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Charge densities of metal in Ge. The charge densities of a number of metals in Ge at the saddle point. Blue and red correspond to regions with minimum and maximum charge, respectively. Isovalues were set to 0.1 eV A À 1 .
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The slow transport of dopants through crystal lattices has hindered the development of novel devices. Typically atoms are contained within deep potential energy wells which necessitates multiple attempts to hop between minimum energy positions. This is because the bonds that constrain atoms are strongest at the minimum positions. As they hop betwee...
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Context 1
... [ D ] is the defect concentration; [h c ] and [e ] are the hole and electron concentrations, respectively. Therefore, unless there are charge compensating species present, low defect formation energies are not a guarantee for these defects to form. From Fig. 1(a), under p-doping conditions neutral and singly negatively charged Pd-vacancy pairs are present, the former will not require a compensating defect while the latter requires singly positively charged defects to compensate, easily accessible under p-type doping conditions. We can now consider possible mechanisms by which Pd can be transported through the Ge lattice. Fig. 2(a) represents the direct interstitial process, Pd i 4 Pd i (schematically shown in Fig. 3), for which the activation energy of migration is only 0.03 eV. This is one of the smallest activation energies of migration ever calculated within a bulk crystalline material. While this is a very low value, there are other defects that exhibit extremely low migration energy in crystalline systems, such as Ag + in a -AgI, which has been reported experimentally to be around 0.05 eV. 30 Another example is helium in tungsten for which the rst principles calculations by Becquart and Domain 31 revealed a migration energy of $ 0.06 eV. Formally the activation energy of di ff usion is de ned as the sum of the formation energy and the migration energy. In that respect, there are two important points that can be deduced from Fig. 1(b) and 2(a). Firstly, there is no need to consider the formation energy of intrinsic point defects as these are not participating in the direct interstitial process. Secondly, as the formation energy of Pd i is lower than Pd Ge under p-type, intrinsic and n-type conditions (up to a Fermi energy of 0.49 eV), once Pd is introduced into the lattice (for example via low energy implantation) its formation energy will not be required in the calculation of the activation energy of di ff usion (usually the additional energy to rearrange Pd from its lowest energy ground state to the interstitial site must be included). There are a number of other ways in which Pd might have been transported. Fig. 2 reports the Pd migration barriers for: the dissociative mechanism (Frank – Turnbull 32 ), the ring- mechanism 11 and the kick-out mechanism. 13 In the dissociative mechanism initially proposed by Frank and Turnbull 32 to explain Cu di ff usion in Ge, Pd i is converted to Pd Ge through the mediation of V Ge via the reaction Pd i + V Ge 4 Pd Ge . The calculated activation energy of migration of this process is 1.11 eV (refer to Fig. 2(b)), far higher compared to the direct interstitial mechanism (0.03 eV). In Ge, vacancy-mediated di ff usion mechanisms via the ring-mechanism of di ff usion are prevalent for n-type and isovalent dopants. 11,26,33 The process would initiate with a Pd atom in a Pd-split- V Ge con guration from which the V Ge must move away to at least the third nearest neighbour site and return along a di ff erent path (refer to the top of Fig. 2(c)). 11 The activation energy of migration of this process is 1.77 eV (Fig. 2(c)), which is higher compared to the equivalent process for oversized atoms such as Sb (1.14 eV) 33 or Sn (1.47 eV). 26 Finally, the kick-out mechanism, Pd i 4 Pd Ge + Ge i , was considered but its migration energy, 2.63 eV, is signi cantly higher compared to all the other mechanisms considered (refer to Fig. 2(d)). To gain insight into whether Pd is unique among species and to identify di ff erences that results in Pd's extreme di ff usion, we studied the migration of ve other metals in Ge, namely Li, Cu, Ag, Pt and Au. These ve metals have higher migration energy barriers (0.14 – 0.54 eV) compared to Pd (see Fig. 4). The two metals that are known experimentally to di ff use via a direct interstitial mechanism in Ge are Li and Cu, 1 for which the calculated migration energies are 0.54 and 0.14 eV, respectively. This compares well with previous experimental work on Li (0.4 – 0.5 eV) 34,35 and Cu (0.084 eV). 