CdGa2Te4: Defect-Chalcopyrite Semiconductor

• CdGa2Te4 is a tetragonal defect-chalcopyrite semiconductor characterized by a direct band gap, strong visible-range absorption, low exciton binding energy, and remarkable stability.
• First-principles studies and SCAPS-1D simulations reveal that optimizing absorber thickness and defect density can achieve efficiencies above 18% in thin-film photovoltaic devices.
• Transport analyses show that CdGa2Te4 exhibits ultralow lattice thermal conductivity, sizeable Seebeck coefficient, and moderate high-temperature stability, making it viable for thermoelectric and thermal-barrier applications.

CdGa$_2$Te$_4$ is a tetragonal defect-chalcopyrite, ordered-vacancy semiconductor in space group I-4 (No. 82) that has been studied by first-principles electronic-structure methods, optical-response calculations, SCAPS-1D device simulation, and BoltzTraP2 transport analysis as a candidate absorber for thin-film photovoltaics and as a chalcogenide for waste-heat recovery and thermal-barrier operation (Rifat et al., 6 Oct 2025, Mishra et al., 2015, Rifat et al., 20 Oct 2025). Across these studies, the compound is consistently treated as a direct-gap semiconductor with strong visible-range absorption, low exciton binding energy, and thermodynamic, dynamic, and mechanical stability, while also exhibiting notable sensitivity to structural distortion and a pronounced dependence of predicted device efficiency on defect density.

1. Crystal chemistry, bonding, and stability

CdGa$_2$Te$_4$ crystallizes in the defect-chalcopyrite tetragonal structure, space group I-4 (No. 82), with optimized GGA-PBEsol lattice parameters $a=b=6.22$ Å and $c=11.92$ Å (Rifat et al., 6 Oct 2025, Rifat et al., 20 Oct 2025). One TB-LMTO/LDA study reported $a=6.18$ Å and $c=12.22$ Å, with tetragonal distortion $\eta=c/(2a)\simeq 0.989$, and compared these values with experiment, $a_{\mathrm{exp}}=6.10$ Å and $_4$0 Å, giving $_4$1 (Mishra et al., 2015). The unit-cell description is consistent at the level of Wyckoff-site occupancy: Cd occupies the 2a site, Ga is split between 2b and 2d, and Te resides at 8g (Rifat et al., 6 Oct 2025, Mishra et al., 2015, Rifat et al., 20 Oct 2025). The reported atomic coordinates differ in representation across studies; one report places Te near $_4$2, while another expresses the Te positions as $_4$3 with $_4$4, $_4$5, and $_4$6 (Rifat et al., 6 Oct 2025, Mishra et al., 2015).

The local coordination is tetrahedral. Each Cd atom is tetrahedrally coordinated by four Te atoms with Cd-Te distances of $_4$7 Å, and each Ga atom has a distorted tetrahedral environment of Te neighbors with Ga-Te bond lengths $_4$8–$_4$9 Å; the Te atoms bridge Cd and Ga centers to form a three-dimensional covalent network (Rifat et al., 6 Oct 2025). Thermodynamic stability is supported by a calculated formation energy $_2$0 eV/atom and cohesive energy $_2$1 eV/atom (Rifat et al., 6 Oct 2025, Rifat et al., 20 Oct 2025).

Dynamic stability was assessed by phonon dispersion and found to be robust: no imaginary frequencies were reported throughout the Brillouin zone, with three acoustic and eighteen optical branches and an evident acoustic-optic gap of about $_2$2 THz (Rifat et al., 20 Oct 2025). Elastic constants $_2$3, $_2$4, $_2$5, $_2$6, $_2$7, and $_2$8 GPa yield Voigt-Reuss-Hill averages $_2$9 GPa, $_4$0 GPa, $_4$1 GPa, and $_4$2 (Rifat et al., 20 Oct 2025). The same study classified the compound as brittle, based on Pugh’s ratio $_4$3 and $_4$4, and as moderately elastically anisotropic, with universal anisotropy index $_4$5 (Rifat et al., 20 Oct 2025).

2. Structural distortion and non-ideal chalcopyrite behavior

A distinct line of work examined CdGa$_4$6Te$_4$7 specifically as a non-ideal defect chalcopyrite, emphasizing the roles of anion displacement and tetragonal distortion (Mishra et al., 2015). In that formulation, the ideal reference structure is defined by $_4$8 and $_4$9, $a=b=6.22$0, while the anion-displacement parameter is written as

$a=b=6.22$1

where $a=b=6.22$2 is the ideal cation-anion bond length (Mishra et al., 2015).

