Quantum confinement explains a dramatic increase in electrical resistivity in silicon sheets of several nanometers thick

Consumer electronics are primarily made from silicon, germanium, copper, and materials that have been used for over 60 years. Why is semiconductor electronics becoming faster and faster this time?

I argue that this is due to miniaturization or the ability to stack more and more transistors in tightly integrated circuits (MicroChip). Some may argue that as the film approaches only 10 nanometers, and even lower thicknesses, we are beginning to reach its miniaturization limit.

These near-2D (2D) materials can be used to build next-generation electronic devices. However, electronic materials such as silicon are reduced in size, making them less energy efficient.

If the silicon film is reduced to about 20-30 nanometers, the electrons will start to bump into the edges of the film, leading to increased resistivity and increased energy dissipation. This phenomenon has been known for decades and is explained by a theory developed by Klaus Fuchs (also known as “atomic spy” who provided classification information about the Manhattan project to the Soviet Union) and E. Helmut Sondheimer.

Papers published in the physical review material show that as new effects begin, things get worse than predicted by the Fuchs-Sandheimer theory as the thickness decreases to less than 10 nanometers. This new effect is due to quantum confinement of electrons.

Quantum confinement makes me refer to a phenomenon in which the energy of quantum particles, such as electrons, increases dramatically when they are limited in space. This effect arises from Heisenberg’s principle of uncertainty. The more precisely the location of the particles, the greater the uncertainty of their momentum and the greater the energy variation.

Recently, I began using general mathematical models to systematically study the implications of quantum confinement for the energy of quantum particles (electrons, phonons) on the properties of actual materials.

The latter takes into account that, according to quantum mechanics, electrons are particles and waves. That is, under the miniaturized confinement of thin sheets, only wavelengths compatible with limited spaces of material are permitted.

This general theory motivated me and my collaborators to provide a parameterless prediction of the electronic properties of materials, consistent with experimental data on ultra-slim and almost 2D materials.

In ultra-thin sheets of silicon, when electrons are narrowed to thin spaces, quantum confinement increases energy. Second, as electrons become more energetic, the band gap that separates valence electrons (which are firmly bound to atoms) from freely moving electrons. Thus, an increase in the bandgap leads to a decrease in the concentration of free electrons available to conduct electricity, leading to an increase in resistivity.

The new mathematical theory I present in this paper shows that this increase in resistivity when decreasing film thickness is very dramatic (an exponential increase with film thickness decreases), and can explain recent experimental data, clearly indicating the predicted exponential increase as the thickness decreases below 10 nm.

The good news is that my theory also explains that this dramatic increase in resistivity can be reduced by carefully adjusting the free electron concentration of silicon nanofilms via doping. This discovery could have great implications for next-generation electronics by providing new methods for manufacturing nanochips that are close to the atomic level.

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