Sulfate replacement of potassium dihydrogen phosphate (KDP) was studied by the first-principles simulation method and the density of of its states was calculated. We found that sulfate can reduce the band gap of KDP crystal to 3.90eV (318nm), which is consistent with the experimental work of others and indicates that sulfate may be a source of the low damage threshold.
© 2006 Optical Society of America
Potassium dihydrogen phosphate KH2PO4 (KDP), which belongs to a family of ferroelectric crystals in which covalently bonded molecular PO4 units are linked by a network of hydrogen-bonds . This is a remarkable material due to the combination of nonlinear optical and electro-optical properties  and the speed at which large single crystals can be grown [3,4]. This unique combination of properties makes KDP technologically important and is an important nonlinear optical material with many applications in laser physics, such as frequency doublers and triplers on large aperture laser systems as the National Ignition Facility and the Laser Megajoule . Understanding the susceptibility of KDP crystals to laser induced damage at high laser fluence that is an order of magnitude below the expected intrinsic break-down limits has been a long- standing issue .
2. Calculation and results
In our work, an ab initio study of [SO4]2- in KDP is presented. [SO4]2- is a common impurity ion in KDP raw materials so that point defects of [PO4]3- replaced by [SO4]2- are easily created during crystal growth. The ab initio calculations that were performed are based on the density-functional theory (DFT) with CASTEP implementation  and ultra-soft pseudopotentials . The Perdew-Burke-Ernzerhof gradient-corrected functional  was used to calculate the exchange-correction energy. The kinetic energy cutoff for the plane-wave basis was set at 680eV, yielding a convergence for a higher total energy than 1meV/atom. Convergence tests for 2×2×2, 4×4×4, and5×5×5 division along the reciprocal-lattice directions in the primitive unit cell of the pure KDP system according to the Monkhorst-Pack scheme  have shown that the total energy converges better than 0.1meV/atom  if a 4×4×4 k-point grid is used. An appropriately scaled grid was used for the KDP supercells that contain the defect, a technique that yields good converged results for the total energy. In our calculations, a tetragonal supercell consisting of eight KH2PO4 formula units was used with the conventional lattice constant of a=7.45927 Å, b=7.45927Å and c=6.95749Å .
3. Discussions and result
Our aim was to try to find different sources of the low damage threshold in KDP crystal. The same simulation model that was adopted by Liu et al.  and Wang et al. was used,  which makes comparisons between different works possible. Figure 1 is the DOS (density of states) of KDP crystal that contains [SO4]2-. Despite the well-known intrinsic deficiencies of DFT in yielding too low band gaps compared to experiments, Fig. 1 shows that the band gap of KDP crystal was reduced to 3.90eV (318nm), although the DFT and experimental values of pure KDP crystal are 5.9eV and 7.2eV respectively .
Carr et al. employed a novel experimental approach in order to understand the mechanisms of laser induced damage of KDP crystals. A damage threshold vs wavelength graph was generated. Two notable sharp steps centered at 2.55eV (487nm) and 3.90eV (318nm) are clearly demonstrated in their experimental results (Fig. 2). The steps located at 2.55 and 3.90eV are close to integer fractions of 0.78eV (band gap of pure KDP crystal). They proposed a defect assisted multi-step photon mechanism to analyze the experimental results. 
The effects of H defects to laser damage were investigated by Liu et al. and they indicate that the band gap for the neutral interstitial H and positive charged H vacancy were greatly reduced to 2.6 and 2.5eV respectively .
This result is consistent with the first sharp step at 2.55eV and suggests that H defects may be a source of the low damage threshold in KDP . The results of the present study are consistent with the experimental work of Carr et al.  The band gap of the KDP crystal has been reduced to 3.90eV (318nm) which can induce absorption of laser at 318nm. So, it can be speculated that the sulfate substitution accounts to some extent for the second sharp step. Much more experimental work on this topic will be done in the following months and the result will be reported later.
The DOS of KDP crystal with defects of sulfate substitution has been calculated. It has been found that the band gap of the crystal decreases, which might a source of the low damage threshold in KDP crystal.
This work was supported by the National Natural Science Foundation of China 10676019, the Institute of Crystal Materials of Shandong University, and the Key Laboratory of Crystal Materials of China.
References and links
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