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Correlation between strain and defects in Bi implanted Si
Journal of Physics and Chemistry of Solids 93 (2016) 27–32
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Correlation between strain and defects in Bi implanted Si C. Palade a,b, A.-M. Lepadatu a, A. Slav a, M.L. Ciurea a,c, S. Lazanu a,n a b c
National Institute of Materials Physics, 405A Atomistilor Str., 077125 Magurele, Romania University of Bucharest, Faculty of Physics, 405 Atomistilor Str, 077125 Magurele, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucuresti, Romania
art ic l e i nf o
a b s t r a c t
Article history: Received 27 October 2015 Received in revised form 18 January 2016 Accepted 8 February 2016 Available online 9 February 2016
The strain in Si containing group-V impurities is a topical subject of study due to its potential applications in quantum computing. In this paper we study 209Bi implanted Si concerning the correlation between the strain produced by stopped Bi ions and trapping characteristics of the defects resulted from implantation. The depths distributions of stopped ions and primary defects are simulated and the distributions of permanent defects are modelled for Si implanted with low fluence 209Bi ions of 28 MeV kinetic energy. For comparison, these depths distributions were similarly calculated for 127I ions with the same fluence and energy, implanted in Si. The results are compared with each other and correlated with the characteristics of traps in these systems, previously obtained. We demonstrate that the intensity of the strain field is the most important factor in changing of trap parameters, while the superposition between the region with strain and the region where defects are located is a second order effect. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Field of strain Ion irradiation defects Trapping centres Modelling the distribution of defects
1. Introduction The system of electron and nuclear spins of donor atoms in silicon is an excellent quantum bit (qubit) candidate for quantum information processing [1,2], and it is expected to be a better solution in respect to superconducting qubits which show relatively fast decoherence rates, insufficient for maintaining quantum information throughout the course of computation. In isotopically enriched 28Si (I¼0), the coherence times are improved in comparison to natural Si, due to the removal of the residual nuclear spins of 29Si, which has the natural abundance of 4.7%, and is the only one isotope of natural Si with nonzero nuclear spin (I¼ 1/2) [3,4]. The interest in Bi doped Si materials suddenly increased in the last years, based on this potential application. Clock transitions with coherence times of several seconds (at 5 K), much longer than those characterizing superconducting qubits, were reported [5–7]. In parallel, studies on the nuclear spin of ionised 31P donors in isotopically purified 28Si have demonstrated even higher coherence times, in the order of tens of minutes or even higher, at room temperature [8,9]. Recently it was reported that the quadrupolar interaction of group-V donors with nuclear spin I41/2 with electric field gradients can be manipulated by applying elastic strain to the host crystal, for mechanical tuning the nuclear spin of ionised donors [10,11], with the benefit of scalable local addressing the qubits. The strain is applied locally by piezoactuators on the scale of nanometres in Ref. [10], while in Ref. [11] n
Corresponding author. E-mail address: lazanu@infim.ro (S. Lazanu).
http://dx.doi.org/10.1016/j.jpcs.2016.02.005 0022-3697/& 2016 Elsevier Ltd. All rights reserved.
the defects created during Si implantation modify the nuclear electric quadrupole interaction of the nuclear quadrupole moment with the electron wavefunction. The relation between electric field gradient tensors and lattice strain was theoretically substantiated [12,13] based on experimental data from nuclear acoustic resonance [14]. For Si, this topic only recently appeared in the literature, in relation to the mentioned applications in quantum computing [10]. In the present paper we aim to study the system 209Bi–Si from the point of view of the relation between the strain field produced by Bi ions (bigger and heavier than the Si host atoms) and the trapping properties of the defects produced during Bi implantation, particularly of the relation between strain field intensity and the relative depth distributions of both strain field and defects. For this, we comparatively analyse Si single crystals implanted with Bi and I ions, both of energy 28 MeV and fluence 5 1011 ions/cm2, which have a lower range than the depth of the samples, and are stopped inside. Both Bi and I ions being bigger and heavier than Si atoms produce a local strain in Si, which is more intense in Bi implanted Si. On the other hand, during their penetration into Si, the ions generate lattice defects. Based on the simulations of depth distributions of stopped ions and of primary defects respectively, we model the production of point defects and their depth distributions. The trap parameters of these irradiation defects were previously obtained by modelling the experimental thermally stimulated current without applied bias curves measured on similar Si samples, implanted with Bi and I ions [15,16], considering the effect of strain. The differences in the characteristics of the trapping centres corresponding to Si samples with Bi and I are correlated and explained based on the results of simulations of ion penetration into Si and on the peculiarities of the fields of strain.
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2. Spatial distribution of the strain fields and defects
and I
6þ
8.36 µm
5x10
ions penetration in Si
The range of both ions of kinetic energy 28 MeV and 3° disoriented in respect to the (100) axis of Si is much smaller than the sample thickness, and consequently they are stopped inside. In order to simulate their penetration into the Si lattice, we used the Monte Carlo code Crystal Transport and Range of Ions in Matter (CTRIM) [19], based on the binary collision approximation. In contrast to the SRIM (Stopping and Range of Ions in Matter) code [20] that simulates the penetration of ions in amorphous targets, CTRIM takes into account the crystal structure and the orientation of the ion beam in respect to the lattice. So, the programme follows the incoming particle and all the particles it sets in motion until they fall below a selected low kinetic energy. It is known that the competition between nuclear and electronic stopping for different ions is a function of ion characteristics (charge and mass numbers) and energy. So, when entering the sample, both Bi and I ions lose energy predominantly by ionisation. Being lighter, I ions penetrate farther into Si. It is known that with the increase of the atomic mass and charge numbers of the ion, the maximum of the nuclear energy loss is shifted to higher energies, and the value of the maximum is also higher, this being correlated with a higher displacement damage production. The nuclear energy loss is the highest near the end of the range, i.e. at low ion energies, and consequently in this region the concentration of defects is also higher, as it will be seen further. In the following, we are interested only in distributions in the depth of the sample, due to the uniformity of the irradiation on the surface. The distributions of stopped ions are nearly Gaussian, with the maxima located at 4.77 and 8.36 mm for Bi and I ions, respectively [15,16]. These distributions are illustrated in Fig. 1, where the centre (projected range) and the standard deviations (range straggling) of each of them are marked. One can see that the distribution of Bi ions is much narrower, steeper than the distribution of I ions. Each stopped ion, being bigger (rBi ¼1.70 Å and rI ¼1.28 Å) and heavier (ABi ¼209 and AI ¼127) than the atoms of the host lattice (rSi ¼1.17 Å, ASi ¼28) produces a local deformation of the lattice. The strain fields produced by all stopped ions add together. The two ions, Bi and I, being differently distributed in the depth of Si, create different configurations of the field of strain. So, the departure of each of the ions studied from the Si atoms of the host lattice (mass, size, electronic configuration) is different, and it is expected that the magnitudes of created strain are also different. 2.2. Simulation of the distributions of primary defects produced by Bi and I ions in Si The depth distributions of the vacancies created by the two types of ions, as a consequence of the energy transmitted to the atomic motion, as obtained from CTRIM are represented comparatively in Fig. 2. These distributions are asymmetrical, with the maxima situated at 4.25 mm and 7.35 mm, giving a total number of vacancies
-5
0 0.0
5.0x104
1.0x105
Depth [A] Fig. 1. Depth distribution of stopped Bi and I ions, with the projected range and standard deviation (range straggling) marked.
