Drift-diffusion Simulations Research Articles

On the Origin of the Ideality Factor in Perovskite Solar Cells

AbstractThe measurement of the ideality factor (nid) is a popular tool to infer the dominant recombination type in perovskite solar cells (PSC). However, the true meaning of its values is often misinterpreted in complex multilayered devices such as PSC. In this work, the effects of bulk and interface recombination on the nid are investigated experimentally and theoretically. By coupling intensity‐dependent quasi‐Fermi level splitting measurements with drift diffusion simulations of complete devices and partial cell stacks, it is shown that interfacial recombination leads to a lower nid compared to Shockley–Read–Hall (SRH) recombination in the bulk. As such, the strongest recombination channel determines the nid of the complete cell. An analytical approach is used to rationalize that nid values between 1 and 2 can originate exclusively from a single recombination process. By expanding the study over a wide range of the interfacial energy offsets and interfacial recombination velocities, it is shown that an ideality factor of nearly 1 is usually indicative of strong first‐order non‐radiative interface recombination and that it correlates with a lower device performance. It is only when interface recombination is largely suppressed and bulk SRH recombination dominates that a small nid is again desirable.

Dominant recombination mechanism in perovskite solar cells: A theoretical study

Different recombination losses have been shown to play a role in the photocurrent and photovoltage loss of lead halide perovskite solar cells. While it is believed that trap density is extremely small in high-efficiency perovskite cells, trap-assisted recombination cannot be ruled out due to the existence of tail states, for instance at the grain boundaries. In this study, the optical and electrical performance of a perovskite solar cell of the structure: ITO/PEDOT:PSS/CH3NH3PbI3/PC61BM/LiF/Al was modelled using numerical drift-diffusion simulations with embedded optical modelling via the transfer matrix method. The total recombination was calculated as the sum of bimolecular recombination and recombination via tail states. The influence of charge carrier mobility on photovoltaic parameters (short-circuit current, fill factor, open-circuit voltage, and power conversion efficiency) of perovskite solar cells was studied. Next, the impact of Urbach energy on the recombination process was investigated by simulation of bimolecular and tail state recombination rates as a function of voltage for various values of Urbach energy. It was shown that by increasing the Urbach energy, the bimolecular recombination rate decreases, but the tail state recombination rate increases at all voltages. Furthermore, the slope of the open-circuit voltage-light intensity curve, the light ideality factor, demonstrates the dominant recombination at different Urbach energy levels. It was found that the slope increases from 1.04 at EU = 25 meV to1.65 at EU = 150 meV. It can be concluded that the bimolecular recombination is the dominant recombination at low EU, while the tail state recombination overcomes the bimolecular recombination at high EU.

Exploring performances of hybrid perovskites tin-based photovoltaic solar cells: Non-equilibrium Green's functions and macroscopic approaches

We used two computational approaches to study hybrid perovskites tin-based photovoltaic solar cells. The first approach is based on electronic transport properties with density functional theory in combination to non-equilibrium Green's function formalism. We have investigated the transmission spectra and density of states. It was observed that the transmission gap decreases when it moves from MASnI3 to MASnBr3 exhibiting a larger electronic transport, thanks to delocalization of electronic state. The second approach is based on the drift-diffusion simulation, from which hybrid perovskites tin-based photovoltaic solar cells parameters were found notably dependent on the perovskite absorber layer thickness. The solar cell performance could be improved with surface recombination velocities in the range of 1–101 cm/s and 102–103 cm/s reaching efficiency of 16.07% and 12.52% for MASnIBr2 and MASnBr3.

Buildup of Triplet-State Population in Operating TQ1:PC71BM Devices Does Not Limit Their Performance

Triplet generation in organic solar cells has been considered a major loss channel. Determining the density of the triplet-state population in an operating device is challenging. Here, we employ transient absorption (TA) spectroscopy on the quinoxaline-thiophene copolymer TQ1 blended with PC71BM, quantify the transient charge and triplet-state densities, and parametrize their generation and recombination dynamics. The charge recombination parameters reproduce the experimentally measured current-voltage characteristics in charge carrier drift-diffusion simulations, and they yield the steady-state charge densities. We demonstrate that triplets are formed by both geminate and nongeminate recombination of charge carriers and decay primarily by triplet-triplet annihilation. Using the charge densities in the rate equations describing triplet-state dynamics, we find that triplet-state densities in devices are in the range of charge carrier densities. Despite this substantial triplet-state buildup, TQ1:PC71BM devices exhibit only moderate geminate recombination and significantly reduced nongeminate charge recombination, with reduction factors between 10-4 and 10-3 compared to Langevin recombination.

