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Differential Hall characterisation of ultrashallow doping in advanced Si-based materials
Materials Science and Engineering B 154–155 (2008) 229–233
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Differential Hall characterisation of ultrashallow doping in advanced Si-based materials N.S. Bennett a,∗ , N.E.B. Cowern a , A.J. Smith b , M. Kah b , R.M. Gwilliam b , B.J. Sealy b , T.C.Q. Noakes c , P. Bailey c , D. Giubertoni d , M. Bersani d a
School of Electrical, Electronic and Computer Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK Surrey Ion Beam Centre, University of Surrey, Guildford GU2 7XH, UK Daresbury Medium-Energy Ion Scattering Facility, Daresbury Laboratory, Warrington WA4 4AD, UK d Fondazione Bruno Kessler, Via Sommarive 18, 38050 Povo, Trento, Italy b c
a r t i c l e
i n f o
Article history: Received 8 May 2008 Received in revised form 14 August 2008 Accepted 8 October 2008 Keywords: Electrical measurements Hall effect Silicon Antimony Arsenic Ion implantation
a b s t r a c t Strained Si channels are commonly used by manufacturers to enhance CMOS performance and research into novel channel materials (SiGe and Ge) is well underway. How these materials affect the electrical properties of the impurities used to dope them is largely unclear and the ability to accurately characterise dopant activation is key to finding this out. In the case of Si, since much is known about the relationship between carrier concentration and mobility, dopant activation can be assessed by competing techniques, however for the newer materials this information is not available. This paper demonstrates the differential Hall technique as a method capable of satisfying these gaps in our knowledge of dopant activation and mobility. Previously we have shown the technique, which combines Hall effect measurements with successive native oxide removal, can measure independent carrier and mobility profiles with resolution better than 1 nm for B-implanted Si and SOI. Presently we show the technique is extendable to characterise n-type dopants (Sb and As) and importantly, can be applied to novel substrates (focussing here on strained Si). In addition, the inherent assumption of the technique – uniform layer removal – is investigated and shown reasonable. Complementary ion beam analysis is used to show how we investigate and correct for Hall scattering effects and designated software is used to apply necessary corrections, transforming raw data into reproducible and highly resolved, carrier and mobility profiles. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Characterising dopant electrical properties following ion implantation and annealing is rapidly becoming as much of a challenge for modern CMOS technologies as actually creating highly activated ultrashallow junctions [1]. It is essential that electrical properties of doped layers can be successfully determined and information on dopant electrical activation and mobility at different depths within a device is of fundamental importance. Global characterisation of a sample is traditionally done using a four-point probe (4PP) system to measure sheet resistance (RS ) through a doped layer. This method does not determine the values which contribute to the measured RS , i.e. mobility and carrier concentration. By performing a resistance measurement alone on a doped strained layer, it is difficult to attribute contributions to any
∗ Corresponding author. Tel.: +44 1912 225648; fax: +44 1912 228180. E-mail address: [email protected] (N.S. Bennett). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.10.003
strain-induced difference in resistance to either a change in carrier mobility or in carrier concentration. While strain is well known to change electron and hole mobility, the level of adjustment is very dependent on the intensity and type of strain. Therefore without a measurement technique capable of separating the individual contributions, any investigation into doping effects in strained Si is difficult. Only Hall or scanning capacitance measurements in conjunction with a resistance measurement can separate the two characteristics to give a greater understanding of electrical properties by providing carrier density and mobility within the doped layer. With careful manipulation both techniques can be used to realise carrier and mobility depth profiles via differential Hall measurements (DHMs) [2] or scanning capacitance microscopy (SCM) [3]. However DHMs are advantageous since they avoid calibration or ‘direct inversion’ [4] required when converting an SCM profile to a carrier profile. Typically in bulk silicon, spreading resistance profiling (SRP) is used to realise depth characteristics. This can be achieved by measuring resistance along a sample with a very low angle bevel, effectively providing resistance as a function of depth. Spreading
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N.S. Bennett et al. / Materials Science and Engineering B 154–155 (2008) 229–233
resistance can be converted to a profile of doping density using a corrective model. Sophisticated adaptations of SRP, such as scanning spreading resistance profiling (SSRP), have been shown to be capable of characterising doping profiles with better than nanometre resolution [5]. Recently a similar approach using a micro-4PP to characterise resistance along the bevel has been shown as a promising technique [6]. Like SRP/SSRP however, this technique is subject to certain limitations: 2. The key advantage of the differential Hall technique For any technique that measures only a resistance profile, certain assumptions have to be made in order to determine a charge carrier profile. If the mobility and resistivity profiles are not measured independently then the carrier concentration is inferred from the resistivity profile under the assumption that carrier concentration varies in accordance with an assumed mobility. While much data exists to describe how electron and hole mobilities vary with carrier concentration in silicon [7], limited information is available in the case of strained silicon, or indeed for SiGe or strained SiGe. Hence for these competing techniques, strain and SiGe creates a problem. In contrast, differential Hall can measure the active carrier and mobility profiles independently without any assumption on the magnitude of mobility. 3. The assumption of uniform layer removal The differential Hall procedure is a layer removal technique that relies on the reaction of silicon with oxygen at room temperature, allowing the formation of a thin native surface oxide that can be etched away. The oxide formation consumes silicon atoms from the sample surface as it grows and each profile step uses a short dip in buffered hydrofluoric (HF) acid to selectively remove all or part of the oxide. The sample is then dipped in water to remove excess HF and allow the oxide to regrow. The surface oxide is of the order of one or two nanometres in thickness but a depth resolution of less than a nanometre is achievable where part of the oxide is etched during a single HF dip. The oxide removal rate is assumed to stay constant throughout the course of a profile and so the as-measured profile is plotted with each data point spaced at regular intervals, calculated as an average of the total etched depth divided by the number of points. Literature exists however to suggest that the etch rate is significantly affected by doping concentration [8] which for ion-implanted samples implies that distortions to the carrier concentration and mobility profiles will occur as a result of non-uniform etching. Experiments have been performed to attempt to justify this assumption that the etch rate remains reasonably constant. 4. Experimental verification of uniform layer removal Differential Hall profiling was carried out for both Sb and As implants in silicon and strained silicon substrates. Ordinarily each profile can be left to continue until the carrier concentration becomes low and zero-bias depletion becomes large meaning measurements of the layer doping are no longer possible. In these experiments, some profiles were intentionally stopped short of completion purely for etch rate analysis. Ultrashallow doping was carried out using 2 keV Sb or As ion implantation at a range of doses (1014 cm−2 to 1015 cm−2 ) in both p-type bulk Si and strained Si substrates (0.7% biaxial tensile strain). Samples from each wafer were annealed at a temperature in the range 600–800 ◦ C to give various doping profiles. Using photolithography and a mesa etch, each sample is fashioned into a cloverleaf-shaped structure. Sam-
Fig. 1. SIMS profiles for 2 keV, 2 × 1014 cm−2 Sb implants in strained Si and bulk Si samples followed by annealing at 700 ◦ C for 10 s. The arrows represent the shallowest and deepest depths of etch-profiling that were carried out.