per ion of 7.17 104 and 5.72 104 for Bi and I ions, respectively. The asymmetry of the distributions of vacancies, i.e. their tails toward the sample surface, is explained by primary defects (vacancies and interstitials) creation in atomic collision cascades, having the source in the primary knock-on atoms. So, in each interaction, if the energy transmitted to the atom exceeds the threshold energy for displacements, the atom leaves its site in the lattice, creating a vacancy–interstitial pair. The self-interstitial, which is the recoil created in the primary interaction, can be the source of a cascade of displacements if it has enough energy. Hence near the trajectory of the heavy ion, vacancies and interstitials are created in pairs. 2.3. Modelling of the distributions of stable defects following Bi and I irradiation As in Si both interstitials and vacancies have a very fast and long range migration [21], they interact either between themselves or with the defects and impurities present in the lattice via migration, recombination and annihilation, thus forming stable point defects which are related to interstitials or to vacancies. The main impurities present in our samples are O, C (both with concentrations in the order of 1015–1016 at/cm3) and P (5 1011–5 1012 at/cm3). In the frame of the theory of diffusion – limited reactions, the process of Bi I
3
Vacancies [1/ion/A]
2.1. Simulation of Bi
6þ
Bi I
4.77µm
1x10-4
Stopped ions [1/A]
The experimental data are from our previous work, Refs. [15,16]. High resistivity Si wafers grown by the floating zone technique, of 2 in. diameter and 280 mm thickness (from Siltronix), contain natural abundances of Si isotopes, i.e. 92.2% 28Si (I¼0), 4.7% 29Si (I¼1/2) and 3.1% 30Si (I¼ 0). They were irradiated with 209Bi6þ and 127I6þ ions at the tandem accelerator of Uppsala University [17]. Both ions had the same kinetic energy and fluence of 28 MeV and 5 1011 ions/cm2, respectively. The irradiation nonuniformity on the Si surface was less than 5%, and the beam axis was disoriented in respect to (100) direction by 3° [15,16]. The irradiations were performed at room temperature, and the samples were not annealed for Bi activation [18], but they were kept at room temperature between irradiation and measurements.
4.25 µm
CTRIM, 30 off
2 7.35 µm
1
0
0.0
5.0x104
1.0x105
Depth [A] Fig. 2. Depth distribution of vacancies created in Si following the irradiation with Bi and I ions, of 28 MeV kinetic energy.
C. Palade et al. / Journal of Physics and Chemistry of Solids 93 (2016) 27–32
formation of stable defects is described by a system of coupled differential equations, having as initial conditions the concentrations of impurities and of vacancies and interstitials, and as parameters the rates of formation of defects. In the present case, due to the impurities considered, the processes taken into account are: – – – –
annihilation of vacancies and interstitials: V+I→Si migration of interstitials to sinks: I→sinks formation of divacancies: V+V⇔V2 formation and decomposition of defect VO (A centre): V+O ⇔ VO – formation and decomposition of defect VP (E centre): V+P ⇔ VP – formation of interstitial carbon Ci: C+I ⇔ Ci – formation of CiOi and CiCs centres: Ci +Cs⇔Ci Cs and Ci +Oi⇔Ci Oi The general form of the reaction rate is: K ~v exp (−E /kT ), where v is the vibration frequency, E is the activation energy of the process taken from Ref. [22] and T is the temperature. The coupling of the equations is through the concentrations of vacancies and/or interstitials. Under these conditions, the following defects form: divacancy (V2), vacancy–oxygen (VO), vacancy–phosphorous (VP), interstitial carbon–substitutional carbon (CiCs) and interstitial carbon–interstitial oxygen (CiOi). It is known from the literature [23] that the distribution of stable defects does not coincide with the distribution of primary defects. On one side, this is due to the preferential forward momentum of recoiling Si atoms that makes interstitial related defects to be located deeper into the sample with respect to the ion range, contrary to vacancy related ones that have the peak displaced toward the surface, and on the other side to the long range migration of primary defects. As we do not have knowledge of values of the concentrations of impurities in our samples, we calculated the distribution of stable defects starting from the distribution of vacancy–interstitial pairs for two uniform distributions of P, O and C impurities in silicon: (a) P: 4 1012 at/cm3, O: 1015 at/cm3 and C: 5 1015 at/cm3; (b) P: 5 1011 at/cm3, O: 1015 at/cm3 and C: 1015 at/cm3, using the phenomenological quantitative model based on diffusion limited reactions from Refs. [24,25]. In these calculations we neglected the migration of vacancies and interstitials, and used their distributions (Fig. 2) obtained from simulation. We took into consideration the reactions of annihilation of vacancies and interstitials, of selfinterstitial migration to sinks, and of V2, VO, VP, Ci, CiCs and CiOi formation and decomposition, as the samples were both irradiated and kept at room temperature and in this temperature interval these defects are stable.
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By solving the associated system of differential equations, the time dependence of the concentrations of defects is found. The distributions of stable defects in the depth of Si, illustrated in Figs. 3 and 4, for the case of Bi and I irradiation, respectively are the asymptotic solutions. The differences between the distributions of different defects are due only to the reaction kinetics, i.e. to the reactions in which they are involved and to the associated activation energies. As specified, two uniform distributions of P, O and C impurities in silicon were investigated, (a) and (b). The results for the depth distributions of defects in the doping case (a) are represented in Fig. 3a, and for doping case (b) in Fig. 3b, respectively. Filled symbols correspond to the concentrations of defects obtained for doping (a), while same symbols but empty are used for defect concentrations for doping (b). In Fig. 3a and b the distributions of stable defects are normalised to the highest maximum between them, i.e. to the maximum of CiCs corresponding to case (a). On the same graph, the distribution of vacancies is also represented, normalised to its own maximum. For the case of Bi irradiation, one can see that the distributions of all stable defects, with the exception of VO, follow the distribution of vacancies. In the two cases we analysed, characterised by the same concentration of O, the distributions and even the concentrations of CiOi defects are nearly similar, as are the concentrations of VO. The excess of C in case (a) conduces to the increase of the concentration of CiCs. The shapes of V2 distributions are similar, and similar to the shape of V distribution, but a little bit wider. In spite of the fact that P concentration is very low, its variation is important as it is directly seen in the variation of V2 concentration. The shaded area illustrates the depth distribution of stopped Bi ions, which is Gaussian, and has the extension corresponding to its one standard deviation. It extends mainly in the region of decreasing concentrations of the majority of defects, and the percentage of defects located in the region with strain to the total number of defects created by irradiation is about 33% in case (a) and 29% in case (b). For any of the dopings (a) or (b), the percentages corresponding to each defect are very close to each other, excepting VO, and smaller than the global ratio. The depth distributions of defects produced by I irradiation and represented in Fig. 4a and b present characteristics close to those in Fig. 3a and b, associated with Bi irradiation. For I irradiation, the percentage of defects located in the region with strain (one standard deviation of the Gaussian corresponding to stopped ions) to the total number of defects created by irradiation is about 50% in case (a) and 42% in case (b). The comparison between the relative concentrations of defects created by the two ions shows that the maximum concentrations
Fig. 3. Depth distributions of the following defects: VO, VP, V2, Ci, CiOi, CiCs produced in Si (100) by irradiation with Bi ions of 28 MeV kinetic energy and of 5 1011 cm 2 fluence, normalised to CiCs concentration corresponding to impurity concentrations (a) and depth distribution of vacancies, normalised to its maximum. Shaded area: region with stopped ions (one standard deviation). (a) Doping case (a) and (b) doping case (b). The impurity concentrations are those from the text.
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Fig. 4. Depth distributions of the following defects: VO, VP, V2, Ci, CiOi, CiCs produced in Si (100) by irradiation with I ions of 28 MeV kinetic energy and of 5 1011 cm 2 fluence, normalised to CiCs concentration corresponding to impurity concentrations (a) and depth distribution of vacancies, normalised to its maximum. Shaded area: region with stopped ions (one standard deviation). (a) Doping case (a) and (b) doping case (b). The impurity concentrations are those from the text.
of CiCs defects created in both case (a) and (b) of Si doping, following Bi and I irradiation, are in the ratio of vacancies created per ion, i.e. 7.17 104/(5.72 104). From the analysis of the distributions of point defects, we found that all radiation-induced defects have non-uniform distributions, in both Bi and I irradiated samples. The depth distributions of all defects, except VO, closely follow the distribution of vacancies and interstitials, have the same peak positions but are wider. There is an important superposition between the region with high concentrations of defects and the region with stopped ions, although the region with stopped ions is deeper located in respect to the sample surface in both cases analysed. This superposition is different in the case of Bi and I irradiation, making the ratio between the number of defects located in the strain region and the total number of defects variable with the irradiation ion. This superposition also depends on the concentration of impurities in the sample, but in both case (a) and (b) of doping it increases from Bi to I irradiation, i.e. is lower for the heaviest ion, which has also narrower distribution of stopped ions.