13 The charge density plots shown in Fig. 5 are those of the metal atoms at the saddle point. The charge density distribution is indicative of the degree of bonding between the defect atoms and the Ge host lattice. A distinct feature to note in Fig. 5 is the ability of metals with low migration energies to exhibit enhanced bonding with their neighbouring Ge atoms. Only Li, which has a migration energy of 0.54 eV, does not form bonds while at the saddle point. The Frank – Turnbull 32 mechanism for Pd di ff usion can be relevant when there is a supersaturation of lattice vacancies, for example when Ge is irradiated or under a supply of V Ge from the surface or dislocations. The kick-out mechanism in which Pd i displaces a Ge atom has an energy barrier of 2.63 eV, whereas, the reverse reaction has a barrier of only 0.65 eV (see Fig. 2(d)). It is therefore possible, given the low interstitial formation energies, to create a high concentration of Pd atoms that can di ff use via a direct interstitial mechanism, which will follow a Frank – Turnbull mechanism when encountering a V Ge forming Pd Ge . This can then be displaced by Ge i with a low barrier. This interplay between the three mechanisms above (direct interstitial, Frank – Turnbull and the kick-out mechanisms) can provide a pathway for di ff usion of Pd in Ge at a low energy penalty, making this defect relatively very mobile. Interestingly, experi- ments could include the introduction of a supersaturation of Ge i ( via proton irradiation, ref. 36) and Pd atoms. This would lead to novel defect engineering strategies by providing another way to control native point defects in Ge. vation energies? The di ff usion process in a crystalline solid can be seen as a series of bond breaking and bond forming steps. The saddle point therefore corresponds to the highest energy step, where the atom has typically broken all its bonds with its neighbours. However, as is shown in Fig. 5, most transition metal atoms (TM) form extended bonds even at the saddle point. In other words, they maintain bonding states with their neighbouring atoms throughout the di ff usion journey. This feature was also noted by Kamon et al. 37 who concluded that ultra-fast di ff usion of metals in Si was due to the formation of six-fold coordinated bonds between the metal and the neighbouring Si atoms. In that study Kamon et al. 37 investigated 3d TMs in Si using the full potential augmented plane wave (FLAPW) method and calculated migration energy barriers that were far higher compared to Pd in Ge (the lowest being 0.25 eV for Co in Si). In order to develop a further qualitative explanation, crystal orbital Hamilton population (COHP) 38 – 40 analysis of the Pd – Ge and Li – Ge interactions ( i.e. between atoms with the lowest and highest migration energies respectively) was performed at the migration saddle point. The COHP and the integrated COHP (ICOHP) are shown in Fig. 6 (the ordinate represents the COHP for which positive or negative values correspond to bonding or antibonding interactions, respectively). The ICOHP calculated up to the Fermi level of the Pd – Ge interaction is À 0.76 eV indicating that bonding states are favoured for Pd at the saddle point. Fig. 5(a) hints that Li is not sharing electrons with its neighbouring Ge atoms. This is con rmed by ICOHP which has a value of 1.58 eV up to E . Defect formation energy calculations reveal that for Pd in Ge substitutional and interstitial Pd defects are dominant for Fermi levels extending over the entire band gap. Having iden- ti ed the charge states of the migrating species and the preferred migration pathway, we showed that Pd exhibits an anomalously low migration energy, much lower than that of the other ve TM species investigated here. The ability of TMs to di ff use so quickly is a consequence of how it maintains bonding states throughout the di ff usion process. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Computational time was provided by the Shaheen supercom- puter and Research Computing resources at KAUST and the High Performance Computing (HPC) facility of Imperial College London. 1 C. Claeys and E. Simoen, Germanium-based technologies: from materials to devices , Elsevier, 2007. 2 M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schie er, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist and H. Sigg, Analysis of enhanced light emission from highly strained germanium microbridges, Nat. Photonics , 2013, 7 , 467 – 473. 3 H. Bracht, S. P. Nicols, W. Walukiewicz, J. P. Silveira, F. Briones and E. E. Haller, Large disparity between gallium and antimony self-di ff usion in gallium antimonide, Nature , 2000, 451 , 652 – 657. 4 E. Kendrick, J. Kendrick, K. S. Knight, M. S. Islam and P. R. Slater, Cooperative mechanisms of fast-ion conduction in gallium-based oxides with tetrahedral moieties, Nat. Mater. , 2007, 6 , 871 – 875. 5 S.-I. Nishimura, G. Kobayashi, K. Ohoyama, R. Kanno, M. Yashima and A. Yamada, Experimental visualization of lithium di ff usion in Li x FePO 4 , Nat. Mater. , 2008, 7 , 707 – 711. 6 M. J. D. Rushton and A. Chroneos, Impact of uniaxial strain and doping on ...