Physics of trap assisted photomultiplication in vertical organic photoresistors

Several experimental groups have reported recently an intriguing high level of gain (Photomultiplication) in vertical organic photoresistance (as well as in other technologies, such as perovskite for instance). This mechanism is sometimes named as “Trap-Assisted Photomultiplication.” This paper investigates the origin of this mechanism by means of drift diffusion simulations, analytical theory, and experiments, considering the particular case of PCDTBT:PC60BM photoresistors, although some conclusions are likely to apply in other technologies. It turns out that an excess of charges (induced by electron–hole carrier generation) may trigger additional carrier injection, leading to photomultiplication, under specific circumstances. We call this mechanism “gain by injection enhancement.” Electron (respectively, hole) trapping for P only (respectively, N only) devices can play this role efficiently. As these additional carriers came from contacts, significant dark current injection is thus needed to achieve a large value of gain, explaining why this mechanism can occur only in P (or N) only photoresistors (and not photodiodes or intrinsic photoresistors, i.e., with midgap contacts). In such devices, however, the detectivity remains intrinsically limited by the high level of dark injection currents required to get gain, and consequently, this type of device may be interesting, in particular, in technologies where it is not possible to achieve low dark currents using photodiodes. However, penalized by the slow trap dynamics, the cut-off frequency of these devices remains extremely low (<100 Hz). Also, this gain takes a high value only at low irradiance, making photoresistor responsivity light dependent. All these results bring new light in analyzing and optimizing photoresistors, opening a large field of investigation to take advantage of gain by injection enhancement.

Correlating hysteresis phenomena with interfacial charge accumulation in perovskite solar cells.

The property of charge extraction at the contact between the perovskite and electron selective layer (ESL) is vital to the photovoltaic performance of perovskite solar cells (PSCs). The J-V hysteresis phenomenon is frequently observed when the PSC is limited by inefficient charge transfer across the perovskite/ESL interface. Drift-diffusion simulations are performed so as to correlate the hysteresis with the quality of the perovskite/ESL junction. A generalized charge exchange model is introduced into drift-diffusion equations for describing the dynamics of charge extraction at the perovskite/ESL contact. Our simulations demonstrate that inefficient charge extraction is one of the causes of j-V hysteresis. This is because limited charge transfer gives rise to a depletion domain in the ESL, and hence promotes the interfacial accumulation of charge carriers as well as movable ions. Furthermore, it is found that the incorporation of surface recombination into drift-diffusion simulations enables the loss in open circuit voltage to be simulated in PSCs with different charge transfer properties. The simulation results indicate that j-V hysteresis can be suppressed by improving the charge extraction property and suppressing surface recombination.

Identification of recombination losses and charge collection efficiency in a perovskite solar cell by comparing impedance response to a drift-diffusion model.

Interpreting the impedance response of perovskite solar cells (PSCs) is significantly more challenging than for most other photovoltaics. This is for a variety of reasons, of which the most significant are the mixed ionic-electronic conduction properties of metal halide perovskites and the difficulty in fabricating stable, and reproducible, devices. Experimental studies, conducted on a variety of PSCs, produce a variety of impedance spectra shapes. However, they all possess common features, the most noteworthy of which is that they have at least two features, at high and low frequency, with different characteristic responses to temperature, illumination and electrical bias. The impedance response has commonly been analyzed in terms of sophisticated equivalent circuits that can be hard to relate to the underlying physics and which complicates the extraction of efficiency-determining parameters. In this paper we show that, by a combination of experiment and drift-diffusion (DD) modelling of the ion and charge carrier transport and recombination within the cell, the main features of common impedance spectra are well reproduced by the DD simulation. Based on this comparison, we show that the high frequency response contains all the key information relating to the steady-state performance of a PSC, i.e. it is a signature of the recombination mechanisms and provides a measure of charge collection efficiency. Moreover, steady-state performance is significantly affected by the distribution of mobile ionic charge within the perovskite layer. Comparison between the electrical properties of different devices should therefore be made using high frequency impedance measurements performed in the steady-state voltage regime in which the cell is expected to operate.

