English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a theoretical analysis of electronic structure evolution in thegroup-IV alloy Ge$_{1-x}$Pb$_{x}$ based on density functional theory. Forordered alloy supercells we demonstrate the emergence of a singlet conductionband (CB) edge state, suggesting the emergence of a direct band gap for Pbcompositions as low as $x \approx 1$%. However, application of hydrostaticpressure reveals Pb-induced hybridisation, with the CB edge state in aGe$_{63}$Pb$_{1}$ ($x = 1.56$%) supercell retaining primarily indirect (GeL$_{6c}$) character. For an ordered Ge$_{15}$Pb$_{1}$ ($x = 6.25$%) supercellwe find that the CB edge has acquired primarily direct (Ge $\Gamma_{7c}$)character, confirming the presence of an indirect- to direct-gap transition.The importance of alloy disorder is highlighted by investigating the impact onthe electronic structure of the formation of a nearest-neighbour Pb-Pb pair.Having established the importance of short-range disorder, we analyse theelectronic structure evolution as a function of $x$ using a series of 128-atomspecial quasi-random structures (SQSs). Our calculations reveal a strongreduction (increase) of the band gap (spin-orbit splitting energy), by $\approx100$ meV ($\approx 40$ meV) per % Pb replacing Ge. We find an indirect- todirect-gap transition occurring in a narrow composition range centred about $x\approx 7$%, close to which composition we calculate that the alloy becomessemimetallic. Further analysis suggests that long-range order introduced byBorn von Karman (supercell) boundary conditions leads to overestimated energysplitting of the Ge L$_{6c}$-derived CB states in the 128-atom SQSs. Accountingfor these finite-size effects, we expect a direct band gap to emerge inGe$_{1-x}$Pb$_{x}$ for $x \gtrsim 3 - 4$%.

First principles analysis of electronic structure evolution and the indirect- to direct-gap transition in Ge$_{1-x}$Pb$_{x}$ group-IV alloys