Context 2
... energy in crystalline systems, such as Ag + in a -AgI, which has been reported experimentally to be around 0.05 eV. 30 Another example is helium in tungsten for which the rst principles calculations by Becquart and Domain 31 revealed a migration energy of $ 0.06 eV. Formally the activation energy of di ff usion is de ned as the sum of the formation energy and the migration energy. In that respect, there are two important points that can be deduced from Fig. 1(b) and 2(a). Firstly, there is no need to consider the formation energy of intrinsic point defects as these are not participating in the direct interstitial process. Secondly, as the formation energy of Pd i is lower than Pd Ge under p-type, intrinsic and n-type conditions (up to a Fermi energy of 0.49 eV), once Pd is introduced into the lattice (for example via low energy implantation) its formation energy will not be required in the calculation of the activation energy of di ff usion (usually the additional energy to rearrange Pd from its lowest energy ground state to the interstitial site must be included). There are a number of other ways in which Pd might have been transported. Fig. 2 reports the Pd migration barriers for: the dissociative mechanism (Frank – Turnbull 32 ), the ring- mechanism 11 and the kick-out mechanism. 13 In the dissociative mechanism initially proposed by Frank and Turnbull 32 to explain Cu di ff usion in Ge, Pd i is converted to Pd Ge through the mediation of V Ge via the reaction Pd i + V Ge 4 Pd Ge . The calculated activation energy of migration of this process is 1.11 eV (refer to Fig. 2(b)), far higher compared to the direct interstitial mechanism (0.03 eV). In Ge, vacancy-mediated di ff usion mechanisms via the ring-mechanism of di ff usion are prevalent for n-type and isovalent dopants. 11,26,33 The process would initiate with a Pd atom in a Pd-split- V Ge con guration from which the V Ge must move away to at least the third nearest neighbour site and return along a di ff erent path (refer to the top of Fig. 2(c)). 11 The activation energy of migration of this process is 1.77 eV (Fig. 2(c)), which is higher compared to the equivalent process for oversized atoms such as Sb (1.14 eV) 33 or Sn (1.47 eV). 26 Finally, the kick-out mechanism, Pd i 4 Pd Ge + Ge i , was considered but its migration energy, 2.63 eV, is signi cantly higher compared to all the other mechanisms considered (refer to Fig. 2(d)). To gain insight into whether Pd is unique among species and to identify di ff erences that results in Pd's extreme di ff usion, we studied the migration of ve other metals in Ge, namely Li, Cu, Ag, Pt and Au. These ve metals have higher migration energy barriers (0.14 – 0.54 eV) compared to Pd (see Fig. 4). The two metals that are known experimentally to di ff use via a direct interstitial mechanism in Ge are Li and Cu, 1 for which the calculated migration energies are 0.54 and 0.14 eV, respectively. This compares well with previous experimental work on Li (0.4 – 0.5 eV) 34,35 and Cu (0.084 eV). 13 The charge density plots shown in Fig. 5 are those of the metal atoms at the saddle point. The charge density distribution is indicative of the degree of bonding between the defect atoms and the Ge host lattice. A distinct feature to note in Fig. 5 is the ability of metals with low migration energies to exhibit enhanced bonding with their neighbouring Ge atoms. Only Li, which has a migration energy of 0.54 eV, does not form bonds while at the saddle point. The Frank – Turnbull 32 mechanism for Pd di ff usion can be relevant when there is a supersaturation of lattice vacancies, for example when Ge is irradiated or under a supply of V Ge from the surface or dislocations. The kick-out mechanism in which Pd i displaces a Ge atom has an energy barrier of 2.63 eV, whereas, the reverse reaction has a barrier of only 0.65 eV (see Fig. 2(d)). It is therefore possible, given the low interstitial formation energies, to create a high concentration of Pd atoms that can di ff use via a direct interstitial mechanism, which will follow a Frank – Turnbull mechanism when encountering a V Ge forming Pd Ge . This can then be displaced by Ge i with a low barrier. This interplay between the three mechanisms above (direct interstitial, Frank – Turnbull and the kick-out mechanisms) can provide a pathway for di ff usion of Pd in Ge at a low energy penalty, making this defect relatively very mobile. Interestingly, experi- ments could include the introduction of a supersaturation of Ge i ( via proton irradiation, ref. 36) and Pd atoms. This would lead to novel defect engineering strategies by providing another way to control native point defects in Ge. vation energies? The di ff usion process in a crystalline solid can be seen as a series of bond breaking and bond forming steps. The saddle point therefore corresponds to the highest energy