4. Numerical simulation of the electronic properties of the LiCAF host

LiCAF is a colquiriite-type fluoride with a hexagonal crystal structure belonging to the P-31c space group (group number 163). It is optically a uniaxial crystal with two formula units per unit cell. Six fluorine (F) atoms surround a lithium (Li), calcium (Ca), or aluminum (Al) atom. Each Li, Ca, and Al cation occupies a deformed octahedral site as shown in Figure 3a. This structure is also described by an alternative stacking of metallic and fluorine atom layers parallel to the c-axis [49–51]. The fraction coordinates of the representative atoms in the unit cell are shown in Table 1.

First-principles density functional theory (DFT) calculations are used to obtain the optimized volume, electronic band structure, total and partial density of states (DOS), and the band gap

Figure 3. (a) Colquiriite-type structure of LiCAF and (b) first Brillouin zone of the hexagonal unit cell of a LiCAF crystal.


Table 1. Atomic positions of the LiCAF atoms.

in this crystal [21, 22]. Following the success of Ce:LiCAF, lasing from Ce3+:LiSrAlF6 was reported. It can also be pumped with the fourth harmonic of a Nd:YAG laser and it has similar laser properties as the Ce:LiCAF crystal [23, 47]. Figure 1 summarizes the tunable wavelength

Ce:LiCAF has the following advantages over the other known Ce3+-doped fluoride hosts: (1) the strong absorption band at 266 nm would allow direct optical pumping by the fourth harmonics of the Nd:YAG laser; (2) the wide fluorescence band offers a tuning range from the 280 to 320 nm for possible pulse compression; (3) the gain cross-section of Ce:LiCAF (6

dyes. This is significant when using this crystal in power amplifiers; (5) the nanosecond lifetime of Ce:LiCAF maybe too short to for regenerative amplifications, but this is sufficiently

Figure 2 shows the energy level structure of Ce3+ doped into a fluoride host. The ground state

state, respectively. The exact positions of these energy levels would depend on the specific host. Lasing in the UV is based on the electric dipole-allowed interconfigurational 5d-4f transitions. In contrast, conventional trivalent lanthanide laser crystals, such as Nd:YAG, uses the intraconfigurational 4f-4f transition that results to infrared (IR) emission. As a result, UV

). The excited state 5d configuration also has two energy levels, <sup>2</sup>

F5/2 and <sup>2</sup>

) is high, even higher compared to the Ti:Sapphire. This property is ideal for building

) of Ce:LiCAF is higher than organic

F7/2, which are separated by 0.2793 eV

) and 6.475 eV (52,226 cm<sup>1</sup>

D3/2 and <sup>2</sup>

) from the ground

D5/2,

regions of the five currently known Ce-doped lasers.

a laser resonator; (4) the saturation fluence (~115 mJ/cm2

long to allow multi-pass amplification.

138 Numerical Simulations in Engineering and Science

4f configuration has two energy levels, <sup>2</sup>

which are separated by 6.166 eV (49,733 cm<sup>1</sup>

Figure 2. Energy level structure of Ce3+ doped into a fluoride host.

3. Cerium ion dopant

10<sup>18</sup> cm2

(2253 cm<sup>1</sup>

energies of the LiCAF crystal. These calculations employed the projector-augmented wave (PAW) method as implemented within the Vienna Ab Initio Simulation Package (VASP) [52– 57], with a plane-wave basis cutoff of 500 eV and a hybrid density functional, which uses the full Perdew-Burke-Ernzerhof (PBE) [58, 59] correlation energy but mixes 65% PBE exchange with 35% exact exchange [60–63]. The initial charge density and wave function was generated using a 3 � 3 � 1 Monkhorst-Pack k-point grid. For the band structure and DOS diagrams, the k-points were chosen following the first Brillouin zone and the path Γ ! M ! K ! A ! L ! H shown in Figure 3b [64].

The electronic band structure of LiCAF along the high symmetry lines of the first Brillouin zone is shown in Figure 4. The maximum of the valence band is located at the k-point between M and K while the conduction band minima is at the Γ point. Therefore, LiCAF has an indirect band gap with a band gap energy of 12.23 eV. This result is 3.30% and 10.51% different from the experimentally obtained band gap energies of 12.65 eV and 11.07 eV, respectively [65–67]. Figure 5 shows the total and partial DOS of LiCAF. The maximum valence band is derived from the fluorine 2p states whereas the aluminum 4 s and fluorine 3 s states contribute to the minimum conduction band.

