multiscale/multiphysics simulation of electronic and ... · university of rome “tor vergata” -...

University of Rome “Tor Vergata” - Dep. Electronic Engineering

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Multiscale/Multiphysics simulation of electronic and optoelectronic devices

Department of Electronic Engineering,

University of Rome “Tor Vergata”, Italy

Acknowledgments:

EU H2020 Projects (CHIPSCOPE)

Aldo Di Carlo, Matthias Auf der Maur


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7Downscaling of MOSFETs

Increasing importance of quantum/non-equilibrium effects

Increasing complexity/breakdown of classical TCAD models

Increasing need for predictive simulation tools

Solution ….. atomistic simulations !


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7Coaxially-gated CNT-FET (C-CNTFET)

VGS=0.2V

VDS=0

PotentialCharge

Calculation performed with Density Functional TB + Non Eq. Green Functions


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7Gate induced CNT deformation

VGATE = 5 V

Ang.

An

g.

GATE

GATE

Forces

Repulsion forces can locally (under the gate) increase the CNT radius (1-2 %)

New effects appear such as Negative Quantum Capacitance (Latessa Phys.

Rev. B 72, 035455)


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7Transport in Carbon Nanotube

We have performed Molecular Dynamics simulations of a reactive collision of a

biased nanotube (V=100mV) and benzyne (C6H4) and we have calculated the

current flowing in the nanotube at each MD step

[Following the NASA MD simulations (J. Han, A. Globus, R. Jaffe, G. Deardorff)]

v = 0.6 Å/ps


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A

A

BB

CC

DI = 20%

CNT without C6H4

RCN-C6H4 = 10KW

RCN = 8 KW


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7Atomistic methods

At the nanoscale “every atom matters!”

Density Functional TB + NEGF + scattering

[PRL 100, 136801 (2008)]

Power dissipated in the C60 molecule is 10 nW

Power calculated as I x V = 10 mW !!!!

- Si dangling bond

- OH passivated dangling bond

H-passivated SiNW with one

A. Pecchia, A. Di Carlo, Rep. Prog. Phys. 67 (2004) 1497


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7Micro/macro scale

In a real device also micro and macro scale should

be considered

• Devices should be accessible from a macro scale

• micro/macro scale details are as important as nanoscale features

(temperature distribution, electrostatics, strain, air gap, etc.)

• Number of atoms cannot grow to much in simulations

• 30 years of experience with Drift-diffusion matters !

(M. Stetler Intel)

Nano, micro and macro scale should be

combined in a multiscale/multiphysics

approach


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7The multiscale problem

Circuit level

QM

nm mm mmLength scale

Elementary processesModel structures, short time scale

Few 1000 atoms, max. 10 ps

Nanostructures/processesincreasing technological relevance

Up to 1.000.000 Atoms 100 ns

classical

Force fields MM

Microstructure

Finite elements

Architecture

Circuit Level

Mesoscopic scales -1 billion atoms and more

technologically real processes

Emprical

Semi-empirical

Ab initio

Typical Pentium 4 MOSFET section


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7Multiscale methods in material science

Time

Propagation of a shock wave in a crystal- central region is treated at the atomistic level (MM)

- external part are treated in the continuous approx. (FEM)

Atomistic

FEM

FEM

Courtesy of G. Anciaux


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7Multiscale simulations: TiberCAD

Circuit simulation Macro-Microscopic description

(Strain, Drift-Diffusion , Heat, etc)

Nanoscale

description

www.tiberlab.com

Synthesis

Analysis


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7Multiscale components

Finite Element Method

Atomistic local basis

- FEM is the method in engineering problems

(deformation/strain, heat, Maxwell, etc. etc.)

-Drift-diffusion (DD) like schemes have been

solved with box integration methods.

- DD-FEM have been heavily developed in

the last 20 years in the Math community

(Hecht, Marrocco, Brezzi, Sacco, Chen)

- many FEM library in GPL

- Localized basis approach are very well

suited for device simulations

- Empirical approaches (ETB)

- Aproximate DFT (DFTB)

- Full DFT (Siesta, DMOL, etc.)


