Intermediate-phase method for computing the natural band offset between two materials with dissimilar structures

The band offset between different semiconductors is an important physical quantity determining carrier transport properties near the interface in heterostructure devices. Computation of the natural band offset is a longstanding challenge. We propose an intermediate-phase method to predict the natural band offset between two structures with different symmetry, for which the superlattice model cannot be directly constructed. With this method and the intermediate phases obtained by our searching algorithm, we successfully calculate the natural band offsets for two representative systems: (i) zinc-blende CdTe and wurtzite CdS and (ii) diamond and graphite. The calculation shows that the valence band maximum (VBM) of zinc-blende CdTe lies 0.71 eV above that of wurtzite CdS, close to the result 0.76 eV obtained by the three-step method. For the natural band offset between diamond and graphite which could not be computed reliably with any superlattice methods, our calculation shows that the Fermi level of graphite lies 1.51 eV above the VBM of diamond using an intermediate phase. This method, under the assumption that the transitivity rule is valid, can be used to calculate the band offsets between any semiconductors with different symmetry on condition that the intermediate phase is reasonably designed.

Figure 1

Schematic illustration of the intermediate-phase method for the natural band offset calculation between $L$ and $R$. $X$ is an intermediate phase. Letters in brackets are surface indexes.

Figure 2

Bulk structures of (a) CdTe (zinc-blende), (b) CdS (wurtzite), and (d) the intermediate phase $\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}$, and heterostructures of (c) ${\mathrm{CdTe}}^{\prime \prime }\left(001\right)\text{/}{\mathrm{CdS}}^{\prime }\left(100\right)$, (e) ${\mathrm{CdTe}}^{\prime \prime }\left(001\right)\text{/}\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}\left(001\right)$, and (f) ${\mathrm{CdS}}^{\prime }\left(100\right)\text{/}\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}\left(010\right)$. Red, green, and blue spheres represent Cd, Te, and S atoms, respectively. Atoms having dangling bonds are indicated with black lines in (c).

Figure 3

(a) The procedures for calculating the valence band offset between CdTe (ZB) and CdS (WZ) using the intermediate phase $\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}$. In the first, second, and fifth steps, we stretch (or compress) the lattice of CdTe or CdS to make it match with $\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}$. In the third and fourth steps, we build heterostructures of $\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}\text{/}{\mathrm{CdTe}}^{\prime \prime }$ and $\mathrm{C}{\mathrm{d}}_4\mathrm{T}{\mathrm{e}}_3\mathrm{S}\text{/}{\mathrm{CdS}}^{\prime }$, respectively. Lattice constants $\left(\AA \right)$ are listed below the sketch models of crystals. (b) The calculated results of core-level alignment in each step and the valence band offset between CdTe and CdS with the core level of CdTe $\left(\mathrm{Cd}1s\right)$ set to be 0 eV.

Figure 4

Bulk structures of (a) diamond, (b) graphite, and (c) the intermediate phase C-16 and heterostructures of (d) diamond'(111)/C-16(001) and (e) graphite(001)/C-16(001). Gray, brown, and violet spheres represent the carbon atoms in diamond, graphite, and C-16, respectively. (f) The calculated results of core-level alignment and the band offset between diamond and graphite with the core level of diamond $\left(C1s\right)$ set to be 0 eV. The core-level alignment between diamond and diamond' is obtained through the three-step method. Lattice constants $\left(\AA \right)$ are listed below the rectangles.