µ₀_e,h× exp (

β_e,h

√

|F |⃗ )

, (2.12)

where µ is the carrier mobility, µ₀is zero-field mobility, β is the field activation parameter, and ⃗F is the electric field. The subscripts (e,h) represent electron and hole, respectively.

Figure 2.3: (a) The schematic illustration of carrier hopping process in organic materials.

(b) The carrier mobility change with different electric fields in organic materials [1].

2.1.1.3 Exciton Diffusion Solver

『As we have mentioned before, the radiative mechanism of OLEDs is different from the traditional solid-state lighting device. To demonstrate the performance of different types of OLEDs, considering both singlet and triplet excitons is needed. In this thesis, an exciton diffusion solver which considers the interaction of both singlet and triplet excitons is developed. Furthermore, most exciton behaviors are considered in this exciton solver, including exciton radiative and non-radiative decay, electron- and hole-induced TPQ, TSA, TTF, and TTA. Singlet and triplet exciton diffusion equations are shown in the following:

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dn^S_ex

dt =∇r·(

D_ex^S∇rn^S_ex)

−(

k_r^S+ k_nr^S + k_e^Sn + k_h^Sp + k_{T S}n^T_ex) n^S_ex +1

2γn²_T + G^S_ex,

(2.13)

dn^T_ex

dt =∇r·(

D^T_ex∇rn^T_ex)

−(

k_r^T + k^T_nr+ k^T_en + k^T_hp + k_{T S}n^S_ex) n^T_ex

− γn²T + G^T_ex,

(2.14)

where n_ex is the exciton density distribution, D_ex is the exciton diffusion coeffi- cient, k_ris radiative exciton constant, k_nr is non-radiative exciton constant, k_eis electron- induced triplet-polaron quenching rate constant, k_his hole-induced triplet-polaron quench- ing rate constant, and G_exis the initial exciton density distribution, generations of singlet exciton and triplet are 1/4 and 3/4 of radiative recombination rate (R) from Poisson-DD solver, respectively. And superscript (S, T) represents singlet and triplet excitons, respec- tively. γ is the exciton annihilation coefficient, n is electron carrier density, and p is hole carrier density.』[2]

『As we have mentioned before, the typical exciton diffusion equation only considers exciton diffusion in bulk materials. However, many studies have shown that exciton can not diffuse from low exciton energy material to high exciton energy material. Hence, we introduce the energy transfer rate of both singlet and triplet exciton in our exciton diffusion equation. This energy transfer rate would be utilized to interface between EML and HLT/

ETL to demonstrate the exciton transfer at the interface between two different exciton energy materials [95, 96]. Figure 2.4 shows that the exciton transfer rate at interface, which transfers from i+1/2 and i-1/2 to the interface, can be described as the following:

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W_i+1/2 = w₀exp

[E_T,i+1/2− ET,i−1/2

2k_bT

]

; (2.15)

W_i_−1/2= w₀exp

[E_T,i_−1/2− ET,i+1/2

2k_bT

]

, (2.16)

where W_i+1/2 and W_i_−1/2 are exciton (both singlet and triplet exciton) transfer rates from i+1/2 and i-1/2 to the interface, respectively. w₀ is the exciton transfer rate’s pref- actor, and w₀ is fixed to 1×10¹² s⁻¹in this thesis [97, 98]. E_T,i+1/2 and E_T,i_−1/2 are the energy of triplet exciton at sites of i+1/2 and i-1/2, respectively. Equations (2.15) and (2.16) represent the transfer rate of triplet exciton. Moreover, these equations also can be implemented to singlet exciton.

And equations (2.15) and (2.16) can be introduced into typical exciton diffusion model [equations (2.14) and (2.13)]. At the interface of heterojunction, the flow-in and flow-out of exciton flow are the same, so the continuity equation of exciton can be shown as the following:

∇r· (Dex∇rnex) = Wi+1/2nex,i+1/2− Wi−1/2nex,i−1/2, (2.17)

The schematic figure of exciton transfer rate at the interface is shown in figure 2.4.

The exciton flow from i+1/2 to the interface is greater than the exciton flow from i-1/2 to the interface when the triplet energy at the position of i+1/2 is more significant than it at the position of i-1/2. The energy transfer of exciton (both singlet and triplet) can be simulated by this modification.』[4]

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Figure 2.4: Schematic illustration of triplet exciton density flow at the interface between two different materials [4].

