We study physical principles of optimal design of a nanoscale multiwell heterostructure functioning as an electrostatic energy storage device. We performed numerical optimization of the multiwell trapping potential for electrons in the nanostructure with the goal to obtain the maximum possible static polarizability of the system. The response of the heterostructure is modeled microscopically using nonlocal linear response theory within the random phase approximation. Three main design strategies are identified which lead to the maximization of the stored energy. We found that the efficiency of each strategy crucially depends on the temperature and the broadening of electron levels. The stored energy for optimized heterostructures can exceed the nonoptimized ones by a factor of 450. These findings provide a theoretical basis for the development of new nanoscale capacitors with high energy density storage capabilities.
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