Coupled Electro-Thermal Simulation of MOSFETs

2009 ◽  
Author(s):  
Chunjian Ni ◽  
Zlatan Aksamija ◽  
Jayathi Y. Murthy ◽  
Umberto Ravaioli
Keyword(s):  
Thermal Transport ◽  
Phonon Scattering ◽  
Field Effect Transistors ◽  
Device Simulation ◽  
Heat Fluxes ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Conduction Model ◽  
Electron Phonon Scattering

Thermal transport in metal-oxide-semiconductor field effect transistors (MOSFETs) due to electron-phonon scattering is simulated using phonon generation rates obtained from an electron Monte Carlo device simulation. The device simulation accounts for a full band description of both electrons and phonons considering 22 types of electron-phonon scattering events. Detailed profiles of phonon emission/absorption rates in the physical and momentum spaces are generated and are used in a MOSFET thermal transport simulation with a recently-developed anisotropic relaxation time model based on the Boltzmann transport equation (BTE). Comparisons with a Fourier conduction model reveal that the anisotropic heat conduction model predicts higher maximum temperatures because it accounts for the bottlenecks in phonon scattering pathways. Heat fluxes leaving the boundaries associated with different phonon polarizations and frequencies are also examined to reveal the main modes responsible for transport. It is found that though the majority of the heat generation is in the optical modes, the heat generated in the acoustic modes is not negligible. The modes primarily responsible for the transport of heat are found to be medium-to-high frequency acoustic phonon modes.

Simulation of Sub-Micron Thermal Transport in a MOSFET Using a Hybrid Fourier-BTE Model

2010 ◽  
Author(s):  
James M. Loy ◽  
Dhruv Singh ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Transport ◽  
Source Term ◽  
Phonon Scattering ◽  
Phonon Dispersion ◽  
Computational Cost ◽  
Phonon Transport ◽  
Boltzmann Transport ◽  
Hybrid Solver ◽  
Solution Methodology ◽  
Electron Phonon Scattering

Self-heating has emerged as a critical bottleneck to scaling in modern transistors. In simulating heat conduction in these devices, it is important to account for the granularity of phonon transport since electron-phonon scattering occurs preferentially to select phonon groups. However, a complete accounting for phonon dispersion, polarization and scattering is very expensive if the Boltzmann transport equation (BTE) is used. Moreover, difficulties with convergence are encountered when the phonon Knudsen number becomes small. In this paper we simulate a two-dimensional bulk MOSFET hotspot problem using a partially-implicit hybrid BTE-Fourier solver which is significantly less expensive than a full BTE solution, and which shows excellent convergence characteristics. Volumetric heat generation from electron-phonon collisions is taken from a Monte Carlo simulation of electron transport and serves as a heat source term in the governing transport equations. The hybrid solver is shown to perform well in this highly non-equilibrium situation, matching the solutions obtained from a pure all-BTE solution, but at significantly lower computational cost. The paper establishes that this new model and solution methodology are viable for the simulation of thermal transport in other emerging transistor designs and in other nanotechnology applications as well.

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar
Keyword(s):  
Gallium Nitride ◽  
Transport Equation ◽  
Thermal Transport ◽  
Hot Spot ◽  
Boltzmann Transport Equation ◽  
Significant Loss ◽  
Computational Time ◽  
Boltzmann Transport ◽  
Phonon Modes ◽  
Fourier Model

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

High-Mobility SiC MOSFETs with Alkaline Earth Interface Passivation

2016 ◽  
Vol 858 ◽  
pp. 671-676 ◽  
Author(s):  
Daniel J. Lichtenwalner ◽  
Vipindas Pala ◽  
Brett A. Hull ◽  
Scott Allen ◽  
John W. Palmour
Keyword(s):  
Nitric Oxide ◽  
Field Effect ◽  
Alkaline Earth ◽  
Phonon Scattering ◽  
Breakdown Strength ◽  
Field Effect Transistors ◽  
Oxide Semiconductor ◽  
Field Effect Mobility ◽  
Channel Mobility ◽  
Alkaline Earth Elements

