Intermediate Band Studies of Substitutional V 2 + , Cr 2 + , and Mn 2 + Defects in ZnTe Alloys

Featured Application: This work conﬁrms the emission band of Cr 2 + 0.03 Zn 0.97 Te comes from the transitions from the defect excited state to the ground state. Abstract: We present ﬁrst-principles total-energy density functional calculations to study the intermediate band states of substitutional V 2 + , Cr 2 + , and Mn 2 + ions in ZnTe alloys. The intermediate band states of substitutional transition metal defects of TM 2 + x Zn 1 − x Te ( TM = V, Cr, Mn) alloys are examined as their atomic, structural, and electronic analysis. Our ﬁndings show that the scissor-corrected transitions due to Jahn-Teller e ﬀ ects lead to the wavelengths 2530 nm and 2695 nm in the emission spectra. Our ﬁndings agree with previously reported experimental results.


Introduction
The ultrashort pulse lasers of infrared (IR) light have gained great attentions for ophthalmic, surgical, dental, therapeutic, and aesthetic medical applications. The pulses from the picosecond (ps) to femtosecond (fs) require less energy to ablate biological tissues and the accuracy is in the micrometer range. At the micrometer point of the tissue through which the ultrashort pulse passes, tiny harmless carbon dioxide and water vapor bubbles are generated. Solid-state diode laser offers a number of advantages over conventional laser sources, such as reduced power consumption, better spectral purity, increased lifetime and low costs, all of which are continuously improving. It is the best and only way to promote a new high-technology development on ultrafast diode lasers. The fabrications of group II-VI laser-diodes (LDs) have become quite important for ultra-short coherent light sources. Divalent chromium doped lasers of the II-VI family emitting in the mid-infrared (mid-IR) (2-3 µm) have recently matured to the commercial continuous-wave lasers. The passively mode-locked femtosecond Cr 2+ :ZnSe laser was first reported in 2006, generating~100 fs pulses at up to 75 mW power around 2.5 µm wavelength [1]. The first Kerr-lens mode-locked (KLM-locked) Cr 2+ :ZnSe laser has two distinct regimes. In the first, the output power and duration of the high-power soliton regime of Cr 2+ :ZnSe laser is about 300 mW and 100 fs, respectively. In contrast, the output power and pulse duration of the chirped pulse regime of Cr 2+ :ZnSe laser is about 170 mW and 1 ps, respectively [2]. In addition, another KLM-locked Cr 2+ :ZnSe can generate 95 fs pulses with an output power as high as 40 mW around 2420 nm wavelength [3]. Furthermore, the first chirped-mirror dispersion controlled KLM Cr 2+ :ZnSe laser using a semiconductor saturable absorbing mirror (SESAM) can generate nearly transform-limited 80 fs pulses at 80 mW output power around 2.4 µm wavelength [4].
On the other hand, Cr 2+ :ZnS lasers have been extensively studied both experimentally and theoretically. The zinc-blende ZnS has the larger band gap of 3.8 eV, higher thermal conductivity of 27 W/mK, higher thermal shock parameter of 7.1 W/m 1/2 , and lower dn/dT of 46 × 10 −6 K −1 , compared respectively to 2.8 eV, 18 W/mK, 5.3 W/m 1/2 , and 70 × 10 −6 K −1 in ZnSe [5,6]. Therefore, the fabrication of Cr 2+ :ZnS lasers has shown the promising prospect for high-power applications. The first continuous-wave (CW) tunable Cr 2+ :ZnS laser was first introduced using the direct diode-pumping at 1.67 µm and generating 100 mW output power of the broadly CW tunable over~280 nm around 2.3 µm wavelength [7]. Furthermore, the first mode-locked CW Cr 2+ :ZnS laser, passively mode-locked by a multiple quantum well InAs/GaSb based SESAM, generated~1.1 ps pulses at 125 mW of output power around 2.45 µm [8]. Recently, the first single-crystalline KLM femtosecond Cr 2+ :ZnS laser was reported, generating high power up to 200 mW stable around 2.4 µm wavelength and clean 110 fs pulses at 180 MHz repetition rate [9]. To date, output average power up to 800 mW at 49.9 MHz repetition rate, and pulse duration as short as 34 fs at 2.4 µm wavelength have been determined experimentally using the KLM-locked femtosecond Cr 2+ :ZnS oscillator pumped by two single-emitter InP C-Mount laser diodes [10]. Due to promising unique properties advanced Cr 2+ doped II-VI materials for medical lasers have attracted tremendous recent attention from both fundamental and practical viewpoints and their applications have become a hot and active field in the world range wide.