step, where the atom has typically broken all its bonds with its neighbours. However, as is shown in Fig. 5, most transition metal atoms (TM) form extended bonds even at the saddle point. In other words, they maintain bonding states with their neighbouring atoms throughout the di ff usion journey. This feature was also noted by Kamon et al. 37 who concluded that ultra-fast di ff usion of metals in Si was due to the formation of six-fold coordinated bonds between the metal and the neighbouring Si atoms. In that study Kamon et al. 37 investigated 3d TMs in Si using the full potential augmented plane wave (FLAPW) method and calculated migration energy barriers that were far higher compared to Pd in Ge (the lowest being 0.25 eV for Co in Si). In order to develop a further qualitative explanation, crystal orbital Hamilton population (COHP) 38 – 40 analysis of the Pd – Ge and Li – Ge interactions ( i.e. between atoms with the lowest and highest migration energies respectively) was performed at the migration saddle point. The COHP and the integrated COHP (ICOHP) are shown in Fig. 6 (the ordinate represents the COHP for which positive or negative values correspond to bonding or antibonding interactions, respectively). The ICOHP calculated up to the Fermi level of the Pd – Ge interaction is À 0.76 eV indicating that bonding states are favoured for Pd at the saddle point. Fig. 5(a) hints that Li is not sharing electrons with its neighbouring Ge atoms. This is con rmed by ICOHP which has a value of 1.58 eV up to E . Defect formation energy calculations reveal that for Pd in Ge substitutional and interstitial Pd defects are dominant for Fermi levels extending over the entire band gap. Having iden- ti ed the charge states of the migrating species and the preferred migration pathway, we showed that Pd exhibits an anomalously low migration energy, much lower than that of the other ve TM species investigated here. The ability of TMs to di ff use so quickly is a consequence of how it maintains bonding states throughout the di ff usion process. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Computational time was provided by the Shaheen supercom- puter and Research Computing resources at KAUST and the High Performance Computing (HPC) facility of Imperial College London. 1 C. Claeys and E. Simoen, Germanium-based technologies: from materials to devices , Elsevier, 2007. 2 M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schie er, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist and H. Sigg, Analysis of enhanced light emission from highly strained germanium microbridges, Nat. Photonics , 2013, 7 , 467 – 473. 3 H. Bracht, S. P. Nicols, W. Walukiewicz, J. P. Silveira, F. Briones and E. E. Haller, Large disparity between gallium and antimony self-di ff usion in gallium antimonide, Nature , 2000, 451 , 652 – 657. 4 E. Kendrick, J. Kendrick, K. S. Knight, M. S. Islam and P. R. Slater, Cooperative mechanisms of fast-ion conduction in gallium-based oxides with tetrahedral moieties, Nat. Mater. , 2007, 6 , 871 – 875. 5 S.-I. Nishimura, G. Kobayashi, K. Ohoyama, R. Kanno, M. Yashima and A. Yamada, Experimental visualization of lithium di ff usion in Li x FePO 4 , Nat. Mater. , 2008, 7 , 707 – 711. 6 M. J. D. Rushton and A. Chroneos, Impact of uniaxial strain and doping on oxygen di ff usion in CeO 2 , Sci. Rep. , 2014, 4 , 6068. 7 S. R. Herd, P. Chaudhari and M. H. Brodsky, Metal contact induced crystallization in lms of amorphous silicon and germanium, J. Non-Cryst. Solids , 1972, 7 , 309. 8 M. Miyasaka, K. Makihira, T. Asano, E. Polychroniadis and J. Stoemenos, In situ observation of nickel metal-induced lateral crystallization of amorphous silicon thin lms, Appl. Phys. Lett. , 2002, 80 , 944. 9 T. H. Phung and C. Zhu, Palladium-induced crystallization of germanium with varied palladium thicknesses, J. Electrochem. Soc. , 2010, 157 , H755 – H758. 10 A. Chroneos and H. Bracht, Di ff usion of n-type dopants in germanium, Appl. Phys. Rev. , 2014, 1 , 011301. 11 A. Chroneos, H. Bracht, R. W. Grimes and B. P. Uberuaga, Vacancy-mediated dopant di ff usion activation enthalpies for germanium, Appl. Phys. Lett. , 2008, 92 , 172103. 12 A. Giese, N. A. Stolwijk and H. Bracht, Double-hump di ff usion pro les of copper and nickel in germanium wafers yielding vacancy-related information, Appl. Phys. Lett. , 2000, 77 , 642 – 644. 13 H. Bracht, Copper related di ff usion phenomena in germanium and silicon, Mater. Sci. Semicond. Process. , 2004, 7 , 113 – 124. 14 J. Heyd, G. E. Scuseria and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. , 2003, 118 , 8207. 15 J. Heyd, G. E. Scuseria and M. Ernzerhof, Erratum: Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. , 2006, 124 , 219906. 16 G. Kresse and J. Furthmüller, E ffi cient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys. , 1996, 54 , 11169 – 11186. 17 J. P. ...