Alkaline earth elements Sr and Ba provide SiO2/SiC interface conditions suitable for obtaining high channel mobility metal-oxide-semiconductor field-effect-transistors (MOSFETs) on the Si-face (0001) of 4H-SiC, without the standard nitric oxide (NO) anneal. The alkaline earth elements Sr and Ba located at/near the SiO2/SiC interface result in field-effect mobility (μFE) values as high as 65 and 110 cm2/V.s, respectively, on 5×1015 cm-3 Al-doped p-type SiC. As the SiC doping increases, peak mobility decreases as expected, but the peak mobility remains higher for Ba interface layer (Ba IL) devices compared to NO annealed devices. The Ba IL MOSFET field-effect mobility decreases as the temperature is increased to 150 °C, as expected when mobility is phonon-scattering-limited, not interface-trap-limited. This is in agreement with measurements of the interface state density (DIT) using the high-low C-V technique, indicating that the Ba IL results in lower DIT than that of samples with nitric oxide passivation. Vertical power MOSFET (DMOSFET) devices (1200V, 15A) fabricated with the Ba IL have a 15% lower on-resistance compared to devices with NO passivation. The DMOSFET devices with a Ba IL maintain a stable threshold voltage under NBTI stress conditions of-15V gate bias stress, at 150 °C for 100hrs, indicating no mobile ions. Secondary-ion mass-spectrometry (SIMS) analysis confirms that the Sr and Ba remain predominantly at the SiO2/SiC interface, even after high temperature oxide annealing, consistent with the observed high channel mobility after these anneals. The alkaline earth elements result in enhanced SiC oxidation rate, and the resulting gate oxide breakdown strength is slightly reduced compared to NO annealed thermal oxides on SiC.

Electron-Phonon Scattering in GaN/AlN and GaAs/AlAs Quantum Wells

1997 ◽  
Vol 482 ◽  
Author(s):  
T. F. Forbang ◽  
C. R. McIntyre
Keyword(s):  
Quantum Wells ◽  
Optical Phonon ◽  
Phonon Spectrum ◽  
Phonon Scattering ◽  
Relaxation Times ◽  
Longitudinal Optical ◽  
Longitudinal Optical Phonon ◽  
Phonon Modes ◽  
Optical Phonon Scattering ◽  
Electron Phonon Scattering

AbstractWe have studied the effects on the phonon spectrum and on the electron-longitudinal optical phonon scattering in GaN/AlN and GaAs/AlAs quantum wells. Phonon modes and potentials have been calculated for both systems. Results for emission due to electroninterface phonons interactions are presented. We will discuss the implications for relaxation times and electron mobility due to modified LO-phonon scattering in both systems.

scholarly journals Reduction of Lattice Thermal Conductivity in PbTe Induced by Artificially Generated Pores

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jae-Yeol Hwang ◽  
Eun Sung Kim ◽  
Syed Waqar Hasan ◽  
Soon-Mok Choi ◽  
Kyu Hyoung Lee ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Pore Structure ◽  
Transport Properties ◽  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Lattice Thermal Conductivity ◽  
Phonon Scattering ◽  
Phonon Modes ◽  
Thermal Transport Properties

Highly dense pore structure was generated by simple sequential routes using NaCl and PVA as porogens in conventional PbTe thermoelectric materials, and the effect of pores on thermal transport properties was investigated. Compared with the pristine PbTe, the lattice thermal conductivity values of pore-generated PbTe polycrystalline bulks were significantly reduced due to the enhanced phonon scattering by mismatched phonon modes in the presence of pores (200 nm–2 μm) in the PbTe matrix. We obtained extremely low lattice thermal conductivity (~0.56 W m−1 K−1at 773 K) in pore-embedded PbTe bulk after sonication for the elimination of NaCl residue.