2.2 Simulation of Optical Property

2.2.1 Finite-Difference Time-Domain Method

Our previous study has mentioned before: 『In this thesis, FD-TD method is utilized to calculate the optical field of PSCs. This 2D FD-TD solver is an in-house optic field solver which is developed by our laboratory [99]. The main idea of FD-TD is solving Maxwell’s equation (equations (2.18)-(2.19)) in the domain of both space and time. The main Maxwell’s equation is shown in the following:

∇ × ⃗E = −µ∂ ⃗H

∂t ; (2.18)

∇ × ⃗H = ε∂ ⃗E

∂t, (2.19)

where ⃗E is the electric field, ⃗H is the magnetic field, µ is permeability, and ε is permittivity.

The periodic boundary condition (PBC) is implemented on two sides of the PSCs

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to save computational costs. Furthermore, The perfectly matched layer (PML) is implemented to prevent repeated reflections from the top layer.』[83]

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Chapter 3 The Carrier Transportation in Host-Guest System

”This chapter will discuss carrier transportation in the organic Host-Guest system.

We developed a simulation program to estimate carrier mobility with a variety of doping concentrations in an organic host-guest system. Several host-guest systems have verified this simulation program, including our experimental measurement (provided by Prof.

Lee’s group) and previous publications from other groups. Implementing doping to generate a host-guest system is the primary method to fabricate the EML of high-performance OLEDs, including Ph-, TTF-, and TADF-OLEDs. It is worth noting that doping technology in organic-based devices is a variety of traditional semiconductor-based devices. For organic-based devices, doping means mixing two a variety of organic materials with a specific proportion through thermal evaporation. The higher and lower proportions materials are called the host and guest materials, respectively. Many studies have shown that the properties of carrier transportation would be dramatically affected by doping. The mobility changing with various doping concentrations shows a non-linear change, which is unpredictable. Moreover, controlling the balance of carrier mobility is a vital issue in achieving high-performance OLEDs. Hence, understanding the mobility change in the

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organic host-guest system is crucial. This simulation program is utilized in the following section to estimate the organic host-guest system’s mobility and explain the physical mechanism behind this non-linear change. The guest states would act as traps when the dopant concentration is low. Hence, carriers are localized in these guest states, and carrier mobility declines sharply. However, the guest states would act as tunnels when the dopant concentration is high because the guest state can cluster together to form tunnels.

The carrier mobility approaches those of the pure guest material gradually.』[1]

And these results are accepted and published on Physical Review Materials [1] (DOI:

10.1103/PhysRevMaterials.4.125602). These data, tables, figures, and parts of contents are re-used from Physical Review Materials [1]. American Physics Society has authorized this re-using. The re-use permission licence is shown in Appendix B: Re-use Permission Licence.

3.1 Modelling Section

”The modified Poisson-DD solver is applied to simulate the OLEDs device characteristics. The details about Poisson-DD solver can refer to section 2.1.

3.1.1 Space-Charge-Limited Current Model

The space-charge-limited current (SCLC) model is a standard approach to extracting electron and hole carrier mobility characteristics for the organic-based devices because some studies show that the carrier mobilities of thin-film and thick bulk are different [100–

102]. We can fabricate HOD and EOD, measure the J-V curve, and extract the mobility using the SCLC model by experimental measurement. In this simulated work, the SCLC

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model is implemented to calculate the carrier mobility under a variety of conditions of the host-guest system. Figure 3.1 shows that the typical characteristics of the J-V curve can be separated into two regions at lower and higher voltages. In the Ohmic region, the current density is mainly affected by contact and sheet resistance. While the SCLC region, the J-V curve shows a linear trend under the logarithm plotting, and the slope indicates pure material properties. Hence, in this work, the mobility can be calculated under a high electric field [6.4× 10⁵V/cm]. The SCLC model can be expressed as follows:

J = 9 8εµV_ap²

L³ (3.1)

where J is the current density at a specific bias, ε is the dielectric constant, µ is the carrier mobility, V_ap is the applied bias, and the L is the length of the whole OLED.

Moreover, this model can be modified by introducing the Poole-Frenkel mobility model, which can be expressed:

J = 9

8εµ₀exp(β

√F )⃗ V_ap²

L³ (3.2)

Then, we can utilize this equation to extract the parameters of mobility from the characteristics of J-V curves under a variety of doping concentrations.

3.1.2 Ising Model

Many studies have shown that the organic-based host-guest systems are not purely random systems because the interactions between molecules would attract themselves and reorganize by the force of interactions [103]. Ising model is a primary method to describe

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Figure 3.1: A typical experimental J-V curve which shows Ohmic and SCLC regimes [5].

the kinetic process of the host-guest system affected by the interactions between molecules [104–106]. Therefore, we applied the Ising model to generate the modeling map that considers two dimensions. Figure 3.2 shows the simulation flowchart of the Ising model in this work.

Figure 3.2: The simulation flowchart of Ising model [1].

