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Ballisticity of the Linear response Transport in Nanometric Silicon Devices

This study investigates the ballistic transport phenomena in 40nm N+NN+ silicon structures, highlighting the limitations of conventional macroscopic models under strong nonequilibrium conditions. Utilizing Boltzmann and Poisson equations, we employ a deterministic numerical solver based on nth-order spherical harmonics expansion to analyze the transport characteristics. Results show significant ballistic transport at high biases, evidenced by velocity overshoot and unique distribution functions. Our findings reveal that linear response behavior in nanometric devices differs fundamentally from bulk materials and can exhibit negative ballistic peaks.

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Ballisticity of the Linear response Transport in Nanometric Silicon Devices

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  1. EIT4 Ballisticity of the Linear response Transport in Nanometric Silicon Devices C. Jungemann Institute for Electronics Bundeswehr UniversityNeubiberg, Germany

  2. Outline • Introduction • Theory • Results for 40nm N+NN+ structure • High bias • Zero bias • Conclusions

  3. Introduction

  4. Introduction 1D 40nm N+NN+ structure • Macroscopic models (DD, HD) fail for strong nonequilibrium due toBallistic transport! • Macroscopic models also fail near equilibrium in nanometric devices!Why?

  5. Theory

  6. Theory • Boltzmann and Poisson equations • Deterministic solver based on an nth-order Spherical harmonics expansion • Newton-Raphson method to solve the nonlinear system of equations • Modena electron model (analytical band structure)

  7. Theory

  8. Results 1D 40nm silicon N+NN+ structure Transport is in x-direction

  9. Results Biased at 0.5V Velocity overshoot is a sign of (quasi-)ballistic transport

  10. Results Scattering dominated Biased at 0.5V Quasi-ballistic

  11. Results Distribution function at 0.5V

  12. Results Distribution function at 0.5V

  13. Results Scattering dominated Linear response without zero order Quasi-ballistic

  14. Results Differential distribution function at equilibrium

  15. Conclusions

  16. Conclusions • Ballistic transport occurs in nanometric devices at high bias • The linear response of the distribution function shows ballistic peaks at zero bias in regions with large built-in fields • The ballistic peaks of the linear response can be negative • Linear response in nanometric devices with large built-in fields is fundamentally different from the bulk case

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