Theory — Finite elements

On this page, we present the fundamental finite-element-method-based theoretical models that underpin QTCAD for semiconductor quantum devices.

In Section 1 to Section 9, we describe the mathematical models defining each solver in the device simulator, along with physical quantities that can be calculated using these solvers.

In Section 10 and Section 11, we consider the theoretical concepts that underlie the transport simulator.

Additionally in Section 12, we describe the theory behind the qubit simulator.

Finally in Section 13, we provide a list of the available materials in QTCAD.

• 1. Poisson solvers
• 2. Band alignment in heterostructures
• 3. Schrödinger solvers
• 4. Operators
• 5. Multivalley effective-mass theory solver
• 6. Lever arm theory
• 7. Schrödinger–Poisson solver
• 8. Many-body solver
• 9. Exchange interaction theory
• 10. Transport in the Coulomb blockade regime
• 11. The nonequilibrium Green’s function (NEGF) formalism
• 12. Quantum control
• 13. Material list