A variance-reduced electrothermal Monte Carlo method for semiconductor device simulation

This paper is concerned with electron transport and heat generation in semiconductor devices. An improved version of the electrothermal Monte Carlo method is presented. This modification has better approximation properties due to reduced statistical fluctuations. The corresponding transport equations are provided and results of numerical experiments are presented

Some properties of the kinetic equation for electron transport in semiconductors

The paper studies the kinetic equation for electron transport in semiconductors. New formulas for the heat generation rate are derived by analyzing the basic scattering mechanisms. In addition, properties of the steady state distribution are discussed and possible extensions of the deviational particle Monte Carlo method to the area of electron transport are proposed

A Multicarrier Technique for Monte Carlo Simulation of Electrothermal Transport in Nanoelectronics

The field of microelectronics plays an important role in many areas of engineering and science, being ubiquitous in aerospace, industrial manufacturing, biotechnology, and many other fields. Today, many micro- and nanoscale electronic devices are integrated into one package. e capacity to simulate new devices accurately is critical to the engineering design process, as device engineers use simulations to predict performance characteristics and identify potential issues before fabrication. A problem of particular interest is the simulation of devices which exhibit exotic behaviors due to non-equilibrium thermodynamics and thermal effects such as self-heating. Frequently, it is desirable to predict the level of heat generation, the maximum temperature and its location, and the impact of these thermal effects on the current-voltage (IV) characteristic of a device. is problem is furthermore complicated by nanoscale device dimensions. As the ratio of surface area to volume increases, boundary effects tend to dominate the transfer of energy through a device. Effects such as quantum confinement begin to play a role for nanoscale devices as geometric feature sizes approach the wavelength of the particles involved. Classical approaches to charge transport and heat transfer simulation such as the drift-diffusion approach and Fourier’s law, respectively, do not provide accurate results at these length scales. Instead, the transport processes are governed by the semi-classical Boltzmann transport equation (BTE) with quantum corrections derived from the Schrodinger equation ̈ (SE). In this work, a technique is presented for coupling a 3D phonon Monte Carlo (MC) simulation to an electron multi-subband Monte Carlo (MSBMC) simulation. Both carrier species are first examined separately. An electron MC simulation of bulk silicon, a silicon n-i-n diode, and an intrinsic-channel fin-field effect transistor (FinFET) structure are also presented. A 3D phonon MC algorithm is demonstrated in bulk silicon, a silicon thin film, and a silicon nanoconstriction. These tests verify the correctness of the MC framework. Finally, a novel carrier scattering system which directly accounts for the interaction be- tween the two particle populations inside a nanoscale device is shown. e tool developed supports quantum size effects and is shown to be capable of modeling the exchange of energy between thermal and electronic particle systems in a silicon FinFET

Some properties of the kinetic equation for electron transport in semiconductors

The paper studies the kinetic equation for electron transport in semiconductors. New formulas for the heat generation rate are derived by analyzing the basic scattering mechanisms. In addition, properties of the steady state distribution are discussed and possible extensions of the deviational particle Monte Carlo method to the area of electron transport are proposed

Coupled quantum-classical transport in silicon nanowires

We present an extended hydrodynamic model describing the transport of electrons in the axial direction of a silicon nanowire. This model has been formulated by closing the moment system derived from the Boltzmann equation on the basis of the maximum entropy principle of Extended Thermodynamics, coupled to the Schr¨odinger-Poisson system. Explicit closure relations for the high-order fluxes and the production terms are obtained without any fitting procedure, including scattering of electrons with acoustic and non polar optical phonons. We derive, using this model, the electron mobility