lattice strain over the depth containing stopped ions, so it depends on the product between the number of stopped ions and the strain created by each of them and also on the thickness containing stopped ions. In its turn, the local strain is related to the mass, size and electronic configuration of I and Bi ions, i.e. it is related to the differences between each of them and Si, and the number of ions is the same in both cases. The information about the parameters of trapping centres (activation energy, concentration, capture cross section) and on the intensity of the average permanent electric field corresponding to strain is extracted by modelling the experimental relaxation currents recorded during temperature increase (using the method of thermally stimulated currents without applied bias) [15,16,28]. By measuring the relaxation currents, we found that the main difference between Bi and I irradiated samples is the strong retrapping of charge carriers in the samples with Bi ions, and the weak retrapping regime in the samples with I ions. By comparatively analysing the information obtained from modelling of experimental curves on Bi and I implanted Si [15,16] it results that:
3. Trap parameters and discussion
– All defects (V2, VO, CiCs, CiOi) are found in both cases as it results by comparing the trap parameters determined by the fitting procedure with those reported in the literature [29]. – In Bi irradiated samples the energy levels of all traps are broadened with Gaussian distributions (18–30 meV), while in I irradiated samples, for each trap a discrete energy level is determined. – The capture cross sections of traps in Bi irradiated Si depend on temperature as 1/T2, while for I irradiated samples temperature independent capture cross sections were found. – The average electric field corresponding to strain is two times more intense in Bi irradiated samples than in I irradiated ones, although the region with stopped ions, i.e. with electric field gradient is narrower.
As the Si samples irradiated with the two ions are from the same single crystal, are similarly oriented in respect to the beam, and the two ions have similar fluencies and kinetic energies, we considered that the same defects are produced, and we used this hypothesis in modelling the distributions of defects in the previous section. In order to study the influence of the field of strain due to stopped ions on the defects produced by irradiation, we chose the method of thermally stimulated currents without applied bias, which is characterized by a superlinear dependence of the current on the concentration of trapping centres [26,27]. Details on the measurements, as well as on the result of modelling the experimental curves can be found for Bi and I irradiation in Refs. [15,16] respectively. In the measurements of thermally stimulated currents without applied bias, the traps are first filled with charge carriers by illumination at low temperature, then the sample is heated up with low constant rate and the relaxation current is recorded. As no electric field is applied, charge carriers move in an electric field, which in the present case has two components. The first is due to the still trapped carriers on non-uniformly distributed centres, at each temperature, while the second is an average electric field corresponding to the strain created by stopped ions. This average electric field has the meaning of integral of the electric field gradient corresponding to
Because the only difference between the samples irradiated with Bi and I ions is the ion itself, all the other conditions being the same (ion beam orientation in respect to Si lattice, ion kinetic energy, ion charge, sizes of the samples, temperature) the observed differences were attributed to the differences in the strain produced in the two cases considered. By putting together the information obtained from the simulation of distributions of stopped ions and defects in the depth of the sample under the irradiated surface, i.e. the percentage of defects located in the region with strain, and the information obtained from modelling of experimental relaxation current
C. Palade et al. / Journal of Physics and Chemistry of Solids 93 (2016) 27–32
curves (meaning the intensity of electric field corresponding to strain, and trap defect parameters) we conclude that the magnitude of strain has the main influence in modifying trap parameters, and the superposition between the region with strain and the region with defects is a second order effect. On the other hand, one must also consider that the defects themselves could produce strain as they break the symmetry of the lattice. The models for the electronic structure of most of them are based on the electron paramagnetic resonance, which provided information about the symmetry of the defect. This method has been extensively exploited by Watkins and co-workers who proposed models for VO [30], VP [31], V2 [32], Ci [33], CiOi [34] and CiCs [35] defects in irradiated silicon. The strain due to defects has been considered to be the source of the electric field gradient in Ref. [11], and its quadrupolar interaction with the electric quadrupole moment of 209Bi (I¼ 9/2) was considered for use in local control of single qubits [10]. The present results are of interest for the use of 209Bi donors in Si in applications related to encoding and processing quantum information, particularly in producing a shift of the nuclear magnetic resonance due to the quadrupole interaction of the Bi nuclear spin with an electric field gradient, which could be due to the strain produced by the presence of Bi stopped ions resulting from implantation. The results concerning the modifications of trap parameters produced by the strain field are also useful for the design and manufacturing of microelectronic devices incorporating strain, as piezoresistive strain sensors [36], quantum well lasers with lattice-mismatched heterostructures [37], magnetomechanical actuators [38,39], strain enhanced MOSFETs as FinFET [40,41] and superjunction VDMOS [42].
4. Conclusions In order to evidence the influence of strain on Bi implanted silicon, we made a comparative analysis of Si containing I and Bi ions, both bigger and heavier than Si host atoms, hence both producing local deformations in the lattice. Bi and I ions were introduced by irradiating high resistivity Si float zone wafers with these ions, of energy 28 MeV and 5 1011 cm 2 fluence. We considered two uniform distributions of impurities of (a) 4 1012 P/cm3, 1015 O/cm3 and 5 1015 C/cm3 and (b) 5 1011 P/cm3, 1015 O/cm3 and 1015 C/cm3. The distributions of stopped ions and of primary defects were simulated, and the distributions of stable defects were derived using a model of diffusion-limited reactions of primary defects between themselves and with the impurities present in the lattice. For both Bi and I irradiation, we found that all radiation-induced defects have nonuniform distributions that follow the distribution of vacancies and interstitials (same peak positions, but wider) excepting the VO defect. The superposition between the region with high concentrations of defects and the region with stopped ions is significant, but differs as a function of the irradiation ion and concentration of doping impurities. The ratio between the concentration of defects located in the strain region and the total concentration of defects is 33% and 29% for Bi, and 50% and 42% for I for uniform distributions of impurities corresponding to the cases (a) and (b) respectively. The only difference between Bi and I irradiated Si is the ion nature, all other characteristics for the irradiation (kinetic energy of the ions, ions charge, fluence, relative orientation beam-Si crystal axes) and the samples used (producer, impurities, resistivity) being similar. We can conclude that the strain intensity is the main factor determining the modifications of the parameters of trapping centres, and its spatial superposition on the region with trapping centres is a second order effect.
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These results are of interest for the development of quantum bits in which the quadrupolar interaction in Si containing group-V donors with I 4I/2 enables the tuning of nuclear magnetic resonance of ionised donors by electrical field gradients, obtained, e.g. from strain. The modifications of trap parameters produced by strain are useful for the community working in design and manufacturing of microelectronic devices incorporating strain (piezoresistive strain sensors, strain enhanced MOSFETs). In a broader context, these results are of interest for strain engineering, understood as the field that studies how the physical properties of materials can be tuned by controlling the elastic strain fields applied to them, and which has become a critical feature of highperformance electronics as it enables significant device performance enhancements.
Acknowledgements This work was supported by the Romanian Ministry of National Education through the NIMP Core Programme PN09-450101.