Context 3
... [ D ] is the defect concentration; [h c ] and [e ] are the hole and electron concentrations, respectively. Therefore, unless there are charge compensating species present, low defect formation energies are not a guarantee for these defects to form. From Fig. 1(a), under p-doping conditions neutral and singly negatively charged Pd-vacancy pairs are present, the former will not require a compensating defect while the latter requires singly positively charged defects to compensate, easily accessible under p-type doping conditions. We can now consider possible mechanisms by which Pd can be transported through the Ge lattice. Fig. 2(a) represents the direct interstitial process, Pd i 4 Pd i (schematically shown in Fig. 3), for which the activation energy of migration is only 0.03 eV. This is one of the smallest activation energies of migration ever calculated within a bulk crystalline material. While this is a very low value, there are other defects that exhibit extremely low migration energy in crystalline systems, such as Ag + in a -AgI, which has been reported experimentally to be around 0.05 eV. 30 Another example is helium in tungsten for which the rst principles calculations by Becquart and Domain 31 revealed a migration energy of $ 0.06 eV. Formally the activation energy of di ff usion is de ned as the sum of the formation energy and the migration energy. In that respect, there are two important points that can be deduced from Fig. 1(b) and 2(a). Firstly, there is no need to consider the formation energy of intrinsic point defects as these are not participating in the direct interstitial process. Secondly, as the formation energy of Pd i is lower than Pd Ge under p-type, intrinsic and n-type conditions (up to a Fermi energy of 0.49 eV), once Pd is introduced into the lattice (for example via low energy implantation) its formation energy will not be required in the calculation of the activation energy of di ff usion (usually the additional energy to rearrange Pd from its lowest energy ground state to the interstitial site must be included). There are a number of other ways in which Pd might have been transported. Fig. 2 reports the Pd migration barriers for: the dissociative mechanism (Frank – Turnbull 32 ), the ring- mechanism 11 and the kick-out mechanism. 13 In the dissociative mechanism initially proposed by Frank and Turnbull 32 to explain Cu di ff usion in Ge, Pd i is converted to Pd Ge through the mediation of V Ge via the reaction Pd i + V Ge 4 Pd Ge . The calculated activation energy of migration of this process is 1.11 eV (refer to Fig. 2(b)), far higher compared to the direct interstitial mechanism (0.03 eV). In Ge, vacancy-mediated di ff usion mechanisms via the ring-mechanism of di ff usion are prevalent for n-type and isovalent dopants. 11,26,33 The process would initiate with a Pd atom in a Pd-split- V Ge con guration from which the V Ge must move away to at least the third nearest neighbour site and return along a di ff erent path (refer to the top of Fig. 2(c)). 11 The activation energy of migration of this process is 1.77 eV (Fig. 2(c)), which is higher compared to the equivalent process for oversized atoms such as Sb (1.14 eV) 33 or Sn (1.47 eV). 26 Finally, the kick-out mechanism, Pd i 4 Pd Ge + Ge i , was considered but its migration energy, 2.63 eV, is signi cantly higher compared to all the other mechanisms considered (refer to Fig. 2(d)). To gain insight into whether Pd is unique among species and to identify di ff erences that results in Pd's extreme di ff usion, we studied the migration of ve other metals in Ge, namely Li, Cu, Ag, Pt and Au. These ve metals have higher migration energy barriers (0.14 – 0.54 eV) compared to Pd (see Fig. 4). The two metals that are known experimentally to di ff use via a direct interstitial mechanism in Ge are Li and Cu, 1 for which the calculated migration energies are 0.54 and 0.14 eV, respectively. This compares well with previous experimental work on Li (0.4 – 0.5 eV) 34,35 and Cu (0.084 eV). 13 The charge density plots shown in Fig. 5 are those of the metal atoms at the saddle point. The charge density distribution is indicative of the degree of bonding between the defect atoms and the Ge host lattice. A distinct feature to note in Fig. 5 is the ability of metals with low migration energies to exhibit enhanced bonding with their neighbouring Ge atoms. Only Li, which has a migration energy of 0.54 eV, does not form bonds while at the saddle point. The Frank – Turnbull 32 mechanism for Pd di ff usion can be relevant when there is a supersaturation of lattice vacancies, for example when Ge is irradiated or under a supply of V Ge from the surface or dislocations. The kick-out mechanism in which Pd i displaces a Ge atom has an energy barrier of 2.63 eV, whereas, the reverse reaction has a barrier of only 0.65 eV (see Fig. 2(d)). It is therefore possible, given