The same study reported that relaxation away from the ideal structure changes both electronic and optical behavior. For CdGa$a=b=6.22$3Te$a=b=6.22$4, the band gap increases from $a=b=6.22$5 eV to $a=b=6.22$6 eV, corresponding to $a=b=6.22$7 eV and a relative change of about $a=b=6.22$8 (Mishra et al., 2015). The physical interpretation given is that anion displacement $a=b=6.22$9 and tetragonal distortion $c=11.92$0 alter cation-anion bond lengths and local symmetry, modify the overlap of Te $c=11.92$1 and Ga $c=11.92$2 orbitals, strengthen the crystal-field splitting at the valence-band maximum, raise $c=11.92$3, and slightly lower $c=11.92$4 (Mishra et al., 2015).

Optically, the joint density of states was reported to remain nearly unchanged by distortion, whereas the optical matrix elements $c=11.92$5 are reduced by $c=11.92$6 in the non-ideal structure relative to the ideal one (Mishra et al., 2015). This distinction is central to the interpretation of why structural distortion can significantly reshape dielectric response without comparably large changes in the underlying band-counting picture. The same analysis further states that anisotropy becomes more pronounced upon distortion because $c=11.92$7 deviates from unity, leading to different polarization responses along and perpendicular to the $c=11.92$8-axis (Mishra et al., 2015).

3. Electronic structure and band-edge character

Electronic-structure calculations consistently classify CdGa$c=11.92$9Te$a=6.18$0 as a direct-gap semiconductor, but the reported reciprocal-space location of the direct gap differs across studies (Rifat et al., 6 Oct 2025, Rifat et al., 20 Oct 2025). One GGA-PBEsol calculation gives a direct gap at $a=6.18$1 with $a=6.18$2 eV, while HSE06 yields $a=6.18$3 eV and mBJ yields $a=6.18$4 eV (Rifat et al., 6 Oct 2025). Another first-principles study reports a direct band gap at the $a=6.18$5 point, with the same GGA-PBEsol gap of $a=6.18$6 eV and the same HSE06 gap of $a=6.18$7 eV (Rifat et al., 20 Oct 2025). A TB-LMTO/LDA treatment also found a direct gap at $a=6.18$8, with the ideal and distorted structures giving $a=6.18$9 and $c=12.22$0 eV, respectively (Mishra et al., 2015). The direct-gap character is therefore common to all cited calculations, while the $c=12.22$1-point assignment is not uniform.

The density of states likewise shows broad agreement on semiconducting character with some variation in orbital assignment. One study states that the valence-band top is dominated by Te-5$c=12.22$2 states from about $c=12.22$3 eV to $c=12.22$4 eV, while the conduction-band bottom is composed mainly of Ga-4$c=12.22$5 and Te-5$c=12.22$6 hybrid states, with minor Cd-4$c=12.22$7 contributions appearing about $c=12.22$8–$c=12.22$9 eV above the Fermi level (Rifat et al., 6 Oct 2025). Another reports zero states at $\eta=c/(2a)\simeq 0.989$0, with Te-5$\eta=c/(2a)\simeq 0.989$1 dominating both valence and conduction edges and Ga-4$\eta=c/(2a)\simeq 0.989$2 hybridization entering the projected density of states (Rifat et al., 20 Oct 2025). In both accounts, $\eta=c/(2a)\simeq 0.989$3-derived chalcogen states dominate the band edges.

Carrier masses have been reported as light for electrons and substantially heavier for holes. The effective masses are $\eta=c/(2a)\simeq 0.989$4 and $\eta=c/(2a)\simeq 0.989$5 (Rifat et al., 6 Oct 2025, Rifat et al., 20 Oct 2025). A parabolic near-edge description was also used in one study,

$\eta=c/(2a)\simeq 0.989$6

highlighting the conventional effective-mass picture near the gap (Mishra et al., 2015).