In recent applications, the ZnTe crystal shows attractive detection performances at frequencies below the Reststrahlen band (<5.3 THz for ZnTe) with a broadband (FWHM = 100 nm) femtosecond (fs) laser [11]. The complex dielectric constant of materials or biological and medical research was detected using THz pulses in electro-optic crystals, but the waveform distortions of THz pulses due to effects of phase mismatch, dispersive propagation, and absorption become more severe with the increase of crystal thickness. The (110)-oriented ZnTe crystal as thick as 3 mm has proven to work for the frequency below 3 THz without remarkable distortions. In view of the difficulty in the crystal growth of <110> ZnTe wafers due to the high melting point of 1568 K and structural defects, a temperature gradient solvent method under Te-rich condition with subwavelength microstructure on the ZnTe crystal surface by reactive ion etching was performed to obtain the optical level of ZnTe crystals [12]. In this case, the analysis of the bulk resistivity under a bias voltage of 1 V indicates that ZnTe:V (Zn 1−x Mn x Te) shows higher resistivity of 10 8 -10 9 Ω·cm (200-400 Ω·cm) than intrinsic ZnTe of 50-100 Ω·cm. The manganese-doped ZnTe crystal can enhance the THz emitter and sensor by 10~19% and 17~28%, respectively. The ZnTe:V crystal can increase the detection sensitivity by 20-30%. In applications requiring the use of the copper doping in cadmium telluride (CdTe) solar cells while limiting the diffusion of copper due to copper as interstitial defects with high mobility, the Cu-doped ZnTe film was selected for the back contacts in the CdTe photovoltaic devices [13]. The CdTe photovoltaic device with a ZnTe layer shows a better open-circuit voltage of 841 mV, a higher short-circuit current of 26.7 mA/cm 2 , and an external quantum efficiency as high as 17.66%. On the theoretical side, a full-potential linearized augmented plane wave (FP-LAPW) and the local orbital (LO) calculations for structural, electronic, and optical properties of zinc blende and wurtzite phases of the ZnTe indicated that the zinc blende ZnTe appears to be the most stable at room temperature [14]. The reflectivity of zinc blende and wurtzite phases of the ZnTe are about 30% and 38%, respectively, which show that the zinc blend phase ZnTe has good transmittance in the visible range, better than the wurtzite one.
For ultrashort coherent light sources, the production of transition metal-doped zinc chalcogenides has become very important. In the particular cases of ZnS, ZnSe, and ZnTe alloys individually doped with Cr 2+ , Co 2+ , Ni 2+ , or Fe 2+ , previous studies have shown that the transition metal ions in the II-VI compounds are susceptible to distortions of tetragonal symmetry [15]. Moreover, the tetragonal deformation leads to Jahn-Teller effects which further split the ground and excited states. For examples in Cr 2+ doped ZnS, ZnSe, and ZnTe alloys the wavelengths of room-temperature emission spectra are all between 1900 and 2700 nm, suggesting the emission bands from the transitions from the metastable excited state to the ground state. Furthermore, divalent chromium doped lasers of the II-VI family emitting in the mid-infrared (mid-IR) (2070-2420 nm) have been reported, such as Cr 2+ :ZnS, Cr 2+ :ZnSe, and Cr 2+ :ZnTe. The emission-quantum yield is as high as 100% at 300K, but the transition in detail is less explainable [16]. In order to explain intermediate band states of substitutional transition metal defects in the II-VI compounds, we investigate the atomic structures, band structures and electronic structures of TM 2+ x Zn 1−x Te (TM = V, Cr, Mn) alloys, in which the transition metal ion TM 2+ is distributed on the substitutional site.

