Rare earth substitutional impurities in germanium: A hybrid density functional theory study

Abstract

The Heyd, Scuseria, and Ernzerhof (HSE06) hybrid functional by means of density functional theory has been used to modelled the electronic and structural properties of rare earth (RE) substitutional impurities in germanium (RE Ge). The formation and charge state transition energies for the RE Ge (RE = Ce, Pr, Er and Eu) were calculated. The energy of formation for the neutral charge state of the RE Ge lies between −0.14 and 3.13 eV. The formation energy result shows that the Pr dopant in Ge (Pr Ge) has the lowest formation energy of −0.14 eV, and is most energetically favourable under equilibrium conditions. The RE Ge induced charge state transition levels within the band gap of Ge. Shallow acceptor levels were induced by both the Eu (Eu Ge) and Pr (Pr Ge) dopants in Ge. The Ce Ge and Er Ge exhibited properties of negative-U ordering with effective-U values of −0.85 and −1.07 eV, respectively.

Electronic properties and defect levels induced by group III substitution–interstitial complexes in Ge

“…Table 1 displays the results of the calculated bond length (BL) of impurity atom with the nearest neighbour Ge atom or impurity atom with the nearest neighbour impurity, and the difference between BL and nearest neighbour Ge-Ge bond length (D). The calculated Ge-Ge nearest neighbour bond length of 2.48 Å is in agreement with previous results [3,5]. For the substitution-interstitial complex of Ge formed by Ga and B, the bond length of Ga-B atoms when a Ga atom is occupying the Ge atom lattice site and B an interstitial atom is 0.43 Å relatively lower than the bond length of the nearest neighbour Ge-Ge atoms.…”

“…Semiconductor material such as Ge, has great advantageous higher carrier mobilities, low dopant activation temperature and smaller band-gap properties relatively to Si. Ge is becoming increasingly important for applications in the field of microelectronics [1][2][3][4][5]. The high carrier mobility unique property of Ge enhances its use for a device where high electron-hole mobility is required [1].…”

“…Despite the huge effort made so far towards the study and understanding of point defect processes in several materials, they remain undiscovered defects which have not been investigated, and hence the defect levels are not known. Defect-complexes in semiconductor are well known to induce active defect levels in their host [2,[18][19][20][21][22]. For example, in SiC and diamond, the nitrogen-vacancy (NV) centre is a well known defect-complex which has great application in qubit [18,23,24].…”

“…Furthermore, B i can also be trapped by a substitutional boron, oxygen or carbon impurities in Si to form complex defects such as B i B Si , B i O i and and B i C Si [20]. While some results of the defect levels induced by the substitution-interstitial complexes in Ge have been reported [2][3][4][5], the substitution-interstitial complexes (X Ge Y i : where X Ge and Y i represent X substitution and Y interstitial in Ge, respectively) including the Ga Ge B i , Ga Ge In i , In Ge B i , In Ge Al i , Al Ge In i and In Ge Ga i defect levels induced in Ge are not yet understood, hence the motivation of this report. The electronic properties and defects levels induced by In, Ga, Al and B substitutionalinterstitial complexes in Ge, were predicted using the Heyd, Scuseria and Ernzerhof (HSE06) [28] hybrid functional within the framework of the density functional the-ory (DFT).…”

“…3. The intersection of the charge states i.e when the charge states have the same formation energy is the charge state transition level and the corresponding Fermi energy is the defect energy level.…”