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

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

3 Introduction

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

5 Theory

6 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 Biased at 0.5V Quasi-ballistic Scattering dominated

11 Results Distribution function at 0.5V

12 Results Distribution function at 0.5V

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

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