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There is a wide variety of electronic structure calculation cooperating with symbolic computation. The main purpose of the latter is to play an auxiliary role (but not without importance) to the former. In the field of quantum physics [1-9], researchers sometimes have to handle complicated mathematical expressions, whose derivation seems almost beyond human power. Thus one resorts to the intensive use of computers, namely, symbolic computation [10-16]. Examples of this can be seen in various topics: atomic energy levels, molecular dynamics, molecular energy and spectra, collision and scattering, lattice spin models and so on [16]. How to obtain molecular integrals analytically or how to manipulate complex formulas in many body interactions, is one such problem. In the former, when one uses special atomic basis for a specific purpose, to express the integrals by the combination of already known analytic functions, may sometimes be very difficult. In the latter, one must rearrange a number of creation and annihilation operators in a suitable order and calculate the analytical expectation value. It is usual that a quantitative and massive computation follows a symbolic one; for the convenience of the numerical computation, it is necessary to reduce a complicated analytic expression into a tractable and computable form. This is the main motive for the introduction of the symbolic computation as a forerunner of the numerical one and their collaboration has won considerable successes. The present work should be classified as one such trial. Meanwhile, the use of symbolic computation in the present work is not limited to indirect and auxiliary part to the numerical computation. The present work can be applicable to a direct and quantitative estimation of the electronic structure, skipping conventional computational methods

C-plane (polar) and m-plane (nonpolar) GaN/ZnO heterostructures have been fabricated by pulsed laser deposition at room temperature, and their electronic structures have been characterized by synchrotron radiation photoemission spectroscopy. Based on the binding energies of core levels and valence band maximum values, the valence band offsets have been found to be 0.7 AE 0.1 and 0.9 AE 0.1 eV for polar and nonpolar GaN/ZnO heterojunctions, respectively. Both heterostructures show type-II band configurations with conduction band offsets of 0.8 AE 0.1 and 1.0 AE 0.1 eV, respectively. GaN and ZnO show upward and downward band bending toward the interface in the nonpolar GaN/ZnO heterojunction. However, both GaN and ZnO show upward band bending toward the interface in the polar heterojunction, which is attributed to negative charges. Analysis of N 1s spectra has revealed that N-O bonds exist only at the polar interface, which probably caused the formation of the negative charges.

c -plane and a-plane AlN films have been grown on single-crystal ZnO substrates by pulsed laser deposition at room temperature. The electronic structures of c-plane and a-plane AlN/ZnO heterojunctions have been characterized by synchrotron radiation photoemission spectroscopy. Based on the binding energies of core-levels and valence-band maximum values, the valence-band offsets have been found to be 0.4±0.1 and 0.1±0.1 eV for the c-plane and a-plane AlN/ZnO heterojunctions, respectively. Both heterojunctions show type-II band configurations with conduction band offsets of 3.0±0.1 and 2.7±0.1 eV, respectively. The potential on the ZnO side bends downward toward the interface for the a-plane AlN/ZnO heterojunction. However, that bends upward toward the interface for the c-plane AlN/ZnO heterojunction. This phenomenon is explained well by the effect of spontaneous polarization in AlN and ZnO.

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