Download Coupling Electrons, Phonons, and Photons for Nonequilibrium

Coupling Electrons, Phonons, and Photons for Nonequilibrium
Transport Simulation
Irena Knezevic, Department of Electrical and Computer Engineering, University of Wisconsin-Madison
[email protected]
Keywords: multiphysics, quantum transport, nonequilibrium, nanostructure, time-dependent
Project Scope
The objective of this project is to develop versatile computational tools for accurate simulation of the farfrom-equilibrium and time-dependent quantum transport in realistic semiconductor nanostructures driven by highintensity dc or ac electromagnetic fields. The key challenge in simulating nonequilibrium time-dependent
transport is that one must capture the strong coupling between electrons, phonons, and electromagnetic fields in
the same simulation, self-consistently and at every time step.
Relevance to MGI
This project relates closely to experimental measurements of
electronic, thermal, and optical properties of a variety of
semiconductor nanostructures. For example, we predicted that
uniformly doped double-barrier tunneling structures would act as
emitters of THz-frequency radiation [1]; these are being fabricated
by the PI’s collaborators. The inclusion of nonequilibrium
phonons affects measured performance of quantum cascade lasers
(QCLs) in significant ways, leading to much better agreement
between theory and experiment in the temperature performance
[2]. Considering that QCLs are the highest-power coherent light
sources at midinfrared and THz frequencies, this work
significantly advances our understanding of the coupling between
electrons and phonons in QCLs, aiding their widespread
applications (Fig. 1).
Figure 1. Nonequilibrium phonon occupation
number (red – high, blue – low) at different
fields and temperatures versus in-plane and
cross-plane momentum in a GaAs-based
midinfrared quantum cascade laser. The
excess phonons exist only near the Brillouin
zone center, but their population is drastically
higher than in equilibrium. They strongly
affect electronic transport, largely by
amplifying electron scattering with phonon
absorption. From Shi and Knezevic [2].
Technical Progress
With high-intensity fields, considerable energy is pumped into
the electron and hole systems, which relax by transferring much of
it to the lattice; thereby, both electronic and lattice (phonon)
systems are far from equilibrium. With high-frequency excitation,
both interband and intraband electronic transitions potentially
occur, and details of the interaction between the the electronic systems and the fields are critical to capture. Three
main directions have been undertaken during the course of this project (currently 2 years and 4 months in): a)
high-frequency or time-dependent transport in nanostructures [1,3,4], b) nonequilibrium phonons in quantum
cascade lasers (good example system for high-field dc transport) [2], and c) phonon transport in realistic confined
structures of experimentally relevant sizes [5]. Under a), we calculated the ac conductivity, dielectric function and
plasmon dispersion of graphene, with focus on the role of substrate impurities [3]. We also showed that selfsustained THz-frequency current oscillations occur in uniformly doped double-barrier tunneling structures, a
phenomenon well documented at much lower frequencies in superlattices [1]. Under direction b), we
demonstrated how critical it is to account for the coupled dynamics of electrons and phonons in far-fromequilibrium systems, especially at low temperatures. We have for the first time fully quantified the influence of
nonequilibrium phonons on QCL operation (Fig. 1). Under c), we
have developed a full-dispersion phonon Monte Carlo algorithms
for 2D systems with hexagonal symmetry, like graphene
nanoribbons, and elucidated the universal phonon transport
features in nanowires with rough correlated surfaces (Fig. 2).
Future Plans
The work under a) and b) will merge as we include coherent
tunneling effects with Wigner Monte Carlo along with
nonequilibrium phonon effects for unprecedented accuracy in the
modeling of heterostructures and superlattices far from
equilibrium (Fig. 3). We will extend the effort to systems with 2D
transport and look at how highly delocalized carriers, such as
electrons in quantum point contacts at low temperatures, couple
with light and how they respond to time-varying biasing. We will
complete the work on the dielectric function and plasmons in
graphene nanoribbons and look into ways to “numerically” excite
plasmons in graphene-based nanostructures with very accurate
electronic and dielectric properties. Emergent related work is on
diffusion of excitons through carbon nanotube composites.
