Abstract
In order to calculate the critical concentration for the metal–insulator transition in doped semiconductors, we study a model of randomly positioned interacting hydrogenic atoms within the one-electron approximation. We calculate approximate eigenfunctions for the system with the standard linear combination of atomic orbital variation method, considering explicitly the nonorthogonality of hydrogenic 1s orbitals. We then compute the correlation length using the concept of quantum connectivity, which we developed to study the localization transition in other disordered quantum-mechanical models. Finally, we employ a finite-size scaling analysis to determine the critical impurity concentration nc. If the isolated impurities have a Bohr radius a, then we find that Rc≡n1/3ca=0.250±0.011, which is in good agreement with experiment (Rc=0.26±0.05).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
