/Development of Band-to-Band Tunneling Modeling in Boltzmann Transport Equation

Development of Band-to-Band Tunneling Modeling in Boltzmann Transport Equation

Leuven | More than two weeks ago

Tunneling in ultra-scaled transistors – friend or enemy?

The semiconductor industry constantly grapples with challenges in scaling down field-effect-transistors (FETs) to improve performance and functionality. However, this endeavor is fraught with obstacles. Miniaturizing devices involves shorter channel lengths, thinner oxides, and metals, resulting in intensified electric fields. These intensified electric fields often trigger adverse effects like off-state junction leakage and gate-induced drain leakage.



Among these effects, band-to-band tunneling plays a crucial role (BTBT). BTBT can be considered as a detrimental phenomenon because it exacerbates impact ionization, thereby further complicating device behavior. Additionally, BTBT can contribute to device ageing mechanisms – such as hot-carrier degradation – and thus additionally limit transistor lifetime. On the other hand, recently a novel transistor architecture based on BTBT was proposed (steep-slope transistors) and reported to be very promising for further FET scaling.  To summarize, mitigating device degradation should rely on modeling how BTBT affects carrier and current density distributions within FETs. These modeling studies should also enable optimization of the steep-slope transistor architecture and hence help in further transistor scaling.


Hence, the aim of this master's thesis internship is to develop and validate a modeling framework for band-to-band tunneling. The developed BTBT model will be integrated into our carrier transport simulator ViennaSHE. The MS student will conduct a comprehensive literature review and mathematical derivation of mainstream band-to-band tunneling models followed by implementation of this phenomenon in the simulator ViennaSHE. This activity assumes collaboration with reliability and device modeling researchers, software developers, and device architecture designers, thereby making her/him part of imec team.


Type of work:

  • 50% literature review and mathematical derivation
  • 50% modeling work



  1. Kane, E. O. (1960). Zener tunneling in semiconductors. Journal of Physics and Chemistry of Solids12(2), 181-188.
  2. J. L. Moll, (1970). “Physics of semiconductors,” pp. 248–249, 3rd edition. 
  3. Liou, J. J. (1990). Modeling the tunnelling current in reverse-biased p/n junctions. Solid State Electronics33(7).
  4. Schenk, A. (1993). Rigorous theory and simplified model of the band-to-band tunneling in silicon. Solid-State Electronics36(1), 19-34.
  5. Jungemann, C., et. al., Stable discretization of the Boltzmann equation based on spherical harmonics, box integration, and a maximum entropy dissipation principle. Journal of applied physics100(2).
  6. Rupp, K. (2009). Numerical solution of the Boltzmann transport equation using spherical harmonics expansions (Doctoral dissertation).
  7. Rupp, K., et. al., (2010). Matrix compression for spherical harmonics expansions of the Boltzmann transport equation for semiconductors. Journal of Computational Physics229(23), 8750-8765.
  8. Hong, S. M., Pham, A. T., & Jungemann, C. (2011). Deterministic solvers for the Boltzmann transport equation. Springer Science & Business Media.
Development of band

Type of project: Thesis

Duration: 6-9 months

Required degree: Master of Science, Master of Engineering Science

Required background: Electrotechnics/Electrical Engineering, Nanoscience & Nanotechnology, Physics

Supervising scientist(s): For further information or for application, please contact: Ethan Kao (Ethan.Kao@imec.be) and Stanislav Tyaginov (Stanislav.Tyaginov@imec.be) and Michel Houssa (houssa@imec.be)

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