ples are characterised electrically according to the van der Pauw principle [9] and carrier density and Hall mobility is realised using Hall effect measurements. These are carried out using a permanent magnet, creating a 0.3 T magnetic field. Successive rounds of resistance and Hall measurements are carried out following a cycle of oxide growth and etching. Samples undergo oxidation for a time of between 5 and 60 s depending on the desired oxide thickness and etching for a time between 5 and 30 s depending on the amount of oxide to be removed. The etch time should be varied according to the concentration of acid used; in this case 5% buffered HF was employed. Profiles have been performed to depths in the range 3–15 nm. The total etched depth is measured following profiling using a Talystep, a method validated on selected samples using atomic force microscopy [10]. This allows the average etch depth per step to be calculated. Fig. 1 shows secondary-ion mass spectroscopy (SIMS) profiles for two of the samples under test, in this case Sb implanted at a dose of 2 × 1014 cm−2 in both Si and strained Si. SIMS shows that by changing the etch depth between 3 and 15 nm the Sb concentration is varied across ∼3 orders of magnitude. By performing profiling to a range of depths, any variation in the amount of material etched at different stages in the profile should be evident and concentration-dependent etch variations should be obvious. In Fig. 2 etch rate results are compared for 2 keV Sb-implanted Si and strained Si. By comparing the etch rates in Fig. 2 no significant variation is observable irrespective of how deep the profile penetrates, suggesting in this case, variations in Sb concentration is having little effect on the oxide formation and subsequent etch. The average etch rate is 0.57 nm/etch step for silicon and 0.59 nm/step in the strained case, implying also that strain has minimal effect on the etch rate. In these cases the standard deviation is 0.05 and 0.04 nm, respectively, highlighting the satisfactory etch uniformity. In Fig. 3 etch rate results are compared for 2 keV As-implanted strained and unstrained Si. Each sample has undergone a similar oxidation and etch sequence. Profiles have been performed to depths in the range 3–14 nm, the total etched depth measured using Talystep and the average etch rate calculated accordingly. By comparing the etch rates in Fig. 3, again no significant variation is observable irrespective of how deep the profile goes, suggesting that like the Sb case, varying As concentration has no effect on the native oxide growth/etch process. For As, the average etch rate is 0.60 nm/step for silicon and 0.59 nm/step in the strained case, implying again that strain has minimal effect on the etch
N.S. Bennett et al. / Materials Science and Engineering B 154–155 (2008) 229–233
231
mobility (C ) according to Ns =
r e.RHs
(1)
C =
RHs H = r.S r
(2)
where RHs is the sheet Hall coefficient, S is sheet resistivity, H is Hall mobility and e is the charge of an electron (or, where appropriate, a hole) [11]. While r is mathematically simple to apply, it is however difficult to attain analytically because of the complicated scattering mechanisms involved, differences depending on dopant species and potential variations as a function of doping concentration [12]. An added complication in this work is that we compare doping in different Si-based substrate materials where again, the Hall scattering factor might be different [13]. In the study by Alzanki [14] when considering Sb-doped silicon, a Hall scattering factor of unity is used. This is based on the good agreement found between a Rutherford backscattering (RBS) determination of the Sb substitutional fraction and the electron density measured by Hall measurement. For 40 keV Sb implants in silicon the Sb substitutional fraction after annealing was deduced as between 94% and 95%. In comparison, the electrically active fraction measured by Hall measurements was between 92% and 95%. This indicates that assuming r is equal to one is reasonable for Sb doping when the Sb concentration peaks at ∼2 × 1020 cm−3 . The work
Fig. 2. Total etched depth during profiling plotted against the number of etch steps carried out in the course of the profile for (a) Sb-implanted Si and (b) Sb-implanted strained Si.