Mathematical Analysis of Charge and Heat Flow in Organic Semiconductor Devices

Organische Halbleiterbauelemente sind eine vielversprechende Technologie, die das Spektrum der optoelektronischen Halbleiterbauelemente erweitert und etablierte Technologien basierend auf anorganischen Halbleitermaterialien ersetzen kann. Für Display- und Beleuchtungsanwendungen werden sie z. B. als organische Leuchtdioden oder Transistoren verwendet. Eine entscheidende Eigenschaft organischer Halbleitermaterialien ist, dass die Ladungstransporteigenschaften stark von der Temperatur im Bauelement beeinflusst werden. Insbesondere nimmt die elektrische Leitfähigkeit mit der Temperatur zu, so dass Selbsterhitzungseffekte, einen großen Einfluss auf die Leistung der Bauelemente haben. Mit steigender Temperatur nimmt die elektrische Leitfähigkeit zu, was wiederum zu größeren Strömen führt. Dies führt jedoch zu noch höheren Temperaturen aufgrund von Joulescher Wärme oder Rekombinationswärme. Eine positive Rückkopplung liegt vor. Im schlimmsten Fall führt dieses Verhalten zum thermischen Durchgehen und zur Zerstörung des Bauteils. Aber auch ohne thermisches Durchgehen führen Selbsterhitzungseffekte zu interessanten nichtlinearen Phänomenen in organischen Bauelementen, wie z. B. die S-förmige Beziehung zwischen Strom und Spannung. In Regionen mit negativem differentiellen Widerstand führt eine Verringerung der Spannung über dem Bauelement zu einem Anstieg des Stroms durch das Bauelement. Diese Arbeit soll einen Beitrag zur mathematischen Modellierung, Analysis und numerischen Simulation von organischen Bauteilen leisten. Insbesondere wird das komplizierte Zusammenspiel zwischen dem Fluss von Ladungsträgern (Elektronen und Löchern) und Wärme diskutiert. Die zugrundeliegenden Modellgleichungen sind Thermistor- und Energie-Drift-Diffusion-Systeme. Die numerische Diskretisierung mit robusten hybriden Finite-Elemente-/Finite-Volumen-Methoden und Pfadverfolgungstechniken zur Erfassung der in Experimenten beobachteten S-förmigen Strom-Spannungs-Charakteristiken wird vorgestellt.Organic semiconductor devices are a promising technology to extend the range of optoelectronic semiconductor devices and to some extent replace established technologies based on inorganic semiconductor materials. For display and lighting applications, they are used as organic light-emitting diodes (OLEDs) or transistors. One crucial property of organic semiconductor materials is that charge-transport properties are heavily influenced by the temperature in the device. In particular, the electrical conductivity increases with temperature, such that self-heating effects caused by the high electric fields and strong recombination have a potent impact on the performance of devices. With increasing temperature, the electrical conductivity rises, which in turn leads to larger currents. This, however, results in even higher temperatures due to Joule or recombination heat, leading to a feedback loop. In the worst case, this loop leads to thermal runaway and the complete destruction of the device. However, even without thermal runaway, self-heating effects give rise to interesting nonlinear phenomena in organic devices, like the S-shaped relation between current and voltage resulting in regions where a decrease in voltage across the device results in an increase in current through it, commonly denoted as regions of negative differential resistance. This thesis aims to contribute to the mathematical modeling, analysis, and numerical simulation of organic semiconductor devices. In particular, the complicated interplay between the flow of charge carriers (electrons and holes) and heat is discussed. The underlying model equations are of thermistor and energy-drift-diffusion type. Moreover, the numerical approximation using robust hybrid finite-element/finite-volume methods and path-following techniques for capturing the S-shaped current-voltage characteristics observed in experiments are discussed

FINITE ELEMENT AND IMAGING APPROACHES TO ANALYZE MULTISCALE ELECTROTHERMAL PHENOMENA

Electrothermal effects are crucial in the design and optimization of electronic devices. Thermoreflectance (TR) imaging enables transient thermal characterization at submicron to centimeter scales. Typically, finite element methods (FEM) are used to calculate the temperature profile in devices and ICs with complex geometry. By comparing theory and experiment, important material parameters and device characteristics are extracted. In this work we combine TR and FEM with image blurring/reconstruction techniques to improve electrothermal characterization of micron and nanoscale devices

Ballistic charge transport in a triple-gate silicon nanowire transistor

In this paper we investigate the electrostatics and charge transport in a triplegate Silicon Nanowire transistor. The quantum confinement in the transversal dimension of the wire have been tackled using the Schr¨odinger equation in the Effective Mass Approximation coupled to the Poisson equation. This system have been solved efficiently using a Variational Method. The charge transport along the longitudinal dimension of the wire has been considered using the semiclassical approximation, in the ballistic regime

