ViennaEMC

ViennaEMC is a header-only C++17 library for semiconductor carrier transport simulation using the Multi-Valley Ensemble Monte Carlo (EMC) method. It is developed at the Institute for Microelectronics at TU Wien.

What it does

The Ensemble Monte Carlo method simulates the quantum-mechanical transport of charge carriers (electrons, holes) through a semiconductor by tracking a statistical ensemble of representative particles. Each particle drifts under the applied electric field and is scattered stochastically by phonons, impurities, and other mechanisms. The distribution of carrier momenta and energies evolves from these microscopic events, giving macroscopic observables such as drift velocity, energy, and valley occupancy.

ViennaEMC extends the classical EMC method with:

Multi-valley analytical band structures — parabolic and non-parabolic, isotropic and anisotropic effective masses, with the Herring–Vogt transformation for anisotropic valleys.
Pluggable scatter mechanisms — acoustic phonon, optical phonon (zero- and first-order intervalley), Fröhlich (polar-optical) in 3D and 2D, Coulomb scattering, grain boundary scattering, and more. New mechanisms can be added by subclassing emcScatterMechanism.
Self-scattering (null-scattering) — the standard technique that lets every particle share the same time step regardless of its local scatter rate.
Particle–particle interactions via FMM — long-range Coulomb forces between moving carriers and fixed donors, computed with ScalFMM.
Poisson solver coupling — for full device simulations (MOSFETs, resistors) the electrostatic potential is solved self-consistently on a grid.
Hot-carrier dynamics in metal-halide perovskites — a dynamic phonon bath (emcPhononBath) tracks the out-of-equilibrium LO phonon occupation N_q per wave-vector bin, coupled to an acoustic reservoir in a three-temperature carrier/LO/acoustic model. Fröhlich scatter rates are rebuilt every time step from the evolving occupation, capturing the hot-phonon bottleneck and the acoustic cascade. On top of this the hotCarrierMHP example builds a full bipolar device model — electrons and holes sharing the bath, carrier–carrier and electron–hole scattering, radiative and Auger recombination, Pauli band filling, and energy-selective extraction from which open-circuit voltage and power conversion efficiency are computed.

Library architecture

ViennaEMC is header-only: all classes live under include/. No library file needs to be compiled — you only link against ScalFMM (for FMM examples) and OpenMP.

include/
├── emcDevice.hpp              — simulation domain (geometry, doping, temperature)
├── emcMaterial.hpp            — material constants (dielectric, mass density, …)
├── emcSimulation.hpp          — top-level device simulation loop
├── emcScatterHandler.hpp      — manages scatter table construction and selection
├── emcConstants.hpp           — physical constants (SI units)
│                                # hot-carrier modules (examples/hotCarrierMHP)
├── emcPhononBath.hpp          — three-temperature LO/acoustic phonon bath (HPB + acoustic cascade)
├── emcCarrierCarrierScatter.hpp   — intra-species carrier–carrier scattering
├── emcInterCarrierScatter.hpp     — electron–hole scattering (reduced-mass frame)
├── emcRecombination.hpp       — radiative (Bnp) + Auger (CCCH/CHHS) recombination
├── emcEnergySelectiveContact.hpp  — energy-selective carrier extraction
├── emcPauliExclusion.hpp      — Lugli–Ferry band filling on a k-space occupancy grid
├── emcHotCarrierOutput.hpp    — Fermi–Dirac fit → carrier temperature, V_OC, PCE
├── ParticleType/
│   ├── emcParticleType.hpp    — base class; holds valleys + scatter mechanisms
│   ├── emcElectron.hpp        — concrete electron particle type
│   ├── emcHole.hpp            — concrete hole particle type (bipolar transport)
│   └── emcAcceptor.hpp        — acceptor particle type
├── ValleyTypes/
│   ├── emcParabolicIsotropValley.hpp
│   ├── emcNonParabolicIsotropValley.hpp
│   ├── emcParabolicAnisotropValley.hpp
│   ├── emcNonParabolicAnistropValley.hpp
│   └── …SingleLayer variants  — 2D transport (e.g. MoS₂)
└── ScatterMechanisms/
    ├── emcAcousticScatterMechanism.hpp
    ├── emcFroehlichInteraction.hpp          — equilibrium Fröhlich (3D)
    ├── emcHotPhononFroehlichMechanism.hpp   — HPB Fröhlich with dynamic N_q
    ├── emcZeroOrderInterValleyScatterMechanism.hpp
    ├── emcFirstOrderInterValleyScatterMechanism.hpp
    ├── emcCoulombScatterMechanism.hpp
    └── …SingleLayer variants

The examples/ directory contains standalone programs that use the library. Each example has its own CMakeLists.txt and can be studied as a template for new simulations.