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7TiberCAD structure

LibMesh

Petsc Slepc Pardiso

GMSH

Devise (ISE)Paraview

Techplot

GMV

Modeler and meshPostprocess

Mathematical libraries

Development is done in C++ / C / Fortran in Linux, porting to other

UNIX-like environments and Windows has been achieved

TiberCAD 2.5 is available at www.tiberlab.com

VISIT

Feast


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7TiberCAD: Multiphysics models

– Mechanical deformation with any kind of constrain

– Semiconductor Strain including piezoelectric effect

– Drift-Diffusion transport of electrons / holes / excitons /

Ions (+ Poisson)

– Heat transport (Fourier and Boltzmann related methods)

– Quantum mechanics based with k.p envelope function

approximation

– Atomistic description via Empirical Tight-Binding (sp3d5s*,

or any other basis) and Density Functional TB

– NEGF library

– Classical molecular mechanics

– Maxwell solver


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7Multiscale methods

domain 1 domain 2

BRIDGE METHOD • the domains are contiguous

and linked through n-1

dimensional regions.

• each domain providesboundary conditions to

adjacent domains.

domain 2

domain 1

OVERLAP METHOD

• the domains are overlapped

• each domain computes

physical quantities that act as

parameters to the otherdomain.


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Multiscale simulations: BRIDGE method

1) Strain: Continuum elasticity model and

Valence force field


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7Continuum Elasticity model (CE)

Whenever we deal with device composed by crystals with different

lattice constant, we have to deal with strain.

Lattice match Lattice mismatch

This PDE is solved with FEM technique

GaN dot in a/AlGaN

nanocolumns


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7Valence Force Field (VFF)

We included a Keating model to calculate strain at an atomistic level

The equilibrium position is that one which minimizes U.We use a nonlinear conjugate gradient minimization technique.

Advantages:• Most efficient atomistic technique. • Description beyond effective medium (random alloy)• Include internal strain• More accurate for some classes of nanostructures

2


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Spherical InAs quantum dot in GaAs box16 nm cubic box (200 000 atoms).

Multiscale strain: Mixing VFF and CE

Good agreement a few nanometers outside the dot but CE fails in the Dot

region. VFF is CPU demanding

exx

ezz


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Now atomistic structure is only defined in a smaller box (4nm) with 4000 atoms

Multiscale strain

1) Solve CE everywhere with lattice match boundary condition at the substrate

2) Apply displacement to atoms3) Fix external atoms as a boundary

condition for VFF(bridge method)

4) Solve VFF in the smaller structure5) Join results

CE/VFF approach


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Multiscale simulations: OVERLAP method

Nitride-based Nanorod : Drift-Diffusion, ETB and k.p


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7GaN Nanorods Structures

Diameter and pitch:

< 100nm through > 5µm (both)

Large area (scalability up to 8inch)

Quality requirements (no or few defects)

Facts

A. WaagBraunschweig University of Technology


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7Simulation of GaN/alGaN nanowire LED

Atomistic

Continuum

Continuum

M. Auf der Maur et al. IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 5, MAY 2011

Multiscale CE/VFF Strain calculation


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7Phase space and overlap Multiscale

Energy

Position

n-AlGaN p-AlGaNGaN

Active region

CB

VBQuantum

density: ETB

Quantum

density: ETB

Classical density

Drift-Diffusion Transport


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7Models: Empirical Tight Binding (ETB)

Tight-binding approach: expand wave function in atomic orbitals

,

, )()(j

jj RrCr

Atomic orbital index

Atomic site

jiji HH , jijiS ,

Matrix elements can be calculated by using e.g. density functional theory

(DFT) or used as empirical fitting parameters (Empirical Tight Binding).

We use a transferable sp3d5s* parametrization (Jancu et al. Phys. Rev. B

57, 1998)

Strain (from VFF) is included by means of Harrison scaling:

0

jsite,atomic orbitals,

,,

jjiji CESH

Ci

orbital

atomic site

px

pypz

s

n

d

dVV

0

0,


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7The advent of Graphic Cards

W. Rodriguez et al. Computer Physics Communications 185, 2510 (2014); J.Comp. Electr.

14(2):593–603, (2015).

By using cost effective Graphic Cards (1000 euro) is it possible to have a

High Performing Computing on Personal Workstation. GPU are very

suited also for Atomistic calculations


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7ETB/k.p/Poisson/Drift-Diffusion

The electrostatic potential and current flow lines around the intrinsic part of the

column. Classical and quantum results. The selfconsistent EFA/ETB/drift-diff. results

shows also the contours of the electron and hole densities at half of the mean density

inside the intrinsic region.

Classical Quantum


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7Current and radiative recombinations

classical simulations: radiative

recombinations originates from a region very

close to the surface of the column,

quantum simulations: radiative recombination

results to be mainly concentrated at the center

of the quantum disk due to the spatial

confinement of the carriers.