rate. For As doping the standard deviations are 0.04 and 0.03 nm, respectively for unstrained and strained materials. Additionally, the change in dopant species appears to have little impact on the etch rate. Determining the average etch rate is significant since it gives an indication of the average depth resolution when profiling. Due to surface states, the resolution tends to be slightly improved at the rising peak of the profile but is worse in the profile tail. In our previous work [2] a resolution of ∼0.3 nm was demonstrated for B-doped Si or SOI. For the Sb- and As-doped Si or strained Si samples measured here, a mean depth resolution of ∼0.6 nm is established. In light of the results in Figs. 2 and 3 the assumption that layer removal is uniform throughout profiling seems reasonable. 5. Transforming the as-measured profile 5.1. Hall scattering correction When measuring a differential Hall profile, certain corrective procedures are often necessary and should be applied to the asmeasured profile. The necessary presence of a magnetic field in order to make a Hall measurement can provoke varying degrees of carrier scattering that distort the measured carrier concentration and Hall mobility, requiring a correction factor. The Hall scattering factor (r) affects the sheet carrier density (Ns) and conductivity
Fig. 3. Total etched depth during profiling plotted against the number of etch steps carried out in the course of the profile for (a) As-implanted Si and (b) As-implanted strained Si.
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of Nylandsted-Larsen et al. [15] has shown that RBS measurements can give an over-estimated substitutional Sb fraction for Sb concentrations in excess of 4.5 × 1020 cm−3 since above this metastable solubility limit Sb tends to cluster with vacancies, or form precipitates at elevated temperatures. Sb contained in Sb-vacancy complexes occupies near-substitutional lattice sites and appears as substitutional Sb in channelling experiments. In order to avoid this complication, experiments to investigate Hall scattering were designed with maximum Sb concentrations of ∼4.5 × 1020 cm−3 [16] and SIMS confirmed that in practise the maximum solubility was only slightly higher, with a peak at 5.0 × 1020 cm−3 . RBS and other channelling experiments proceed by directing an ion beam through an obvious channel of the crystalline lattice under test. In this case a spectrum is assembled that contains information about Sb present between lattice sites of the host substrate. Clearly, any Sb in the channel is non-substitutional in the silicon lattice. By directing the beam in a so-called ‘random’ crystallographic direction, a spectrum characteristic of the overall proportion of Sb in the host is determined, irrespective of its substitutionality. By looking at the relative quantities of random and channel-dwelling Sb, an estimate for the substitutional fraction of Sb can be made. While every substitutional dopant may not necessarily contribute electrically it is generally accepted that for a dopant atom to act as a donor or acceptor it should be substitutional in the host lattice. Therefore the calculated substitutional fraction at least provides an upper limit for the carrier density assuming the implanted dose is known. Conveniently Sb dose can be deduced from the random spectrum and is confirmed in these experiments by SIMS. When characterising ultrashallow implants the resolution of RBS become a terminal limiting factor because of the relatively high energetics of the beam. One way to overcome this issue is to use medium-energy ion scattering (MEIS). MEIS is a refinement of RBS with enhanced depth and angle resolution as a result of the 4 He+ ion beam having a much lower energy, here 100 keV, as opposed to >1 MeV. Pieces of both Si and strained Si wafers, implanted with 2 keV Sb to a dose of either 1 × 1014 cm−2 or 2 × 1014 cm−2 and annealed at 700 ◦ C for 10 s, were examined with MEIS, Hall measurements and SIMS. The implanted Sb dose for each sample was deduced from MEIS using dedicated software [17]. The electron density, measured using the Hall effect, was also measured for each sample. The electrically active Sb fraction is calculated from the ratio of the electron density and Sb dose. The substitutional Sb fraction is estimated from MEIS data. Channelling was done with the ∼120 nA incident beam aligned to (1 1 1) and the detector positioned along (−1 1 1), with a scattering angle of 70.12◦ . The fraction of Sb detected as non-substitutional was deduced from the ratio of the channelled and random Sb counts. This is easily converted to a substitutional Sb fraction. A summary of the results from the experimental techniques is presented in Table 1. As the electrically active fraction cannot be greater than the substitutional fraction, an estimate for the Hall scattering factor can be made by taking a ratio of the two. In the case of Sb-doped Si and in good agreement with the findings of Alzanki, a Hall scattering factor of 1.0 is found, as shown in Table 1. This implies that no correction is required to the as-measured carrier density or mobility values.
Fig. 4. Carrier concentration and mobility profiles as a function of depth for Sbdoped Si and strained Si measured using the differential Hall technique. Doping is created using 2 keV, 1015 cm−2 Sb implantation followed by 10 s annealing at 700 ◦ C.
Likewise, Table 1 shows that the same correction factor, r = 1.0, is applicable for Sb-doped strained silicon. It is worth noting from Table 1 that for the 2 × 1014 cm−2 dose, a greater substitutional Sb fraction and higher electron density is measured for Sb-doped strained Si compared to bulk Si which supports previous findings on Sb activation enhancement in strained Si [18]. 5.2. Surface states correction The final correction that is applied to the as-measured Hall profile is required as a result of carrier trapping in surface states. This is due to the sudden break of lattice structure at the air/surface boundary where unsaturated bonds readily react to give discrete surface states [19]. Any charge on these states will attract or repel electrons, an effect that is neutralised by ionised acceptors or donors, leaving the Fermi level pinned within the forbidden gap [20]. This phenomenon leads to the measured carrier profile being a distorted version of the true profile because the Hall measurement technique assumes that current is uniformly distributed through the layer under test. Importantly, distortions due to surface states can be accurately corrected for and a practical procedure to do this has been publicized by Yeo et al. [21]. Software implementing the procedure of Yeo et al. has been developed to carryout the carrier profile correction. The measured Hall mobility profile is easier to correct since the magnitude of the ‘real’ mobility will be the same as in the as-measured case because mobility is independent of etched thickness. The mobility data points should however be fitted to the correct depth, which are the same depths as the equivalent corrected carrier concentration data points.
