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One major concern of channel engineering in nanotransistors is the coupling of the conduction channel to the source/drain contacts. In a number of previous publications, we have developed a semiempirical quantum model in quantitative agreement with three series of experimental transistors. On the basis of this model, an overlap parameter 0≤C≤1 can be defined as a criterion for the quality of the contact-to-channel coupling: A high level of C means good matching between the wave functions in the source/drain and in the conduction channel associated with a low contact-to-channel reflection. We show that a high level of C leads to a high saturation current in the ON-state and a large slope of the transfer characteristic in the OFF-state. Furthermore, relevant for future device miniaturization, we analyze the contribution of the tunneling current to the total drain current. It is seen for a device with a gate length of 26 nm that for all gate voltages, the share of the tunneling current becomes small for small drain voltages. With increasing drain voltage, the contribution of the tunneling current grows considerably showing Fowler–Nordheim oscillations. In the ON-state, the classically allowed current remains dominant for large drain voltages. In the OFF-state, the tunneling current becomes dominant.
In a series of recent papers we have established a semiempirical model for quantum transport in a nanotransistor. Here we apply this model to characterize four industrial transistors with gate lengths ranging between 22 nm and 30 nm finding excellent quantitative agreement between theory and experiment. Adjusting our semiempirical model to the experimental output traces, three calibration parameters are found: First, the height of the source–drain barrier, second, the device temperature, and, third, the overlap parameter. The overlap parameter describes the wave function overlap between the source/drain contact and the conduction channel. With the aid of the calibration parameters the considered devices can be classified in three groups: A first group (G1) with good contact-channel coupling and a high saturation current, a second group (G2) with intermediate values and a third group (G3) with poor contact-channel coupling and a small saturation current. We calculate the gate capacitance of the transistors: At threshold voltage a peak of the gate capacitance is observed which is associated with a jump in the overlap parameter. This finding is most pronounced in G1, weaker in G2 and absent in G3. We attribute it to favorable screening conditions in G1 leading to a smooth transition between the contacts and the conduction channel. Our results indicate that this screening effect is favored by an efficient release of the Ohmic heat.
Quantized thermal Conductance via Phononic heat transport in nanoscale devices at low temperatures
(2014)
We study phononic heat transport in nanoscale devices. In the nonequilibrium Green's function formalism, an analytical small-frequency expansion of the phonon current transmission is derived for an arbitrary oscillator chain with typical contact-device-contact structure. Applying this expansion in a Landauer formula, it is possible to construct a systematic low-temperature expansion of the thermal conductance. It follows that quantized thermal conductance occurs as a plateau of the thermal conductance divided by the temperature within second order of the temperature expansion for completely heterogeneous systems as long as the product of force constant and oscillator mass is identical in both contacts, independent of the scattering area. Beyond this plateau, the higher-order terms of the low-temperature expansion yield a finite-temperature correction exhibiting the form of a cubic power law depending on the details of the scattering area. These findings are in agreement with experiments and numerical calculations. Our general results are applied to a double junction chain, where we find as the first phenomenon beyond our low-temperature expansion a second plateau. This plateau is associated with a thermal phase averaging of the phonon transmission, which leads for increasing temperatures to an independence of the thermal conductance from the device length.
We consider a thermal model for an integrated circuit including its chip environment. As the simplest choice, the
active device layer (integrated circuit) consists of an array of replicas of the same quantum device with the same
time depended average temperature. Modeling the chip
environment we assume this active layer is sandwiched
between two coplanar heat reservoirs. The top heat reservoir represents the wiring layer of the chip (‘back-end of line’). Its temperature is predominantly determined by the dissipated Joule heat in the wiring, typically in the order of one hundred degrees of Celsius.
The bottom reservoir represents the cooling unit at about
room-temperature. We solve the coupled equations describing
thermal transport between the active layer and
surrounding heat reservoirs and electrical transport in the
quantum devices. The stationary working temperatures of the considered quantum devices can be found from a fix-point problem. A proper linearization of the complete
time-depended problem yields the stability of these fixpoints. Numerical solutions for a device layer consisting of identical nano-transistors are given for selected parameters.
Recently, we have suggested a scale-invariant numerical model for a planar nanotransistor based on a Fowler-Nordheim-type of formula. In this this model we introduce a set of approximations to obtain simple analytical expressions for the drain current in the off-state regime. For this purpose the saddle point approximation is applied to the Fowler-Nordheim integral. Furthermore, we are using the WKB-expression for transmission coefficient and a series approximation for Fermi-Dirac integrals by Mc Dougal and Stoner to evaluate the supply function. The resulting analytical formula is in qualitative agreement with the traces of an experimental transistor. It becomes quite simple for small gate voltages, i.e. in the deep off-state regime. Systematic steps to improve our approximations towards a quantitative agreement are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Die neue Landesregierung möchte Berlin beim Klimaschutz unter den Metropolen weltweit als Vorreiter etablieren. Die Erarbeitung der Machbarkeitsstudie „Klimaneutrales Berlin 2050“ im Auftrag der Senatsverwaltung für Stadtentwicklung und Umwelt soll auf diesem und für diesen Weg ein zentraler Baustein sein. Sie soll mögliche Entwicklungspfade für die Handlungsfelder Energiebereitstellung, Wohnen, Konsum, Wirtschaft und Mobilität aufzeigen sowie Maßnahmen und Leitprojekte für ein klimafreundliches Berlin vorschlagen. Koordiniert wird das Projekt vom Potsdamer Institut für Klimafolgenforschung (PIK). Der Anhang soll vor allem einen Kurzüberblick über die zur Erreichung des Klimaneutralitäts-Ziel vorgeschlagenen Maßnahmen geben.