the low interstitial formation energies, to create a high concentration of Pd atoms that can di ff use via a direct interstitial mechanism, which will follow a Frank – Turnbull mechanism when encountering a V Ge forming Pd Ge . This can then be displaced by Ge i with a low barrier. This interplay between the three mechanisms above (direct interstitial, Frank – Turnbull and the kick-out mechanisms) can provide a pathway for di ff usion of Pd in Ge at a low energy penalty, making this defect relatively very mobile. Interestingly, experi- ments could include the introduction of a supersaturation of Ge i ( via proton irradiation, ref. 36) and Pd atoms. This would lead to novel defect engineering strategies by providing another way to control native point defects in Ge. vation energies? The di ff usion process in a crystalline solid can be seen as a series of bond breaking and bond forming steps. The saddle point therefore corresponds to the highest energy step, where the atom has typically broken all its bonds with its neighbours. However, as is shown in Fig. 5, most transition metal atoms (TM) form extended bonds even at the saddle point. In other words, they maintain bonding states with their neighbouring atoms throughout the di ff usion journey. This feature was also noted by Kamon et al. 37 who concluded that ultra-fast di ff usion of metals in Si was due to the formation of six-fold coordinated bonds between the metal and the neighbouring Si atoms. In that study Kamon et al. 37 investigated 3d TMs in Si using the full potential augmented plane wave (FLAPW) method and calculated migration energy barriers that were far higher compared to Pd in Ge (the lowest being 0.25 eV for Co in Si). In order to develop a further qualitative explanation, crystal orbital Hamilton population (COHP) 38 – 40 analysis of the Pd – Ge and Li – Ge interactions ( i.e. between atoms with the lowest and highest migration energies respectively) was performed at the migration saddle point. The COHP and the integrated COHP (ICOHP) are shown in Fig. 6 (the ordinate represents the COHP for which positive or negative values correspond to bonding or antibonding interactions, respectively). The ICOHP calculated up to the Fermi level of the Pd – Ge interaction is À 0.76 eV indicating that bonding states are favoured for Pd at the saddle point. Fig. 5(a) hints that Li is not sharing electrons with its neighbouring Ge atoms. This is con rmed by ICOHP which has a value of 1.58 eV up to E . Defect formation energy calculations reveal that for Pd in Ge substitutional and interstitial Pd defects are dominant for Fermi levels extending over the entire band gap. Having iden- ti ed the charge states of the migrating species and the preferred migration pathway, we showed that Pd exhibits an anomalously low migration energy, much lower than that of the other ve TM species investigated here. The ability of TMs to di ff use so quickly is a consequence of how it maintains bonding states throughout the di ff usion process. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Computational time was provided by the Shaheen supercom- puter and Research Computing resources at KAUST and the High Performance Computing (HPC) facility of Imperial College London. 1 C. Claeys and E. Simoen, Germanium-based technologies: from materials to devices , Elsevier, 2007. 2 M. J. Süess, R. Geiger, R. A. Minamisawa, G. Schie er, J. Frigerio, D. Chrastina, G. Isella, R. Spolenak, J. Faist and H. Sigg, Analysis of enhanced light emission from highly strained germanium microbridges, Nat. Photonics , 2013, 7 , 467 – 473. 3 H. Bracht, S. P. Nicols, W. Walukiewicz, J. P. Silveira, F. Briones and E. E. Haller, Large disparity between gallium and antimony self-di ff usion in gallium antimonide, Nature , 2000, 451 , 652 – 657. 4 E. Kendrick, J. Kendrick, K. S. Knight, M. S. Islam and P. R. Slater, Cooperative mechanisms of fast-ion conduction in gallium-based oxides with tetrahedral moieties, Nat. Mater. , 2007, 6 , 871 – 875. 5 S.-I. Nishimura, G. Kobayashi, K. Ohoyama, R. ...
Citations
... Metallic diffusion in semiconductors such as Ge is both scientifically and technologically important [30,[61][62][63][64][65]. For example, Giese et al. [30] have studied the diffusion of nickel and copper in Ge to derive information regarding the vacancy-mediated Ge self-diffusion coefficient and the concentration of vacancies with respect to temperature. ...
... For example, Giese et al. [30] have studied the diffusion of nickel and copper in Ge to derive information regarding the vacancy-mediated Ge self-diffusion coefficient and the concentration of vacancies with respect to temperature. From a technological viewpoint metals such as copper, nickel, and palladium are used as crystallization inducers in the metal-induced lateral crystallization (MILC) method which is an efficient way to produce large grain crystals [64]. ...