System requirements

Requirement	Minimum version	Notes
Linux	any recent	Tested on Ubuntu 22.04+
C++ compiler	GCC 9 / Clang 10	Must support C++17 and OpenMP
CMake	3.12
Git	any	Required to fetch ScalFMM
Internet access	—	Only during `make buildDependencies`
Intel MKL	optional	Used by ScalFMM for BLAS/LAPACK; LAPACK/OpenBLAS can substitute

ScalFMM is the only external dependency and is downloaded and built automatically by CMake the first time you run make buildDependencies.

Building

Step 1 — Clone and configure

git clone https://github.com/ViennaTools/ViennaEMC.git
cd ViennaEMC
mkdir build && cd build

# Configure (release build, examples enabled)
cmake .. -DCMAKE_BUILD_TYPE=Release -DVIENNAEMC_BUILD_EXAMPLES=ON

If you want to install the library to a custom prefix instead of /usr/local:

cmake .. -DCMAKE_BUILD_TYPE=Release \
         -DVIENNAEMC_BUILD_EXAMPLES=ON \
         -DCMAKE_INSTALL_PREFIX=/path/to/install

Step 2 — Build dependencies

This downloads ScalFMM from its Git repository and compiles it. It only needs to run once and may take several minutes depending on your machine and internet connection.

make buildDependencies

After it completes, re-run CMake so it can find the newly built ScalFMM:

cmake ..

Note: If you already have ScalFMM installed, skip this step and pass -Dscalfmm_DIR=/path/to/scalfmm/install to the cmake command instead.

Step 3 — Build the examples

make -j$(nproc)

This compiles all examples in parallel. Each executable is placed under build/examples/<name>/.

Step 4 — Run an example

The executables write their output to the directory from which they are invoked, so change into the example's build folder first:

cd build/examples/bulkSimulation
./bulkSimulation

Output files (.txt) appear in the same directory and can then be plotted with the provided Python scripts (see Plotting results).

Examples

Bulk Silicon

Path: examples/bulkSimulation/ Executable: build/examples/bulkSimulation/bulkSimulation

Simulates electron transport in bulk silicon under a constant applied electric field. The conduction band is modelled with six equivalent X-valleys (non-parabolic, anisotropic). Scatter mechanisms: acoustic phonon deformation potential, zero-order intervalley phonon scattering.

What you can study:

Steady-state drift velocity vs. field strength (velocity–field characteristic)
Average carrier energy vs. field
Valley occupancy as electrons scatter between the six X-valleys

Key parameters to tune in bulkSimulation.cpp:

Parameter	Default	Description
`appliedFieldStrength`	1 kV/cm	Magnitude of the background electric field
`appliedFieldDirection`	`{1,0,0}`	Direction (automatically normalised)
`totalTime`	3 ps	Total simulation time
`dt`	1 fs	Time step

Output files: avgEnergy<valley>.txt, avgVelocity<valley>.txt, valleyOccupation.txt

Bulk Silicon with FMM particle–particle interactions

Path: examples/bulkSimulationFMM/ Executable: build/examples/bulkSimulationFMM/bulkSimulationFMM

Same as the bulk silicon example but adds real-space Coulomb forces between electrons and between electrons and fixed ionised donors, computed with the Fast Multipole Method (ScalFMM). Useful for studying screening and carrier–carrier scattering effects.

Additional requirement: ScalFMM must be built (handled by make buildDependencies).

Single-layer MoS₂

Path: examples/singleLayerMoS2/ Executable: build/examples/singleLayerMoS2/singleLayerMoS2

Simulates 2D electron transport in a monolayer of MoS₂. The simulation is 2D: valleys and scatter mechanisms use the SingleLayer variants in include/. Scatter mechanisms: acoustic and optical phonons (2D Fröhlich interactions available).

What you can study:

2D drift velocity vs. field
Effects of different valley parameterisations (several literature models are available via a compile-time flag)

2D MOSFET

Path: examples/mosfet2D/ Executable: build/examples/mosfet2D/mosfet2D

Simulates an n-channel silicon MOSFET in 2D. The device geometry, doping profile, contacts, and gate potential are defined in the source file. The Poisson equation is solved self-consistently at each time step.