Furthermore, the generating process shows in the following steps: (1) a cubic grid

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is generated with a size of 10 Å, which is decided by the average iridium-iridium dis- tance in iridium compounds (the crystal structure is shown in figure 3.3). As shown in figure 3.4(a), the map is randomly assigned to 0 or 1, which means to host and guest materials, respectively. (2) The exchange energy of adjacent sites is applied to this system, and the elements in the original map can exchange according to a probability calculated by the energy change in this system. This energy change can be determined by the following equation:

ε_i = −JIsing

2

∑

j

(δ_i,j− 1) (3.3)

where δ_i,j is the Kronecker delta function. The probability can then be expressed as

P (∆ε) = exp(−∆ε/kBT )

1 + exp(−∆ε/kBT ) (3.4)

where J_Isingis the interaction energy, which equals to k_BT , where k_Bis Boltzmann’s con- stant and T is temperature. Figure 3.4(b) shows the map after considering the Ising model.

Figure 3.3: The crystal structure of iridium compound. And the cif file of FIrpic and Ir(ppy)3 refer to these studies [6, 7]. And it’s based on the Cambridge Crystallographic Data Centre (CCDC) database [1].

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Figure 3.4: (a) The map is generated by randomly assigning in which one and zero corresponding host and guest material, respectively. (b) The map is re-distributed by 2D Ising model which corresponds the influence of interaction energy between host and guest materials. (c) The map is assigned by Gaussian-averaging method, a number from 0 and 1 means the carrier (electron and hole) can transport in a sub-state of guest material, and DOS is modified by this number. Furthermore, the doping concentration is fixed in these figures (20%) [1].

3.1.3 Gaussian Averaging Method

The Gaussian averaging method is implemented to demonstrate the carrier transportation in the tail state for organic materials in order to describe hopping process of carrier.

Figure 3.5 shows that the Gaussian averaging method. For guest materials, the sub-state is determined by the Gaussian averaging method which can be expressed as the following:

ζ^†(x, y) =

Nx

∑

i=1 Ny

∑

j=1

ζ(x, y) exp

[(x− i)²+ (y− j)² 2σ²

]

Nx

∑

i=1 Ny

∑

j=1

exp

[(x− i)² + (y− j)² 2σ²

] (3.5)

where ζ^†are the elements of the host-guest system after application of the Gaussian aver- aging method and ζ are the initial elements of the host-guest system, N_x and N_y are the maximum nodes in the x and y directions, and σ is the broadening factor in the Gaussian function.

After considering the Gaussian averaging method, the modeling map changes to fig-

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Guest Material (0) Host Material (1) σ

Figure 3.5: The schematic diagram of Gaussian-averaging method. The distribution of host (blue) and guest (red) materials are decided by a randomly assigning and 2D Ising model [1].

ure 3.4(c). The value in figure 3.4(c) between 0 and 1 represents that the carrier (electron or hole) can transport in a sub-state of the guest material, and the DOS is modified by this change. In this work, the modeling domain is set as 100 (nm) rm× 100 (nm). However, this setting cannot represent the actual situation of the host-guest system. Hence, calculat- ing the average of characteristics is utilized by generating numerous maps with a variety of seeding numbers. Figure 3.6 shows that the error converges small enough to present the actual situation when the number of seeding is more significant than 100. Hence, the 100 a variety of seeding maps are adopted to obtain convergent results for all cases in this work.』[1]

3.2 Model Correctness Verification

”The accuracy of this transport model will be examined by a variety of doping com- binations. Figure 3.7 shows the materials utilized in the following sections. These parameters of Gaussian density of state and the Poole-Frenkel mobility model we applied

有機發光二極體以及鈣鈦礦太陽能電池的電性以及光學元件模擬

Graduate Institute of Photonics and Optoelectronics College of Electrical Engineering and Computer Science

National Taiwan University Doctoral Dissertation

Acknowledgements

摘要

Abstract

Contents

List of Figures

List of Tables

Chapter 1 Introduction

1.1 Background

1.1.1 Organic Light-Emitting Diodes

1.1.2 Perovskite Solar Cells

1.2 Motivation

1.2.1 Organic Light-Emitting Diodes

1.2.2 Perovskite Solar Cells

Chapter 2 Methodology

2.1 Simulation of Electrical Property

2.1.1 Poisson and Dirft-Diffusion Equation

2.2 Simulation of Optical Property

2.2.1 Finite-Difference Time-Domain Method

Chapter 3 The Carrier Transportation in Host-Guest System

3.1 Modelling Section

3.1.1 Space-Charge-Limited Current Model

3.1.2 Ising Model

3.1.3 Gaussian Averaging Method

3.2 Model Correctness Verification