The physical principles are studied for the optimal design of a quantummultiwell heterostructure working as an electrostatic energy storage device. Weperformed the search for an optimal multiwell trapping potential for electronsthat results in the maximum static palarizability of the system. The responseof the heterostructure is modeled quantum mechanically using nonlocal linearresponse theory. Three main design strategies are identified, which lead to themaximization of the stored energy. We found that the efficiency of eachstrategy crucially depends on the temperature and the broadening of electronlevels. The energy density for optimized heterostructures can exceed thenonoptimized value by a factor more than $400$. These findings provide a basisfor the development of new nanoscale capacitors with high energy densitystorage capabilities.
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