A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs

2011 ◽  
Vol 10 (2) ◽  
pp. 305-338 ◽  
Author(s):  
Tiao Lu ◽  
Gang Du ◽  
Xiaoyan Liu ◽  
Pingwen Zhang
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Semiconductor Device ◽  
Field Effect Transistors ◽  
Mean Free Path ◽  
Transport Problem ◽  
Oxide Semiconductor ◽  
Double Gate ◽  
Boltzmann Transport ◽  
Volume Method

AbstractWe propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared out source/drain contacts. A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved. We propose a second order finite volume method based on the positive and flux conservative (PFC) method to discretize the Boltzmann transport equations (BTEs). The transport part of the BTEs is split into two problems. One is a 1D transport problem in the position space, and the other is a 2D transport problem in the wavevector space. In order to reduce the splitting error, the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems. The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated. Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Chunjian Ni ◽  
Jayathi Y. Murthy
Keyword(s):  
Relaxation Time ◽  
Transport Equation ◽  
Thermal Transport ◽  
Relaxation Times ◽  
Boltzmann Transport Equation ◽  
Phonon Transport ◽  
Oxide Semiconductor ◽  
Boltzmann Transport ◽  
Scattering Model ◽  
Anisotropic Relaxation

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

Coupled Non-Equilibrium Green’s Function (NEGF) Electron-Phonon Interaction in Thermoelectric Materials

2011 ◽  
Author(s):  
T. D. Musho ◽  
D. G. Walker
Keyword(s):  
Thermoelectric Materials ◽  
Thermal Transport ◽  
Phonon Scattering ◽  
Computational Method ◽  
Direct Result ◽  
Inelastic Electron ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Scattering ◽  
Non Equilibrium

Over the last decade, nano-structured materials have shown a promising avenue for enhancement of the thermoelectric figure of merit. These performance enhancements in most cases have been a direct result of selectively modifying certain geometric attributes that alter the thermal or electrical transport in a desirable fashion. More often, models used to study the electrical and/or thermal transport are calculated independent of each other. However, studies have suggested electrical and thermal transport are intimately linked at the nanoscale. This provides an argument for a more rigorous treatment of the physics in an effort to capture the response of both electrons and phonons simultaneously. A simulation method has been formulated to capture the electron-phonon interaction of nanoscale electronics through a coupled non-equilibrium Greens function (NEGF) method. This approach is unique because the NEGF electron solution and NEGF phonon solution have only been solved independently and have never been coupled to capture a self-consistent inelastic electron-phonon scattering. One key aspect of this formalism is that the electron and phonon description is derived from a quantum point of view and no correction terms are necessary to account for the probabilistic nature of the transport. Additionally, because the complete phonon description is solved, scattering rates of individual phonon frequencies can be investigated to determine how electron-phonon scattering of particular frequencies influences the transport. This computational method is applied to the study of Si/Ge nanostructured superlattice thermoelectric materials.

Interface Trap Density and Mobility Characterization of Silicon Carbide MOSFET Inversion Layers

2009 ◽  
Vol 615-617 ◽  
pp. 801-804 ◽  
Author(s):  
Vinayak Tilak ◽  
Kevin Matocha ◽  
Greg Dunne
Keyword(s):  
Silicon Carbide ◽  
Electric Field ◽  
Doping Concentration ◽  
Phonon Scattering ◽  
Field Effect Transistors ◽  
Inversion Layer ◽  
Oxide Semiconductor ◽  
Conduction Band Edge ◽  
Interface Trap ◽  
Surface Electric Field

Silicon Carbide (SiC) based metal oxide semiconductor field effect transistors (MOSFETs) were fabricated and characterized using gated hall measurements with different p-type substrate doping concentration (7.2X1016cm-3 and 2X1017 cm-3). An interface trap state density of 5X1013 cm-2eV-1 was observed nearly 0.1 eV above the conduction band edge leading to the conclusion that these states are present in the silicon dioxide rather than the interface. The Hall mobility of the MOSFETs decreased from 26.5 to 20 cm2/Vs as the doping was increased from 7.2X1016 to 2X1017cm-3. The decrease in mobility is primarily due to an increase in the surface electric field that causes an increase in surface roughness scattering. The inversion layer mobility when plotted as a function of average surface electric field is not independent of doping concentration as is the case in silicon MOSFETs because the dominant scattering mechanism is not phonon scattering.

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