Exact Solution of the Electrostatic Problem for a Single Electron Multijunction Trap

We present an exact solution for the potential profile of a biased single electron trap. Analytical expressions for the total free energy as well as the corresponding charging energy, barrier height for a trapped electron in the store island, and threshold voltage for a single charge transfer are derived. This enables us to demonstrate the important role of well capacitance Cw in determining the barrier height of the trapped electron, and to show that systems with small well capacitance are not suitable for studying the single electron trap. Our techniques are applicable to a variety of other single charge tunneling systems.