Intermediate Band States
The geometry optimizations of ZnTe and TM 2+ 0.25Zn0.75Te (TM = V, Cr, Mn) through DFT-GGA calculations were shown in Figures 2-4. We clearly see that the HOMO levels of ZnTe are localized on the Te atoms in the left panel of Figure 2. The LUMO isosurfaces are significantly different from the HOMO isosurfaces. The LUMO levels of ZnTe are not only around Te atoms but also around Zn atoms. In the right panel of Figure 2 it can be clearly seen that |1>, |0>, |−1>, and |−2> levels of

Intermediate Band States
The geometry optimizations of ZnTe and TM 2+ 0.25 Zn 0.75 Te (TM = V, Cr, Mn) through DFT-GGA calculations were shown in Figures 2-4. We clearly see that the HOMO levels of ZnTe are localized on the Te atoms in the left panel of Figure 2. The LUMO isosurfaces are significantly different from the HOMO isosurfaces. The LUMO levels of ZnTe are not only around Te atoms but also around Zn atoms. In the right panel of Figure 2 it can be clearly seen that |1>, |0>, |−1>, and |−2> levels of V 2+ 0.25 Zn 0.75 Te are in the bottom of the forbidden gap of the ZnTe or between the valence E 0 and conduction E 1 band of the ZnTe. The extremely narrow band gap cannot emit in the IR laser. Furthermore, the eight-atom zinc-blende ZnTe and Cr 2+ 0.25 Zn 0.75 Te models are shown in Figure 3 The results in the right panel of Figure 3 inform that the Cr 2+ ions in the ZnTe compounds lead to Jahn-Teller effects which further split the ground and excited states. It can be seen that Cr 2+ 0.25 Zn 0.75 Te is a good laser gain medium with the multi-level system, which the upper |1>, |0>, |−1>, and |−2> levels may lead to a significant population inversion.
Moreover, the eight-atom zinc-blende ZnTe and Mn 2+ 0.25 Zn 0.75 Te models are shown in Figure 4. It can be clearly seen that there is not any level of Mn 2+ 0.25 Zn 0.75 Te in the forbidden gap of the ZnTe. The Mn 2+ 0.25 Zn 0.75 Te is a two-level system, where it is hard to achieve population inversion in the two-level system. Figure 5a shows a two-level system with the ground state 0 and the excited state 3 indicating that the rate of absorption is the same as one of spontaneous emission or stimulated emission. It is hard to achieve population inversion in the two-level system. The idea laser gain medium with the multi-level system, such as four-level system as shown in Figure 5b, may lead to a significant population inversion. The stimulated emission occurs from level 2 to level 1 and is the basis of photon amplification and the basic mechanism of the laser action. Our eight-atom Cr 2+ 0.25 Zn 0.75 Te model is the only one of the four-level system where the population inversion could be achieved.    [23,24], respectively, showing that the band gaps are strongly influenced by the two-valent species.  Table 1. The lattice constants of strain relaxed lattices of V 2+ 0.25Zn0.75Te, Cr 2+ 0.25Zn0.75Te, Mn 2+ 0.25Zn0.75Te are, respectively, 0.16%, 0.48%, and 0.16% larger than the one of ZnTe. The data also show the band gap of TM 2+ 0.25Zn0.75Te decreases as the dopant atom is substituted by ZnTe in the alloy, yielding a long-wavelength emission or a narrow band gap from the TM 2+ ion. The calculated band gap of ZnTe of 1.23 eV is in excellent agreement with the other theoretical value of 1.4 eV [22]. We note that the band gaps of V 2+ 0.25Zn0.75Te and Cr 2+ 0.25Zn0.75Te are somewhat lower than other theoretical gaps of V0.25Zn0.75Te and Cr0.25Zn0.75Te obtained by FP-LAPW calculations without using the two-valent chromium and vanadium [23,24], respectively, showing that the band gaps are strongly influenced by the two-valent species. Previous studies reported that the infrared femtosecond lasers using transition metals doped II-VI materials with transition metal compositions up to 3% [25][26][27]. Therefore, our models with transition metals compositions of 25% cannot refer to reality. In order to compare with the experimental observations of transition metals Cr 2+ doped ZnTe materials with low concentration we modeled 64-atom zinc-blende ZnTe and Cr 2+ 0.03Zn0.97Te. In fact, as we will show below, the use of the 64-atom large cell allows us to prove that the ZnTe