arXiv subjects

Abhijeet Paul

Publications and source records attributed to Abhijeet Paul.

18 recordsLinked to original sources

arXiv2011

An efficient algorithm to calculate intrinsic thermoelectric parameters based on Landauer approach

The Landauer approach provides a conceptually simple way to calculate the intrinsic thermoelectric (TE) parameters of materials from the ballistic to the diffusive transport regime. This method relies on the calculation of the number of propagating modes and the scattering rate for each mode. The modes are calculated from the energy dispersion (E(k)) of the materials which require heavy computation and often supply energy relation on sparse momentum (k) grids. Here an efficient method to calculate the distribution of modes (DOM) from a given E(k) relationship is presented. The main features of this algorithm are, (i) its ability to work on sparse dispersion data, and (ii) creation of an energy grid for the DOM that is almost independent of the dispersion data therefore allowing for efficient and fast calculation of TE parameters. The inclusion of scattering effects is also straight forward. The effect of k-grid sparsity on the compute time for DOM and on the sensitivity of the calculated TE results are provided. The algorithm calculates the TE parameters within 5% accuracy when the K-grid sparsity is increased up to 60% for all the dimensions (3D, 2D and 1D). The time taken for the DOM calculation is strongly influenced by the transverse K density (K perpendicular to transport direction) but is almost independent of the transport K density (along the transport direction). The DOM and TE results from the algorithm are bench-marked with, (i) analytical calculations for parabolic bands, and (ii) realistic electronic and phonon results for $Bi_{2}Te_{3}$.

cond-mat.mes-hall↗

arXiv2011

Relating electronic structure to thermoelectric device performance

Realistic thermoelectric modeling and simulation tools are needed to explain the experiments and for device design. In this paper, we present a simple computational technique to make use of rigorous band structure calculations in thermoelectric device design. Our, methodology, based on Landauer theory, provides a way to benchmark effective mass level models against rigorous band structures. It can also be used for determining the temperature-dependent Fermi-level from a given doping density and numerically generated density-of-states, which can then be used with the numerically generated distribution of channels to evaluate the temperature dependent electrical conductivity, thermopower, and electronic thermal conductivity. We illustrate the technique for silicon, for which well-calibrated band structure and transport data is available, but the technique is more generally suited to complex thermoelectric materials and provides an easy way to make use of first principles band structure calculations in device design.

cond-mat.mes-hall↗

arXiv2011

Shape and orientation effects on the ballistic phonon thermal properties of ultra-scaled Si nanowires

The effect of geometrical confinement, atomic position and orientation of Silicon nanowires (SiNWs) on their thermal properties are investigated using the phonon dispersion obtained using a Modified Valence Force Field (MVFF) model. The specific heat ($C_{v}$) and the ballistic thermal conductance ($κ^{bal}_{l}$) shows anisotropic variation with changing cross-section shape and size of the SiNWs. The $C_{v}$ increases with decreasing cross-section size for all the wires. The triangular wires show the largest $C_{v}$ due to their highest surface-to-volume ratio. The square wires with [110] orientation show the maximum $κ^{bal}_{l}$ since they have the highest number of conducting phonon modes. At the nano-scale a universal scaling law for both $C_{v}$ and $κ^{bal}_{l}$ are obtained with respect to the number of atoms in the unit cell. This scaling is independent of the shape, size and orientation of the SiNWs revealing a direct correlation of the lattice thermal properties to the atomistic properties of the nanowires. Thus, engineering the SiNW cross-section shape, size and orientation open up new ways of tuning the thermal properties at the nanometer regime.

cond-mat.mes-hall↗

arXiv2011

Influence of cross-section geometry and wire orientation on the phonon shifts in ultra-scaled Si nanowires

