Optimization of amorphous semiconductors and low-/high- k dielectrics through percolation and topological constraint the
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troduction In contrast to cements and glasses, the essence of a semiconductor is the manipulation of electron transport.1 One may question the relevance to semiconductors of the Phillips– Thorpe inspired molecular rigidity concepts described in the Introductory article of this issue.2,3 However, many key transitions in the semiconductor electronic structure bear striking similarities to the percolation and mechanical rigidity transitions exhibited in glassy and other noncrystalline solids.3 As we illustrate in this article, such electronic transitions can be important in optimizing semiconductors for specific applications and, in some cases, offer the potential to realize new devices that could further revolutionize the world.4,5 We additionally demonstrate how rigidity percolation plays a more direct role in insulating high- and low-dielectric-constant (high-/low-k) materials. This is important to achieve voltage-controlled electronic transport in commercial semiconductor devices that have already made a significant technological impact.6
Semiconductor metal–insulator transitions As their name implies, semiconductors are neither ideal conductors nor insulators. However, the ability to tune their conductivity over many orders of magnitude and manipulate
the majority carrier type via the deliberate introduction of impurities (doping) has made them indispensible.1 The unique properties exhibited by semiconductors are a result of their electronic structure—the existence of a bandgap with most of the allowed electronic states in the lower valence band being occupied and only a few allowed states in the upper conduction band being occupied. Whether a state is full, partially filled, or empty is governed by Fermi–Dirac statistics and is described by the Fermi level (EF), which is defined as the energy level where there is a 50% probability of occupancy at any given time (see Figure 1a).7 What makes semiconductors so useful and interesting is the possibility of adjusting EF and hence conductivity via the intentional introduction of impurities or defects (dopants) to create states just above or below the conduction and valence bands, respectively. In ideal conditions, semiconductors are perfect insulators at cryogenic temperatures due to lack of thermal activation of electrons into the conduction band. At such temperatures, dopant states in low concentrations remain localized and are unable to contribute to conductivity. However, as the dopant concentration is increased, a critical concentration is eventually reached where the dopant states become delocalized and form a percolating path of extended states.8,9 At this point, the
Michelle M. Paquette, Department of Physics and Astronomy, University of Missouri–Kansas City, USA; [email protected] Bradley J. Nordell, Extreme Light Laboratory, Department of Physics and Astronomy, University of Nebraska–Lincoln; and University of Missouri–Kansas City, USA; [email protected] Anthony N. Caruso, Department of Physics and Astronomy, University of Missouri–Kansas City, USA; carusoan@um
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