Strong Magnetic Field, Quantum Well D ~ - The Center Of The Bound State

Recently the properties of neutral shallow donor center D0 and negative shallow donor center D- in quantum wells with magnetic field have received a great deal of attention[1,2]. The research for the binding energy of D- centers is important to the transition energy and the optical and the magneto-optical absorption of shallow center D-There have been some theoretical and experimental investigations[1,4,5,6,7,8] about three-dimensional and two-dimensional D-centers in magnetic field, but have no works discussed the D~ centers in quantum wells in the strong magnetic field limited. If the magnetic field is strong enough, the number of bound states of D~ centers is countless in three dimensional material, however in two dimensions only four bound states are found. So in theory, the numbers of bound states should be more and more versus the width of well becomes wider. A finite quantum well can be regarded as three dimension material when the well width approached to infinite or to zero (the infinite quantum well can be regarded as two-dimension when well width approached to zero). The purpose of this paper is to calculate the distribution of D- centers' bound states along with the variation of the width of the quantum well. We want to understand the confine effect through our calculation that the system received from the quantum well.The generic methods for the calculation about the binding energy of D- centers are variational and diffusion quantum Monte Carlo methods. Because the result obtained from the variation methoddepends delicately on the form of the trial wave function, we won't use this method in our calculation. We solve the secular equation for the system's binding energy. E. D.M.Whittaker and A.J.Shields[3] calculated the states of the quantum-well negatively charged exciton X- in a perpendicular magnetic field with this method. The basis states they used are products of an axial (z) part, determined by the quantum well confinement, and an in plane (r,6) Landau-level wave function. We adopted the same basis states as they used to construct the quantum-well D~ centers' wave function. We obtained the system energy and binding energy of ground and some low-lying excited states by solving the equation Hnm-E=0. Different fromthe variational method's result closely depending on the form of the trial wave function, our result has high accuracy as long as the matrix we used is big enough.The system we selected is the positive donor ion located in the centers of GaAslGaAsAl quantum well (doped density of Al is 0.33) in the process of calculation. We take the center of well as the origin of coordinates. We noticed that the electron's effective mass is different in the well and in the barrier, but didn't pay attention to the mismatch of the dielectric constant. The expansion for matrix involved in different Landau levels. Compared with the Lowest-Landau-level approximation method, our result has higher accuracy for D~ centers with lower magnetic field.We calculated the states' binding energy in finite and infinitequantum well with different width of well such as 10 A , 20 A 30 A 50 A 70 A 100 A . We obtained the well width that some low-lying excited states appeared in strong field and in fixed well width thevalue of magnetic field when these states began appear. We found that the number of bound states becomes more and more versus the quantum well wider, at the same time the critical magnet value becomes lower and lower.