Engineering of the cross-section shape and size of ultra-scaled Si nanowires (SiNWs) provides an attractive way for tuning their structural properties. The acoustic and optical phonon shifts of the free-standing circular, hexagonal, square and triangular SiNWs are calculated using a Modified Valence Force Field (MVFF) model. The acoustic phonon blue shift (acoustic hardening) and the optical phonon red shift (optical softening) show a strong dependence on the cross-section shape and size of the SiNWs. The triangular SiNWs have the least structural symmetry as revealed by the splitting of the degenerate flexural phonon modes and The show the minimum acoustic hardening and the maximum optical hardening. The acoustic hardening, in all SiNWs, is attributed to the decreasing difference in the vibrational energy distribution between the inner and the surface atoms with decreasing cross-section size. The optical softening is attributed to the reduced phonon group velocity and the localization of the vibrational energy density on the inner atoms. While the acoustic phonon shift shows a strong wire orientation dependence, the optical phonon softening is independent of wire orientation.

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arXiv2011

Strain effects on the thermal properties of ultra-scaled Si nanowires

The impact of uniaxial and hydrostatic stress on the ballistic thermal conductance ($κ_{l}$) and the specific heat ($C_{v}$) of [100] and [110] Si nanowires are explored using a Modified Valence Force Field phonon model. An anisotropic behavior of $κ_{l}$ and isotropic nature of $C_{v}$ under strain are predicted for the two wire orientations. Compressive (tensile) strain decreases (increases) $C_{v}$. The $C_{v}$ trend with strain is controlled by the high energy phonon sub-bands. Dominant contribution of the low/mid (low/high) energy bands in [100] ([110]) wire and their variation under strain governs the behavior of $κ_{l}$.

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arXiv2011

Atomistic study of electronic structure of PbSe nanowires

Lead Selenide (PbSe) is an attractive `IV-VI' semiconductor material to design optical sensors, lasers and thermoelectric devices. Improved fabrication of PbSe nanowires (NWs) enables the utilization of low dimensional quantum effects. The effect of cross-section size (W) and channel orientation on the bandstructure of PbSe NWs is studied using an 18 band $sp^3d^5$ tight-binding theory. The bandgap increases almost with the inverse of the W for all the orientations indicating a weak symmetry dependence. [111] and [110] NWs show higher ballistic conductance for the conduction and valence band compared to [100] NWs due to the significant splitting of the projected L-valleys in [100] NWs.

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arXiv2011

Atomistic approach to alloy scattering in $Si_{1-x}Ge_{x}$

SiGe alloy scattering is of significant importance with the introduction of strained layers and SiGe channels into CMOS technology. However, alloy scattering has till now been treated in an empirical fashion with a fitting parameter. We present a theoretical model within the atomistic tight-binding representation for treating alloy scattering in SiGe. This approach puts the scattering model on a solid atomistic footing with physical insights. The approach is shown to inherently capture the bulk alloy scattering potential parameters for both n-type and p-type carriers and matches experimental mobility data.

cond-mat.mes-hall↗

arXiv2011

Interface trap density metrology from sub-threshold transport in highly scaled undoped Si n-FinFETs

Channel conductance measurements can be used as a tool to study thermally activated electron transport in the sub-threshold region of state-of-art FinFETs. Together with theoretical Tight-Binding (TB) calculations, this technique can be used to understand the evolution of source-to-channel barrier height (Eb) and of active channel area (S) with gate bias (Vgs). The quantitative difference between experimental and theoretical values that we observe can be attributed to the interface traps present in these FinFETs. Therefore, based on the difference between measured and calculated values of (i) S and (ii) |dEb/dVgs| (channel to gate coupling), two new methods of interface trap density (Dit) metrology are outlined. These two methods are shown to be very consistent and reliable, thereby opening new ways of analyzing in situ state-of-the-art multi-gate FETs down to the few nm width limit. Furthermore, theoretical investigation of the spatial current density reveal volume inversion in thinner FinFETs near the threshold voltage.

