A phase-shifting mask (PSM) is expected to enhance optical lithography in the very large-scale integrated/very-high-speed-integrated-circuit era. PSM changes the phase of light to cause destructive interference at the edge with an original light. The use of PSM improves both resolution and depth of focus without significantly altering the existing exposure system.
In order to acquire the resolution for deep-ultraviolet (DUV) lithography, it requires proper transmittance and transmittance slope at the energy of light source in inspection and lithography process. Chromium aluminum oxide has been proposed as a candidate material for PSM in DUV optical lithography, but it is difficult to meet the requirements of transmittance slope using chromium aluminum oxide. When nitrogen is substituted for oxygen in Cr-Al-O system, it shows a proper transmittance slope through the control of composition, thickness, etc. Such optical properties are closely related to the electronic structure of material. Accordingly, understanding the electronic structure of chromium aluminum oxynitride is important to develop the mask material.
The electronic structure of chromium aluminum oxide and oxynitride is investigated theoretically and experimentally. The electronic structure is calculated and compared with the results of photoelectron spectroscopy such as X-ray photoelectron spectroscopy (XPS) and ultraviolet photoelectron spectroscopy (UPS). Lattice simulation (LS) and molecular dynamics (MD) are used to determine atomic structure of crystalline and amorphous phase. Then the embedded cluster model within the framework of discrete variational (DV)-Xα method is employed to investigate the electronic structure of their optimized structures. The several model clusters, formulated with different atomic concentration, are chosen to simulate atomic structures in both crystalline and amorphous phase. Simulation is verified by comparing calculated partial density of states (PDOS) with the results of photoelectron spectroscopy.
PDOS, which calculated by DV-Xα method with embedded cluster model, is well consistent with photoelectron spectra of chromium aluminum oxide and chromium aluminum oxynitride systems. In chromium aluminum oxide system, valence band consists of O 2p orbital that is the highest occupied molecular orbital (HOMO). Lowest unoccupied molecular orbital (LUMO) is partially unoccupied Cr 3d. Band gap, defined as the difference between LUMO and HOMO level, increases slowly from 4.01 to 6.09 eV with the concentration of aluminum oxide below 0.9 mole fraction. As the composition close to pure aluminum oxide, band gap increases abruptly to the band gap of pure aluminum oxide (∼10 eV). When nitrogen is substituted for oxygen in Cr-Al-O system, N 2p level appears between O 2p and Cr 3d level. So the valence band of chromium aluminum oxynitride becomes broader and the band gap becomes smaller than that of chromium aluminum oxide. This N 2p orbital should closely relate to the transmittance slope in Cr-Al-O-N systems.
In order to verify the valence band structure precisely, valence band photoemission experiments were carried out at 4B1 beam line of Pohang Light Source. The results shows that the valence band of Cr-Al-O-N system was consisted of partially occupied Cr 3d and N 2p orbital in the energy region of 0-7 eV.
The electronic structure of chromium aluminum oxide and oxynitride can be elucidated for PSM application through the theoretical calculation in quantum scale and experimental verification.
