Charged donor in a narrow quantum well in the presence of in-plane crossedmagnetic and electric fields

An analytical approach to the problem of a negatively charged donor in a na rrow quantum well (QW) in the presence of crossed magnetic and electric fie lds is developed. The width of the QW is taken to be much less than the imp urity radius and the magnetic length. Both magnetic and electric fields are directed parallel to the heteroplanes, The impurity centre is positioned a nywhere within the QW The adiabatic approximation is used: the motion of th e electron in the direction perpendicular to the heteroplanes is much faste r than that parallel to the heteroplanes. The explicit dependences of the t otal energy of the charged donor upon the parameters of the well and extern al field strengths are obtained. The dependences of the binding energy of t he charged donor on the width of the well and the position of the impurity within the well are studied. It is shown that a displacement of the impurit y centre from the mid-point of the QW leads to a decrease of the binding en ergy. The relative position of the impurity within the narrow well affects strongly the dependence of the binding energy on the width of the well, A r ed shift of the energy and the detachment rate of the quasi-two-dimensional charged donor both caused by the weak electric field are calculated explic itly. The red shift can be balanced by the blue shift induced by the magnet ic field. Using the parameters associated with GaAs and InGaN QWs estimates of the values expected for an experiment are made.