References [1] B.E. Kane, A silicon-based nuclear spin quantum computer, Nature 393 (1998) 133. [2] T.D. Ladd, F. Jelezko, R. Laamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Quantum computers, Nature 464 (2010) 45. [3] R.E. George, W. Witzel, H. Riemann, N.V. Abrosimov, N. Nötzel, M.L. W. Thewalt, J.J.L. Morton, Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si, Phys. Rev. Lett. 105 (2010) 067601. [4] A.M. Tyryshkin, S. Tojo, J.J.L. Morton, H. Riemann, N.V. Abrosimov, P. Becker, H. J. Pohl, T. Schenkel, M.L.W. Thewalt, K.M. Itoh, S.A. Lyon, Electron spin coherence exceeding seconds in high-purity silicon, Nat. Mater. 11 (2012) 143. [5] C.D. Weis, C.C. Lo, V. Lang, A.M. Tyryshkin, R.E. George, K.M. Yu, J. Bokor, S. A. Lyon, J.J.L. Morton, T. Schenkel, Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon 28, Appl. Phys. Lett. 100 (2012) 172104. [6] G.W. Morley, P. Lueders, M.H. Mohammady, S.J. Balian, G. Aeppli, C.W.M. Kay, W.M. Witzel, G. Jeschke, T.S. Monteiro, Quantum control of hybrid nuclear– electronic qubits, Nat. Mater. 12 (2013) 103. [7] G. Wolfowicz, A.M. Tyryshkin, R.E. George, H. Riemann, N.V. Abrosimov, P. Becker, H.J. Pohl, M.L.W. Thewalt, S.A. Lyon, J.J.L. Morton, Atomic clock transitions in silicon-based spin qubits, Nat. Nanotechnol. 8 (2013) 561. [8] M. Steger, K. Saeedi, M.L.W. Thewalt, J.J.L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, Quantum information storage for over 180 s using donor spins in a 28Si “semiconductor vacuum”, Science 336 (2012) 1280. [9] K. Saeedi, S. Simmons, J.Z. Salvail, P. Dluhy, H. Riemann, N.V. Abrosimov, P. Becker, H.-J. Pohl, J.J.L. Morton, M.L.W. Thewalt, Donors in silicon 28, Science 342 (2013) 830. [10] D.P. Franke, F.M. Hrubesch, M. Künzl, H.-W. Becker, K.M. Itoh, M. Stutzmann, F. Hoehne, L. Dreher, M.S. Brandt, Phys. Rev. Lett. 115 (2015) 057601. [11] P.A. Mortemousque, S. Rosenius, G. Pica, D.P. Franke, T. Sekiguchi, A. Truong, M. P. Vlasenko, L.S. Vlasenko, M.S. Brandt, R.G. Elliman, K.M. Itoh, Quadrupole Shift of Nuclear Magnetic Resonance of Donors in Silicon at Low Magnetic Field, arXiv:1506.04028v1, 2015. [12] S. Hafizuddin, N.C. Mohapatra, A first-principles theory of the strain-effect electric field gradient in cubic metals due to point defects, J. Phys. F: Met. Phys. 16 (1986) 217–232. [13] C. Brusewitz, U. Vetter, H. Hofsass, Determination of gradient elastic tensors: stress and strain dependencies of electric field gradients in cubic and hexagonal systems, J. Phys.: Condens. Matter 27 (2015) 055401. [14] R.K. Sundforst, Determination of the gradient-elastic tensors for AIIIBV compounds using nuclear acoustic resonance, Phys. Rev. 177 (1969) 1221–1230. [15] M.L. Ciurea, S. Lazanu, A. Slav, C. Palade, Strain-induced modification of trap parameters due to the stopped ions in Bi-irradiated Si, EPL 108 (2014) 36004. [16] S. Lazanu, A. Slav, A.-M. Lepadatu, I. Stavarache, C. Palade, G. Iordache, M. L. Ciurea, Effects produced by iodine irradiation on high resistivity silicon, Appl. Phys. Lett. 101 (2012) 242106. [17] G. Possnert, AMS with the Uppsala EN tandem accelerator, Nucl. Instrum. Methods Phys. Res. B 5 (1984) 159–161. [18] R. Baron, G.A. Shifrin, O.J. Marsh, J.W. Mayer, Electrical behavior of group III and V implanted dopants in silicon, J. Appl. Phys. 40 (1969) 3702–3719. [19] Crystal-TRIM (04/1D -last revision May 2004), developed by Matthias Posselt 1991–2005, Forschungszentrum Rossendorf, Dresden, Germany. [20] SRIM-The Stopping and Range of Ions in Matter, developed by James F. Ziegler, 〈〈http://www.srim.org〉〉. [21] M. Suezawa, N. Fukata, Y. Iijima, I. Yonenaga, Formation and migration
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[22]
[23]
[24]
[25]
[26] [27]
[28] [29] [30] [31]
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energies of a vacancy and an interstitial in a high-purity Si crystal determined by detecting complexes of point defects and hydrogen: evaluation of activation energies of self-diffusion, Jpn. J. Appl. Phys. 53 (2014) 091302. I. Lazanu, S. Lazanu, The role of primary point defects in the degradation of silicon detectors due to hadron and lepton irradiation, Phys. Scr. 74 (2006) 201–207. P. Lévêque, N.H. Kortegaard, P. Pellegrino, A. Hallen, B.G. Svensson, A. Yu Kuznetsov, J. Wong-Leung, C. Jagadish, V. Privitera, Vacancy and interstitial depth profiles in ion-implanted silicon, J. Appl. Phys. 93 (2003) 871–877. I. Lazanu, S. Lazanu, Long-term damage induced by hadrons in silicon detectors for uses at the LHC-accelerator and in space missions, Phys. Scr. 67 (2003) 388–394. S. Lazanu, I. Lazanu, Systematic study related to the role of initial impurities and irradiation rates in the formation and evolution of complex defects in silicon for detectors in HEP experiments, Phys. Scr. 69 (2004) 376–384. D. Petre, I. Pintilie, T. Botila, M.L. Ciurea, Trapping levels in Bi12SiO20 crystals, J. Appl. Phys. 76 (1994) 2216–2219. V. Iancu, M.L. Ciurea, M. Draghici, Modeling of optical charging spectroscopy investigation of trapping phenomena in nanocrystalline porous silicon, J. Appl. Phys. 94 (2003) 216–223. M.L. Ciurea, V. Iancu, M.R. Mitroi, Trapping phenomena in silicon-based nanocrystalline semiconductors, Solid-State Electron. 51 (2007) 1328–1337. P. Pichler P, Intrinsic Point Defects, Impurities and Their Diffusion in Silicon, Springer Verlag, Wien, 2004. G.D. Watkins, J.W. Corbett, Defects in irradiated silicon. I. Electron spin resonance of the Si-A center, Phys. Rev. 121 (1961) 1001–1013. G.D. Watkins, J.W. Corbett, Defects in irradiated silicon: electron paramagnetic resonance and electron-nuclear double resonance of the Si-E center, Phys. Rev. 134 (1964) A1359–A1377.
[32] G.D. Watkins, J.W. Corbett, Defects in irradiated silicon: electron paramagnetic resonance of the divacancy, Phys. Rev. 138 (1965) A543–A555. [33] G.D. Watkins, K.L. Brower, EPR observation of the isolated interstitial carbon atom in silicon, Phys. Rev. Lett. 36 (1976) 1329. [34] J.M. Trombetta, G.D. Watkins, Identification of an interstitial carbon-interstitial oxygen complex in silicon, Appl. Phys. Lett. 51 (1987) 1103–1105. [35] L.W. Song, G.D. Watkins, EPR identification of the single-acceptor state of interstitial carbon in silicon, Phys. Rev. B 42 (1990) 5759–5764. [36] A.A. Barlian, W.-T. Park, J.R. Mallon Jr, A. Rastegar, B.L. Pruitt, Review: semiconductor piezoresistance for microsystems, Proc. IEEE Inst. Electr. Electron. Eng. 97 (2009) 513–552. [37] M.M.S. Polash, M.S. Alam, International Conference on Electrical Engineering and Information & Communication Technology (ICEEICT) 1–5, 2014. [38] S.V. Kumar, S. Seenithurai, M.M. Raja, M. Mahendran, Structural and magnetic properties of sputter-deposited polycrystalline Ni–Mn–Ga ferromagnetic shape-memory thin films, J. Electron. Mater. 44 (2015) 3761–3767. [39] J. Cui, C.-Y. Liang, E.A. Paisley, A. Sepulveda, J.F. Ihlefeld, G.P. Carman, C. S. Lynch, Generation of localized strain in a thin film piezoelectric to control individual magnetoelectric heterostructures, Appl. Phys. Lett. 107 (2015) 092903. [40] T. van Hemert, R.J.E. Hueting, Piezoelectric strain modulation in FETs, IEEE Trans. Electron. Devices 60 (2013) 3265–3268. [41] H. Achour, B. Cretu, E. Simoen, J.-M. Routoure, R. Carin, A. Benfdila, M. Aoulaiche, C. Claeys, Identification of Si film traps in p-channel SOI FinFETs using low temperature noise spectroscopy, Solid-State Electron. 112 (2015) 1–6. [42] A. Naugarhiya, S. Dubey, P.N. Kondekar, A. Naugarhiya, S. Dubey, P. N. Kondekar, Superlattices and microstructures, Superlattices Microstruct. 85 (2015) 461–468.