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arXiv2011

Full 3D Quantum Transport Simulation of Atomistic Interface Roughness in Silicon Nanowire FETs

The influence of interface roughness scattering (IRS) on the performances of silicon nanowire field-effect transistors (NWFETs) is numerically investigated using a full 3D quantum transport simulator based on the atomistic sp3d5s* tight-binding model. The interface between the silicon and the silicon dioxide layers is generated in a real-space atomistic representation using an experimentally derived autocovariance function (ACVF). The oxide layer is modeled in the virtual crystal approximation (VCA) using fictitious SiO2 atoms. <110>-oriented nanowires with different diameters and randomly generated surface configurations are studied. The experimentally observed ON-current and the threshold voltage is quantitatively captured by the simulation model. The mobility reduction due to IRS is studied through a qualitative comparison of the simulation results with the experimental results.

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arXiv2010

Intrinsic Reliability improvement in Biaxially Strained SiGe p-MOSFETs

In this letter we not only show improvement in the performance but also in the reliability of 30nm thick biaxially strained SiGe (20%Ge) channel on Si p-MOSFETs. Compared to Si channel, strained SiGe channel allows larger hole mobility (μh) in the transport direction and alleviates charge flow towards the gate oxide. μh enhancement by 40% in SiGe and 100% in Si-cap SiGe is observed compared to the Si hole universal mobility. A ~40% reduction in NBTI degradation, gate leakage and flicker noise (1/f) is observed which is attributed to a 4% increase in the hole-oxide barrier height (ϕ) in SiGe. Similar field acceleration factor (Γ) for threshold voltage shift (ΔVT) and increase in noise (ΔSVG) in Si and SiGe suggests identical degradation mechanisms.

cond-mat.mes-hall↗

arXiv2010

Tuning lattice thermal conductance by porosity control in ultra-scaled Si and Ge nanowires

Porous nanowires (NWs) with tunable thermal conductance are examined as a candidate for thermoelectric (TE) devices with high efficiency (ZT). Thermal conductance of porous Si and Ge NWs is calculated using the complete phonon dispersion obtained from a modified valence force field (MVFF) model. The presence of holes in the wires break the crystal symmetry which leads to the reduction in ballistic thermal conductance ($σ_{l}$). $[100]$ Si and Ge NWs show similar percentage reduction in $σ_{l}$ for the same amount of porosity. A 4nm $\times$ 4nm Si (Ge) NW shows $\sim$ 30% (29%) reduction in $σ_{l}$ for a hole of radius 0.8nm. The model predicts an anisotropic reduction in $σ_{l}$ in SiNWs, with $[111]$ showing maximum reduction followed by $[100]$ and $[110]$ for a similar hole radius. The reduction in $σ_{l}$ is attributed to phonon localization and anisotropic mode reduction.

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arXiv2010

Interface Trap Density Metrology of state-of-the-art undoped Si n-FinFETs

The presence of interface states at the MOS interface is a well-known cause of device degradation. This is particularly true for ultra-scaled FinFET geometries where the presence of a few traps can strongly influence device behavior. Typical methods for interface trap density (Dit) measurements are not performed on ultimate devices, but on custom designed structures. We present the first set of methods that allow direct estimation of Dit in state-of-the-art FinFETs, addressing a critical industry need.

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arXiv2010

Modified valence force field approach for phonon dispersion: from zinc-blende bulk to nanowires

he correct estimation of thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that the nanowire phonon spectrum differ considerably from the bulk dispersions. This manifests itself in the form of different physical and thermal properties in these wires. We believe that this model and approach will prove beneficial in the understanding of the lattice dynamics in the next generation ultra-scaled semiconductor devices.

cond-mat.mes-hall↗

arXiv2010

Atomistic modeling of the phonon dispersion and lattice properties of free-standing <100> Si nanowires

Phonon dispersions in <100> silicon nanowires (SiNW) are modeled using a Modified Valence Force Field (MVFF) method based on atomistic force constants. The model replicates the bulk Si phonon dispersion very well. In SiNWs, apart from four acoustic like branches, a lot of flat branches appear indicating strong phonon confinement in these nanowires and strongly affecting their lattice properties. The sound velocity (Vsnd) and the lattice thermal conductance (kl) decrease as the wire cross-section size is reduced whereas the specific heat (Cv) increases due to increased phonon confinement and surface-to-volume ratio (SVR).