Design and development of an AlGaN/GaN heterostructure nano‐ATT oscillator: experimental feasibility studies in THz domain

Numerical analysis followed by experimental investigations are done with heterostructure GaN/AlGaN single drift MIxed Tunnelling and Avalanche Transit Time (MITATT) devices grown on Si〈111〉 substrate, at around 1 THz. A generalised self-consistent, nonlinear Mixed Quantum Drift-Diffusion (MQDD) simulator is developed and used for designing p++-n−-n-n++ type room temperature solid-state source within 0.75–1.1 THz regime. The epitaxial heterojunction layers are grown by III–V nitride molecular beam epitaxy which has enabled the realisation of GaN/AlGaN periodic structure on Si〈111〉 substrate with AlN buffer layer. For the first time, the realisation of heterostructure III–V Nitride MITATT oscillator at sub-mm wave/terahertz (THz) frequencies is done. The device is observed to oscillate at 1 THz with ∼4%. A comparison of MQDD model with experimental (On wafer DC testing) results for heterojunction GaN/AlGaN MITATT diodes shows generalised agreement in terms of breakdown voltage (∼27 V) and efficiency (∼4%). First experimental results of GaN/AlGaN heterostructure MITATT diode are reported and compared with the theoretical predictions obtained through MQDD model.

Compact Modeling of Multi-Layered MoS2 FETs Including Negative Capacitance Effect

In this article, we present a channel thickness dependent analytical model for MoS2 symmetric double-gate FETs including negative capacitance (NC) effect. In the model development, first thickness dependent model of the baseline 2D FET is developed, and later NC effect is included in the model using the Landau-Khalatnikov (L-K) relation. To validate baseline model behavior, density functional theory (DFT) calculations are taken into account to obtain numerical data for the $K$ and $\Lambda $ valley dependent effective masses and differences in the energy levels of N-layer (N = 1, 2, 3, 4, and 5) MoS2. The calculated layer dependent parameters using DFT theory are further used in a drift-diffusion simulator to obtain electric characteristics of the baseline 2D FET for model validation. The model shows excellent match for drain current and total gate capacitance of baseline FET and NCFET against the numerical simulation.

A drift-diffusion simulation model for organic field effect transistors: on the importance of the Gaussian density of states and traps

The nature of charge transport in organic materials depends on several important aspects, such as the description of the density of states, and the charge mobility model. Therefore specific models describing electronic properties of organic semiconductors must be considered. We have used an organic based drift-diffusion model for the electrical characterization of organic field effect transistors (OFETs) utilizing either small molecules or polymers. Furthermore, the effect of interface traps, bulk traps, and fixed charges on transistor characteristics are included and investigated. Finally, simulation results are compared to experimental measurements, and conclusions are drawn out in terms of transistor performance parameters including threshold voltages, and field-dependent mobilities.

Hot electron effects on the operation of potential well barrier diodes

A study has just been carried out on hot electron effects in GaAs/Al0.3Ga0.7As potential well barrier (PWB) diodes using both Monte Carlo (MC) and drift-diffusion (DD) models of charge transport. We show the operation and behaviour of the diode in terms of electric field, mean electron velocity and potential, mean energy of electrons and Γ-valley population. The MC model predicts lower currents flowing through the diode due to back scattering at anode (collector) and carrier heating at higher bias. At a bias of 1.0 V, the current density obtained from experimental result, MC and DD simulation models are 1.35, 1.12 and 1.77 μA/μm2 respectively. The reduction in current over conventional model, is compensated to a certain extent because less charge settles in the potential well and so the barrier is slightly reduced. The DD model results in higher currents under the same bias and conditions. However, at very low bias specifically, up to 0.3 V without any carrier heating effects, the DD and MC models look pretty similar as experimental results. The significant differences observed in the I–V characteristics of the DD and MC models at higher biases confirm the importance of energy transport when considering these devices.

Impact of Fin Line Edge Roughness and Metal Gate Granularity on Variability of 10-nm Node SOI n-FinFET

We report the numerical simulation study on the characteristic variability of 10-nm SOI Multi Fin n-FET due to the impact of random fluctuation sources such as gate work function variability induced by metal gate granularity (MGG) and Fin line edge roughness (LER) using quantum corrected 3-D drift diffusion (DD) simulation framework. The statistical simulation predictions reveal that for ultra downscaled SOI FinFET, the MGG predominantly affects device threshold voltage. Similarly, the LER sources are found to strongly influence the variability of device short channel effect immunity and channel mobility of carriers. Both MGG and long correlation length LER are found to strongly influence the overlap and outer fringing parasitic capacitances variability, resulting in increased variability of device intrinsic speed. It is predicted that the presence of combined random fluctuation sources results in the increased variability of threshold mismatch index ( $A_{\text {VT}}$ ) for the sub-10-nm SOI FinFET technology.