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Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Correlation between strain and defects in Bi implanted Si C. Palade a,b, A.-M. Lepadatu a, A. Slav a, M.L. Ciurea a,c, S. Lazanu a,n a b c
National Institute of Materials Physics, 405A Atomistilor Str., 077125 Magurele, Romania University of Bucharest, Faculty of Physics, 405 Atomistilor Str, 077125 Magurele, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucuresti, Romania
art ic l e i nf o
a b s t r a c t
Article history: Received 27 October 2015 Received in revised form 18 January 2016 Accepted 8 February 2016 Available online 9 February 2016
The strain in Si containing group-V impurities is a topical subject of study due to its potential applications in quantum computing. In this paper we study 209Bi implanted Si concerning the correlation between the strain produced by stopped Bi ions and trapping characteristics of the defects resulted from implantation. The depths distributions of stopped ions and primary defects are simulated and the distributions of permanent defects are modelled for Si implanted with low fluence 209Bi ions of 28 MeV kinetic energy. For comparison, these depths distributions were similarly calculated for 127I ions with the same fluence and energy, implanted in Si. The results are compared with each other and correlated with the characteristics of traps in these systems, previously obtained. We demonstrate that the intensity of the strain field is the most important factor in changing of trap parameters, while the superposition between the region with strain and the region where defects are located is a second order effect. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Field of strain Ion irradiation defects Trapping centres Modelling the distribution of defects
1. Introduction The system of electron and nuclear spins of donor atoms in silicon is an excellent quantum bit (qubit) candidate for quantum information processing [1,2], and it is expected to be a better solution in respect to superconducting qubits which show relatively fast decoherence rates, insufficient for maintaining quantum information throughout the course of computation. In isotopically enriched 28Si (I¼0), the coherence times are improved in comparison to natural Si, due to the removal of the residual nuclear spins of 29Si, which has the natural abundance of 4.7%, and is the only one isotope of natural Si with nonzero nuclear spin (I¼ 1/2) [3,4]. The interest in Bi doped Si materials suddenly increased in the last years, based on this potential application. Clock transitions with coherence times of several seconds (at 5 K), much longer than those characterizing superconducting qubits, were reported [5–7]. In parallel, studies on the nuclear spin of ionised 31P donors in isotopically purified 28Si have demonstrated even higher coherence times, in the order of tens of minutes or even higher, at room temperature [8,9]. Recently it was reported that the quadrupolar interaction of group-V donors with nuclear spin I41/2 with electric field gradients can be manipulated by applying elastic strain to the host crystal, for mechanical tuning the nuclear spin of ionised donors [10,11], with the benefit of scalable local addressing the qubits. The strain is applied locally by piezoactuators on the scale of nanometres in Ref. [10], while in Ref. [11] n
Corresponding author. E-mail address: lazanu@infim.ro (S. Lazanu).
http://dx.doi.org/10.1016/j.jpcs.2016.02.005 0022-3697/& 2016 Elsevier Ltd. All rights reserved.
the defects created during Si implantation modify the nuclear electric quadrupole interaction of the nuclear quadrupole moment with the electron wavefunction. The relation between electric field gradient tensors and lattice strain was theoretically substantiated [12,13] based on experimental data from nuclear acoustic resonance [14]. For Si, this topic only recently appeared in the literature, in relation to the mentioned applications in quantum computing [10]. In the present paper we aim to study the system 209Bi–Si from the point of view of the relation between the strain field produced by Bi ions (bigger and heavier than the Si host atoms) and the trapping properties of the defects produced during Bi implantation, particularly of the relation between strain field intensity and the relative depth distributions of both strain field and defects. For this, we comparatively analyse Si single crystals implanted with Bi and I ions, both of energy 28 MeV and fluence 5 1011 ions/cm2, which have a lower range than the depth of the samples, and are stopped inside. Both Bi and I ions being bigger and heavier than Si atoms produce a local strain in Si, which is more intense in Bi implanted Si. On the other hand, during their penetration into Si, the ions generate lattice defects. Based on the simulations of depth distributions of stopped ions and of primary defects respectively, we model the production of point defects and their depth distributions. The trap parameters of these irradiation defects were previously obtained by modelling the experimental thermally stimulated current without applied bias curves measured on similar Si samples, implanted with Bi and I ions [15,16], considering the effect of strain. The differences in the characteristics of the trapping centres corresponding to Si samples with Bi and I are correlated and explained based on the results of simulations of ion penetration into Si and on the peculiarities of the fields of strain.
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2. Spatial distribution of the strain fields and defects
and I
6þ
8.36 µm
5x10
ions penetration in Si
The range of both ions of kinetic energy 28 MeV and 3° disoriented in respect to the (100) axis of Si is much smaller than the sample thickness, and consequently they are stopped inside. In order to simulate their penetration into the Si lattice, we used the Monte Carlo code Crystal Transport and Range of Ions in Matter (CTRIM) [19], based on the binary collision approximation. In contrast to the SRIM (Stopping and Range of Ions in Matter) code [20] that simulates the penetration of ions in amorphous targets, CTRIM takes into account the crystal structure and the orientation of the ion beam in respect to the lattice. So, the programme follows the incoming particle and all the particles it sets in motion until they fall below a selected low kinetic energy. It is known that the competition between nuclear and electronic stopping for different ions is a function of ion characteristics (charge and mass numbers) and energy. So, when entering the sample, both Bi and I ions lose energy predominantly by ionisation. Being lighter, I ions penetrate farther into Si. It is known that with the increase of the atomic mass and charge numbers of the ion, the maximum of the nuclear energy loss is shifted to higher energies, and the value of the maximum is also higher, this being correlated with a higher displacement damage production. The nuclear energy loss is the highest near the end of the range, i.e. at low ion energies, and consequently in this region the concentration of defects is also higher, as it will be seen further. In the following, we are interested only in distributions in the depth of the sample, due to the uniformity of the irradiation on the surface. The distributions of stopped ions are nearly Gaussian, with the maxima located at 4.77 and 8.36 mm for Bi and I ions, respectively [15,16]. These distributions are illustrated in Fig. 1, where the centre (projected range) and the standard deviations (range straggling) of each of them are marked. One can see that the distribution of Bi ions is much narrower, steeper than the distribution of I ions. Each stopped ion, being bigger (rBi ¼1.70 Å and rI ¼1.28 Å) and heavier (ABi ¼209 and AI ¼127) than the atoms of the host lattice (rSi ¼1.17 Å, ASi ¼28) produces a local deformation of the lattice. The strain fields produced by all stopped ions add together. The two ions, Bi and I, being differently distributed in the depth of Si, create different configurations of the field of strain. So, the departure of each of the ions studied from the Si atoms of the host lattice (mass, size, electronic configuration) is different, and it is expected that the magnitudes of created strain are also different. 2.2. Simulation of the distributions of primary defects produced by Bi and I ions in Si The depth distributions of the vacancies created by the two types of ions, as a consequence of the energy transmitted to the atomic motion, as obtained from CTRIM are represented comparatively in Fig. 2. These distributions are asymmetrical, with the maxima situated at 4.25 mm and 7.35 mm, giving a total number of vacancies
-5
0 0.0
5.0x104
1.0x105
Depth [A] Fig. 1. Depth distribution of stopped Bi and I ions, with the projected range and standard deviation (range straggling) marked.
per ion of 7.17 104 and 5.72 104 for Bi and I ions, respectively. The asymmetry of the distributions of vacancies, i.e. their tails toward the sample surface, is explained by primary defects (vacancies and interstitials) creation in atomic collision cascades, having the source in the primary knock-on atoms. So, in each interaction, if the energy transmitted to the atom exceeds the threshold energy for displacements, the atom leaves its site in the lattice, creating a vacancy–interstitial pair. The self-interstitial, which is the recoil created in the primary interaction, can be the source of a cascade of displacements if it has enough energy. Hence near the trajectory of the heavy ion, vacancies and interstitials are created in pairs. 2.3. Modelling of the distributions of stable defects following Bi and I irradiation As in Si both interstitials and vacancies have a very fast and long range migration [21], they interact either between themselves or with the defects and impurities present in the lattice via migration, recombination and annihilation, thus forming stable point defects which are related to interstitials or to vacancies. The main impurities present in our samples are O, C (both with concentrations in the order of 1015–1016 at/cm3) and P (5 1011–5 1012 at/cm3). In the frame of the theory of diffusion – limited reactions, the process of Bi I
3
Vacancies [1/ion/A]
2.1. Simulation of Bi
6þ
Bi I
4.77µm
1x10-4
Stopped ions [1/A]
The experimental data are from our previous work, Refs. [15,16]. High resistivity Si wafers grown by the floating zone technique, of 2 in. diameter and 280 mm thickness (from Siltronix), contain natural abundances of Si isotopes, i.e. 92.2% 28Si (I¼0), 4.7% 29Si (I¼1/2) and 3.1% 30Si (I¼ 0). They were irradiated with 209Bi6þ and 127I6þ ions at the tandem accelerator of Uppsala University [17]. Both ions had the same kinetic energy and fluence of 28 MeV and 5 1011 ions/cm2, respectively. The irradiation nonuniformity on the Si surface was less than 5%, and the beam axis was disoriented in respect to (100) direction by 3° [15,16]. The irradiations were performed at room temperature, and the samples were not annealed for Bi activation [18], but they were kept at room temperature between irradiation and measurements.