Excited state absorption (ESA), which is prevalent in rare-earth-doped fluorides operating in the UV region, has been observed in both Ce3+:LiCaAlF6 (Ce:LiCAF) and Ce3+:LiSrAlF6 (Ce: LiSAF). However, experimental investigations reveal that Ce:LiSAF experiences ESA to a greater extent compared to Ce:LiCAF and therefore, the conversion efficiency of a Ce:LiSAF laser is lower. ESA results from an electron being promoted from the 5d excited state configuration of Ce3+ to the conduction band of the LiCAF host [24, 68]. Therefore, the onset of ESA strongly depends on the host. If the conduction band minimum of the host is close to the 5d excited state level of the activator ion, then ESA will be greater in this laser material. Similar band structure and DOS calculations performed for LiSAF reveal that the band gap energy of LiSAF is 11.79 eV, which is 0.44 eV smaller than LiCAF [62]. Associated with the strong ESA is color center formation or solarization, which happens due to an electron getting trapped at impurities in the conduction band of the host as shown in Figure 6 [27]. Under UV excitation, color centers can be created due to solarization. Broad absorption bands in energies other than the band gap then appear as a result of color center-formation. The Ce3+ ions that are doped in

the LiCAF or LiSAF host tend to occupy the Ca2+ or Sr2+ octahedral sites [29]. The CeF6 cluster in LiSAF will then have to compensate for the disparity in the size of the Ce3+ ion, which is 1.15 Å, and the Sr2+ ion, which is 1.27 Å. This compensation makes LiSAF prone to defects such as cracks and impurities during crystal growth [69]. For comparison, the size of the Ca2+ ion in LiCAF, which is 1.14 Å, is similar to that of the Ce3+ ion. Ce:LiCAF does not exhibit as much defects as Ce:LiSAF under the same growth conditions [69]. The larger amount of cracks and defect in Ce:LiSAF as well as the significant ESA as described above result to more pronounced solarization in this crystal. Both ESA and solarization compete with the lasing process and these

Ultrashort Pulse Generation in Ce:LiCAF Ultraviolet Laser http://dx.doi.org/10.5772/intechopen.73501 141

Figure 6. Excited state absorption (ESA) and color center formation in Ce3+-doped fluoride gain media [27].

results to lower laser conversion efficiency.

Figure 5. Total and projected density of states of LiCAF host.

Figure 4. Simulated electronic band structure of LiCAF host crystal.

Figure 5. Total and projected density of states of LiCAF host.

energies of the LiCAF crystal. These calculations employed the projector-augmented wave (PAW) method as implemented within the Vienna Ab Initio Simulation Package (VASP) [52– 57], with a plane-wave basis cutoff of 500 eV and a hybrid density functional, which uses the full Perdew-Burke-Ernzerhof (PBE) [58, 59] correlation energy but mixes 65% PBE exchange with 35% exact exchange [60–63]. The initial charge density and wave function was generated using a 3 � 3 � 1 Monkhorst-Pack k-point grid. For the band structure and DOS diagrams, the k-points were chosen following the first Brillouin zone and the path Γ ! M ! K ! A ! L ! H

The electronic band structure of LiCAF along the high symmetry lines of the first Brillouin zone is shown in Figure 4. The maximum of the valence band is located at the k-point between M and K while the conduction band minima is at the Γ point. Therefore, LiCAF has an indirect band gap with a band gap energy of 12.23 eV. This result is 3.30% and 10.51% different from the experimentally obtained band gap energies of 12.65 eV and 11.07 eV, respectively [65–67]. Figure 5 shows the total and partial DOS of LiCAF. The maximum valence band is derived from the fluorine 2p states whereas the aluminum 4 s and fluorine 3 s states contribute to the

Excited state absorption (ESA), which is prevalent in rare-earth-doped fluorides operating in the UV region, has been observed in both Ce3+:LiCaAlF6 (Ce:LiCAF) and Ce3+:LiSrAlF6 (Ce: LiSAF). However, experimental investigations reveal that Ce:LiSAF experiences ESA to a greater extent compared to Ce:LiCAF and therefore, the conversion efficiency of a Ce:LiSAF laser is lower. ESA results from an electron being promoted from the 5d excited state configuration of Ce3+ to the conduction band of the LiCAF host [24, 68]. Therefore, the onset of ESA strongly depends on the host. If the conduction band minimum of the host is close to the 5d excited state level of the activator ion, then ESA will be greater in this laser material. Similar band structure and DOS calculations performed for LiSAF reveal that the band gap energy of LiSAF is 11.79 eV, which is 0.44 eV smaller than LiCAF [62]. Associated with the strong ESA is color center formation or solarization, which happens due to an electron getting trapped at impurities in the conduction band of the host as shown in Figure 6 [27]. Under UV excitation, color centers can be created due to solarization. Broad absorption bands in energies other than the band gap then appear as a result of color center-formation. The Ce3+ ions that are doped in

shown in Figure 3b [64].

140 Numerical Simulations in Engineering and Science

minimum conduction band.

Figure 4. Simulated electronic band structure of LiCAF host crystal.

Figure 6. Excited state absorption (ESA) and color center formation in Ce3+-doped fluoride gain media [27].

the LiCAF or LiSAF host tend to occupy the Ca2+ or Sr2+ octahedral sites [29]. The CeF6 cluster in LiSAF will then have to compensate for the disparity in the size of the Ce3+ ion, which is 1.15 Å, and the Sr2+ ion, which is 1.27 Å. This compensation makes LiSAF prone to defects such as cracks and impurities during crystal growth [69]. For comparison, the size of the Ca2+ ion in LiCAF, which is 1.14 Å, is similar to that of the Ce3+ ion. Ce:LiCAF does not exhibit as much defects as Ce:LiSAF under the same growth conditions [69]. The larger amount of cracks and defect in Ce:LiSAF as well as the significant ESA as described above result to more pronounced solarization in this crystal. Both ESA and solarization compete with the lasing process and these results to lower laser conversion efficiency.
