Vacancy-mediated dopant diffusion activation enthalpies for germanium

Abstract

Electronic structure calculations are used to predict the activation enthalpies of diffusion for a range of impurity atoms ͑aluminium, gallium, indium, silicon, tin, phosphorus, arsenic, and antimony͒ in germanium. Consistent with experimental studies, all the impurity atoms considered diffuse via their interaction with vacancies. Overall, the calculated diffusion activation enthalpies are in good agreement with the experimental results, with the exception of indium, where the most recent experimental study suggests a significantly higher activation enthalpy. Here, we predict that indium diffuses with an activation enthalpy of 2.79 eV, essentially the same as the value determined by early radiotracer studies. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2918842͔ Germanium ͑Ge͒ has the potential to replace silicon ͑Si͒ in advanced nanoelectronic devices because of the higher mobility of holes and electrons, compatibility with Si manufacturing processes, increased dopant solubility, and smaller band gap. 1 The precise control required for the fabrication of these devices would be greatly aided by an accurate determination of the diffusion properties of impurities in Ge. 2 This is particularly important for donor impurities for which activation control can be problematic. 3 In previous studies, it has been concluded that most impurities mainly occupy substitutional lattice sites in Ge and, with the exception of boron ͑B͒, dopant diffusion is mainly mediated by vacancies ͑V͒ as interstitial mechanisms typically have significantly higher activation enthalpies. 2, Aluminium ͑Al͒, gallium ͑Ga͒, indium ͑In͒, and B are acceptor atoms that can potentially be used as p-type dopants in Ge technology. Recent experiments 4 on B diffusion in Ge yield an activation enthalpy of 4.65 eV that agrees with earlier results, but the absolute values of the B diffusion coefficients are several orders of magnitude lower than those reported earlier. 5 Previous experimental studies on Al diffusion yield activation enthalpies in the range of 3.2-3.45 eV. 6,7 Södervall et al. 8 obtained an activation enthalpy of 3.31 eV for Ga diffusion in Ge. This value is supported by the more recent experimental studies of Riihimäki et al. 9 who determined an activation enthalpy of 3.21 eV for Ga diffusion in Ge via a V-mediated mechanism. The spread in the data reported for the activation enthalpy of In diffusion in Ge is especially large ͑0.85 eV͒. The radiotracer studies of Pantaleev 10 suggest a value of 2.78 eV, whereas the In profiles measured by Dorner et al. 11 by means of secondary ion mass spectrometry ͑SIMS͒ yield a value of 3.63 eV.Carbon ͑C͒, Si, and tin ͑Sn͒ are important isovalent impurities. C atoms have been observed to be relatively immobile; however, they can retard the diffusion of phosphorus ͑P͒, arsenic ͑As͒, and antimony ͑Sb͒ atoms in Ge. 26,27 Recent experimental studies by Silvestri et al. 15 ͑using SIMS͒ concluded that Si diffusion in Ge is mediated by V with an activation enthalpy of 3.32 eV, whereas previous studies ...

Intrinsic and extrinsic diffusion of indium in germanium

“…5 The diffusion experiments reported by Dorner et al, 17,20 Södervall et al, 18 and Riihimäki et al 19 yield diffusion activation enthalpies for Al, Ga, and In that clearly exceed the activation enthalpy of self-diffusion. 21,22 Considering the DFT calculations of Chroneos et al, 23,24 these results seem to be in conflict with the picture on a vacancy-mediated acceptor diffusion that predict diffusion activation enthalpies below 3 eV for Al, Ga, and In. In order to verify the diffusion activation enthalpy, we report in this paper experiments on the intrinsic and extrinsic diffusion of In in Ge.…”

“…This has been concluded from self-and foreign-atom diffusion studies 7,21,22,[27][28][29][30] and confirmed by atomistic calculations. 15,23,[30][31][32][33] In particular, the simultaneous diffusion of self-and dopant atoms in isotopically controlled Ge heterostructures have revealed that vacancies in Ge are mainly doubly negatively charged under intrinsic and n-type doping conditions. 7,34 However, the preferred charge state of V under p-type doping is not known.…”

Vacancy-oxygen defects in p-type Si1−xGex

“…[1][2][3][4][5] An enabling factor is the advent of high dielectric constant (high-k) dielectrics that allow the departure from the prerequisite to use native oxides such as SiO 2 in Si-based devices. [6][7][8] Si 1-x Ge x is a random alloy with the diamond structure that has one lattice site that can be occupied by either Si or Ge.…”

The vacancy in silicon: A critical evaluation of experimental and theoretical results

“…9 Recent theoretical calculations of the activation enthalpy of P, As, and Sb diffusion in Ge not only reproduce the decreasing diffusion activation enthalpy with increasing size of the dopants but also agree quantitatively with the experimental results. 10 Uberuaga et al 11 predicted an activation enthalpy of 3.1 eV for Ge self-diffusion that is in excellent agreement with the experimental result of 3.09 eV reported by Werner et al 8 This agreement between experimental and theoretical results on the activation enthalpies of self-and dopant diffusion holds true for Ge and also for Si ͑see below͒ in the case an alternative functional, such as the B3YLP, is used in density functional theory ͑DFT͒ calculations, as discussed by Uberuaga et al 11 Previous DFT calculations 3-5 are known to underestimate the formation energies of defects in Si and Ge due to the lack of exact exchange in these functionals. [12][13][14][15] Although these are well converged studies employing supercells of up to 512 atoms and Brillouin-zone sampling with 2 3 k-points, the 3.17-3.29 eV values predicted for the V-formation enthalpy in Si 3,5 are a severe underestimation and are therefore not appropriate to facilitate comparison with the experimental studies that support 3.6 eV for selfdiffusion via V in Si.…”