Table 1 A summary of results and analysis for Sb-implanted Si and strained Si substrates from MEIS and Hall measurements.
Si Si -Si -Si
A, Sb dose (cm−2 ) [MEIS]
B, Electron density (cm−2 ) [Hall]
C, Electrically active Sb fraction (%) [= 100(B/A)]
D, Random Sb counts [MEIS]
E, Channelled Sb counts [MEIS]
F, Chemically substitutional Sb fraction (%) [= 100 − 100(E/D)]
Hall scattering factor [= F/C]
1.90 × 1014 9.0 × 1013 2.00 × 1014 9.0 × 1013
1.23 × 1014 7.03 × 1013 1.68 × 1014 7.05 × 1013
65% 78% 84% 78%
9,900 6,832 12,995 4,030
3533 1228 2655 940
64% 82% 80% 77%
1.0 1.0 1.0 1.0
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6. Differential Hall profiles In Fig. 4, independent carrier and mobility profiles for n-doped Si and strained Si are presented. Each profile has been corrected for surface depletion and Hall scattering effects, although in this case the Hall scattering factor is unity. The profiles consist of data points with better than nanometre resolution. Not only does the differential Hall technique allow us to separate the conductivity contributions of carrier concentration and mobility, but depth information is also realised. The key advantage of this technique over competing methods is illustrated by the fact that by measuring independent carrier and mobility profiles we can distinguish that strain has an effect on both the activation and electron mobility in Sb-doped substrates. Interested readers can find many additional profiles for both Sb and As in Ref. [18]. 7. Conclusion In the case where information is sought about dopant properties in strained silicon or any novel substrate, the differential Hall technique provides an advantage over other techniques since it is capable of separating the relative carrier concentration and mobility contributions to the conductivity of the doped layer under test. In this paper the inherent assumption of the technique – uniform layer removal – has been tested and shown to be reasonable. Similarly, correction procedures to the as-measured profile have been discussed and where necessary, corrections are implemented for the carrier and mobility profiles we present. These factors combine to give rise to a technique capable of accurately determining dopant carrier and mobility profiles as a function of depth for ultrashallowdoped layers. The introduction of strained Si and strained/unstrained SiGe materials is likely to play a key role in future CMOS and therefore
233
a technique capable of reliably measuring independent activation and mobility properties for ultrashallow doping is likely to be an indispensable characterisation tool. References [1] W. Vandervorst, AIP Conference Proceedings, vol. 931, 2007, p. 233. [2] N.S. Bennett, A.J. Smith, B. Colombeau, R. Gwilliam, N.E.B. Cowern, B.J. Sealy, Mater. Sci. Eng. B 305 (2005) 124–125. [3] F. Giannazzo, V. Raineri, S. Mirabella, G. Impellizzeri, F. Priolo, Appl. Phys. Lett. 88 (2006) 043117. [4] F. Giannazzo, Ph.D. Thesis, University of Catania, Italy, 2002. [5] P. Eyben, T. Janssens, W. Vandervorst, Mater. Sci. Eng. B 45 (2005) 124–125. [6] T. Clarysse, P. Eyben, B. Parmentier, B. Van Daele, A. Satta, W. Vandervorst, R. Lin, D.H. Petersen, P.F. Nielsen, J. Vac. Sci. Technol. B 26 (2008) 317. [7] G. Masetti, M. Severi, S. Solmi, IEEE Trans. Electron Devices ED-30 (7) (1983) 764. [8] M.C. Roberts, Electrochemical Society Extended Abstracts, 85-2, 1985, 677. [9] L.J. Van der Pauw, Philips Res. Rep. 13 (1958) 1. [10] A.J. Smith, Ph.D. Thesis, University of Surrey, U.K., 2006. [11] HL5900PC Hall Profiler System User Manual Issue 2.0, U.K., 2001. [12] P. Norton, T. Braggins, H. Levinstein, Phys. Rev. B 8 (12) (1973) 5632. [13] L. Romano, E. Napolitani, V. Privitera, S. Scalese, A. Terrasi, S. Mirabella, M.G. Grimaldi, Mater. Sci. Eng. B 102 (2003) 49. [14] T. Alzanki, Ph.D. Thesis, University of Surrey, U.K., 2004. [15] A. Nylandsted Larsen, F.T. Pedersen, G. Weyer, R. Galloni, R. Rizzoli, A. Armigliato, J. Appl. Phys. 59 (6) (1986) 1908. [16] TRIM Software, http://srim.org/. [17] QUARKMEIS Software, http://www.quarksimulation.com. [18] N.S. Bennett, N.E.B. Cowern, A.J. Smith, R.M. Gwilliam, B.J. Sealy, L. O’Reilly, P.J. McNally, G. Cooke, H. Khyerandish, Appl. Phys. Lett. 89 (2006) 182122; N.S. Bennett, A.J. Smith, R.M. Gwilliam, B.J. Sealy, N.E.B. Cowern, L. O’Reilly, P.J. McNally, J. Vac. Sci. Technol. B 26 (2008) 391; N.S. Bennett, Ph.D. Thesis, University of Surrey, U.K., 2008. [19] A. Many, Y. Goldstein, N.B. Grover, Semiconductor Surfaces, North-Holland, Amsterdam, 1965, p. 165. [20] A. Chandra, C.E.C. Wood, D.W. Woodard, L.F. Eastman, Solid-State Electron. 22 (1979) 645. [21] Y.K. Yeo, R.L. Hengehold, D.W. Elsaesser, J. Appl. Phys. 61 (11) (1987) 5070.
