Impact Of Energy Quantization On Single Electron Transistor Devices And Circuits
Abstract
Although scalingof CMOS technology has been predicted to continue for another decade, novel technological solutions are required to overcome the fundamental limitations of the decananometer MOS transistors. Single Electron Transistor (SET) has attracted attention mainly because of its unique Coulomb blockade oscillations characteristics, ultra low power dissipation and nanoscale feature size. Despite the high potential, due to some intrinsic limitations (e.g., very low current drive) it will be very diﬃcult for SET to compete headtohead with CMOS’s largescale infrastructure, proven design methodologies, and economic predictability. Nevertheless, the characteristics of SET and MOS transistors are quite complementary. SET advocates lowpower consumption and new functionality (related to the Coulomb blockade oscillations), while CMOS has advantages like highspeed driving and voltage gain that can compensate the intrinsic drawbacks of SET. Therefore, although a complete replacement of CMOS by singleelectronics is unlikely in the near future, it is also true that combining SET and CMOS one can bring out new functionalities, which are unmirrored in pure CMOS technology. As the hybridization of CMOSand SET is gaining popularity, silicon SETs are appearing to be more promising than metallic SETs for their possible integration with CMOS. SETs are normally studied on the basis of the classical Orthodox Theory, where quantization of energy states in the island is completely ignored. Though this assumption greatly simpliﬁes the physics involved, it is valid only when the SET is made of metallic island. As one cannot neglect the quantization of energy states in a semi conductive island, it is extremely important to study the eﬀects of energy quantization on hybrid CMOSSET integrated circuits. The main objectives of this thesis are: (1) understand energy quantization eﬀects on SET by numerical simulations; (2) develop simple analytical models that can capture the energy quantization eﬀects; (3)analyze the eﬀects of energy quantization on SET logic inverter, and ﬁnally; (4)developa CAD framework for CMOSSETcosimulation and to study the eﬀects of energy quantization on hybrid circuits using that framework.
In this work the widely accepted SIMON Monte Carlo (MC) simulator for single electron devices and circuits is used to study the eﬀects of energy quantization. So far SIMON has been used to study SETs having metallic island. In this work, for the ﬁrst time, we have shown how one can use SIMON to analyze SET island properties having discrete energy states.It is shown that energy quantization mainly changes the Coulomb Blockade region and drain current of SET devices and thus aﬀects the noise margin, power dissipation, and the propagation delay of SET logic inverter. Anew model for the noise margin of SET inverter is proposed, which includes the energy quantization term. Using the noise margin as a metric, the robustness of SET inverter is studied against the eﬀects of energy quantization. An analytical expression is developed, which explicitly deﬁnes the maximum energy quantization (termedas “Quantization Threshold”)that an SET inverter logic circuit can withstand before its noise margin upper bound crosses the acceptable tolerance limit. It is found that SET inverter designed with CT : CG =0.366 (where CT and CG are tunnel junction and gate capacitances respectively) oﬀers maximum robustness against energy quantization. Then the eﬀects of energy quantization are studied for Current biased SET (CBS), which is an integral part of almost all hybrid CMOSSET circuits. It is demonstrated that energy quantization has no impact on the gain of the CBS characteristics though it changes the output voltage levels and oscillation periodicity. The eﬀects of energy quantization are further studied for two circuits: Negative Diﬀerential Resistance (NDR) and Neurone Cell, which use CBS. A new model for the conductance of NDR characteristics is also formulated that includes the energy quantization term. A novel CAD framework is then developed for CMOSSET cosimulation, whichuses MCsimulator for SET devices alongwithconventional SPICE. Using this framework, the eﬀects of energy quantization are studied for some hybrid circuits, namely, SETMOS, multiband voltage ﬁlter, and multiple valued logic circuits. It is found that energy quantization degrades the performance of hybrid circuit, which could be compensated by properly tuning the bias current of SET devices. Though this study is primarily done by exhaustive MC simulation, eﬀort has also been put to develop ﬁrst order compact model for SET that includes energy quantization eﬀects. Finally it has been demonstrated that the SET behavior under energy quantization can be predicted byslightlymodifyingthe existing SETcompact models that are valid for metallic devices having continuous energy states.
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