Nanoelectronics Fundamentals

Nanoelectronics is the study of nanoscale materials, devices, and systems. Modern practice of science and engineering is founded on three pillars, namely theory, computation, and experiments.

A physical phenomena is always described as a function of time and spatial coordinates \((t,\varvec{{ r}})\). One may Fourier transform the time domain (t) to the frequency domain(\(\omega \)) without losing any information, where \(\omega \) (rad/s) is the angular frequency.

Electronic structure describes how energy levels or spectra are distributed as a function of either real space \((\varvec{{ r}})\) or reciprocal space \((\varvec{{ k}})\). In this chapter, we focus on the Band Diagram or Energy Diagram \(E(\varvec{{ r}})\), and the Band Structure \(E(\varvec{{ k}})\). The method of choice for calculating the electronic structure of nanomaterials is the Quantum mechanics (also called wave mechanics), where the non-relativistic Schrödinger equation is the norm and not an exception. Before going into the details of this new kind of mechanics of the nanostructures and nanomaterials, let us first review some history.

Quantum transport is broadly divided into two regimes, namely Coherent and Incoherent. Coherent transport is the norm in the absence of any scattering process, where the phase of the wavefunction is preserved. Additionally, coherent transport is always an elastic process due to the absence of any scattering events in the channel region.

In this chapter, we discuss ideal and nonideal conduction behavior of various two terminal and three terminal nanodevices based on semiconducting channels. The end of chapter problems encourage the enthusiastic reader to couple NEGF formalism from the previous chapter to the IV characteristics of the nanodevices discussed in this chapter. For the two terminal devices, the channel is connected to the source and the drain contacts, using which one may inject electrons or holes into the channel and extract electrons or holes out of the channel. Source and drain contacts are also referred to as cathode and anode, respectively, with reference to the electron injection and the extraction. For the three terminal devices, the third contact (called gate) is used to electrostatically control the channel to switch the device between ON and OFF states. The current through the gate contact is usually undesirable and hence termed as the gate leakage current.

In the previous chapter, we discuss devices that control the flow of electrons or holes by making use of an electrostatic potential (intrinsic or extrinsic). Charge carriers (electrons and holes) have an additional degree of freedom in the form of spin, which may be thought of as a net magnetic moment pointing in two opposite directions, which are taken as either up-spin (\(\uparrow \)-spin) or down-spin (\(\downarrow \)-spin). In this chapter, we discuss the spin dependent properties of materials and how one may use them in devices—an area of immense scientific and technological interest, known as Spintronics.

Memories are used extensively to store information in a binary manner. A memory circuit is a bistable circuit that may be in the high current (low resistance) state or the low current (high resistance) state. One should note that for the use of nanodevices in computing applications, e.g. micro and nanoprocessors, the ON/OFF current ratio has to be four to six orders of magnitude. However, for memory applications, the ON/OFF current ratio requirement is not as stringent. In fact, a ratio of only 10 or less (in most cases) is considered state of the art for the memory technology.

In this chapter, we discuss various circuits and systems based on the CMOS technology. While, it is simply not possible to cover the broad area of the circuits and systems related to nanoelectronics in a single chapter, we do discuss a few representative circuits and systems, in order to emphasize the key concepts.

In this chapter, we discuss device fabrication at the nanoscale. There are two approaches to nanofabrication, namely the conventional top down approach and the more novel bottom up approach. It is the bottom up approach that is most fascinating due to its emphasis on the use of atoms and molecules as the building blocks during the synthesis and fabrication, whereas in the top down approach, one follows the conventional approach of device scaling. We discuss both approaches with their pros and cons in this chapter.

In this chapter, we introduce various microscopy and spectroscopy techniques. Spectroscopy is the discipline of analyzing the response of a material to various stimuli.