[paper] Model for Cryo-CMOS Subthreshold Swing

Arnout Beckers, Jakob Michl, Alexander Grill, Member IEEE; Ben Kaczer, Marie Garcia Bardon, Bertrand Parvais, Bogdan Govoreanu, Kristiaan De Greve, Gaspard Hiblot, 

and Geert Hellings, Senior Member IEEE

Physics-Based and Closed-Form Model for Cryo-CMOS Subthreshold Swing

in IEEE Transactions on Nanotechnology, vol. 22, pp. 590-596, 2023,

DOI 10.1109/TNANO.2023.3314811.

IMEC, Leuven (B)

Institute for Microelectronics, TU Vienna (A)

Vrije Universiteit Brussel (B)

KU Leuven (B)

Abstract: Cryogenic semiconductor device models are essential in designing control systems for quantum devices and in benchmarking the benefits of cryogenic cooling for high-performance computing. In particular, the saturation of subthreshold swing due to band tails is an important phenomenon to include in low-temperature analytical MOSFET models, as it predicts theoretical lower bounds on the leakage power and supply voltage in tailored cryogenic CMOS technologies with tuned threshold voltages. Previous physics-based modeling required to evaluate functions with no closed-form solutions, defeating the purpose of fast and efficient model evaluation. Thus far, only the empirically proposed expressions are in closed form. This article bridges this gap by deriving a physics-based and closed-form model for the full saturating trend of the subthreshold swing from room down to low temperature. The proposed model is compared against experimental data taken on some long and short devices from a commercial 28-nm bulk CMOS technology down to 4.2 K.

FIG: (a) TEM picture of a mature imec technology node. (b) Electrostatic potential fluctuations near the channel/oxide interface. (c) Gaussian distributed depths of the potential wells. (d) Including the binding energy in the wells in the quantum picture gives a Laplace distribution of P(Eb). (e-f) Convolution (*) of P(Eb) with the sharp-edged 2-D DOS leads to a logistic/Fermi-like DOS function with an exponential tail.

[Purdue e-Pubs] A physics-based compact model for thermoelectric devices

A physics-based compact model for thermoelectric devices

Kyle Conrad, Purdue University; Mark S. Lundstrom, Purdue University (Advisor)

Abstract: Thermoelectric devices have a wide variety of potential applications including as coolers, temperature regulators, power generators, and energy harvesters. During the past decade or so, new thermoelectric materials have been an active area of research. As a result, several new high figure of merit (zT) materials have been identified, but practical devices using these new materials have not yet been reported. A physics-based compact model could be used to simulate a thermoelectric devices within a full system using SPICE-compatible circuit simulators. If such a model accepts measured or simulated material parameters, it would be useful in exploring the system level applications of new materials. In this thesis, the ground work for such a compact model is developed and tested. I begin with a discussion of thermoelectric transport theory within the Landauer formalism. The Landauer formalism is used as the basis of the tool LanTraP, which uses full band descriptions to calculate the distribution of modes and thermoelectric transport parameters, which can serve as the input to a compact model. Next, an equivalent circuit model is presented, explained, and tested using a simple Bi2Te 3 thermoelectric leg. The equivalent circuit is shown to perform well under a variety of DC, transient, and AC small signal operating conditions. With the equivalent circuit it is easy to determine the maximum cold side temperature drop, the maximum cold side heat absorbed, the temperature profile within the leg, the temperature response to a pulsed current, and impedance over a range of frequencies. Finally, Sentaurus®, a computer program that solves the thermoelectric transport equations numerically, is used to compare and benchmark some of the results of the equivalent circuit when considering Si as the thermoelectric material. The equivalent circuit and Sentaurus® simulations produce similar results in DC and transient cases, but in the AC small signal case the two simulations produce slight differences. The results of this work establishes a baseline compact model for thermoelectric devices whose accuracy and capabilities can be extended.

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