Analysis of Quantum Waveguide : Effective Width and Height of Potential for Quantum Wires under Split Gates

In order to apply quantum waveguides to electronic devices, we calculate the electrostatic potential in the split-gate quantum wire and establish the relation between the electrostatic potential and the square well potential which is usually assumed in simulations of these waveguides. The height and width of the square well potential are expressed as simple functions of the gate voltage and their dependencies are clarified. The results may be useful in calculating the characteristics of electronic devices based on quantum waveguides as functions of controllable parameters such as gate voltage.