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
Differential Hall characterisation of ultrashallow doping in advanced Si-based materials N.S. Bennett a,∗ , N.E.B. Cowern a , A.J. Smith b , M. Kah b , R.M. Gwilliam b , B.J. Sealy b , T.C.Q. Noakes c , P. Bailey c , D. Giubertoni d , M. Bersani d a
School of Electrical, Electronic and Computer Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, UK Surrey Ion Beam Centre, University of Surrey, Guildford GU2 7XH, UK Daresbury Medium-Energy Ion Scattering Facility, Daresbury Laboratory, Warrington WA4 4AD, UK d Fondazione Bruno Kessler, Via Sommarive 18, 38050 Povo, Trento, Italy b c
a r t i c l e
i n f o
Article history: Received 8 May 2008 Received in revised form 14 August 2008 Accepted 8 October 2008 Keywords: Electrical measurements Hall effect Silicon Antimony Arsenic Ion implantation
a b s t r a c t Strained Si channels are commonly used by manufacturers to enhance CMOS performance and research into novel channel materials (SiGe and Ge) is well underway. How these materials affect the electrical properties of the impurities used to dope them is largely unclear and the ability to accurately characterise dopant activation is key to finding this out. In the case of Si, since much is known about the relationship between carrier concentration and mobility, dopant activation can be assessed by competing techniques, however for the newer materials this information is not available. This paper demonstrates the differential Hall technique as a method capable of satisfying these gaps in our knowledge of dopant activation and mobility. Previously we have shown the technique, which combines Hall effect measurements with successive native oxide removal, can measure independent carrier and mobility profiles with resolution better than 1 nm for B-implanted Si and SOI. Presently we show the technique is extendable to characterise n-type dopants (Sb and As) and importantly, can be applied to novel substrates (focussing here on strained Si). In addition, the inherent assumption of the technique – uniform layer removal – is investigated and shown reasonable. Complementary ion beam analysis is used to show how we investigate and correct for Hall scattering effects and designated software is used to apply necessary corrections, transforming raw data into reproducible and highly resolved, carrier and mobility profiles. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Characterising dopant electrical properties following ion implantation and annealing is rapidly becoming as much of a challenge for modern CMOS technologies as actually creating highly activated ultrashallow junctions [1]. It is essential that electrical properties of doped layers can be successfully determined and information on dopant electrical activation and mobility at different depths within a device is of fundamental importance. Global characterisation of a sample is traditionally done using a four-point probe (4PP) system to measure sheet resistance (RS ) through a doped layer. This method does not determine the values which contribute to the measured RS , i.e. mobility and carrier concentration. By performing a resistance measurement alone on a doped strained layer, it is difficult to attribute contributions to any
∗ Corresponding author. Tel.: +44 1912 225648; fax: +44 1912 228180. E-mail address: [email protected] (N.S. Bennett). 0921-5107/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2008.10.003
strain-induced difference in resistance to either a change in carrier mobility or in carrier concentration. While strain is well known to change electron and hole mobility, the level of adjustment is very dependent on the intensity and type of strain. Therefore without a measurement technique capable of separating the individual contributions, any investigation into doping effects in strained Si is difficult. Only Hall or scanning capacitance measurements in conjunction with a resistance measurement can separate the two characteristics to give a greater understanding of electrical properties by providing carrier density and mobility within the doped layer. With careful manipulation both techniques can be used to realise carrier and mobility depth profiles via differential Hall measurements (DHMs) [2] or scanning capacitance microscopy (SCM) [3]. However DHMs are advantageous since they avoid calibration or ‘direct inversion’ [4] required when converting an SCM profile to a carrier profile. Typically in bulk silicon, spreading resistance profiling (SRP) is used to realise depth characteristics. This can be achieved by measuring resistance along a sample with a very low angle bevel, effectively providing resistance as a function of depth. Spreading
230
N.S. Bennett et al. / Materials Science and Engineering B 154–155 (2008) 229–233
resistance can be converted to a profile of doping density using a corrective model. Sophisticated adaptations of SRP, such as scanning spreading resistance profiling (SSRP), have been shown to be capable of characterising doping profiles with better than nanometre resolution [5]. Recently a similar approach using a micro-4PP to characterise resistance along the bevel has been shown as a promising technique [6]. Like SRP/SSRP however, this technique is subject to certain limitations: 2. The key advantage of the differential Hall technique For any technique that measures only a resistance profile, certain assumptions have to be made in order to determine a charge carrier profile. If the mobility and resistivity profiles are not measured independently then the carrier concentration is inferred from the resistivity profile under the assumption that carrier concentration varies in accordance with an assumed mobility. While much data exists to describe how electron and hole mobilities vary with carrier concentration in silicon [7], limited information is available in the case of strained silicon, or indeed for SiGe or strained SiGe. Hence for these competing techniques, strain and SiGe creates a problem. In contrast, differential Hall can measure the active carrier and mobility profiles independently without any assumption on the magnitude of mobility. 3. The assumption of uniform layer removal The differential Hall procedure is a layer removal technique that relies on the reaction of silicon with oxygen at room temperature, allowing the formation of a thin native surface oxide that can be etched away. The oxide formation consumes silicon atoms from the sample surface as it grows and each profile step uses a short dip in buffered hydrofluoric (HF) acid to selectively remove all or part of the oxide. The sample is then dipped in water to remove excess HF and allow the oxide to regrow. The surface oxide is of the order of one or two nanometres in thickness but a depth resolution of less than a nanometre is achievable where part of the oxide is etched during a single HF dip. The oxide removal rate is assumed to stay constant throughout the course of a profile and so the as-measured profile is plotted with each data point spaced at regular intervals, calculated as an average of the total etched depth divided by the number of points. Literature exists however to suggest that the etch rate is significantly affected by doping concentration [8] which for ion-implanted samples implies that distortions to the carrier concentration and mobility profiles will occur as a result of non-uniform etching. Experiments have been performed to attempt to justify this assumption that the etch rate remains reasonably constant. 4. Experimental verification of uniform layer removal Differential Hall profiling was carried out for both Sb and As implants in silicon and strained silicon substrates. Ordinarily each profile can be left to continue until the carrier concentration becomes low and zero-bias depletion becomes large meaning measurements of the layer doping are no longer possible. In these experiments, some profiles were intentionally stopped short of completion purely for etch rate analysis. Ultrashallow doping was carried out using 2 keV Sb or As ion implantation at a range of doses (1014 cm−2 to 1015 cm−2 ) in both p-type bulk Si and strained Si substrates (0.7% biaxial tensile strain). Samples from each wafer were annealed at a temperature in the range 600–800 ◦ C to give various doping profiles. Using photolithography and a mesa etch, each sample is fashioned into a cloverleaf-shaped structure. Sam-
Fig. 1. SIMS profiles for 2 keV, 2 × 1014 cm−2 Sb implants in strained Si and bulk Si samples followed by annealing at 700 ◦ C for 10 s. The arrows represent the shallowest and deepest depths of etch-profiling that were carried out.