Figure 2. Thermal conductivity κ in 70-nmwide Si nanowires with exponentially
correlated real-space surface roughness of
correlation length ξ and rms roughness Δ.
The dashed line denotes the Casimir limit, the
lower limit on thermal conductivity that is
obtainable with the specularity model for
phonon interaction with the boundaries. With
real-space roughness, it is clear that a vast
parameter space results in thermal
conductivity below the Casimir limit, as seen
in experiment. From Maurer et al. [5].
Data Management and Open Access
Raw data, source code, and figures are being stored for a minimum of three years past the end of either this
award or publication, whichever is later. The codes will be made publically accessible (GPL-v3) within the next
several years.
References
Figure 3. (Preliminary data) Wigner function
(represented by color) versus position and
wave vector for a THz quantum cascade laser.
Red denotes thenegative values of the Wigner
function, which indicates coherent transport
(tunneling). This type of simulation is
computationally only marginally more
intensive than semiclassical Monte Carlo, but
capture coherent transport very well. Jonasson
and Knezevic, in prep.
[1] O. Jonasson and I. Knezevic, “Coulomb-driven terahertz-frequency
intrinsic current oscillations in a double-barrier tunneling structure,”
Phys. Rev. B 90, 165415 (2014).
[2] Y. B. Shi and I. Knezevic, “Nonequilibrium phonon effects in
midinfrared QCLs,” J. Appl. Phys. 116, 123105 (2014).
[3] F. Karimi and I. Knezevic, “Dielectric function and plasmons in
graphene: a self-consistent field calculation within a Markovian master
equation formalism,” submitted (2015); N. Sule, K. J. Willis, S. C.
Hagness, and I. Knezevic, “Terahertz-frequency electronic transport in
graphene,” Phys. Rev. B 90, 045431 (2014).
[4] I. Knezevic and B. Novakovic, “Time-dependent transport in open
systems based on quantum master equations,” J. Comput. Electron. 12,
363-374 (2013).
[5] S. Mei, L. N. Maurer, Z. Aksamija, and I. Knezevic, “Full-dispersion
Monte Carlo simulation of phonon transport in micron-sized graphene
nanoribbons,” J. Appl. Phys. 116, 164307 (2014); L. N. Maurer et al.
“Universal features of phonon transport in correlated rough
nanowires,” submitted.
Publications
1. Y. B. Shi and I. Knezevic, “Nonequilibrium phonon effects in midinfrared quantum cascade lasers,”Journal of
Applied Physics 116, 123105 (2014). [PDF]
2. O. Jonasson and I. Knezevic, “Coulomb-driven terahertz-frequency intrinsic current oscillations in a doublebarrier tunneling structure,” Physical Review B 90, 165415 (2014). [PDF]
3. N. Sule, K. J. Willis, S. C. Hagness, and I. Knezevic, “Terahertz-frequency electronic transport in graphene,”
Physical Review B 90, 045431 (2014). [PDF]
4. S. Mei, L. N. Maurer, Z. Aksamija, and I. Knezevic, “Full-dispersion Monte Carlo simulation of phonon
transport in micron-sized graphene nanoribbons,” Journal of Applied Physics 116, 164307 (2014). [PDF]
5. I. Knezevic and B. Novakovic, “Time-dependent transport in open systems based on quantum master
equations,” Journal of Computational Electronics 12, 363-374 (2013). [PDF]
6. L. N. Maurer, Z. Aksamija, E. B. Ramayya, A. H. Davoody, and I. Knezevic, “Universal Dimensional Scaling
of Phonon Transport in Correlated Rough Nanowires,” submitted.
7. O. Jonasson and I. Knezevic, “On the Boundary Conditions for the Wigner Transport Equation,” submitted.
8. F. Karimi and I. Knezevic, “Dielectric function and plasmons in graphene: a self-consistent field calculation
within a Markovian master equation formalism,” submitted.