VENUS: A Vertical-Cavity Surface-Emitting Laser Electro-Opto-Thermal NUmerical Simulator

The properties of vertical-cavity surface-emitting lasers (VCSELs) are investigated by means of a multiphysical Vcsel Electro-opto-thermal NUmerical Simulator (VENUS). VENUS includes a three-dimensional vectorial electromagnetic code, a description of the quantum well optical response, a heat equation solver, and a quantum-corrected drift-diffusion simulator. The proposed suite includes coupling mechanisms often overlooked in VCSEL simulation and allows to reassess the impact of parameters, which can be critically dependent on implementation details inaccessible in commercial codes. The agreement with experimental results holds the promise of the application of this framework to the computer-aided design of innovative VCSEL concepts.

Polarization Effect Due to Discreteness of Dopants in Nanoscale MOSFETs

We study the polarization effects associated with the discreteness of dopants at the interface in metal–oxide–semiconductor field-effect-transistors (MOSFETs) by drift-diffusion simulations. A charge distribution model, which reproduces the long-range Coulomb potential consistently with a dielectric mismatch at the interface between semiconductor substrate and oxide, is incorporated into simulations, and the impact on statistical variability in threshold voltage in nanoscale MOSFETs is clarified. We explicitly and quantitatively show, for the first time, that the threshold voltage is shifted due to the polarization charge at the interface induced by the discreteness of dopants in the semiconductor substrate.

Impact of a Doping-Induced Space-Charge Region on the Collection of Photogenerated Charge Carriers in Thin-Film Solar Cells Based on Low-Mobility Semiconductors

Unintentional doping of the active layer is a source for lowered device performance in organic solar cells. The effect of doping is to induce a space-charge region within the active layer, generally resulting in increased recombination losses. In this work, the impact of a doping-induced space-charge region on the current-voltage characteristics of low-mobility solar cell devices has been clarified by means of analytical derivations and numerical device simulations. It is found that, in case of a doped active layer, the collection efficiency of photo-generated charge carriers is independent of the light intensity and exhibits a distinct voltage dependence, resulting in an apparent electric-field dependence of the photocurrent. Furthermore, an analytical expression describing the behavior of the photocurrent is derived. The validity of the analytical model is verified by numerical drift-diffusion simulations and demonstrated experimentally on solution-processed organic solar cells. Based on the theoretical results, conditions of how to overcome charge collection losses caused by doping are discussed. Furthermore, the presented analytical framework provides tools to distinguish between different mechanisms leading to voltage dependent photocurrents.

Theoretical Study of InAlN/GaN High Electron Mobility Transistor (HEMT) with a Polarization-Graded AlGaN Back-Barrier Layer

An inserted novel polarization-graded AlGaN back barrier structure is designed to enhance performances of In0.17Al0.83N/GaN high electron mobility transistor (HEMT), which is investigated by the two-dimensional drift-diffusion simulations. The results indicate that carrier confinement of the graded AlGaN back-barrier HEMT is significantly improved due to the conduction band discontinuity of about 0.46 eV at interface of GaN/AlGaN heterojunction. Meanwhile, the two-dimensional electron gas (2DEG) concentration of parasitic electron channel can be reduced by a gradient Al composition that leads to the complete lattice relaxation without piezoelectric polarization, which is compared with the conventional Al0.1Ga0.9N back-barrier HEMT. Furthermore, compared to the conventional back-barrier HEMT with a fixed Al-content, a higher transconductance, a higher current and a better radio-frequency performance can be created by a graded AlGaN back barrier.

