Electronic States of a Shallow Hydrogenic Donor Impurity in Different Shaped Semiconductor Quantum Wells

The shallow hydrogenic donor impurity states in square, V-shaped, and parabolic quantum wells arestudied in the framework of effective-mass envelope-function theory using the plane wave basis. The first four impurityenergy levels and binding energy of the ground state are more easily calculated than with the variation method. Thecalculation results indicate that impurity energy levels decrease with the increase of the well width and decrease quicklywhen the well width is small. The binding energy of the ground state increases until it reaches a maximum value, andthen decreases as the well width increases. The results are meaningful and can be widely applied in the design of variousoptoelectronic devices.