What you can study:

I–V characteristics (drain current vs. drain–source voltage at different gate voltages)
Carrier concentration and velocity profiles along the channel

Results in this example were validated against the classical EMC simulator CEMC from ViennaWD. See the example's README.md for a detailed description of the device structure and parameter definitions.

2D Resistor

Path: examples/resistor2D/ Executable: build/examples/resistor2D/resistor2D

Simulates a uniformly doped silicon resistor in 2D. A simpler device than the MOSFET — useful as a starting point for understanding the device simulation workflow before tackling the MOSFET.

Hot-Carrier Dynamics in Metal-Halide Perovskites

Path: examples/hotCarrierMHP/ Executable: build/examples/hotCarrierMHP/hotCarrierMHP

Simulates photo-excited hot-carrier cooling and device operation in a bulk metal-halide perovskite (MHP). It extends the single-carrier hot-phonon-bottleneck model of Faber, Filipovic, Koster, J. Phys. Chem. Lett. 2024, 15, 12601 into a bipolar, three-temperature device simulation.

What it models

Hot-phonon bottleneck (HPB) — carriers emit LO phonons (Fröhlich); the LO occupation N_q rises above its equilibrium value N_0 and stimulated re-absorption slows further cooling. emcPhononBath tracks N_q per wave-vector bin and updates it each step as
```
Nq[i] += (nEmitted[i] - nAbsorbed[i]) / Dph  -  (dt / tauLO) * (Nq[i] - Nstar)
```
where Dph = q² dq Vsim / (2π²) is the number of phonon modes in the bin and tauLO is the Klemens lifetime. The Fröhlich rates are rebuilt every step from the current N_q.
Acoustic cascade — a three-temperature carrier/LO/acoustic model in which the LO decay target Nstar follows a finite-lifetime acoustic reservoir (lifetime tau_ac) that the LO modes back-heat, so the bottleneck persists longer. An optional Ridley channel (LO → LA + TO) competes with Klemens decay.
Bipolar transport — electrons and holes share the phonon bath, with intra-species carrier–carrier and inter-species electron–hole scattering.
Recombination — radiative (Bnp) and Auger (CCCH/CHHS); Auger returns the gap energy to a surviving carrier (Auger reheating).
Band filling — Lugli–Ferry Pauli blocking on a k-space occupancy grid.
Energy-selective contact (ESC) — extraction through a window [E_ex ± ΔE/2], from which the working open-circuit voltage and PCE are computed.

Optionally, --use_multimode 1 resolves the two IR-active MAPbI₃ LO branches instead of a single effective mode.

Running the example

Every mechanism and material parameter is a command-line flag — there are no compile-time switches. Run from the build folder:

cd build/examples/hotCarrierMHP

# Full default model (MAPbI3, all mechanisms on)
./hotCarrierMHP

# Equilibrium-phonon reference (HPB off)
./hotCarrierMHP --use_hot_phonon 0

# CsSnI3 presets with a selective device contact
./hotCarrierMHP --material sn --E_ex 0.2 --delta_E 0.05

# Acoustic-lifetime study, reproducible, larger box for low shot noise
./hotCarrierMHP --tau_ac 10e-12 --box 200e-9 --seed 1

At the end of a run the console prints the working V_OC, extraction yield, and PCE. A default run (100 nm box, 10 ps) finishes in well under a minute; the larger boxes used for low-noise or band-filling runs take longer.

Key command-line flags

Defaults are for MAPbI₃; --material sn switches to CsSnI₃ presets. Times are in seconds, energies in eV, densities in m⁻³. Boolean flags take 0/1.

