The (16 atom) conventional unit cell of is shown. (a) indicates the crystalline structure. (b) shows the defect in and figure (c) indicates the crystalline structure of .
Projected density of states for bulk . The Fermi energy is the zero of energy.
Calculated phase diagram for the Cu–Al–S system indicating the stable phases in the vicinity of . and indicates Cu-rich, Al-rich regions. Since is defined through Eq. (2), the also indicates a S-poor region. The diagonal line which links the and axes represents a sulfur rich region with .
Defect formation energies at the border of the stability region. This region is defined by the lines connecting the points 1–2-3–4 in Fig. 3.
Defect formation energies at the four corners of the stability region of (Fig. 3). At these four points, labeled 1, 2, 3, and 4, the chemical potentials have fixed values, and the defect formation energy is a function of the Fermi energy, whose values range have been assumed to be vary from the VBM up to the CBM. The breaking points of each line indicate the transition energies between different charged states of the defect. In each plot, vertical dashed-dotted lines mark the and -type doping limits, and a red dashed-dotted line indicates the equilibrium Fermi energy , which has been calculated self-consistently using the neutrality condition [Eq. (3)] at a temperature of 900 K.
Calculated defect transition energies as defined by Eq. (12). Their precise values are given in Table III. The transitional charge states are indicated in parenthesis. The thick black lines at the top and bottom represent the CBM and VBM respectively.
Convergence on the value of for increasing system size.
Calculated lattice constants for . The experimental values (Ref. 1) are given in parenthesis.
Calculated transition energies of vacancies and substitutional defects as defined by Eq. (12). The corresponding charge states for these transitions are given in parentheses. The transition energies are relative to the VBM for acceptors and to the CBM for donors. The transition energy in is below the VBM.
Observed PL emissions on samples. The synthesis methods are indicated in the second column. The temperature at which the PL emission was observed and its corresponding intensity and FWHM are indicated in the third and fourth columns. Columns five and six show the proposed experimental and theoretical origins of the observed PL emissions: (A) FE recombination; excitonic emission bound to a neutral donor; excitonic emission bound to a singly-charged donor; radiative recombination of a free hole and a donor; excitonic emission bound to a neutral acceptor; excitonic emission bound to a singly-charged acceptor; radiative recombination of a free electron and an acceptor (free-to-bound emission); and is a donor acceptor pair recombination. The subscript s indicates a strong PL intensity.
Calculated values of the PL emission energies, , associated with different defect states in . is the calculated band gap and is the FE binding energy. The second column shows the form Eq. (17) adopt depending on the type of PL emission and the defects involved. The values of the electronic transition energies used on the expressions on the second column were taken from Table III.
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