The efficiency of $\mathrm{CuIn}{\mathrm{Se}}_2$ based solar cell devices could improve significantly if $\mathrm{CuGa}{\mathrm{Se}}_2$, a wider band gap chalcopyrite semiconductor, could be added to the $\mathrm{CuIn}{\mathrm{Se}}_2$ absorber layer. This is, however, limited by the difficulty of doping $n$-type $\mathrm{CuGa}{\mathrm{Se}}_2$ and, hence, in its alloys with ${\mathrm{CuInSe}}_2$. Indeed, wider-gap members of semiconductor series are often more difficult to dope than lower-gap members of the same series. We find that in chalcopyrites, there are three critical values of the Fermi energy $E_F$ that control $n$-type doping: (i) $E_F^{n,\mathrm{pin}}$ is the value of $E_F$ where the energy to form Cu vacancies is zero. At this point, the spontaneously formed vacancies ($=$acceptors) kill all electrons. (ii) $E_F^{n,\mathrm{comp}}$ is the value of $E_F$ where the energy to form a Cu vacancy equals the energy to form an $n$-type dopant, e.g., ${\mathrm{Cd}}_{\mathrm{Cu}}$. (iii) $E_F^{n,\text{site}}$ is the value of $E_F$ where the formation of Cd-on-In is equal to the formation of Cd-on-Cu. For good $n$-type doping, $E_F^{n,\mathrm{pin}}$, $E_F^{n,\mathrm{comp}}$, and $E_F^{n,\text{site}}$ need to be as high as possible in the gap. We find that these quantities are higher in the gap in $\mathrm{CuIn}{\mathrm{Se}}_2$ than in $\mathrm{CuGa}{\mathrm{Se}}_2$, so the latter is difficult to dope $n$-type. In this work, we calculate all three critical Fermi energies and study theoretically the best growth condition for $n$-type $\mathrm{CuIn}{\mathrm{Se}}_2$ and $\mathrm{CuGa}{\mathrm{Se}}_2$ with possible cation and anion doping. We find that the intrinsic defects such as ${\mathrm{V}}_{\mathrm{Cu}}$ and ${\mathrm{In}}_{\mathrm{Cu}}$ or ${\mathrm{Ga}}_{\mathrm{Cu}}$ play significant roles in doping in both chalcopyrites. For group-II cation (Cd, Zn, or Mg) doping, the best $n$-type growth condition is $\mathrm{In}∕\mathrm{Ga}$-rich, and maximal Se-poor, which is also the optimal condition for stabilizing the intrinsic ${\mathrm{In}}_{\mathrm{Cu}}∕{\mathrm{Ga}}_{\mathrm{Cu}}$ donors. Bulk $\mathrm{CuIn}{\mathrm{Se}}_2$ can be doped at equilibrium $n$-type, but bulk $\mathrm{CuGa}{\mathrm{Se}}_2$ cannot be due to the low formation energy of intrinsic Cu-vacancy. For halogen anion doping, the best $n$-type materials growth is still under $\mathrm{In}∕\mathrm{Ga}$-rich, and maximal Se-poor conditions. These conditions are not best for halogen substitutional defects, but are optimal for intrinsic ${\mathrm{In}}_{\mathrm{Cu}}∕{\mathrm{Ga}}_{\mathrm{Cu}}$ donors. Again, $\mathrm{CuGa}{\mathrm{Se}}_2$ cannot be doped $n$-type by halogen doping, while $\mathrm{CuIn}{\mathrm{Se}}_2$ can.

The schematic diagram of different Sn-5s and I-5p antibonding strengths of FASnI ₃ and MASnI ₃ due to various bond lengths of Sn–I.

Partially inverse spinel CoFe₂O₄, which may be prepared through various heat treatments, differs remarkably from the ideal inverse spinel in many properties. The structure of partially inverse spinel CoFe₂O₄ as well as its electronic and magnetic properties through a systemic theoretical calculation of (Co_1−x Fe _x )_Tet(Co _x Fe_2−x )_OctO₄ (x = 0, 0.25, 0.5, 0.75 and 1.0) have been investigated by the generalized gradient approximation (GGA) + U approach. It is found that the Co and Fe ions prefer their high spin configurations with higher spin moments at octahedral sites in all the studied cases, in line with experimental observations. The Co ions at the octahedral sites favour being far away from each other in the partial inverse spinels, which also show half metallicity at certain inversion degrees.

First-principles calculations are used to explore the geometry, bonding, and electronic properties of MoS${}_2$/Ti${}_2$C and MoS${}_2$/Ti${}_2$C$Y_2$ ($Y$ $=$ F and OH) semiconductor/metal contacts. The structure of the interfaces is determined. Strong chemical bonds formed at the MoS${}_2$/Ti${}_2$C interface result in additional states next to the Fermi level, which extend over the three atomic layers of MoS${}_2$ and induce a metallic character. The interaction in MoS${}_2$/Ti${}_2$C$Y_2$, on the other hand, is weak and not sensitive to the specific geometry, and the semiconducting nature thus is preserved. The energy level alignment implies weak and strong $n$-type doping of MoS${}_2$ in MoS${}_2$/Ti${}_2$CF${}_2$ and MoS${}_2$/Ti${}_2$C(OH)${}_2$, respectively. The corresponding $n$-type Schottky barrier heights are 0.85 and 0.26 eV. We show that the MoS${}_2$/Ti${}_2$CF${}_2$ interface is close to the Schottky limit. At the MoS${}_2$/Ti${}_2$C(OH)${}_2$ interface, we find that a strong dipole due to charge rearrangement induces the Schottky barrier. The present interfaces are well suited for application in all-two-dimensional devices.

The observation of an antisymmetric magnetoresistance in a trilayer van der Waals heterostructure Fe ₃ GeTe ₂ /graphite/Fe ₃ GeTe ₂ .