4.25 µm
CTRIM, 30 off
2 7.35 µm
1
0
0.0
5.0x104
1.0x105
Depth [A] Fig. 2. Depth distribution of vacancies created in Si following the irradiation with Bi and I ions, of 28 MeV kinetic energy.
C. Palade et al. / Journal of Physics and Chemistry of Solids 93 (2016) 27–32
formation of stable defects is described by a system of coupled differential equations, having as initial conditions the concentrations of impurities and of vacancies and interstitials, and as parameters the rates of formation of defects. In the present case, due to the impurities considered, the processes taken into account are: – – – –
annihilation of vacancies and interstitials: V+I→Si migration of interstitials to sinks: I→sinks formation of divacancies: V+V⇔V2 formation and decomposition of defect VO (A centre): V+O ⇔ VO – formation and decomposition of defect VP (E centre): V+P ⇔ VP – formation of interstitial carbon Ci: C+I ⇔ Ci – formation of CiOi and CiCs centres: Ci +Cs⇔Ci Cs and Ci +Oi⇔Ci Oi The general form of the reaction rate is: K ~v exp (−E /kT ), where v is the vibration frequency, E is the activation energy of the process taken from Ref. [22] and T is the temperature. The coupling of the equations is through the concentrations of vacancies and/or interstitials. Under these conditions, the following defects form: divacancy (V2), vacancy–oxygen (VO), vacancy–phosphorous (VP), interstitial carbon–substitutional carbon (CiCs) and interstitial carbon–interstitial oxygen (CiOi). It is known from the literature [23] that the distribution of stable defects does not coincide with the distribution of primary defects. On one side, this is due to the preferential forward momentum of recoiling Si atoms that makes interstitial related defects to be located deeper into the sample with respect to the ion range, contrary to vacancy related ones that have the peak displaced toward the surface, and on the other side to the long range migration of primary defects. As we do not have knowledge of values of the concentrations of impurities in our samples, we calculated the distribution of stable defects starting from the distribution of vacancy–interstitial pairs for two uniform distributions of P, O and C impurities in silicon: (a) P: 4 1012 at/cm3, O: 1015 at/cm3 and C: 5 1015 at/cm3; (b) P: 5 1011 at/cm3, O: 1015 at/cm3 and C: 1015 at/cm3, using the phenomenological quantitative model based on diffusion limited reactions from Refs. [24,25]. In these calculations we neglected the migration of vacancies and interstitials, and used their distributions (Fig. 2) obtained from simulation. We took into consideration the reactions of annihilation of vacancies and interstitials, of selfinterstitial migration to sinks, and of V2, VO, VP, Ci, CiCs and CiOi formation and decomposition, as the samples were both irradiated and kept at room temperature and in this temperature interval these defects are stable.
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By solving the associated system of differential equations, the time dependence of the concentrations of defects is found. The distributions of stable defects in the depth of Si, illustrated in Figs. 3 and 4, for the case of Bi and I irradiation, respectively are the asymptotic solutions. The differences between the distributions of different defects are due only to the reaction kinetics, i.e. to the reactions in which they are involved and to the associated activation energies. As specified, two uniform distributions of P, O and C impurities in silicon were investigated, (a) and (b). The results for the depth distributions of defects in the doping case (a) are represented in Fig. 3a, and for doping case (b) in Fig. 3b, respectively. Filled symbols correspond to the concentrations of defects obtained for doping (a), while same symbols but empty are used for defect concentrations for doping (b). In Fig. 3a and b the distributions of stable defects are normalised to the highest maximum between them, i.e. to the maximum of CiCs corresponding to case (a). On the same graph, the distribution of vacancies is also represented, normalised to its own maximum. For the case of Bi irradiation, one can see that the distributions of all stable defects, with the exception of VO, follow the distribution of vacancies. In the two cases we analysed, characterised by the same concentration of O, the distributions and even the concentrations of CiOi defects are nearly similar, as are the concentrations of VO. The excess of C in case (a) conduces to the increase of the concentration of CiCs. The shapes of V2 distributions are similar, and similar to the shape of V distribution, but a little bit wider. In spite of the fact that P concentration is very low, its variation is important as it is directly seen in the variation of V2 concentration. The shaded area illustrates the depth distribution of stopped Bi ions, which is Gaussian, and has the extension corresponding to its one standard deviation. It extends mainly in the region of decreasing concentrations of the majority of defects, and the percentage of defects located in the region with strain to the total number of defects created by irradiation is about 33% in case (a) and 29% in case (b). For any of the dopings (a) or (b), the percentages corresponding to each defect are very close to each other, excepting VO, and smaller than the global ratio. The depth distributions of defects produced by I irradiation and represented in Fig. 4a and b present characteristics close to those in Fig. 3a and b, associated with Bi irradiation. For I irradiation, the percentage of defects located in the region with strain (one standard deviation of the Gaussian corresponding to stopped ions) to the total number of defects created by irradiation is about 50% in case (a) and 42% in case (b). The comparison between the relative concentrations of defects created by the two ions shows that the maximum concentrations
Fig. 3. Depth distributions of the following defects: VO, VP, V2, Ci, CiOi, CiCs produced in Si (100) by irradiation with Bi ions of 28 MeV kinetic energy and of 5 1011 cm 2 fluence, normalised to CiCs concentration corresponding to impurity concentrations (a) and depth distribution of vacancies, normalised to its maximum. Shaded area: region with stopped ions (one standard deviation). (a) Doping case (a) and (b) doping case (b). The impurity concentrations are those from the text.
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Fig. 4. Depth distributions of the following defects: VO, VP, V2, Ci, CiOi, CiCs produced in Si (100) by irradiation with I ions of 28 MeV kinetic energy and of 5 1011 cm 2 fluence, normalised to CiCs concentration corresponding to impurity concentrations (a) and depth distribution of vacancies, normalised to its maximum. Shaded area: region with stopped ions (one standard deviation). (a) Doping case (a) and (b) doping case (b). The impurity concentrations are those from the text.
of CiCs defects created in both case (a) and (b) of Si doping, following Bi and I irradiation, are in the ratio of vacancies created per ion, i.e. 7.17 104/(5.72 104). From the analysis of the distributions of point defects, we found that all radiation-induced defects have non-uniform distributions, in both Bi and I irradiated samples. The depth distributions of all defects, except VO, closely follow the distribution of vacancies and interstitials, have the same peak positions but are wider. There is an important superposition between the region with high concentrations of defects and the region with stopped ions, although the region with stopped ions is deeper located in respect to the sample surface in both cases analysed. This superposition is different in the case of Bi and I irradiation, making the ratio between the number of defects located in the strain region and the total number of defects variable with the irradiation ion. This superposition also depends on the concentration of impurities in the sample, but in both case (a) and (b) of doping it increases from Bi to I irradiation, i.e. is lower for the heaviest ion, which has also narrower distribution of stopped ions.