Flag	Default (pb / sn)	Description
`--material`	`pb`	Presets: `pb` = MAPbI₃, `sn` = CsSnI₃
`--use_hot_phonon`	`1`	Hot-phonon bottleneck (dynamic N_q)
`--use_acoustic`	`1`	Acoustic reservoir (three-temperature model)
`--use_holes`	`1`	Bipolar transport (electrons + holes)
`--use_recomb`	`1`	Radiative + Auger recombination
`--use_cc`	`1`	Carrier–carrier scattering
`--use_esc`	`1`	Energy-selective extraction
`--use_bf`	`0`	Pauli band filling (selects the large box)
`--use_multimode`	`0`	Two-branch (multi-mode) Fröhlich coupling
`--ridley_w`	`0`	Ridley LO→LA+TO branching fraction (0–1)
`--E_photon`	`3.1`	Pump photon energy
`--E_ex` / `--delta_E`	`0.4` / `0.05`	ESC window centre / width
`--density`	`1e24`	Carrier density (10²⁴ m⁻³ ≈ 10¹⁸ cm⁻³)
`--tau_ac`	`30e-12`	Acoustic-reservoir lifetime
`--tau_lo`	`2e-12` / `0.1e-12`	LO (Klemens) phonon lifetime
`--box`	auto	Cubic box side [m]; `0` auto-selects (100 nm, or 464 nm with `--use_bf`)
`--total_time`	`10e-12`	Simulation time
`--seed`	`0`	RNG seed; `0` = wall-clock, nonzero = reproducible

Further overrides: --eps_hi, --eps_lo, --mass_e, --mass_h, --omega_lo, --omega_to, --tau_to, --tau_ex, --E_gap, --T_lat.

Output files

The driver writes five time series. Each filename carries a suffix encoding the enabled mechanisms — HPB or EQ, then _AC (acoustic), _MM (multi-mode), _RID (Ridley), _BF (band filling), _1C (single-carrier), _ESC (extraction). The full default model, for example, writes carrierTempHPB_AC_ESC.txt.

File (before suffix)	Columns	Description
`avgEnergyElectrons` / `avgEnergyHoles`	`t <E>[eV]`	Mean carrier energy vs time
`phononOccupation`	`t N_LO [N_ac T_ac] [N_TO T_TO]`	LO occupation, plus acoustic (and Ridley TO) reservoir when enabled
`nrCarriers`	`t N_e N_h N_esc_e N_esc_h`	Surviving and extracted carrier counts
`carrierTemp`	`t T_MB_e T_MB_h T_FD_e μ_e T_FD_h μ_h`	Maxwell–Boltzmann and Fermi–Dirac carrier temperatures / chemical potentials

Reproducibility: particle moves run over OpenMP threads, each with its own RNG stream, so the seed and the thread count together define a trajectory. Pin OMP_NUM_THREADS and pass a nonzero --seed for repeatable runs.

Building and running tests

cd build
cmake .. -DVIENNAEMC_BUILD_TESTS=ON
make buildTests
ctest --output-on-failure

Installing as a library

To install the headers and CMake config files to a system or custom path:

cd build
cmake .. -DCMAKE_INSTALL_PREFIX=/path/to/install
make install

This copies:

Headers to <prefix>/include/ViennaEMC/
CMake package files to <prefix>/lib/cmake/ViennaEMC/

To uninstall:

make uninstall

Integrating into your own CMake project

After installing, add the following to your project's CMakeLists.txt:

find_package(ViennaEMC REQUIRED
             PATHS "/path/to/install/lib/cmake/ViennaEMC")

add_executable(myApp main.cpp)
target_include_directories(myApp PUBLIC ${VIENNAEMC_INCLUDE_DIRS})
target_link_libraries(myApp PRIVATE ${VIENNAEMC_LIBRARIES})

A minimal simulation program has this structure:

#include <emcDevice.hpp>
#include <ParticleType/emcElectron.hpp>
#include <ValleyTypes/emcNonParabolicIsotropValley.hpp>
#include <ScatterMechanisms/emcFroehlichInteraction.hpp>
// ... include your particle handler

int main() {
    // 1. Define material and device geometry
    emcMaterial<double> material(eps_r, mass_density, ni, v_sound, bandgap);
    emcDevice<double, 3> device{material, maxPos, spacing, tempK};
    device.addConstantDopingRegion({0,0,0}, maxPos, dopingDensity);

    // 2. Define carrier type, valley(s), and scatter mechanism(s)
    std::map<int, std::unique_ptr<emcParticleType<...>>> particleTypes;
    particleTypes[0] = std::make_unique<emcElectron<double, DeviceType>>(nrEnergies, maxEnergy);
    particleTypes[0]->addValley(std::make_unique<emcNonParabolicIsotropValley<double>>(
        relEffMass, constants::me, degFactor, alpha));
    particleTypes[0]->addScatterMechanism({0},
        std::make_unique<emcFroehlichEmission3D<double>>(
            0, phononEnergy, relEffMass, eps_hi, eps_lo, tempK, "myMaterial"));

    // 3. Create particle handler, generate particles, run loop
    MyParticleHandler handler(device, particleTypes, field, dt);
    handler.generateInitialParticles();
    for (SizeType step = 0; step < nrSteps; step++)
        handler.moveParticles(dt);
}

The examples/bulkSimulation/ example is the recommended starting point.

