Scattering and adsorption of ballistic phonons by the electron inversion layer in silicon: Theory and experiment (original) (raw)
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In this work, the mechanism for enhanced phonon backscattering in silicon is investigated. An understanding of phonon propagation through substrates has implications for engineering heat flow at the nanoscale, for understanding sources of decoherence in quantum systems, and for realizing efficient phonon-mediated particle detectors. In these systems, phonons that backscatter from the bottom of substrates, within the crystal or from interfaces, often contribute to the overall detector signal. We utilize a microscale phonon spectrometer, comprising superconducting tunnel junction emitters and detectors, to specifically probe phonon backscattering in silicon substrates ($500 lm thick). By etching phonon " enhancers " or deep trenches ($90 lm) around the detectors, we show that the backscattered signal level increases by a factor of $2 for two enhancers versus one enhancer. Using a geometric analysis of the phonon pathways, we show that the mechanism of the backscattered phonon enhancement is due to confinement of the ballistic phonon pathways and increased scattering off the enhancer walls. Our result is applicable to the geometric design and pat-terning of substrates that are employed in phonon-mediated detection devices. V C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4934534\]
Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation
Journal of Applied Physics, 2013
We investigate the effect of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of thicknesses between 1 nm − 16 nm. We employ the modified valence force field method to model the lattice dynamics and the ballistic Landauer transport formalism to calculate the thermal conductance. We consider the major thin layer surface orientations {100}, {110}, {111}, and {112}. For every surface orientation, we study thermal conductance as a function of the transport direction within the corresponding surface plane. We find that the ballistic thermal conductance in the thin layers is anisotropic, with the {110}/<110> channels exhibiting the highest and the {112}/<111> channels the lowest thermal conductance with a ratio of about two. We find that in the case of the {110} and {112} surfaces, different transport orientations can result in ∼ 50% anisotropy in thermal conductance. The thermal conductance of different transport orientations in the {100} and {111} layers, on the other hand, is mostly isotropic. These observations are invariant under different temperatures and layer thicknesses. We show that this behavior originates from the differences in the phonon group velocities, whereas the phonon density of states is very similar for all the thin layers examined. We finally show how the phonon velocities can be understood from the phonon spectrum of each channel. Our findings could be useful in the design of the thermal properties of ultra-thin Si layers for thermoelectric and thermal management applications.
Scattering of phonons from a high-energy grain boundary in silicon: Dependence on angle of incidence
Physical Review B, 2007
We use molecular-dynamics simulation to elucidate phonon scattering from the high-energy ⌺29 twist grain boundary in silicon. In particular, we have computed the dependence of energy transmission through the grain boundary on the wavelength and angle of incidence. Transmission through the grain boundary is found to be predominantly a function of the incident phonon frequency. In agreement with previous results, modes with wave vectors perpendicular to the grain-boundary plane exhibit relatively large energy-transmission coefficients. However, as the wavelength decreases and frequency increases, the energy transmission through the interface tends to sharply decrease. To develop a comprehensive picture of elastic phonon scattering, we have studied longitudinal-acoustic, transverse-acoustic, and some longitudinal-optical modes. By considering a simple theory that relates the energy-transmission coefficients to the Kapitza conductance, we are able to make a quantitative prediction based on detailed transmission probabilities. Predictions obtained using this model are relevant for comparison to both the classical ͑i.e., high-temperature͒ and quantum ͑i.e., low-temperature͒ regimes. We discuss the temperature dependence of the Kapitza conductance and suggest avenues of inquiry including experimental verification.
Monte Carlo study of electron transport in silicon inversion layers
Physical review, 1993
Electron transport in Si inversion layers at 300 K is studied using a self-consistent Monte Carlo solution of the Boltzmann transport equation coupled to the two-dimensional Poisson equation and the onedimensional Schrodinger equation. Physical elements included in the model are (1) nonparabolicity effects to treat quantization in the inversion layer; (2) static screening of the Coulomb interactions accounting for the population of many subbands; (3) anisotropy of the deformation-potential interaction, shown to be quite important in the case of a two-dimensional electron gas (2DEG); (4) a careful analysis of the dynamic screening of the deformation-potential interaction, showing that the interaction between electrons and acoustic phonons can be approximated by the unscreened interaction in the nondegenerate limit of a 2DEG; and (5) the inclusion of interface Si02 optical phonons. Up to ten subbands have been included to study the 2DEG together with a bulk-transport model employed to handle high-energy electrons. We have obtained mixed results: In the Ohmic regime, we have found a phonon-limited mobility that exhibits the correct dependence on carrier density, but which is about 20%%uo larger than the experimental data. This still represents an improvement upon previous nonempirical theories, and even better quantitative agreement is obtained at the very low and very high carrier densities at which Coulomb scattering and scattering with surface roughness, respectively, control the mobility. At high longitudinal fields we find a bulklike saturated velocity, in agreement with some experimental results, but not with many others that we consider more reliable.
Measurement of ballistic phonon conduction near hotspots in silicon
Applied Physics Letters, 2001
The Fourier law for lattice heat conduction fails when the source of heat is small compared to the phonon mean free path. We provide experimental evidence for this effect using heating and electrical-resistance thermometry along a doped region in a suspended silicon membrane. The data are consistent with a closed-form two-fluid phonon conduction model, which accounts for the severe departure from equilibrium at the hotspot. The temperature rise exceeds predictions based on the Fourier law by 60% when the phonon mean free path is a factor of 30 larger than the resistor thickness. This work is improving the constitutive modeling of heat flow in deep-submicron transistors.
Electron mobility in silicon and germanium inversion layers: The role of remote phonon scattering
Journal of Computational Electronics, 2007
We calculate the electron mobility in Si and Ge inversion layers in single-gate metal-oxide-semiconductor field effect transistors. Scattering with bulk phonons, surface roughness and remote phonons is included in the mobility calculations. Various high-κ dielectric materials are considered for both Si and Ge substrates. Overall, Ge outperforms Si, but in general Ge is more affected by the use of high-κ dielectrics. HfO 2 degrades the mobility substantially compared to SiO 2 for Si substrates and may prohibitively degrade performance. HfO 2 with Ge yields an improvement over Si with a mobility enhancement ≈3× at an electron sheet density of 1 × 10 13 cm −3 .
Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors
Journal of Heat Transfer, 2006
Intense electron-phonon scattering near the peak electric field in a semiconductor device results in nanometer-scale phonon hotspots. Past studies have argued that ballistic phonon transport near such hotspots serves to restrict heat conduction. We reexamine this assertion by developing a new phonon transport model. In a departure from previous studies, we treat isotropic dispersion in all phonon branches and include a phonon emission spectrum from independent Monte Carlo simulations of electron-phonon scattering. We cast the model in terms of a non-equilibrium phonon distribution function and compare predictions from this model with data for ballistic transport in silicon. The solution to the steady-state transport equations for bulk silicon transistors shows that energy stagnation at the hotspot results in an excess equivalent temperature rise of about 13% in a 90 nm gate-length device. Longitudinal optical phonons with non-zero group velocities dominate transport. We find that the resistance associated with ballistic transport does not overwhelm that from the package unless the peak power density approaches 50 W / m 3 . A transient calculation shows negligible phonon accumulation and retardation between successive logic states. This work highlights and reduces the knowledge gaps in the electro-thermal simulation of transistors.