ples are characterised electrically according to the van der Pauw principle [9] and carrier density and Hall mobility is realised using Hall effect measurements. These are carried out using a permanent magnet, creating a 0.3 T magnetic field. Successive rounds of resistance and Hall measurements are carried out following a cycle of oxide growth and etching. Samples undergo oxidation for a time of between 5 and 60 s depending on the desired oxide thickness and etching for a time between 5 and 30 s depending on the amount of oxide to be removed. The etch time should be varied according to the concentration of acid used; in this case 5% buffered HF was employed. Profiles have been performed to depths in the range 3–15 nm. The total etched depth is measured following profiling using a Talystep, a method validated on selected samples using atomic force microscopy [10]. This allows the average etch depth per step to be calculated. Fig. 1 shows secondary-ion mass spectroscopy (SIMS) profiles for two of the samples under test, in this case Sb implanted at a dose of 2 × 1014 cm−2 in both Si and strained Si. SIMS shows that by changing the etch depth between 3 and 15 nm the Sb concentration is varied across ∼3 orders of magnitude. By performing profiling to a range of depths, any variation in the amount of material etched at different stages in the profile should be evident and concentration-dependent etch variations should be obvious. In Fig. 2 etch rate results are compared for 2 keV Sb-implanted Si and strained Si. By comparing the etch rates in Fig. 2 no significant variation is observable irrespective of how deep the profile penetrates, suggesting in this case, variations in Sb concentration is having little effect on the oxide formation and subsequent etch. The average etch rate is 0.57 nm/etch step for silicon and 0.59 nm/step in the strained case, implying also that strain has minimal effect on the etch rate. In these cases the standard deviation is 0.05 and 0.04 nm, respectively, highlighting the satisfactory etch uniformity. In Fig. 3 etch rate results are compared for 2 keV As-implanted strained and unstrained Si. Each sample has undergone a similar oxidation and etch sequence. Profiles have been performed to depths in the range 3–14 nm, the total etched depth measured using Talystep and the average etch rate calculated accordingly. By comparing the etch rates in Fig. 3, again no significant variation is observable irrespective of how deep the profile goes, suggesting that like the Sb case, varying As concentration has no effect on the native oxide growth/etch process. For As, the average etch rate is 0.60 nm/step for silicon and 0.59 nm/step in the strained case, implying again that strain has minimal effect on the etch
N.S. Bennett et al. / Materials Science and Engineering B 154–155 (2008) 229–233
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mobility (C ) according to Ns =
r e.RHs
(1)
C =
RHs H = r.S r
(2)
where RHs is the sheet Hall coefficient, S is sheet resistivity, H is Hall mobility and e is the charge of an electron (or, where appropriate, a hole) [11]. While r is mathematically simple to apply, it is however difficult to attain analytically because of the complicated scattering mechanisms involved, differences depending on dopant species and potential variations as a function of doping concentration [12]. An added complication in this work is that we compare doping in different Si-based substrate materials where again, the Hall scattering factor might be different [13]. In the study by Alzanki [14] when considering Sb-doped silicon, a Hall scattering factor of unity is used. This is based on the good agreement found between a Rutherford backscattering (RBS) determination of the Sb substitutional fraction and the electron density measured by Hall measurement. For 40 keV Sb implants in silicon the Sb substitutional fraction after annealing was deduced as between 94% and 95%. In comparison, the electrically active fraction measured by Hall measurements was between 92% and 95%. This indicates that assuming r is equal to one is reasonable for Sb doping when the Sb concentration peaks at ∼2 × 1020 cm−3 . The work
Fig. 2. Total etched depth during profiling plotted against the number of etch steps carried out in the course of the profile for (a) Sb-implanted Si and (b) Sb-implanted strained Si.
