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4 - Extending CMOS with negative capacitance
- from Section I - CMOS circuits and technology limits
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- By Asif Islam Khan, University of California, Berkeley, Sayeef Salahuddin, University of California, Berkeley
- Edited by Tsu-Jae King Liu, University of California, Berkeley, Kelin Kuhn, Cornell University, New York
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- Book:
- CMOS and Beyond
- Published online:
- 05 February 2015
- Print publication:
- 05 February 2015, pp 56-76
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Summary
Introduction
It is now well recognized that energy dissipation in microchips may ultimately restrict device scaling – the downsizing of physical dimensions that has fueled the fantastic growth of the microchip industry so far [1–6]. But there is a fundamental limit to the dissipation that can be achieved in the transistors that are at the heart of almost all electronic devices. Conventional transistors are thermally activated. A barrier is created that blocks the current and then the barrier height is modulated to control the current flow. This modulation of the barrier changes the number of electrons following the exponential Boltzmann factor, exp(qV / kT). This, in turn, means that a voltage of at least 2.3kT / q (which translates to 60 mV at room temperature) is necessary to change the current by an order of magnitude. In practice, a voltage many times this limit of 60 mV has to be applied to obtain a good ratio of on- and off-currents. As a result, it is not possible to reduce the supply voltage in conventional transistors below a certain point, while still maintaining the healthy on/off ratio that is necessary for robust operation. On the other hand, continuous downscaling is putting an ever larger number of devices in the same area, thereby increasing the energy dissipation density beyond controllable and sustainable limits. This situation is often called Boltzmann’s Tyranny [2], and it has been predicted that unless new principles can be found based on fundamentally new physics, then transistors will die a thermal death [4].
Numerical study of rotational diffusion in sheared semidilute fibre suspension
- Asif Salahuddin, Jingshu Wu, C. K. Aidun
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- Journal:
- Journal of Fluid Mechanics / Volume 692 / 10 February 2012
- Published online by Cambridge University Press:
- 21 December 2011, pp. 153-182
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Fibre-level computer simulation is carried out to study the rotational diffusion and structural evolution of semidilute suspensions of non-Brownian, rigid-rod-like fibres under shear flow in a Newtonian fluid. The analyses use a hybrid approach where the lattice-Boltzmann method is coupled with the external boundary force method. The probability distribution of the orbit constant, , in the semidilute regime is predicted with this method. The paper emphasizes assessment of the characteristics of a rotary diffusion model – anisotropic in nature (Koch, Phys. Fluids, vol. 7, 1995, pp. 2086–2088) – when used in suspensions with fibres of different aspect ratios (ranging from to ) and with different volume concentrations (ranging from to ). A measure of the scalar Folgar–Tucker constant, , is extracted from the anisotropic diffusivity tensor, . The scalar is mostly in the semidilute regime and compares very well with the experimental observations of Stover (PhD thesis, School of Chemical Engineering, Cornell University, 1991) and Stover, Koch & Cohen (J. Fluid Mech., vol. 238, 1992, pp. 277–296). The values provide substantial numerical evidence that the range of (0.0038–0.0165) obtained by Folgar & Tucker (J. Rein. Plast. Compos., vol. 3, 1984, pp. 98–119) in the semidilute regime is actually overly diffusive. The paper also branches out to incorporate anisotropic diffusion (through the use of the Koch model) in the second-order evolution equation for (a second-order orientation tensor). The solution of the evolution equation with the Koch model demonstrates unphysical behaviour at low concentrations. The most plausible explanation for this behaviour is error in the closure approximation; and the use of the Koch model in a spherical harmonics-based method (Montgomery-Smith, Jack & Smith, Compos. A: Appl. Sci. Manuf., vol. 41, 2010, pp. 827–835) to solve for the orientation moments corroborates this claim.