Overview
This project simulates Resonant Tunneling Diodes (RTDs) — nanoscale quantum devices that exploit the wave nature of electrons. Unlike classical electronic components where electrons move as particles over barriers, in RTDs electrons behave as waves that tunnel through potential barriers. When the electron energy aligns with a resonant state trapped between two barriers, transmission probability spikes electrons pass through efficiently. Shift the alignment, and current drops despite increasing voltage.
This phenomenon Negative Differential Resistance (NDR) — makes RTDs uniquely useful for ultra-high-frequency oscillators, multi-valued logic, and terahertz electronics.
Full Paper (PDF) · ResearchGate Preprint
Physics
The Quantum Double-Barrier Structure
Two thin barriers (typically AlGaAs) sandwich a quantum well (GaAs). The well traps quasi-bound states at discrete energies $E_n = n^2\pi^2\hbar^2 / 2m^*w^2$, where $w$ is the well width. When incoming electrons from the source contact have energy matching a quasi-bound state, transmission peaks sharply.
Negative Differential Resistance
The hallmark of RTDs:
- Low bias: resonant level aligns with the Fermi sea → high current
- Peak bias: maximum alignment → peak current
- Valley: level shifts out of alignment → current drops despite higher voltage
This I-V characteristic is purely quantum mechanical — no classical model predicts it.
The NEGF Formalism
The simulator implements the Non-Equilibrium Green’s Function method — the rigorous quantum mechanical framework for calculating electron transport in open systems connected to reservoirs (contacts).
Key components:
- Retarded Green’s Function: $G^R(E) = [(E+i\eta)I - H - \Sigma_L - \Sigma_R]^{-1}$
- Self-Energies $\Sigma_{L,R}$: encode the effect of semi-infinite contacts on the finite device region
- Transmission: $T(E) = \text{Tr}[\Gamma_L G^R \Gamma_R G^A]$ (Landauer-Büttiker formula)
- Current: $I = \frac{2e}{h}\int T(E)[f_L(E) - f_R(E)]dE$
The implementation uses sparse linear algebra for efficiency, discretizing the Hamiltonian on a finite-difference grid with tight-binding coupling.
Computed Quantities
| Output | Description |
|---|---|
| Transmission spectrum $T(E)$ | Energy-resolved tunneling probability |
| I-V characteristics | Current vs. bias showing NDR peak |
| Local Density of States | Spatial map of electron density at each energy |
| Resonance widths | Linewidths of quasi-bound states |
Theoretical Foundation
This work builds on a prior study: “Numerically Solving the Time-Dependent Schrödinger Equation: Analysis of Unitarity, Stability, and Real-Time GPU Implementation” (ResearchGate), which explored wavepacket dynamics and split-operator methods. The RTD simulator extends that foundation from time-dependent dynamics to steady-state quantum transport with open boundary conditions.