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arXiv2010

Thermionic Emission as a tool to study transport in undoped nFinFETs

Thermally activated sub-threshold transport has been investigated in undoped triple gate MOSFETs. The evolution of the barrier height and of the active cross-section area of the channel as a function of gate voltage has been determined. The results of our experiments and of the Tight Binding simulations we have developed are both in good agreement with previous analytical calculations, confirming the validity of thermionic approach to investigate transport in FETs. This method provides an important tool for the improvement of devices characteristics.

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arXiv2008

Simulations of Nanowire Transistors: Atomistic vs. Effective Mass Models

The ballistic performance of electron transport in nanowire transistors is examined using a 10 orbital sp3d5s* atomistic tight-binding model for the description of the electronic structure, and the top-of-the-barrier semiclassical ballistic model for calculation of the transport properties of the transistors. The dispersion is self consistently computed with a 2D Poisson solution for the electrostatic potential in the cross section of the wire. The effective mass of the nanowire changes significantly from the bulk value under strong quantization, and effects such as valley splitting strongly lift the degeneracies of the valleys. These effects are pronounced even further under filling of the lattice with charge. The effective mass approximation is in good agreement with the tight binding model in terms of current-voltage characteristics only in certain cases. In general, for small diameter wires, the effective mass approximation fails.

cond-mat.mtrl-sci↗

arXiv2008

Bandstructure Effects in Silicon Nanowire Hole Transport

Bandstructure effects in PMOS transport of strongly quantized silicon nanowire field-effect-transistors (FET) in various transport orientations are examined. A 20-band sp3d5s* spin-orbit-coupled (SO) atomistic tight-binding model coupled to a self consistent Poisson solver is used for the valence band dispersion calculation. A ballistic FET model is used to evaluate the capacitance and current-voltage characteristics. The dispersion shapes and curvatures are strong functions of device size, lattice orientation, and bias, and cannot be described within the effective mass approximation. The anisotropy of the confinement mass in the different quantization directions can cause the charge to preferably accumulate in the (110) and secondly on the (112) rather than (100) surfaces, leading to significant charge distributions for different wire orientations. The total gate capacitance of the nanowire FET devices is, however, very similar for all wires in all the transport orientations investigated ([100], [110], [111]), and is degraded from the oxide capacitance by ~30%. The [111] and secondly the [110] oriented nanowires indicate highest carrier velocities and better ON-current performance compared to [100] wires. The dispersion features and quantization behavior, although a complicated function of physical and electrostatic confinement, can be explained at first order by looking at the anisotropic shape of the heavy-hole valence band.

cond-mat.mes-hall↗

arXiv2008

Bandstructure Effects in Silicon Nanowire Electron Transport

Bandstructure effects in the electronic transport of strongly quantized silicon nanowire field-effect-transistors (FET) in various transport orientations are examined. A 10-band sp3d5s* semi-empirical atomistic tight-binding model coupled to a self consistent Poisson solver is used for the dispersion calculation. A semi-classical, ballistic FET model is used to evaluate the current-voltage characteristics. It is found that the total gate capacitance is degraded from the oxide capacitance value by 30% for wires in all the considered transport orientations ([100], [110], [111]). Different wire directions primarily influence the carrier velocities, which mainly determine the relative performance differences, while the total charge difference is weakly affected. The velocities depend on the effective mass and degeneracy of the dispersions. The [110] and secondly the [100] oriented 3nm thick nanowires examined, indicate the best ON-current performance compared to [111] wires. The dispersion features are strong functions of quantization. Effects such as valley splitting can lift the degeneracies especially for wires with cross section sides below 3nm. The effective masses also change significantly with quantization, and change differently for different transport orientations. For the cases of [100] and [111] wires the masses increase with quantization, however, in the [110] case, the mass decreases. The mass variations can be explained from the non-parabolicities and anisotropies that reside in the first Brillouin zone of silicon.

cond-mat.mtrl-sci↗