Noise Analysis in Silicon Devices Using 1D and 2D Monte Carlo Simulation Employing the Ramo–Shockley Theorem
Open Access Depositedwhile both yield consistent spectral estimates, the direct autocovariance method reveals the time-domain correlation structure of the noise, which is not accessible through the Welch method alone. Temperature and bias-voltage sweeps performed on the GWU Pegasus high-performance computing cluster validate the framework across operating conditions, recovering the expected injection trends, recombination dynamics, and the transition from thermal-noise-dominated to shot-noise-dominated behavior.
as carriers scatter at random times and in random directions, the terminal current fluctuates around its mean value. Analytical noise models such as the Johnson-Nyquist thermal noise relation and the Schottky shot noise relation describe the average behavior of these fluctuations, but rely on simplifying assumptions that break down in nanoscale devices where electric fields are non-uniform, and carriers are away from equilibrium.A self-consistent ensemble Monte Carlo simulation framework for noise analysis in silicon devices is developed. The framework combines a Monte Carlo transport engine, including acoustic phonon, optical phonon, and ionized-impurity scattering, with a Poisson solver for self-consistent electrostatics and the Ramo-Shockley theorem for instantaneous terminal current extraction. In this methodology, noise is not imposed through external models
The motion of charge carriers in semiconductor devices is fundamentally stochastic. Electrons accelerate under the local electric field, scatter from lattice vibrations and ionized impurities, and follow unpredictable trajectories. This randomness is the origin of electrical noise
rather, it arises directly from the stochastic motion of the carriers. The framework is validated progressively, beginning with bulk silicon transport and extending to resistor structures and p-n diodes in one-dimensional and two-dimensional nanoscale and microscale device configurations. The simulated noise approaches the thermal-noise limit in the resistor and the shot-noise limit in the forward-biased p-n diode. With the inclusion of Shockley-Read-Hall recombination, the framework also captures generation-recombination noise with the expected spectral characteristics. A direct autocovariance-based noise analysis method is introduced alongside the Welch periodogram approach
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