with Cr 2+ dopants as low as 3%, not included in the V 2+ -and Mn 2+ -doped ZnTe, is nearly identical within the four-level system as an 8-atom small cell. The reasons which we have not included doping with V 2+ and Mn 2+ for the larger cell are as following: (a) no level of Mn 2+ 0.25Zn0.75Te in the forbidden gap of the ZnTe, showing a two-level system and limiting to the population inversion, (b) the defect levels of V 2+ 0.25Zn0.75Te in the bottom of the forbidden gap of the ZnTe, showing that the extremely narrow band gap cannot emit in the IR laser, (c) the IR laser emitted in the small cell of Cr 2+ 0.25Zn0.75Te, suggesting that IR laser will be emitted in the large unit of Cr 2+ 0.03Zn0.97Te. According to experimental observations [1][2][3][4][5][6][7][8][9][10]15,16], it is perhaps not  Previous studies reported that the infrared femtosecond lasers using transition metals doped II-VI materials with transition metal compositions up to 3% [25][26][27]. Therefore, our models with transition metals compositions of 25% cannot refer to reality. In order to compare with the experimental observations of transition metals Cr 2+ doped ZnTe materials with low concentration we modeled 64-atom zinc-blende ZnTe and Cr 2+ 0.03 Zn 0.97 Te. In fact, as we will show below, the use of the 64-atom large cell allows us to prove that the ZnTe with Cr 2+ dopants as low as 3%, not included in the V 2+ -and Mn 2+ -doped ZnTe, is nearly identical within the four-level system as an 8- Figure 6. We can be clearly seen that |1>, |0>, |−1>, and |−2> levels of Cr 2+ 0.03 Zn 0.97 Te are in the forbidden gap of the ZnTe. The fundamental gap between the conduction band and defect levels can be corrected with a "scissor operator" to match the photoluminescence (PL) peaks due to the well-known bandgap underestimation of DFT calculations. The calculated band gap of 0.94 eV is corrected by the scissor correction (the scissors operator is 1.63 eV) to approach the PL emission in the 2.57 eV spectral region. |0> and |−1> metastable excited states to E 0 ground state are scaled up to 0.49 eV and 0.46 eV, which the wavelengths are 2530 nm and 2695 nm, respectively. Our results agree with previously reported experimental results [15]. In order to understand how defects in ZnTe alloys we calculate the formation energy and defect formation energy of ZnTe and TM 2+ 0.25 Zn 0.75 Te (TM = V, Cr, Mn). The formation energy E f can be written as where E tot is the total energy of bulk ZnTe; n i and µ i are the number of atoms and the chemical potential of the ith constituent of the bulk. The defect formation energy E d can be determined by the difference of the formation energies between bulks ZnTe and TM 2+ 0.25 Zn 0.75 Te (TM = V, Cr, Mn) and given by where E tot_defect is the total energy of bulk TM 2+ 0.25 Zn 0.75 Te (TM = V, Cr, Mn). n d is the number of TM atoms. µ d and µ Zn are the chemical potential of TM and Zn, respectively. Table 2 lists the results of the formation energy and the defect formation energy for ZnTe and TM 2+ 0.25 Zn 0.75 Te (TM = V, Cr, Mn).
We find that the V 2+ ion preferentially occupies the Zn site, leading to the minimum defect formation energy of 2.441 eV. In contrast, Cr 2+ ion occupies the Zn site and becomes more unstable due to the maximum defect formation energy of 3.158 eV.

Conclusions
The intermediate band states of substitutional transition metal defects in TM 2+ x Zn 1−x Te (TM = V, Cr, Mn) alloys were studied by first-principles calculations. By studying the atomic structures, band structures and electronic structures of 8-atom and 64-atom zinc-blende lattice unit cells, we found that the Cr 2+ ion in the ZnTe compounds leads to Jahn-Teller effects which further split the ground and excited states. Our scissor-corrected wavelengths of the transitions from the metastable excited state to the ground state are 2530 nm and 2695 nm. Our results agree with the corresponding observed experiments [15]. In this case we have succeeded in explaining the intermediate band states of substitutional transition metal defects in the II-VI compounds, which enable us to determine the emission spectra of next generation diode lasers.