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VSP – Vienna Schrödinger Poisson

Fig.1a: Energy well in the inversion layer of a FinFET (3D)
Fig.1a: Energy well in the inversion layer of a FinFET (3D)
Fig.1b: Electron concentration in the inversion layer of a FinFET (3D)
Fig.1b: Electron concentration in the inversion layer of a FinFET (3D)
Fig.2: Wavefunction of a circular nanowire cross-section
Fig.2: Wavefunction of a circular nanowire cross-section
Fig.3: Strain effect
Fig.3: S/P electron concentration and dispersion relation for axial stress
Fig.4: Electron energy spectrum of a RTD
Fig.4: Electron energy spectrum of a RTD
Fig.5: Nano-MOSFET simulated using the 2D NEGF model
Fig.5: Energetically resolved carrier density spectrum of a fully-depleted SOI MOS FET
Fig.6: k-space plots of carrier distribution response (pMOS)
Fig.7: Conductivity of NMOS FinFET channel [Z. Stanojevic, IEDM 2013]
Fig.8: Effective field [S.Takagi, IEEE TED 1994]

Cutting-Edge Quantum-Electronic Simulator

The First Physics-Based Commercial Solver for FinFETs and Nanowires

VSP is a general-purpose device simulator for arbitrary nano-structures, operating on the Schrödinger-Poisson equation system. The simulator includes quantum mechanical solvers for closed-boundary as well as open-boundary problems; VSP is the first commercial solver to simulate quantum effects by true physical models, virtually free of empiric parameters.

Available Physical Models

The closed boundary model setup allows to calculate a self-consistent carrier concentration/distribution in FinFETs or nanowire cross-sections including confinement/quantization effects. The equations systems are solved on tetrahedral and triangular meshes for arbitrary two- and three-dimensional geometries, respectively (see Fig.1 a,b and Fig.2). The Schrödinger solver supports effective mass (EFM) or k⋅p Hamiltonians (including arbitrary strain distribution conditions tensor) (see Fig.3). The model accounts for arbitrary substrate types and channel orientation.

Upcoming Device Types

Hetero-structured semiconductor devices, like resonant tunneling diodes (RTD) and quantum cascade lasers (QCL) can be treated within the closed boundary model for quick estimation of resonant energy levels (Fig.4). The open boundary model allows evaluation of current-voltage characteristics. Using the two-dimensional non-equilibrium Green's functions solver, nano-MOSFETs in the ballistic operation regime can be investigated, as shown in Fig.5.

Integrated Solvers

Closed-boundary (CB) Schrödinger Solver

  • Arbitrary 1D/2D/3D geometries by using unstructured meshes
  • Substrate and channel orientation
  • Multi-band effective mass (EFM) Hamiltonian
  • k⋅p Hamiltonian including strain effect
  • Calculate sub-band ladder (eigen-energies) and wave-functions (incl. overlaps)

Open-boundary (OB) Schrödinger Solver

  • Based on non-equilibrium Green's functions formalisms
  • Multi-band effective mass (EFM) Hamiltonian
  • 1D/2D structured meshes (rectangular)
  • Ballistic and dissipative transport
  • Current voltage characteristic with resonant tunneling states

Kubo-Greenwood Solver

  • Accurate low-field mobility from BTE
  • Including ADP, IVS, IIS, and SRS
  • Novel SRS model

Software Development Kit (SDK)

Details and Example Application

For details about the concept, please refer to Schrödinger-Poisson Simulation of FinFETs.
To take a look on application, see Schrödinger Poisson, demonstrating simulation of nanowires using VSP.

Applications and Benefits

Use VSP to systematically engineer channel transport properties, and boost device performance

  • Quantum mechanical solver for accurate simulation of nano-structures
  • Dimensions: 0D (bulk), 1D (film), 2D (wire), 3D (dot)
  • Accurate simulation of upcoming CMOS technologies
    • FinFETs and nanowire (NW) cross-sections
    • Quantization and tunneling effects
    • Gate leakage calculation
  • Heterostructure semiconductor devices
    • Resonant tunneling devices
    • Quantum-dot (QD) and quantum cascade lasers (QCLs)

General Features

  • N×N up to second-order bipolar k·p band structure
  • Unstructured 3D mesh r-grid / k-grid
  • E and k-based Kubo Greenwood integration
  • Scattering processes: phonons, impurities, surface roughness
  • Linearized Boltzmann transport (Kubo-Greenwood formalism)
  • Ballistic (QTBM) and dissipative carrier transport
  • Novel gate stacks
  • New channel materials: strained Si, Ge, SiGe, InGaAs
  • Extensive and extensible material database

Integrated in GTS Framework

  • Intuitive and versatile graphical user interface
  • Comprehensive scripting interface
  • Available for Windows and Linux platforms