Intermediate Band Studies of Substitutional V²⁺, Cr²⁺, and Mn²⁺ Defects in ZnTe Alloys

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This work confirms the emission band of Cr²⁺_0.03Zn_0.97Te 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 V²⁺, Cr²⁺, and Mn²⁺ ions in ZnTe alloys. The intermediate band states of substitutional transition metal defects of TM²⁺_xZn_1−xTe (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 effects lead to the wavelengths 2530 nm and 2695 nm in the emission spectra. Our findings agree with previously reported experimental results.

1. 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 Cr²⁺: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) Cr²⁺:ZnSe laser has two distinct regimes. In the first, the output power and duration of the high-power soliton regime of Cr²⁺:ZnSe laser is about 300 mW and 100 fs, respectively. In contrast, the output power and pulse duration of the chirped pulse regime of Cr²⁺:ZnSe laser is about 170 mW and 1 ps, respectively [2]. In addition, another KLM-locked Cr²⁺: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 Cr²⁺: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, Cr²⁺: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 Cr²⁺:ZnS lasers has shown the promising prospect for high-power applications. The first continuous-wave (CW) tunable Cr²⁺: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 Cr²⁺: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 Cr²⁺: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 Cr²⁺:ZnS oscillator pumped by two single-emitter InP C-Mount laser diodes [10]. Due to promising unique properties advanced Cr²⁺ 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−xMn_xTe) shows higher resistivity of 10⁸–10⁹ 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/cm², 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 Cr²⁺, Co²⁺, Ni²⁺, or Fe²⁺, 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 Cr²⁺ 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 Cr²⁺:ZnS, Cr²⁺:ZnSe, and Cr²⁺: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 TM²⁺_xZn_1−xTe (TM = V, Cr, Mn) alloys, in which the transition metal ion TM²⁺ is distributed on the substitutional site.

2. Theoretical Approach

We report on ab initio calculations to study the intermediate band states of substitutional transition metal defects in TM²⁺_xZn_1−xTe (TM = V, Cr, Mn) alloys. Our ab initio studies were based on the density functional theory (DFT) methods and calculated with the Vanderbilt ultrasoft pseudopotentials (USPPs) using the Cambridge serial total energy package (CASTEP) [17,18]. The utilized USPPs to efficiently treat ion-electron interactions derived from the projector augmented wave (PAW) method and the generalized gradient approximation (GGA) with the Perdew-Wang (PW91) exchange-correlation functional [19,20]. The electronic configurations for the valence electrons are V: 3s²3p⁶4s²3d³, Cr: 3s²3p⁶4s¹3d⁵, Mn: 4s²3d⁵, Zn: 4s²3d¹⁰, and Te: 4d⁸5p⁴. The ZnTe (space group: 216 F-43m) and TM²⁺_xZn_1-xTe (TM = V, Cr, Mn) alloys were constructed using bulk crystalline configurations with discrete TM²⁺ compositions of 25% and 3% (or x = 0.25 and x = 0.03). The structural properties of TM²⁺_0.25Zn_0.75Te, and TM²⁺_0.03Zn_0.97Te were modeled by substituting one TM²⁺ ion on the Zn site within an 8-atom and 64-atom zinc-blende lattice unit cells, respectively. The 8-atom zinc-blende ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn) models and 64-atom zinc-blende Cr²⁺_0.03Zn_0.97Te model are shown in Figure 1. The Brillouin zones were performed using a 4 × 4 × 4 (2 × 2 × 2) Monkhorst-Pack grid and a 400 eV (150 eV) energy cutoff in TM²⁺_0.25Zn_0.75Te (TM²⁺_0.03Zn_0.97Te). The highest occupied Kohn–Sham orbitals (HOMO) and lowest unoccupied Kohn–Sham orbitals (LUMO) have been used to analyze the intermediate band states of substitutional transition metal defects in TM²⁺_xZn_1-xTe (TM = V, Cr, Mn) alloys. Recent theoretical work confirms that the infrared light emission of 0.852 eV derived from first-principles theoretical models is close to the value 0.842 eV of experimental photoluminescence (PL) defect-peak observations of the twist–bonded dislocation network [21].

3. Intermediate Band States

The geometry optimizations of ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn) through DFT-GGA calculations were shown in Figure 2, Figure 3 and Figure 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 V²⁺_0.25Zn_0.75Te are in the bottom of the forbidden gap of the ZnTe or between the valence E₀ and conduction E₁ band of the ZnTe. The extremely narrow band gap cannot emit in the IR laser.

