3D Monte-Carlo device simulations using an effective quantum potential including electron-electron interactions


Effective quantum potentials describe the physics of quantum-mechanical electron transport in semiconductors more than the classical Coulomb potential. An effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. The effective quantum potential was used in a three-dimensional Monte-Carlo device simulator for calculating the electron-electron and electron-barrier interactions. Simulation results for an SOI transistor are presented and illustrate how the effective quantum potential changes the characteristics compared to the classical potential.

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  1. Gasser, I., Jüngel, A.: The quantum hydrodynamic model for semiconductors in thermal equilibrium. Z. Angew. Math. Phys. 48, 45 (1997)

    MATH  Article  MathSciNet  Google Scholar 

  2. Gardner, C., Ringhofer, C.: Smooth quantum potential for the hydrodynamic model. Phys. Rev. E53, 157 (1996)

    Google Scholar 

  3. Ringhofer, C., et al.: Effective potentials and quantum fluid models: a thermodynamic approach. Int. J. High Speed Elect. Sys. 13(3), 771 (2003).

    Article  MathSciNet  Google Scholar 

  4. Ahmed, S., et al.: Quantum potential approach to modeling nanoscale MOSFETs. J. Comp. Elect. 4(1–2), 57 (2005)

    Article  Google Scholar 

  5. Vasileska, D., et al.: Quantum and Coulomb effects in nanodevices. Int. J. Nanosci. 4(3), 305 (2005)

    Article  Google Scholar 

  6. Ferry, D.: The onset of quantization in ultra-submicron semiconductor devices. Superlatt. Microstruct. 27, 61 (2000)

    Article  Google Scholar 

  7. Ferry, D., Grubin, H.: Modelling of quantum transport in semiconductor devices. Solid State Phys. 49, 283 (1995)

    Article  Google Scholar 

  8. Iafrate, G., et al.: Utilization of quantum distribution functions for ultra-submicron device transport. J. de Physique 42(Colloque C7), 307 (1981)

    Google Scholar 

  9. Wyatt, R.: Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths. Chem. Phys. Lett. 313, 189 (1999)

    Google Scholar 

  10. Wyatt, R.: Quantum wave packet dynamics with trajectories: application to reactive scattering. J. Chem. Phys. 111, 4406 (1999)

    Article  Google Scholar 

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Correspondence to Clemens Heitzinger.

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Heitzinger, C., Ringhofer, C., Ahmed, S. et al. 3D Monte-Carlo device simulations using an effective quantum potential including electron-electron interactions. J Comput Electron 6, 15–18 (2007). https://doi.org/10.1007/s10825-006-0058-x

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  • Monte-Carlo simulation
  • Effective quantum potential
  • Electron-electron interactions