... In that investigation, Tahini et al. [64] considered all the possible diffusion mechanisms (for example, the dissociative or Frank-Turnbull mechanism, the kick-out mechanism, and the ring mechanism); however, the direct interstitial process, Pdi ↔ Pdi, (refer to Figure 5) was the lowest energy way for a Pd atom to diffuse in the Ge lattice. The migration energy for this process is only 0.03 eV, which is one of the lowest energies ever calculated for mass transport in a crystalline material [64]. In this order of magnitude are the migration energies of helium in tungsten and the self-diffusion of silver in α-AgI [64]. ...
Germanium is an important mainstream material for many nanoelectronic and sensor applications. The understanding of diffusion at an atomic level is important for fundamental and technological reasons. In the present review, we focus on the description of recent studies concerning n-type dopants, isovalent atoms, p-type dopants, and metallic and oxygen diffusion in germanium. Defect engineering strategies considered by the community over the past decade are discussed in view of their potential application to other systems.
... In this process, metals such as nickel (Ni) and copper (Cu) are used as crystallization inducers. [9][10][11][12] Ni and Cu can also enter the Si lattice unintentionally, and this contamination can impact Sibased IC and solar-cell devices. [13][14][15] For example, in Si solar cells, the replacement of the relatively expensive silver-pasted front contacts with electroplated Ni and Cu contacts reduces the cell fabrication costs but simultaneously decreases the cell efficiency by the contamination of these fast diffusers. ...
In the present study, nickel and copper fast diffusion in silicon is investigated in the framework of the cBΩ thermodynamic model, which connects point defect parameters with the bulk elastic and expansion properties. All the calculated point defect thermodynamic properties (activation Gibbs free energy, activation enthalpy, activation entropy, and activation volume) exhibit temperature dependence due to the non-linear anharmonic behavior of the isothermal bulk modulus of Si. Calculated activation enthalpies (0.15–0.16 eV for Ni and 0.17–0.19 eV for Cu) are in agreement with the reported experimental results. Small values of calculated activation volumes for both dopants (∼4% of the mean atomic volume) are consistent with the interstitial diffusion of Ni and Cu in Si.
... The specific diffusion process was described phenomenologically by a regrowth model [9]. In a nutshell, the Pd enables out-diffusion of Ga from the GaAs wafer before it quickly diffuses through the Ge layer away from the GaAs surface [11]. The Ge atoms then diffuse into the gallium vacancies below the GaAs wafer surface. ...
III-V nanowires are comprehensively studied because of their suitability for optoelectronic quantum technology applications. However, their small dimensions and the spatial separation of carriers from the wire surface render electrical contacting difficult. Systematically studying ohmic contact formation by diffusion to $n$-doped GaAs nanowires, we provide a set of optimal annealing parameters for Pd/Ge/Au ohmic contacts. We reproducibly achieve low specific contact resistances of $\sim2\times10^{-7}\,\Omega\text{cm}^2$ at room temperature becoming an order of magnitude higher at $T\simeq4.2\,$K. We provide a phenomenological model to describe contact resistances as a function of diffusion parameters. Implementing a transfer-matrix method, we numerically study the influence of the Schottky barrier on the contact resistance. Our results indicate that contact resistances can be predicted using various barrier shapes but further insights into structural properties would require a full microscopic understanding of the complex diffusion processes.
... Consequent studies revealed that the diffusion of most dopants in Ge is mediated by vacancies [39][40][41][42]. Exceptions include copper (Cu), palladium (Pd), Au and Ag (refer to [43] and references therein). Au [10,[44][45][46] and Ag [47,48] diffusion in Ge has been investigated for about six decades. ...
... As it has been previously discussed [21,24] the cBX model is appropriate when a single-diffusion mechanism is operating. Although Au and Ag diffusion in characterized by a single diffusion mechanism dissociative diffusion can be complicated as it requires both vacancies and interstitials, whereas the steps are not as well defined as in other mechanisms (for example the ring-mechanism for vacancy diffusion in Ge [43]). ...
Diffusion properties are technologically important in the understanding of semiconductors for the efficent formation of defined nanoelectronic devices. In the present study we employ experimental data to show that bulk materials properties (elastic and expansivity data) can be used to describe gold and silver diffusion in germanium for a wide temperature range (702–1177 K). Here we show that the so-called cBΩ model thermodynamic model, which assumes that the defect Gibbs energy is proportional to the isothermal bulk modulus and the mean volume per atom, adequately metallic diffusion in germanium.