Furthermore, the eight-atom zinc-blende ZnTe and Cr²⁺_0.25Zn_0.75Te models are shown in Figure 3 The results in the right panel of Figure 3 inform that the Cr²⁺ ions in the ZnTe compounds lead to Jahn-Teller effects which further split the ground and excited states. It can be seen that Cr²⁺_0.25Zn_0.75Te 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 Mn²⁺_0.25Zn_0.75Te models are shown in Figure 4. It can be clearly seen that there is not any level of Mn²⁺_0.25Zn_0.75Te in the forbidden gap of the ZnTe. The Mn²⁺_0.25Zn_0.75Te 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 Cr²⁺_0.25Zn_0.75Te model is the only one of the four-level system where the population inversion could be achieved.

The calculated ground state structures for ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn) and their optical properties (band gaps) are summarized in

Table 1. The lattice constants of optimized atomic structures of ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn) fit other theoretical values. The corresponding band gaps are compared with other calculated values.

Compounds	Lattice Constant (Å)		Energy Gap (eV)
ZnTe	6.19	6.09 a	1.23	1.4 a
V2+0.25Zn0.75Te	6.20	6.22 b	0.25	0.33 b,*
Cr2+0.25Zn0.75Te	6.22	6.22 c	0.49	0.77 c,*
Mn2+0.25Zn0.75Te	6.20		0.68

^a Ref. [22]; ^b Ref. [23]; ^c Ref. [24]; * Note: bang gaps of neutral species, V_0.25Zn_0.75Te and Cr_0.25Zn_0.75Te.

. The lattice constants of strain relaxed lattices of V²⁺_0.25Zn_0.75Te, Cr²⁺_0.25Zn_0.75Te, Mn²⁺_0.25Zn_0.75Te are, respectively, 0.16%, 0.48%, and 0.16% larger than the one of ZnTe. The data also show the band gap of TM²⁺_0.25Zn_0.75Te decreases as the dopant atom is substituted by ZnTe in the alloy, yielding a long-wavelength emission or a narrow band gap from the TM²⁺ 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 V²⁺_0.25Zn_0.75Te and Cr²⁺_0.25Zn_0.75Te are somewhat lower than other theoretical gaps of V_0.25Zn_0.75Te and Cr_0.25Zn_0.75Te 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 Cr²⁺ doped ZnTe materials with low concentration we modeled 64-atom zinc-blende ZnTe and Cr²⁺_0.03Zn_0.97Te. In fact, as we will show below, the use of the 64-atom large cell allows us to prove that the ZnTe with Cr²⁺ dopants as low as 3%, not included in the V²⁺- and Mn²⁺-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 V²⁺ and Mn²⁺ for the larger cell are as following: (a) no level of Mn²⁺_0.25Zn_0.75Te in the forbidden gap of the ZnTe, showing a two-level system and limiting to the population inversion, (b) the defect levels of V²⁺_0.25Zn_0.75Te 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 Cr²⁺_0.25Zn_0.75Te, suggesting that IR laser will be emitted in the large unit of Cr²⁺_0.03Zn_0.97Te. According to experimental observations [1,2,3,4,5,6,7,8,9,10,15,16], it is perhaps not surprising that the II–VI compounds doped with transition metal Cr²⁺ are mature laser materials.

The HOMO and LUMO of ZnTe and Cr²⁺_0.03Zn_0.97Te were calculated as shown in Figure 6. We can be clearly seen that |1>, |0>, |−1>, and |−2> levels of Cr²⁺_0.03Zn_0.97Te 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 E₀ 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 TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn). The formation energy E_f can be written as

E_f = E_tot − Σ n_iμ_i,

(1)

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 TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn) and given by

E_d = E_{tot_defect} − E_tot − n_d (μ_d − μ_Zn),

(2)

where E_{tot_defect} is the total energy of bulk TM²⁺_0.25Zn_0.75Te (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. Formation and defect formation energies of ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn).

	Formation Energy (eV)	Defect Formation Energy (eV)
ZnTe	−3.765	0
V2+0.25Zn0.75Te	−1.325	2.441
Cr2+0.25Zn0.75Te	−0.608	3.158
Mn2+0.25Zn0.75Te	−0.901	2.864

lists the results of the formation energy and the defect formation energy for ZnTe and TM²⁺_0.25Zn_0.75Te (TM = V, Cr, Mn). We find that the V²⁺ ion preferentially occupies the Zn site, leading to the minimum defect formation energy of 2.441 eV. In contrast, Cr²⁺ ion occupies the Zn site and becomes more unstable due to the maximum defect formation energy of 3.158 eV.

4. Conclusions

The intermediate band states of substitutional transition metal defects in TM²⁺_xZn_1−xTe (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 Cr²⁺ 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.