rate. For As doping the standard deviations are 0.04 and 0.03 nm, respectively for unstrained and strained materials. Additionally, the change in dopant species appears to have little impact on the etch rate. Determining the average etch rate is significant since it gives an indication of the average depth resolution when profiling. Due to surface states, the resolution tends to be slightly improved at the rising peak of the profile but is worse in the profile tail. In our previous work [2] a resolution of ∼0.3 nm was demonstrated for B-doped Si or SOI. For the Sb- and As-doped Si or strained Si samples measured here, a mean depth resolution of ∼0.6 nm is established. In light of the results in Figs. 2 and 3 the assumption that layer removal is uniform throughout profiling seems reasonable. 5. Transforming the as-measured profile 5.1. Hall scattering correction When measuring a differential Hall profile, certain corrective procedures are often necessary and should be applied to the asmeasured profile. The necessary presence of a magnetic field in order to make a Hall measurement can provoke varying degrees of carrier scattering that distort the measured carrier concentration and Hall mobility, requiring a correction factor. The Hall scattering factor (r) affects the sheet carrier density (Ns) and conductivity
Fig. 3. Total etched depth during profiling plotted against the number of etch steps carried out in the course of the profile for (a) As-implanted Si and (b) As-implanted strained Si.
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of Nylandsted-Larsen et al. [15] has shown that RBS measurements can give an over-estimated substitutional Sb fraction for Sb concentrations in excess of 4.5 × 1020 cm−3 since above this metastable solubility limit Sb tends to cluster with vacancies, or form precipitates at elevated temperatures. Sb contained in Sb-vacancy complexes occupies near-substitutional lattice sites and appears as substitutional Sb in channelling experiments. In order to avoid this complication, experiments to investigate Hall scattering were designed with maximum Sb concentrations of ∼4.5 × 1020 cm−3 [16] and SIMS confirmed that in practise the maximum solubility was only slightly higher, with a peak at 5.0 × 1020 cm−3 . RBS and other channelling experiments proceed by directing an ion beam through an obvious channel of the crystalline lattice under test. In this case a spectrum is assembled that contains information about Sb present between lattice sites of the host substrate. Clearly, any Sb in the channel is non-substitutional in the silicon lattice. By directing the beam in a so-called ‘random’ crystallographic direction, a spectrum characteristic of the overall proportion of Sb in the host is determined, irrespective of its substitutionality. By looking at the relative quantities of random and channel-dwelling Sb, an estimate for the substitutional fraction of Sb can be made. While every substitutional dopant may not necessarily contribute electrically it is generally accepted that for a dopant atom to act as a donor or acceptor it should be substitutional in the host lattice. Therefore the calculated substitutional fraction at least provides an upper limit for the carrier density assuming the implanted dose is known. Conveniently Sb dose can be deduced from the random spectrum and is confirmed in these experiments by SIMS. When characterising ultrashallow implants the resolution of RBS become a terminal limiting factor because of the relatively high energetics of the beam. One way to overcome this issue is to use medium-energy ion scattering (MEIS). MEIS is a refinement of RBS with enhanced depth and angle resolution as a result of the 4 He+ ion beam having a much lower energy, here 100 keV, as opposed to >1 MeV. Pieces of both Si and strained Si wafers, implanted with 2 keV Sb to a dose of either 1 × 1014 cm−2 or 2 × 1014 cm−2 and annealed at 700 ◦ C for 10 s, were examined with MEIS, Hall measurements and SIMS. The implanted Sb dose for each sample was deduced from MEIS using dedicated software [17]. The electron density, measured using the Hall effect, was also measured for each sample. The electrically active Sb fraction is calculated from the ratio of the electron density and Sb dose. The substitutional Sb fraction is estimated from MEIS data. Channelling was done with the ∼120 nA incident beam aligned to (1 1 1) and the detector positioned along (−1 1 1), with a scattering angle of 70.12◦ . The fraction of Sb detected as non-substitutional was deduced from the ratio of the channelled and random Sb counts. This is easily converted to a substitutional Sb fraction. A summary of the results from the experimental techniques is presented in Table 1. As the electrically active fraction cannot be greater than the substitutional fraction, an estimate for the Hall scattering factor can be made by taking a ratio of the two. In the case of Sb-doped Si and in good agreement with the findings of Alzanki, a Hall scattering factor of 1.0 is found, as shown in Table 1. This implies that no correction is required to the as-measured carrier density or mobility values.
Fig. 4. Carrier concentration and mobility profiles as a function of depth for Sbdoped Si and strained Si measured using the differential Hall technique. Doping is created using 2 keV, 1015 cm−2 Sb implantation followed by 10 s annealing at 700 ◦ C.
Likewise, Table 1 shows that the same correction factor, r = 1.0, is applicable for Sb-doped strained silicon. It is worth noting from Table 1 that for the 2 × 1014 cm−2 dose, a greater substitutional Sb fraction and higher electron density is measured for Sb-doped strained Si compared to bulk Si which supports previous findings on Sb activation enhancement in strained Si [18]. 5.2. Surface states correction The final correction that is applied to the as-measured Hall profile is required as a result of carrier trapping in surface states. This is due to the sudden break of lattice structure at the air/surface boundary where unsaturated bonds readily react to give discrete surface states [19]. Any charge on these states will attract or repel electrons, an effect that is neutralised by ionised acceptors or donors, leaving the Fermi level pinned within the forbidden gap [20]. This phenomenon leads to the measured carrier profile being a distorted version of the true profile because the Hall measurement technique assumes that current is uniformly distributed through the layer under test. Importantly, distortions due to surface states can be accurately corrected for and a practical procedure to do this has been publicized by Yeo et al. [21]. Software implementing the procedure of Yeo et al. has been developed to carryout the carrier profile correction. The measured Hall mobility profile is easier to correct since the magnitude of the ‘real’ mobility will be the same as in the as-measured case because mobility is independent of etched thickness. The mobility data points should however be fitted to the correct depth, which are the same depths as the equivalent corrected carrier concentration data points.