Effect of quantum barrier composition on electro-optical properties of AlGaN-based UVC light emitting diodes

The height of the barrier around the AlGaN quantum well has a strong impact on the external quantum efficiency of UVC light emitting diodes (LEDs) as it affects the carrier confinement, the polarization fields, and the injection efficiency as well as the optical polarization and emission profile of the emitted light. The electro-optical properties such as emission wavelength, optical polarization, and light output power of AlGaN multiple quantum well (MQW) LEDs emitting around 270 nm with Al mole fraction in the AlxGa1−xN barriers between x = 55% and x = 76% are investigated by electroluminescence measurements. In order to analyze the experimental results, 6-band k·p method-based simulations as well as single band Schrödinger-Poisson drift-diffusion simulations have been conducted. It was found that for the same current density of 100 A cm−2 the on-wafer emission power reaches a maximum for an Al mole fraction of x = 67% in the AlxGa1−xN barrier of the Al0.53Ga0.47N MQW (0.84 mW at 40 mA). Furthermore, the emission wavelength decreases and the fraction of transverse-electric polarized light emission increases with increasing Al mole fraction in the barrier. This is consistent with drift-diffusion and k·p simulations, attributing the changes of the emission power primarily to changes in charge carrier injection and electrical confinement in the quantum wells rather than to changes in the optical polarization and light extraction.

Scaling and optimisation of lateral super-junction multi-gate MOSFET for high drive current and low specific on-resistance in sub–50 V applications

The scaling of a non-planar super-junction (SJ) Si MOSFET based on SOI technology for low voltage rating applications (below 50 V) requires a subsequent optimisation of SJ unit. The scaling and the SJ optimisation are carried out with physically based commercial TCAD device simulations by Silvaco. The study is based on a meticulous calibration of drift-diffusion simulations against experimental characteristics of a 1 μm gate length SJ multi-gate MOSFET (SJ-MGFET) aiming at improving density, switching speed, drive current, breakdown voltage (BV), and specific on-resistance (Ron,sp). We investigate scaling of the device architecture to improve the device performance by optimising doping profile to achieve an avalanche-enabled device under a charge balanced condition. The optimised SJ-MGFETs scaled by a factor of 0.5 and 0.25, with a folded alternating U-shaped n/p-SJ drift region pillar of a width of 0.3 μm and a trench depth of 2.7 μm, achieve a low specific on-resistance (Ron,sp) of 7.68 mΩ⋅mm2 and 2.24 mΩ⋅mm2 (VGS = 10 V) and BV of 48 V and 26 V, respectively. The scaled 0.5 μm and 0.25 μm gate length SJ-MGFETs offer a transconductance (gm) of 20 mS/mm and 56 mS/mm at a drain voltage of 0.1 V, respectively, greatly improving the levels of integration in a CMOS architecture.

Consistent Device Simulation Model Describing Perovskite Solar Cells in Steady-State, Transient, and Frequency Domain.

A variety of experiments on vacuum-deposited methylammonium lead iodide perovskite solar cells are presented, including JV curves with different scan rates, light intensity-dependent open-circuit voltage, impedance spectra, intensity-modulated photocurrent spectra, transient photocurrents, and transient voltage step responses. All these experimental data sets are successfully reproduced by a charge drift-diffusion simulation model incorporating mobile ions and charge traps using a single set of parameters. While previous modeling studies focused on a single experimental technique, we combine steady-state, transient, and frequency-domain simulations and measurements. Our study is an important step toward quantitative simulation of perovskite solar cells, leading to a deeper understanding of the physical effects in these materials. The analysis of the transient current upon voltage turn-on in the dark reveals that the charge injection properties of the interfaces are triggered by the accumulation of mobile ionic defects. We show that the current rise of voltage step experiments allow for conclusions about the recombination at the interface. Whether one or two mobile ionic species are used in the model has only a minor influence on the observed effects. A delayed current rise observed upon reversing the bias from +3 to -3 V in the dark cannot be reproduced yet by our drift-diffusion model. We speculate that a reversible chemical reaction of mobile ions with the contact material may be the cause of this effect, thus requiring a future model extension. A parameter variation is performed in order to understand the performance-limiting factors of the device under investigation.

Effect of Imbalanced Charge Transport on the Interplay of Surface and Bulk Recombination in Organic Solar Cells

Surface recombination has a major impact on the open-circuit voltage ($V_\text{oc}$) of organic photovoltaics. Here, we study how this loss mechanism is influenced by imbalanced charge transport in the photoactive layer. As a model system, we use organic solar cells with a two orders of magnitude higher electron than hole mobility. We find that small variations in the work function of the anode have a strong effect on the light intensity dependence of $V_\text{oc}$. Transient measurements and drift-diffusion simulations reveal that this is due to a change in the surface recombination rather than the bulk recombination. We use our numerical model to generalize these findings and determine under which circumstances the effect of contacts is stronger or weaker compared to the idealized case of balanced charge transport. Finally, we derive analytical expressions for $V_\text{oc}$ in the case that a pile-up of space charge is present due to highly imbalanced mobilities.