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Pre-lithiation is the most effective method to overcome the initial capacity loss of high-capacity electrodes and has the potential to be used in beyond-conventional lithium-ion batteries. In this article we focus on two types of pre-lithiation: the first type can be applied to batteries in which the cathode has been fully lithiated but the anode has a large initial capacity loss, such as batteries made with lithium metal oxide cathode and silicon-carbon anode. The second type can be applied to batteries in which both electrodes are initially lithium-free and suffer a loss of lithium during the initial cycles, such as batteries made with sulfurized-polyacrylonitrile cathode and silicon-carbon anode. We describe the pre-lithiation procedures and electrode potential profiles during pre-lithiation corresponding to different pre-lithiation sources for both types of pre-lithiation. We also derive formulas for the theoretical specific energy and energy density that are based entirely on measurable parameters such as specific capacities, porosities, mass densities of two electrodes and extra lithium source, Coulombic efficiencies of electrodes, and the voltage of the cell. These formulas can be applied to different pre-lithiation sources to predict the specific energy of conventional and beyond-conventional lithium-ion batteries as a function of the type of pre-lithiation. 

In this article we use the ensemble Monte-Carlo method to study the frequency comb induced by a periodically excited tunnel junction on a semiconductor. The electron transport is modeled by solving the Boltzmann transport in p-type silicon doped with a concentration of 10 17 cm -3 . For a laser-pulse frequency of 100 MHz, we observe that, if the distance between the STM probe and the second electrode is under 1 μm and we apply a negative bias on the STM tip, the harmonics of the frequency spectrum are not reduced significantly by the electron diffusion and resistance spreading effects in the semiconductor. In this case we obtain a wide frequency comb spectrum, relatively similar to the ones measured experimentally in metals and other materials with high electron conductivity.