Table 1 A summary of results and analysis for Sb-implanted Si and strained Si substrates from MEIS and Hall measurements.
Si Si -Si -Si
A, Sb dose (cm−2 ) [MEIS]
B, Electron density (cm−2 ) [Hall]
C, Electrically active Sb fraction (%) [= 100(B/A)]
D, Random Sb counts [MEIS]
E, Channelled Sb counts [MEIS]
F, Chemically substitutional Sb fraction (%) [= 100 − 100(E/D)]
Hall scattering factor [= F/C]
1.90 × 1014 9.0 × 1013 2.00 × 1014 9.0 × 1013
1.23 × 1014 7.03 × 1013 1.68 × 1014 7.05 × 1013
65% 78% 84% 78%
9,900 6,832 12,995 4,030
3533 1228 2655 940
64% 82% 80% 77%
1.0 1.0 1.0 1.0
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6. Differential Hall profiles In Fig. 4, independent carrier and mobility profiles for n-doped Si and strained Si are presented. Each profile has been corrected for surface depletion and Hall scattering effects, although in this case the Hall scattering factor is unity. The profiles consist of data points with better than nanometre resolution. Not only does the differential Hall technique allow us to separate the conductivity contributions of carrier concentration and mobility, but depth information is also realised. The key advantage of this technique over competing methods is illustrated by the fact that by measuring independent carrier and mobility profiles we can distinguish that strain has an effect on both the activation and electron mobility in Sb-doped substrates. Interested readers can find many additional profiles for both Sb and As in Ref. [18]. 7. Conclusion In the case where information is sought about dopant properties in strained silicon or any novel substrate, the differential Hall technique provides an advantage over other techniques since it is capable of separating the relative carrier concentration and mobility contributions to the conductivity of the doped layer under test. In this paper the inherent assumption of the technique – uniform layer removal – has been tested and shown to be reasonable. Similarly, correction procedures to the as-measured profile have been discussed and where necessary, corrections are implemented for the carrier and mobility profiles we present. These factors combine to give rise to a technique capable of accurately determining dopant carrier and mobility profiles as a function of depth for ultrashallowdoped layers. The introduction of strained Si and strained/unstrained SiGe materials is likely to play a key role in future CMOS and therefore
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a technique capable of reliably measuring independent activation and mobility properties for ultrashallow doping is likely to be an indispensable characterisation tool. References [1] W. Vandervorst, AIP Conference Proceedings, vol. 931, 2007, p. 233. [2] N.S. Bennett, A.J. Smith, B. Colombeau, R. Gwilliam, N.E.B. Cowern, B.J. Sealy, Mater. Sci. Eng. B 305 (2005) 124–125. [3] F. Giannazzo, V. Raineri, S. Mirabella, G. Impellizzeri, F. Priolo, Appl. Phys. Lett. 88 (2006) 043117. [4] F. Giannazzo, Ph.D. Thesis, University of Catania, Italy, 2002. [5] P. Eyben, T. Janssens, W. Vandervorst, Mater. Sci. Eng. B 45 (2005) 124–125. [6] T. Clarysse, P. Eyben, B. Parmentier, B. Van Daele, A. Satta, W. Vandervorst, R. Lin, D.H. Petersen, P.F. Nielsen, J. Vac. Sci. Technol. B 26 (2008) 317. [7] G. Masetti, M. Severi, S. Solmi, IEEE Trans. Electron Devices ED-30 (7) (1983) 764. [8] M.C. Roberts, Electrochemical Society Extended Abstracts, 85-2, 1985, 677. [9] L.J. Van der Pauw, Philips Res. Rep. 13 (1958) 1. [10] A.J. Smith, Ph.D. Thesis, University of Surrey, U.K., 2006. [11] HL5900PC Hall Profiler System User Manual Issue 2.0, U.K., 2001. [12] P. Norton, T. Braggins, H. Levinstein, Phys. Rev. B 8 (12) (1973) 5632. [13] L. Romano, E. Napolitani, V. Privitera, S. Scalese, A. Terrasi, S. Mirabella, M.G. Grimaldi, Mater. Sci. Eng. B 102 (2003) 49. [14] T. Alzanki, Ph.D. Thesis, University of Surrey, U.K., 2004. [15] A. Nylandsted Larsen, F.T. Pedersen, G. Weyer, R. Galloni, R. Rizzoli, A. Armigliato, J. Appl. Phys. 59 (6) (1986) 1908. [16] TRIM Software, http://srim.org/. [17] QUARKMEIS Software, http://www.quarksimulation.com. [18] N.S. Bennett, N.E.B. Cowern, A.J. Smith, R.M. Gwilliam, B.J. Sealy, L. O’Reilly, P.J. McNally, G. Cooke, H. Khyerandish, Appl. Phys. Lett. 89 (2006) 182122; N.S. Bennett, A.J. Smith, R.M. Gwilliam, B.J. Sealy, N.E.B. Cowern, L. O’Reilly, P.J. McNally, J. Vac. Sci. Technol. B 26 (2008) 391; N.S. Bennett, Ph.D. Thesis, University of Surrey, U.K., 2008. [19] A. Many, Y. Goldstein, N.B. Grover, Semiconductor Surfaces, North-Holland, Amsterdam, 1965, p. 165. [20] A. Chandra, C.E.C. Wood, D.W. Woodard, L.F. Eastman, Solid-State Electron. 22 (1979) 645. [21] Y.K. Yeo, R.L. Hengehold, D.W. Elsaesser, J. Appl. Phys. 61 (11) (1987) 5070.