4. Optical response and excitonic regime

The optical response of CdGa$\eta=c/(2a)\simeq 0.989$7Te$\eta=c/(2a)\simeq 0.989$8 is governed by direct interband transitions and strong visible-range absorption (Rifat et al., 6 Oct 2025, Mishra et al., 2015). In the formalism used for the dielectric response,

$\eta=c/(2a)\simeq 0.989$9

with

$a_{\mathrm{exp}}=6.10$0

and

$a_{\mathrm{exp}}=6.10$1

(Mishra et al., 2015).

A first-principles optical study reported that the real part $a_{\mathrm{exp}}=6.10$2 peaks at $a_{\mathrm{exp}}=6.10$3 eV and then decays, confirming non-metallicity, while the imaginary part $a_{\mathrm{exp}}=6.10$4 rises sharply from the absorption edge near $a_{\mathrm{exp}}=6.10$5 eV to a broad maximum at $a_{\mathrm{exp}}=6.10$6 eV (Rifat et al., 6 Oct 2025). The absorption coefficient $a_{\mathrm{exp}}=6.10$7 reaches $a_{\mathrm{exp}}=6.10$8 cm$a_{\mathrm{exp}}=6.10$9 in the visible region, and the steep direct transitions between Te-5$_4$00 valence states and Ga-4$_4$01 conduction states yield $_4$02–$_4$03 cm$_4$04 for $_4$05–$_4$06 eV photons (Rifat et al., 6 Oct 2025). Another study quantified static optical anisotropy in the non-ideal structure as $_4$07, $_4$08, $_4$09, and $_4$10, and noted that the highest $_4$11 peak for $_4$12 at about $_4$13 eV in the non-ideal structure splits into peaks near $_4$14 and $_4$15 eV in the ideal case (Mishra et al., 2015).

Excitonic characteristics have been analyzed within a hydrogenic model,

$_4$16

where $_4$17 is the reduced mass and $_4$18 is the static dielectric constant (Rifat et al., 6 Oct 2025). For CdGa$_4$19Te$_4$20, the reported values are $_4$21, $_4$22, $_4$23, and $_4$24, leading to $_4$25 meV and $_4$26 Å (Rifat et al., 6 Oct 2025). The corresponding exciton dissociation temperature is

$_4$27

and the reported interpretation is that at room temperature excitons readily dissociate into free carriers (Rifat et al., 6 Oct 2025). In the paired CdGa$_4$28Te$_4$29/ZnGa$_4$30Te$_4$31 comparison, the exciton binding energies span $_4$32–$_4$33 meV, Bohr radii $_4$34–$_4$35 Å, and exciton temperatures $_4$36–$_4$37 K (Rifat et al., 6 Oct 2025).

5. Photovoltaic heterostructures and SCAPS-1D simulation

CdGa$_4$38Te$_4$39 has been modeled as the absorber in a thin-film heterostructure of the form Pt / CdS / CdGa$_4$40Te$_4$41 / Cu$_4$42O / Ti using SCAPS-1D (Rifat et al., 6 Oct 2025). The detailed architecture is specified as Pt (front contact) / $_4$43-CdS (100 nm ETL) / $_4$44-CdGa$_4$45Te$_4$46 (1000–1800 nm absorber) / $_4$47-Cu$_4$48O (200 nm HTL) / Ti (back contact) (Rifat et al., 6 Oct 2025). The same source states that the ideal absorber thickness for $_4$49Ga$_4$50Te$_4$51 $_4$52 is $_4$53–$_4$54 nm and that the CdS buffer layer is around $_4$55 nm, while the detailed CdGa$_4$56Te$_4$57 layer set uses a 100 nm CdS buffer (Rifat et al., 6 Oct 2025).

The key CdGa$_4$58Te$_4$59 simulation parameters are absorber thickness $_4$60 nm, acceptor density $_4$61 cm$_4$62, and defect density $_4$63 cm$_4$64 (Rifat et al., 6 Oct 2025). The CdS buffer is assigned $_4$65 nm and $_4$66 cm$_4$67, while the Cu$_4$68O hole-transport layer is assigned $_4$69 nm, $_4$70 cm$_4$71, and $_4$72 cm$_4$73 (Rifat et al., 6 Oct 2025).

