Hypothetical Quantum Wire of Hydrogen

Abstract

A one dimensional quantum nano-wire of hydrogen is hypothetically demonstrated. This nanostructure device has been designed to perform at nanoscale with more efficiency than existing semiconductor based devices. Because this device is smaller and fabrication process is simpler, which are the primary requirements of semiconductor industry. The device has achieved a very flexible physical structure. A framework has been developed in this work that a device of completely non-metal element can behaves like a pure conductor depending on the atomic arrangement and a semiconductor without any significant dopant species presents. Basis function has been used as a computational tool for solving the Schrodinger's Equation for periodic solid composed of hydrogen. By using MATLAB we will produce the E(k)diagram which will give us the expected eigenvalues of the dispersion relation of the wires. A base calculation has been developed to calculate the bandstructure of a quantum wire. Hypothetical quantum wire of hydrogen is a one dimensional device designed in nanometer scale. Our main purpose is to illustrate the procedure for calculating the bandstructure for quantum wire by using the 1D model concept of quantum wire. Electronic structure of the hydrogen wire is demonstrated where numerical solution has been preferred instead of analytical solution for the device. The wire is a one dimensional solid composed of N hydrogen atoms which are actually a lattice of finite range whose unit cell is consisting one atom each. In this structure electrons are free to move only in the x direction and confined in both y- and z- directions.(1) This type of atomic arrangement simply forms a quantum wire of hydrogen atoms. The bandstructure has been calculated by solving Hamiltonian matrix eigenvalue equation. Finite difference method followed to find the eigenvalues of the matrix.(2) In this paper we have developed a quantum wire to investigate its conducting properties with help of the E-k diagram. We have plotted the E-k diagram from dispersion relation which shows the eigenvalues by using MATLAB. The resulting bandstructures of the quantum wire of hydrogen atom and quantum wire of hydrogen dimer establish the solid-state like material property. A model structure for nano-wire transistor of quantum wire of hydrogen has been proposed in this research.