... The entire database has been calculated both at the PBE level of theory, as well as the higher HSE06 level. 3133 The latter can require orders of magnitude more computational power, but is able to correct various shortcomings in PBE such as the incorrectly vanishing bandgap of Ge. 28,29,3437 The availability of this data for a wide range of systems enables the direct quantication of the dierences between both. This has not been previously possible as earlier databases focused on a single level of theory equivalent to PBE. ...
Increased computational resources now make it possible to generate large datasets solely from first principles. Such ‘high-throughput’ screening is employed to create a database of embedding enthalpies for extrinsic point defects and their vacancy complexes in Si and Ge, for 73 impurities from H to Rn. Calculations are performed both at the PBE and HSE06 levels of theory. The dataset is verified by comparison of predicted lowest-enthalpy positions with experimental observations. The effect of temperature on the relative occupation of defect sites is estimated through configurational entropy. Potential applications are demonstrated by selecting optimal vacancy traps, directly relevant to industrial processes such as Czochralski growth as a means to suppress void formation.
... [14] Then eed for high-power applications have called for the development of high-performance electrode materials because they have been am ajor limiting factor in overall rechargeable battery performance.Recently,significant effort has focused on alternatives (i.e., transition-metal oxides and metals,s uch as Si, Sn) for electrode construction to explore potentially low-cost, high-performance materials for replacement of current electrode materials. [13,[15][16][17] As typical new-concept battery materials,o xides (including ternary oxides [18,19] ), sulfides, [20][21][22] and metals [23][24][25] have been extensively investigated due to their distinctive advantages including low cost, their abundance and high storage capacity as electrodes in LIBs and sodium ion batteries (SIBs). [26,27] Among candidate materials,m etals are believed to deliver the highest Li-storage capability owing to simple elemental addition. ...
Germanium-based nanomaterials have emerged as important candidates for next-generation energy-storage devices owing to their unique chemical and physical properties. In this Review, we provide a review of the current state-of-the-art in germanium-based materials design, synthesis, processing, and application in battery technology. The most recent advances in the area of Ge-based nanocomposite electrode materials and electrolytes for solid-state batteries are summarized. The limitations of Ge-based materials for energy-storage applications are discussed, and potential research directions are also presented with an emphasis on commercial products and theoretical investigations.
In the last chapter we examined how to use the kinetics of reactions to model the rate of change of populations, or concentrations. We did not consider the consequences of the motion or spatial transport of these populations. There are multiple mechanisms involved with transport, and in this chapter we will examine one of them, and it is the process of diffusion. A simple example of diffusion arises when a perfume bottle is opened. Assuming the air is still, the perfume molecules move through the air because of molecular diffusion.
This study represents the first direct experimental demonstrations and mechanism proposal regarding abnormal palladium diffusion into Ge. Our experiments indicated that excess Ge atoms among palladium germanide alloy formation indirectly induce the abnormal out-diffusion of mass palladium atoms into Ge. Consequently, palladium germanide alloy on both n- and p-type Ge form Ohmic-like Schottky junctions. To identify this phenomenon, first-principles calculations and technology computer-aided design simulation were used to evaluate the electrical influence of palladium atoms in Ge. We discovered that activated palladium atoms in Ge induce large midgap bulk-trap states, which contribute to a severe increment of trap-assisted tunneling current at the palladium germanide/Ge junction.
PdGe contact fabrication on Ge(001) wafers doped with Ga is investigated using conventional complementary metal-oxide-semiconductor processes. Despite a p-type doping level of ~1.4 × 1020 cm−3, the resistivity of the PdGe contact is found to be twice higher than that of undoped Ge. Ga doping has no influence on the Pd reaction with Ge. However, the doping process and the Salicide process led to the formation of Ga-Pd defects in both sides of the PdGe/Ge interface, resulting from Ga and Pd co-segregation on Ge dislocation loops.
A Systematic study of defects and incorporation of xenon (Xe) and zirconium (Zr) fission products in uranium diboride (UB2) has been investigated using density functional theory (DFT) calculations as implemented in Quantum ESPRESSO code. The incorporation and solution energies show that both FPs (Xe and Zr) are most stable in U vacancies with Zr being more stable than Xe. A volume expansion is observed as the concentration of Xe increases in the fuel matrix while Zr incorporation leads to a contraction. Bader charge analysis is used to establish the formation of Zr-B ionic/covalent bond due to large electron transfer observed while there is only a weak electronic interaction between Xe and the UB2 lattice. Finally, using climbing-image nudged elastic band calculation, we found that the energy barrier of U in UB2 is 0.08 eV higher than B migration energy.