lattice strain over the depth containing stopped ions, so it depends on the product between the number of stopped ions and the strain created by each of them and also on the thickness containing stopped ions. In its turn, the local strain is related to the mass, size and electronic configuration of I and Bi ions, i.e. it is related to the differences between each of them and Si, and the number of ions is the same in both cases. The information about the parameters of trapping centres (activation energy, concentration, capture cross section) and on the intensity of the average permanent electric field corresponding to strain is extracted by modelling the experimental relaxation currents recorded during temperature increase (using the method of thermally stimulated currents without applied bias) [15,16,28]. By measuring the relaxation currents, we found that the main difference between Bi and I irradiated samples is the strong retrapping of charge carriers in the samples with Bi ions, and the weak retrapping regime in the samples with I ions. By comparatively analysing the information obtained from modelling of experimental curves on Bi and I implanted Si [15,16] it results that:
3. Trap parameters and discussion
– All defects (V2, VO, CiCs, CiOi) are found in both cases as it results by comparing the trap parameters determined by the fitting procedure with those reported in the literature [29]. – In Bi irradiated samples the energy levels of all traps are broadened with Gaussian distributions (18–30 meV), while in I irradiated samples, for each trap a discrete energy level is determined. – The capture cross sections of traps in Bi irradiated Si depend on temperature as 1/T2, while for I irradiated samples temperature independent capture cross sections were found. – The average electric field corresponding to strain is two times more intense in Bi irradiated samples than in I irradiated ones, although the region with stopped ions, i.e. with electric field gradient is narrower.
As the Si samples irradiated with the two ions are from the same single crystal, are similarly oriented in respect to the beam, and the two ions have similar fluencies and kinetic energies, we considered that the same defects are produced, and we used this hypothesis in modelling the distributions of defects in the previous section. In order to study the influence of the field of strain due to stopped ions on the defects produced by irradiation, we chose the method of thermally stimulated currents without applied bias, which is characterized by a superlinear dependence of the current on the concentration of trapping centres [26,27]. Details on the measurements, as well as on the result of modelling the experimental curves can be found for Bi and I irradiation in Refs. [15,16] respectively. In the measurements of thermally stimulated currents without applied bias, the traps are first filled with charge carriers by illumination at low temperature, then the sample is heated up with low constant rate and the relaxation current is recorded. As no electric field is applied, charge carriers move in an electric field, which in the present case has two components. The first is due to the still trapped carriers on non-uniformly distributed centres, at each temperature, while the second is an average electric field corresponding to the strain created by stopped ions. This average electric field has the meaning of integral of the electric field gradient corresponding to
Because the only difference between the samples irradiated with Bi and I ions is the ion itself, all the other conditions being the same (ion beam orientation in respect to Si lattice, ion kinetic energy, ion charge, sizes of the samples, temperature) the observed differences were attributed to the differences in the strain produced in the two cases considered. By putting together the information obtained from the simulation of distributions of stopped ions and defects in the depth of the sample under the irradiated surface, i.e. the percentage of defects located in the region with strain, and the information obtained from modelling of experimental relaxation current
C. Palade et al. / Journal of Physics and Chemistry of Solids 93 (2016) 27–32
curves (meaning the intensity of electric field corresponding to strain, and trap defect parameters) we conclude that the magnitude of strain has the main influence in modifying trap parameters, and the superposition between the region with strain and the region with defects is a second order effect. On the other hand, one must also consider that the defects themselves could produce strain as they break the symmetry of the lattice. The models for the electronic structure of most of them are based on the electron paramagnetic resonance, which provided information about the symmetry of the defect. This method has been extensively exploited by Watkins and co-workers who proposed models for VO [30], VP [31], V2 [32], Ci [33], CiOi [34] and CiCs [35] defects in irradiated silicon. The strain due to defects has been considered to be the source of the electric field gradient in Ref. [11], and its quadrupolar interaction with the electric quadrupole moment of 209Bi (I¼ 9/2) was considered for use in local control of single qubits [10]. The present results are of interest for the use of 209Bi donors in Si in applications related to encoding and processing quantum information, particularly in producing a shift of the nuclear magnetic resonance due to the quadrupole interaction of the Bi nuclear spin with an electric field gradient, which could be due to the strain produced by the presence of Bi stopped ions resulting from implantation. The results concerning the modifications of trap parameters produced by the strain field are also useful for the design and manufacturing of microelectronic devices incorporating strain, as piezoresistive strain sensors [36], quantum well lasers with lattice-mismatched heterostructures [37], magnetomechanical actuators [38,39], strain enhanced MOSFETs as FinFET [40,41] and superjunction VDMOS [42].
4. Conclusions In order to evidence the influence of strain on Bi implanted silicon, we made a comparative analysis of Si containing I and Bi ions, both bigger and heavier than Si host atoms, hence both producing local deformations in the lattice. Bi and I ions were introduced by irradiating high resistivity Si float zone wafers with these ions, of energy 28 MeV and 5 1011 cm 2 fluence. We considered two uniform distributions of impurities of (a) 4 1012 P/cm3, 1015 O/cm3 and 5 1015 C/cm3 and (b) 5 1011 P/cm3, 1015 O/cm3 and 1015 C/cm3. The distributions of stopped ions and of primary defects were simulated, and the distributions of stable defects were derived using a model of diffusion-limited reactions of primary defects between themselves and with the impurities present in the lattice. For both Bi and I irradiation, we found that all radiation-induced defects have nonuniform distributions that follow the distribution of vacancies and interstitials (same peak positions, but wider) excepting the VO defect. The superposition between the region with high concentrations of defects and the region with stopped ions is significant, but differs as a function of the irradiation ion and concentration of doping impurities. The ratio between the concentration of defects located in the strain region and the total concentration of defects is 33% and 29% for Bi, and 50% and 42% for I for uniform distributions of impurities corresponding to the cases (a) and (b) respectively. The only difference between Bi and I irradiated Si is the ion nature, all other characteristics for the irradiation (kinetic energy of the ions, ions charge, fluence, relative orientation beam-Si crystal axes) and the samples used (producer, impurities, resistivity) being similar. We can conclude that the strain intensity is the main factor determining the modifications of the parameters of trapping centres, and its spatial superposition on the region with trapping centres is a second order effect.
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These results are of interest for the development of quantum bits in which the quadrupolar interaction in Si containing group-V donors with I 4I/2 enables the tuning of nuclear magnetic resonance of ionised donors by electrical field gradients, obtained, e.g. from strain. The modifications of trap parameters produced by strain are useful for the community working in design and manufacturing of microelectronic devices incorporating strain (piezoresistive strain sensors, strain enhanced MOSFETs). In a broader context, these results are of interest for strain engineering, understood as the field that studies how the physical properties of materials can be tuned by controlling the elastic strain fields applied to them, and which has become a critical feature of highperformance electronics as it enables significant device performance enhancements.
Acknowledgements This work was supported by the Romanian Ministry of National Education through the NIMP Core Programme PN09-450101.
