Analytical closed form expressions for the effective band edges in shallow quantum wells

Shallow quantum wells are widely used in electronic and optoelectronic heterostructure devices. However, to determine the effective band edges, one needs numerical techniques unless the barrier height is infinite. In this letter the nearly free electron approach used in periodic structures is exploited to provide accurate energy level expressions for the electronic ground state in a number of important quantum wells with different shapes. These include the square quantum well without and with an applied transverse electric field.