Thermodynamic modeling of the PbX (X=S,Te) phase diagram using a five sub-lattice and two sub-lattice model

Abstract

Five-sublattice and two-sublattice models have been built to describe the PbX (X=S,Te) semiconductors using the CALPHAD method. The five-sublattice model has three additional sublattices to explicitly model interstitials, electrons, and holes. The experimental literature has been critically reviewed and many high temperature carrier concentration results used in previous assessments have been shown to be unreliable. First-principle calculations for the formation energies of neutral defects and their respective ionization energies have also been incorporated into the models. The models show an improvement over previous assessments of PbTe and are the first time PbS has not been treated as a stoichiometric compound in a CALPHAD assessment.

The importance of phase equilibrium for doping efficiency: iodine doped PbTe

“…In both cases, the material has room temperature carrier concentrations B10 18 cm À3 and bipolar conduction above room temperature in agreement with previous reports. 24,25 The properties of iodine-doped PbTe also vary drastically between Pb-rich and Te-rich conditions (Table 1). Degenerate n-type behavior (410 19 cm À3 ) is measured after annealing doped samples with Pb-rich material at 973 K, while nondegenerate material is reproducibly synthesized when iodinedoped PbTe is equilibrated in Te-rich conditions.…”

“…Contrary to typical chemical intuition applied during synthesis, PbTe (like other ''line compound'' semiconductors) should have different doping properties when it is prepared slightly cation-or anion-rich. This is due to a finite width of the singlephase region near the PbTe composition 24,25 required by configurational entropy considerations. 26 It has been found both experimentally 24,25 and theoretically 27 that Pb-rich PbTe is Fig.…”

“…This is due to a finite width of the singlephase region near the PbTe composition 24,25 required by configurational entropy considerations. 26 It has been found both experimentally 24,25 and theoretically 27 that Pb-rich PbTe is Fig. 1 A schematic, isothermal, ternary phase diagram of a binary semiconductor, AB, doped with C. The single-phase region around the compound AB has a width due to A cation and B anion vacancies and extends towards compounds AC and AC 2 due to solubility of dopant C (both width and extension are exaggerated).…”

A Review of Calphad Modeling of Ordered Phases

“…However, in reality there exists always a small range of solubility and in some cases it is important to model this, for example in compound semiconductors. [22][23][24][25][26] Defects can be vacancies, anti-site atoms, and interstitials and they can also be charged. When developing multicomponent databases the defects considered are…”