List of Figures

• 4.1. Resulting current density from the double grid discretization featuring distinct solution curves from the odd and the even grid points.
• 4.2. Unphysical oscillations in the equilibrium electron density.
• 4.3. Relative error (ratio) of the closure for bulk and for the $L_{{c}} =100$nm device. Error from cumulant closure increases with high bias. Best fit for $c = 2.7$.
• 4.4. Comparison of the average velocity obtained from the SM and ET models with the self-consistent Monte Carlo simulation for the $L_{{c}} =100$nm device.
• 4.5. Comparison of the kurtosis obtained from the SM and ET models with the self-consistent Monte Carlo simulation for the $L_{{c}} =100$nm device.
• 4.6. Comparison of the device currents obtained from the SM and ET models with the self-consistent Monte Carlo simulation for varying channel length.
• 5.1. Conduction band edge of the RTD for different voltages. A linear voltage drop is assumed over a distance of 40 nm.
• 5.2. Influence of phonon scattering on the I/V characteristics of an RTD
• 7.1. The self-consistent potential entering the Schrödinger equation is obtained as a sum from the solution of the Poisson equation and the offset from the bandgap.
• 8.1. Wigner distribution function. Density is very low in large parts of the simulation domain.
• 9.1. Pair generation rate $\gamma (x)$ caused by the Wigner potential for two different voltages
• 9.2. The trajectory split algorithm: At each scattering event the weight of the trajectory is multiplied by 3 and a particle-antiparticle pair is generated.
• 10.1. I-V curve comparing Wigner and von Neumann simulation
• 10.2. Wigner simulation: Comparing ``naive'' and ``correct'' formula for current density at maximum bias
• 10.3. Comparing carrier density from Wigner and von Neumann simulation
• 10.4. Effect of the coherence length in Wigner simulations
• 10.5. Spikes in the transmitted current density resulting from sharp resonances