Plotting results

A Python helper package emcPlottingFiles is provided in helper/emcPlottingFiles/. Install it once:

cd helper
pip install emcPlottingFiles

Required Python packages (installed automatically): numpy, matplotlib, pandas, scipy.

Each example in examples/ contains a Python plotting script. Run it from the directory where the output .txt files were written:

cd build/examples/bulkSimulation
python3 ../../../examples/bulkSimulation/plotBulkResults.py

Generating documentation

The API documentation is generated with Doxygen:

cd docs/doxygen
./make_doxygen.sh
firefox html/index.html

Troubleshooting

ScalFMM build fails with missing Intel MKL include path

If CMake reports a path like /opt/intel/oneapi/compiler/2025.3/include does not exist, this is a mismatch between different oneAPI component versions. Two workarounds:

# Option A: create the missing directory
sudo mkdir -p /opt/intel/oneapi/compiler/2025.3/include

# Option B: remove the conflicting version from pkg-config search path
export PKG_CONFIG_PATH=$(echo $PKG_CONFIG_PATH | tr ':' '\n' \
    | grep -v '2025.3' | tr '\n' ':')
cmake ..

`cannot find -lscalfmm` linker error

This means the CMake config is passing a plain string scalfmm instead of the imported target scalfmm::scalfmm. Check that cmake/ViennaEMCConfig.cmake.in uses:

list(APPEND VIENNAEMC_LIBRARIES scalfmm::scalfmm)

Hot phonon bath: N_q does not change from N_0

This is almost always a sign that the phonon mode density Dph has Vsim in the denominator instead of the numerator. The correct formula in emcPhononBath.hpp is:

T Dph = q * q * dq * Vsim / (T(2) * constants::pi * constants::pi);

Dph should be a large number (order 10⁵ for a 100 nm box with dq = 2×10⁹ m⁻¹).

Very noisy N_q oscillations

This occurs when there are too few phonon modes per bin (small Dph), so each scatter event changes N_q by a large fraction. Solutions:

Use fewer, wider bins: reduce nrPhononBins and increase dq.
For the single-mode approximation, use nrPhononBins = 1 and dq = 2e9 (covers the full Fröhlich q-range).

Compilation errors: stray `@` or `*/` in scatter mechanism headers

C++ block comments are terminated by the first */. Symbols like m*/m_e inside /** … */ comments will prematurely close the comment block. Use m_star/m_e (ASCII only) in block comments. Similarly, avoid Unicode characters such as ε — use ASCII descriptions (eps_inf) instead.

Authors and license

Current maintainer: Lado Filipovic
Former contributors: Laura Gollner, Robin Steiner, Anna Benzer

This library was developed at the Institute for Microelectronics, TU Wien.

See file LICENSE in the base directory for the license terms.

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cmake		cmake
docs		docs
examples		examples
external/upstream		external/upstream
helper/emcPlottingFiles		helper/emcPlottingFiles
include		include
tests		tests
.gitignore		.gitignore
CMakeLists.txt		CMakeLists.txt
LICENSE		LICENSE
README.md		README.md
format-project.sh		format-project.sh

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ViennaEMC

Table of Contents

What it does

Library architecture

System requirements

Building

Step 1 — Clone and configure

Step 2 — Build dependencies

Step 3 — Build the examples

Step 4 — Run an example

Examples

Bulk Silicon

Bulk Silicon with FMM particle–particle interactions

Single-layer MoS₂

2D MOSFET

2D Resistor

Hot-Carrier Dynamics in Metal-Halide Perovskites

What it models

Running the example

Key command-line flags

Output files

Building and running tests

Installing as a library

Integrating into your own CMake project

Plotting results

Generating documentation

Troubleshooting

ScalFMM build fails with missing Intel MKL include path

cannot find -lscalfmm linker error

Hot phonon bath: N_q does not change from N_0

Very noisy N_q oscillations

Compilation errors: stray @ or */ in scatter mechanism headers

Authors and license

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`cannot find -lscalfmm` linker error

Compilation errors: stray `@` or `*/` in scatter mechanism headers

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