Parametric trends in the SCAPS calculations are explicit. Increasing absorber thickness from $_4$74 to $_4$75 nm raises $_4$76 and $_4$77, with saturation beyond about $_4$78 nm, while $_4$79 slightly decreases because of series resistance (Rifat et al., 6 Oct 2025). Raising absorber doping from $_4$80 to $_4$81 cm$_4$82 improves $_4$83 and fill factor, with an optimum $_4$84 cm$_4$85 (Rifat et al., 6 Oct 2025). Increasing defect density from $_4$86 to $_4$87 cm$_4$88 degrades $_4$89, $_4$90, and $_4$91; to obtain an efficiency above $_4$92, the defect density in the absorber layer should be kept below $_4$93 cm$_4$94, and the detailed discussion states that maintaining $_4$95 cm$_4$96 is critical (Rifat et al., 6 Oct 2025). Series resistance $_4$97 reduces fill factor and $_4$98, whereas higher shunt resistance $_4$99 saturates all performance metrics (Rifat et al., 6 Oct 2025). Elevated operating temperature from $_2$00 to $_2$01 K lowers $_2$02 and fill factor but slightly increases $_2$03 due to thermally enhanced carrier generation (Rifat et al., 6 Oct 2025).

Under AM 1.5G illumination at $_2$04 K, the optimized CdS/CdGa$_2$05Te$_2$06/Cu$_2$07O device is reported to achieve $_2$08 mA/cm$_2$09, $_2$10 V, $_2$11, and $_2$12 (Rifat et al., 6 Oct 2025). The same study states that extrapolating to slightly lower defect densities and optimized series/shunt resistances suggests $_2$13 is attainable for $_2$14–$_2$15 nm and $_2$16 cm$_2$17 (Rifat et al., 6 Oct 2025).

6. Thermoelectric transport, thermal management, and broader materials context

Beyond photovoltaic modeling, CdGa$_2$18Te$_2$19 has also been evaluated as a thermoelectric and thermal-barrier material by combining DFT with BoltzTraP2 under the constant-relaxation-time approximation (Rifat et al., 20 Oct 2025). The transport coefficients $_2$20, $_2$21, and $_2$22 were derived from band derivatives, and the figure of merit was defined as

$_2$23

For CdGa$_2$24Te$_2$25, the Seebeck coefficient is positive, indicating $_2$26-type conduction, with $_2$27, a maximum near $_2$28 around $_2$29 K, and a gradual decrease toward about $_2$30 at $_2$31 K (Rifat et al., 20 Oct 2025).

The electrical conductivity scaled by relaxation time rises strongly with temperature, from $_2$32 to $_2$33 at $_2$34 K (Rifat et al., 20 Oct 2025). The electronic thermal conductivity likewise increases, from $_2$35 W/m·K·s at $_2$36 K to $_2$37 W/m·K·s at $_2$38 K, while the lattice thermal conductivity $_2$39, calculated via Slack’s model, is ultralow and sub-1 W/m·K at $_2$40 K (Rifat et al., 20 Oct 2025). The power factor $_2$41 is described qualitatively as increasing with temperature because $_2$42 rises while $_2$43 remains large, and the figure of merit increases from $_2$44 to $_2$45 (Rifat et al., 20 Oct 2025).

The same study extends the discussion to thermal-barrier behavior. The melting temperature inferred from elastic constants is $_2$46 K, the thermal expansion coefficient is $_2$47, and $_2$48 is on the order of $_2$49–$_2$50 W/m·K below $_2$51 K, with a reported minimum $_2$52 W/m·K (Rifat et al., 20 Oct 2025). Combined with moderate $_2$53 and low $_2$54, these values were taken to indicate suitability as a thermal barrier coating below about $_2$55 K (Rifat et al., 20 Oct 2025).

Taken together, the available calculations place CdGa$_2$56Te$_2$57 among multifunctional telluride semiconductors with competitive optoelectronic properties and transport behavior. The photovoltaic literature emphasizes a near-optimal direct band gap, very high visible-range absorption, low exciton binding, and sensitivity to absorber defect density, whereas the transport literature emphasizes ultralow lattice thermal conductivity, sizeable Seebeck coefficient, and moderate high-temperature stability (Rifat et al., 6 Oct 2025, Rifat et al., 20 Oct 2025). The main limitations identified in the photovoltaic study are the synthesis of high-quality films with minimal bulk and interface defects, control of grain boundaries, and the issue of replacing toxic Cd with less hazardous elements; future work was directed toward experimental film growth, heterojunction engineering, and advanced passivation strategies (Rifat et al., 6 Oct 2025).