Tuning Thermal Transport in Thin Films

Decades of research have enabled new understanding of thermal transport at the nanoscale. Leveraging this new understanding to tune heat conduction in thin films (TFs) is of significant interest for both fundamental and applications. This work explores tuning thermal conduction in TFs by structuring, strain engineering, and annealing. Specifically, three approaches are interrogated: 1) nanostructuring to achieve significant in-plane thermal conduction anisotropy in TFs; 2) strain engineering of thermal conductivity (k) of a basic structure in flexible electronics, Au-on-polyimide films, and a representative 2D material, graphene; and 3) high temperature annealing of reduced graphene oxide (RGO) films to enhance k. Nanostructuring is well known as an efficient method to modulate thermal conductivity. Extending beyond previous studies, this work investigates the directional dependence of the thermal conductivity introduced by anisotropic boundaries. Specifically, thickness modulators are introduced in TFs to structurally impact the thermal conduction anisotropy. Simulations, based on the phonon Boltzmann Transport Equation (BTE), demonstrate the ability to tune the in-plane thermal anisotropy ratio across an order of magnitude via modulating the thickness of the thin films. To predict the thermal conductivity of nanostructures, simplified Monte Carlo (MC) methods have been developed considering the expensive computational cost of solving the full BTE. We reevaluate the simplified MC methods and the applicability of these methods is evaluated. Beyond structural engineering, this dissertation explores strain engineering of thermal conductivity in nanostructured materials including flexible TFs and 2D materials. Past experimental study on the impact of strain on thermal conductivity is very limited due to the challenges of measuring k of thin films under controlled strain. This work develops fully suspended devices on flexible substrate for strain control and evaluation of strain-dependent k using a new electrothermal measurement method. By extending conventional electrothermal approaches, the new method allows accurate thermal conductivity measurements with minimal assumptions. Finally, this dissertation investigates annealing as an effective method to tune thermal transport in RGO films. Both the electrical and thermal conductivity increases significantly as the annealing (or reduction) temperature increases. The measured electrical and thermal conductivity are analyzed using a 3D Mott variable range hopping model and a thermal conductivity integral model, respectively. Further, the application of RGO films for high temperature thermoelectrics and extreme temperature sensing is discussed based on the measured electrical and thermal conductivity across a wide temperature range (10 K -3000 K). Key contributions of this dissertation include new understanding of engineering thermal conduction in TFs and characterization of thermal conductivity in strained TFs. The high in-plane thermal anisotropy ratio by nanostructuring is promising for directing heat flow in modern applications. Tuning thermal conductivity by strain control is of significant interest for modern devices with stress/strain such as flexible electronics and other devices with extreme thermomechanical stresses. For materials with an extremely high melting point, annealing at extreme temperatures by Joule heating suspended films enables additional modulation of the thermal conductivity. In summary, this dissertation enhances the understanding of tuning thermal transport with structuring, strain, and annealing through experimental and computational efforts

Reliability of wind turbine power modules using high-resolution wind data reconstruction : a digital twin concept

This study introduces a Digital Twin (DT) framework for the reliability assessment of wind turbine power modules. Its importance is demonstrated by examining the effect of wind turbulence on the electrothermal behaviour and lifetime of machine side power electronic converters and semiconductor devices of direct-drive wind turbines. To this end, an electrothermal model embedded in a turbine model is established, which tracks the changes in wind speed. Using real-world, 1-sec wind speed data, the real device junction temperature profiles and the fatigue experienced by the semiconductor devices are examined for two 10-min periods. Then, these metrics are compared with the corresponding metrics of the same 10-min periods when the wind speed is assumed constant and equal to the 10-min average value, which is often used in traditional device reliability assessment methods using SCADA data. Based on simulation results, the fatigue experienced by the semiconductor devices due to sudden fluctuations of the wind is found to be significantly higher than the fatigue estimated by traditional reliability assessment methods using the SCADA data. Two methods that attempt to reconstruct the wind spectrum (Random Walk Metropolis-Hastings algorithm) and compress the wind speed data (Discrete Wavelet Transform) are proposed. These and/or other similar methods may be integrated into the DT interface to address the issue of the large volume of data required to be stored in DTs