Scattering of a conduction electron by a charged shallow donor located near a semiconductor᎐insulator interface in the semiconductor or by a charged center embedded in the insulator is considered within the model of a hydrogenlike atom in a semi-infinite space. The interface influence is allowed for by spatial confinement of the electron envelope wave function. The impurity electrostatic image at the interface is taken into account. The problem is separable in prolate spheroidal coordinates and thus is solvable exactly. A rapidly convergent expansion is proposed for the angular eigenfunctions. The radial eigenfunctions are calculated directly by numerical integration of the radial boundary value problem. Expansions of the scattering wave function and the scattering amplitude in terms of the eigenfunctions of the problem are obtained. Using the extended and localized state wave functions, the photoionization cross section of a shallow donor near a semiconductor᎐insulator interface is calculated. It is presented as a superposition of the oscillator strengths of transitions to the partial extended eigenstates that constitute the scattering wave function. Near the interface, the cross section is enhanced significantly and redistributed over the direction of photoionized electron escape. The photoionization threshold follows the localized state energy varying with the donor᎐interface distance.