Classical radiative recombinations Quantum radiative recombinations


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Random Atomistic

Structure

Indium fluctuation and optical properties


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Transition energies are correlated with

the effective mean In concentration, given

by the mean concentration weighted by

the electrons’ ground state

Spatial Probability

Density (SPD). 116 samples In0.1GaN

QD random samples

Ground state SPDs for four

different In0.1GaN QD random

samples

- yellow: electron SPD,

- green: hole SPD,

- red dots: In atoms,

- gray dots: Ga atoms.

Localization of the wavefunction


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Electron-hole transition histogram

Spectrum of cumulative el-hl transitions for 116 samples

Optical emission


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7The Green Gap

Phosphor-free white LEDs based on color mixing with high efficacy needs

in particular high efficacy green LEDs.

peak emission efficiency

green gap

K. A. Bulashevich, et al. Phys. Status Solidi (a) 212, 914 (2015).

D. Schiavon, et al. Phys. Status Solidi (b) 250, 283 (2013).


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7Simulation: DriftDiffusion + atomistic

Continuous models are solved in 1D

No in-plane potential fluctuations

10

nm

x 1

0 n

m

su

perc

ell

Model system: 3 nm single quantum well, 15/20/25/30/35% In, p-i-n

structure:

Atomistic models: VFF, ETB

Typical band profile near maximum efficiency:

el-hl overlap is reduced due to QCSE


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7Origin of MME scattering

What is the origin of the strong spread in MME?

Ec Ev

vertical

separation

in-plane separation

Both electrons and holes tend to localize in regions where the In

concentration is higher

However, due to QCSE electrons and holes feel Indium fluctuations on different atomic planes of the QW

In

Ga

N


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7Simulation results vs. experiment

Assume optimistic case: constant A and C (measured values) how

does the peak IQE vary with wavelength?

Schiavon et al., Phys. Status Solidi B 250, No. 2 (2013)

Non-radiative recombinations

Eg

QCSE

Random

alloy

Random alloy fluctuations explain the missing

contribution to the green gap

M. Auf der Maur, et al. PRL 116, 027401 (2016)


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Other Multiscale/Multiphysics examples


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7Organic Solar Cell

e-h generation

rate (from Maxwell solver)

e current (from

Drift-Diffusion solver)


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7Core-Shell GaN/InGaN nanorod

We performed semiclassical simulations of relatively low aspect ratio

circular nanorods with 3 QWs based on the drift-diffusion model:

– Calculate strain

– Do a voltage sweep and calculate carrier transport

– Extract current efficiencies for the different recombination

mechanisms

Symmetry

axis

We make use of circular symmetry to

limit computational cost.


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7Core-Shell Simulation Results

Influence of strain relaxation / polarization field (for 20% In, vrec = 105 cm/s):

• Strain relaxation towards

top and bottom surfaces• Discontinuity of

polarization at top and

bottom surfaces

Carrier accumulation

With polarization

Psp

+ P

pz

Without polarization


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Glass

FTO

c-TiO2

TiO2 + Dye + Polymer

Metal electrode

TEM

Tomography

FIB +

=+

TiO2 Hole-conductor

Mesh & CAD

Cate Ducati , Giorgio Divitini (Cambridge)

Henry Snaith (Oxford)

Fabio Di Fonzo, Agnese Abrusci (IIT)

500 nm

Solid State DSC: Real Morphology


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200 nm !

200nm are not representative of a

several micron size devices.

• Potential profiles, concentration gradients

are on a much larger scale

• Boundary condition are on a micron scale

Micro- and nano-scale should

coexist in the same concurrent

simulation

Photocurrent

Multiscale

simulations

Macro scale

effectivematerial

nano scale

real material

Multiscale approach


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7Embedding of a 2D slice into the effective model

Effective material Effective material

TiO2

Hole conductor

3 um

Photoanode Cathode

Light

180 nm

Real morphology


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7Effect of trap states on the hole current

Traps screened by the ionic

additives (LiTFSI) Traps at the interface

The effect of trapped electrons is to spatially move the hole current

close to the surface TiO2/hole conductor enhancing recombination.

TiO2

Spiro (HTM)

A.Gagliardi et al. Nanoscale, 2015, 7, 1136


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7Conclusions

Multiscale/multiphysics is requested in real modern devices

where different length scales models are linked together.

We presented one of the first consistent attempt to answer

this request.

The main effort was related to the connection between

models. The Multiscale infrastructure has been defined.

The Multiscale framework will be used for design nd

analyses of CHIPSCOPE.

Additional details at http://www.tibercad.org

multiscale/multiphysics simulation of electronic and ... · university of rome “tor vergata” -...

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