Cutting-Edge Quantum-Electronic Simulator

Icon: GTS Vienna Schrödinger-Poisson solver (VSP)

GTS VSP (Vienna Schrödinger-Poisson) is a general-purpose quantum 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 using physical models based on material properties, rather than relying on empirical models and parameters.

The closed boundary model setup allows to calculate the quantum states or subbands as well as the self-consistent carrier concentration in FinFETs or nanowire cross-sections including confinement effects. The Schrödinger-Poisson system is solved on arbitrary one, two and three-dimensional geometries using tetrahedral and triangular meshes. The Schrödinger solver supports effective mass (EM) and k⋅p Hamiltonians that respond to arbitrary stress/strain distributions in the device. The Hamiltonians are automatically rotated to account for arbitrary substrate and channel orientations.

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. The open boundary model allows evaluation of current-voltage characteristics. Using the one, two, and three-dimensional non-equilibrium Green’s functions solver, nano-MOSFETs in the ballistic operation regime can be investigated.


  1. Systematically engineer channel transport properties, and boost device performance.
  2. Accurate simulation of emerging CMOS technologies, path finding beyond CMOS.
  3. Simulate hetero-structure semiconductor devices including quantum effects.
  4. Evaluate new materials.

When channel length or cross-section dimensions approach the free electron wavelength charge carriers become geometrically confined. This strongly affects device physics, such as electrostatic properties and carrier transport; for accurate modeling, it is vital to account for this behavior. GTS VSP can simulate such devices and thus be used to optimize the structure to obtain a desired performance.

In nanometer-scale device or devices with semiconductor hetero-interfaces, quantum wells, quantum wires, and quantum dots can be formed. Corresponding quantum confinement and transport effects arise (e.g. subbands, resonances, jumps), which can only be fully understood and quantitatively explored by using a full Schrödinger solver. GTS VSP can simulate such structures and deliver insights into their internal properties.

New materials can have different and unexpected properties at the macroscopic scale (e.g. terminal characteristics, optical properties). With its customizable material database and its robust solvers VSP is able to predict such material properties in a variety of applications.


Closed-Boundary (CB) Schrödinger Solver

  • Arbitrary 1D/2D/3D geometries by using unstructured meshes
  • Substrate and channel orientation
  • Multi-valley single-band effective mass (EM) Hamiltonian
  • k·p Hamiltonian with arbitrary number of bands
  • Lattice stress/strain effect on band structure automatically included
  • Calculate subband ladder (eigen-energies) and wave-functions

Open-Boundary (OB) Schrödinger Solver

  • Based on non-equilibrium Green’s functions formalism
  • Multi-valley single-band effective mass (EM) Hamiltonian
  • Ballistic transport
  • Current voltage characteristic with resonant tunneling states

Mobility calculation on cross-sections

  • Physical modeling for conductivity and mobility
  • Based on linearized Boltzmann transport equation (BTE)
    – beyond Kubo-Greenwood formula
  • Includes crystal orientation and strain effects
  • Anisotropic band-structure
  • Surface roughness scattering (SRS)
  • Acoustic, optical, and inter-valley phonon scattering (ADP, ODP, IVS)
  • Polar-optical and remote phonon scattering (POP)
  • Local and remote Coulomb scattering including dopants, traps, charges both in bulk and on interfaces
  • Alloy disorder scattering (ADS)



K-space plot
k-space plots of carrier distribution response (pMOS)
  • User-defined N×N unipolar/bipolar k·p band structure models up to second-order in k
  • Structured or unstructured 3D meshes for real-space and k-space
  • Smart and efficient solution of Boltzmann transport equation (BTE) in r-, k- and energy-space
  • Novel gate stacks with remote charges and traps
  • Support for wide range of channel materials: Si, strained Si, Ge, SiGe, GaAs, InGaAs, and others
  • Extensive and extensible material database


  • Integration in the GTS Framework
  • Intuitive and versatile graphical user interface
  • Fastest solvers for linear, nonlinear and eigenvalue problems in the industry
  • Comprehensive scripting interface
  • Efficient multi-core simulation support

Software Development Kit (SDK)

  • Create one’s own VSP models
  • Multi-dimensional implementation

Future-Proof Device Designs with Real Physics

With ever-smaller device features, considering quantum effects is vital for avoiding design risk and understanding device physics. In contrast to empirical descriptions used in most available tools, GTS VSP provides a physical description and insight relying on well-known material properties. GTS VSP is the first commercially available tool capable of accurate simulation of real-world 2D/3D device geometries on a triangular / tetrahedral mesh using a k⋅p Schrödinger Poisson Hamiltonian, including strain effects.

GTS VSP enables you to explore, understand and specifically address quantum-effects in recent and future devices, significantly improving efficiency in the design process.

Want to learn more?

Please check the examples, tutorials, publications and further information in the Related column.
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