References [1] B.E. Kane, A silicon-based nuclear spin quantum computer, Nature 393 (1998) 133. [2] T.D. Ladd, F. Jelezko, R. Laamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Quantum computers, Nature 464 (2010) 45. [3] R.E. George, W. Witzel, H. Riemann, N.V. Abrosimov, N. Nötzel, M.L. W. Thewalt, J.J.L. Morton, Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si, Phys. Rev. Lett. 105 (2010) 067601. [4] A.M. Tyryshkin, S. Tojo, J.J.L. Morton, H. Riemann, N.V. Abrosimov, P. Becker, H. J. Pohl, T. Schenkel, M.L.W. Thewalt, K.M. Itoh, S.A. Lyon, Electron spin coherence exceeding seconds in high-purity silicon, Nat. Mater. 11 (2012) 143. [5] C.D. Weis, C.C. Lo, V. Lang, A.M. Tyryshkin, R.E. George, K.M. Yu, J. Bokor, S. A. Lyon, J.J.L. Morton, T. Schenkel, Electrical activation and electron spin resonance measurements of implanted bismuth in isotopically enriched silicon 28, Appl. Phys. Lett. 100 (2012) 172104. [6] G.W. Morley, P. Lueders, M.H. Mohammady, S.J. Balian, G. Aeppli, C.W.M. Kay, W.M. Witzel, G. Jeschke, T.S. Monteiro, Quantum control of hybrid nuclear– electronic qubits, Nat. Mater. 12 (2013) 103. [7] G. Wolfowicz, A.M. Tyryshkin, R.E. George, H. Riemann, N.V. Abrosimov, P. Becker, H.J. Pohl, M.L.W. Thewalt, S.A. Lyon, J.J.L. Morton, Atomic clock transitions in silicon-based spin qubits, Nat. Nanotechnol. 8 (2013) 561. [8] M. Steger, K. Saeedi, M.L.W. Thewalt, J.J.L. Morton, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, Quantum information storage for over 180 s using donor spins in a 28Si “semiconductor vacuum”, Science 336 (2012) 1280. [9] K. Saeedi, S. Simmons, J.Z. Salvail, P. Dluhy, H. Riemann, N.V. Abrosimov, P. Becker, H.-J. Pohl, J.J.L. Morton, M.L.W. Thewalt, Donors in silicon 28, Science 342 (2013) 830. [10] D.P. Franke, F.M. Hrubesch, M. Künzl, H.-W. Becker, K.M. Itoh, M. Stutzmann, F. Hoehne, L. Dreher, M.S. Brandt, Phys. Rev. Lett. 115 (2015) 057601. [11] P.A. Mortemousque, S. Rosenius, G. Pica, D.P. Franke, T. Sekiguchi, A. Truong, M. P. Vlasenko, L.S. Vlasenko, M.S. Brandt, R.G. Elliman, K.M. Itoh, Quadrupole Shift of Nuclear Magnetic Resonance of Donors in Silicon at Low Magnetic Field, arXiv:1506.04028v1, 2015. [12] S. Hafizuddin, N.C. Mohapatra, A first-principles theory of the strain-effect electric field gradient in cubic metals due to point defects, J. Phys. F: Met. Phys. 16 (1986) 217–232. [13] C. Brusewitz, U. Vetter, H. Hofsass, Determination of gradient elastic tensors: stress and strain dependencies of electric field gradients in cubic and hexagonal systems, J. Phys.: Condens. Matter 27 (2015) 055401. [14] R.K. Sundforst, Determination of the gradient-elastic tensors for AIIIBV compounds using nuclear acoustic resonance, Phys. Rev. 177 (1969) 1221–1230. [15] M.L. Ciurea, S. Lazanu, A. Slav, C. Palade, Strain-induced modification of trap parameters due to the stopped ions in Bi-irradiated Si, EPL 108 (2014) 36004. [16] S. Lazanu, A. Slav, A.-M. Lepadatu, I. Stavarache, C. Palade, G. Iordache, M. L. Ciurea, Effects produced by iodine irradiation on high resistivity silicon, Appl. Phys. Lett. 101 (2012) 242106. [17] G. Possnert, AMS with the Uppsala EN tandem accelerator, Nucl. Instrum. Methods Phys. Res. B 5 (1984) 159–161. [18] R. Baron, G.A. Shifrin, O.J. Marsh, J.W. Mayer, Electrical behavior of group III and V implanted dopants in silicon, J. Appl. Phys. 40 (1969) 3702–3719. [19] Crystal-TRIM (04/1D -last revision May 2004), developed by Matthias Posselt 1991–2005, Forschungszentrum Rossendorf, Dresden, Germany. [20] SRIM-The Stopping and Range of Ions in Matter, developed by James F. Ziegler, 〈〈http://www.srim.org〉〉. [21] M. Suezawa, N. Fukata, Y. Iijima, I. Yonenaga, Formation and migration
32
[22]
[23]
[24]
[25]
[26] [27]
[28] [29] [30] [31]
C. Palade et al. / Journal of Physics and Chemistry of Solids 93 (2016) 27–32
energies of a vacancy and an interstitial in a high-purity Si crystal determined by detecting complexes of point defects and hydrogen: evaluation of activation energies of self-diffusion, Jpn. J. Appl. Phys. 53 (2014) 091302. I. Lazanu, S. Lazanu, The role of primary point defects in the degradation of silicon detectors due to hadron and lepton irradiation, Phys. Scr. 74 (2006) 201–207. P. Lévêque, N.H. Kortegaard, P. Pellegrino, A. Hallen, B.G. Svensson, A. Yu Kuznetsov, J. Wong-Leung, C. Jagadish, V. Privitera, Vacancy and interstitial depth profiles in ion-implanted silicon, J. Appl. Phys. 93 (2003) 871–877. I. Lazanu, S. Lazanu, Long-term damage induced by hadrons in silicon detectors for uses at the LHC-accelerator and in space missions, Phys. Scr. 67 (2003) 388–394. S. Lazanu, I. Lazanu, Systematic study related to the role of initial impurities and irradiation rates in the formation and evolution of complex defects in silicon for detectors in HEP experiments, Phys. Scr. 69 (2004) 376–384. D. Petre, I. Pintilie, T. Botila, M.L. Ciurea, Trapping levels in Bi12SiO20 crystals, J. Appl. Phys. 76 (1994) 2216–2219. V. Iancu, M.L. Ciurea, M. Draghici, Modeling of optical charging spectroscopy investigation of trapping phenomena in nanocrystalline porous silicon, J. Appl. Phys. 94 (2003) 216–223. M.L. Ciurea, V. Iancu, M.R. Mitroi, Trapping phenomena in silicon-based nanocrystalline semiconductors, Solid-State Electron. 51 (2007) 1328–1337. P. Pichler P, Intrinsic Point Defects, Impurities and Their Diffusion in Silicon, Springer Verlag, Wien, 2004. G.D. Watkins, J.W. Corbett, Defects in irradiated silicon. I. Electron spin resonance of the Si-A center, Phys. Rev. 121 (1961) 1001–1013. G.D. Watkins, J.W. Corbett, Defects in irradiated silicon: electron paramagnetic resonance and electron-nuclear double resonance of the Si-E center, Phys. Rev. 134 (1964) A1359–A1377.
[32] G.D. Watkins, J.W. Corbett, Defects in irradiated silicon: electron paramagnetic resonance of the divacancy, Phys. Rev. 138 (1965) A543–A555. [33] G.D. Watkins, K.L. Brower, EPR observation of the isolated interstitial carbon atom in silicon, Phys. Rev. Lett. 36 (1976) 1329. [34] J.M. Trombetta, G.D. Watkins, Identification of an interstitial carbon-interstitial oxygen complex in silicon, Appl. Phys. Lett. 51 (1987) 1103–1105. [35] L.W. Song, G.D. Watkins, EPR identification of the single-acceptor state of interstitial carbon in silicon, Phys. Rev. B 42 (1990) 5759–5764. [36] A.A. Barlian, W.-T. Park, J.R. Mallon Jr, A. Rastegar, B.L. Pruitt, Review: semiconductor piezoresistance for microsystems, Proc. IEEE Inst. Electr. Electron. Eng. 97 (2009) 513–552. [37] M.M.S. Polash, M.S. Alam, International Conference on Electrical Engineering and Information & Communication Technology (ICEEICT) 1–5, 2014. [38] S.V. Kumar, S. Seenithurai, M.M. Raja, M. Mahendran, Structural and magnetic properties of sputter-deposited polycrystalline Ni–Mn–Ga ferromagnetic shape-memory thin films, J. Electron. Mater. 44 (2015) 3761–3767. [39] J. Cui, C.-Y. Liang, E.A. Paisley, A. Sepulveda, J.F. Ihlefeld, G.P. Carman, C. S. Lynch, Generation of localized strain in a thin film piezoelectric to control individual magnetoelectric heterostructures, Appl. Phys. Lett. 107 (2015) 092903. [40] T. van Hemert, R.J.E. Hueting, Piezoelectric strain modulation in FETs, IEEE Trans. Electron. Devices 60 (2013) 3265–3268. [41] H. Achour, B. Cretu, E. Simoen, J.-M. Routoure, R. Carin, A. Benfdila, M. Aoulaiche, C. Claeys, Identification of Si film traps in p-channel SOI FinFETs using low temperature noise spectroscopy, Solid-State Electron. 112 (2015) 1–6. [42] A. Naugarhiya, S. Dubey, P.N. Kondekar, A. Naugarhiya, S. Dubey, P. N. Kondekar, Superlattices and microstructures, Superlattices Microstruct. 85 (2015) 461–468.