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Energy efficiency in digital circuits is limited by the subthreshold swing (SS), which defines how abruptly a transistor switches between its ON and OFF-states. The SS is particularly important for circuits targeting minimum-energy computation which operate in the subthreshold region between the ON and OFF-states of the transistor. The SS of MOSFET devices is fundamentally limited by thermionic emission, which has inspired a search for new devices whose SS can reach below the Boltzmann thermal limit. Tunnel field-effect transistors (TFETs) have emerged as a post-CMOS candidate with low (steep) SS and have been investigated using an evolving selection of geometries and materials that yield continuously improving device performance and circuit performance estimates. To unify previous works and guide future TFET iterations, this article provides a comprehensive theory on minimum-energy operation in the subthreshold region for steep-SS devices. We show that the optimal supply voltage for energy minimization and minimum obtainable energy are both proportional to the SS, and that a fundamental limit exists for the required $I_{\mathrm{\scriptstyle {ON}}}/I_{\mathrm{\scriptstyle {OFF}}}$ to achieve operation at the minimum-energy point. We explore how device knobs affect the optimization space for minimum-energy operation, and analyze how common TFET nonidealities affect the potential for minimum-energy operation.

Not all computing problems are created equal. The inherent complexity of processing certain classes of problems using digital computers has inspired the exploration of alternate computing paradigms. Coupled oscillators exhibiting rich spatio-temporal dynamics have been proposed for solving hard optimization problems. However, the physical implementation of such systems has been constrained to small prototypes. Consequently, the computational properties of this paradigm remain inadequately explored. Here, we demonstrate an integrated circuit of thirty oscillators with highly reconfigurable coupling to compute optimal/near-optimal solutions to the archetypally hard Maximum Independent Set problem with over 90% accuracy. This platform uniquely enables us to characterize the dynamical and computational properties of this hardware approach. We show that the Maximum Independent Set is more challenging to compute in sparser graphs than in denser ones. Finally, using simulations we evaluate the scalability of the proposed approach. Our work marks an important step towards enabling application-specific analog computing platforms to solve computationally hard problems., Designing efficient analog dynamical systems for solving hard optimization problems remains a challenge. Here, the authors demonstrate a dynamical system of thirty oscillators with reconfigurable coupling to compute optimal/near-optimal solutions to the hard Maximum Independent Set problem with over 90% accuracy.

We present a quasi-analytical model for Tunnel Field Effect Transistors (TFETs) that includes the microscopic physics and chemistry of interfaces and non-idealities. The ballistic band-to-band tunneling current is calculated by modifying the well known Simmons equation for oxide tunneling, where we integrate the Wentzel-Kramers-Brillouin tunneling current over the transverse modes. We extend the Simmons equation to finite temperature and non-rectangular barriers using a two-band model for the channel material and an analytical channel potential profile obtained from Poisson’s equation. The two-band model is parametrized first principles by calibrating with hybrid Density Functional Theory calculations and extended to random alloys with a band unfolding technique. Our quasi-analytical model shows quantitative agreement with ballistic quantum transport calculations. On top of the ballistic tunnel current, we incorporate higher order processes arising at junctions coupling the bands, specifically interface trap assisted tunneling and Auger generation processes. Our results suggest that both processes significantly impact the off-state characteristics of the TFETs—Auger, in particular, being present even for perfect interfaces. We show that our microscopic model can be used to quantify the TFET performance on the atomistic interface quality. Finally, we use our simulations to quantify circuit level metrics such as energy consumption.We present a quasi-analytical model for Tunnel Field Effect Transistors (TFETs) that includes the microscopic physics and chemistry of interfaces and non-idealities. The ballistic band-to-band tunneling current is calculated by modifying the well known Simmons equation for oxide tunneling, where we integrate the Wentzel-Kramers-Brillouin tunneling current over the transverse modes. We extend the Simmons equation to finite temperature and non-rectangular barriers using a two-band model for the channel material and an analytical channel potential profile obtained from Poisson’s equation. The two-band model is parametrized first principles by calibrating with hybrid Density Functional Theory calculations and extended to random alloys with a band unfolding technique. Our quasi-analytical model shows quantitative agreement with ballistic quantum transport calculations. On top of the ballistic tunnel current, we incorporate higher order processes arising at junctions coupling the bands, specifically interface t...