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High resolution elastic recoil detection
Nuclear Instruments and Methods in Physics Research B 219–220 (2004) 333–343 www.elsevier.com/locate/nimb
High resolution elastic recoil detection G. Dollinger a
a,* ,
A. Bergmaier a, L. Goergens a, P. Neumaier a, W. Vandervorst b, S. Jakschik c
Physik Department E12, Technische Universit€at M€unchen, D-85748 Garching, Germany b IMEC, Kapeldreef, Belgium c Infineon Technologies, Dresden, Germany
Abstract The quantitative analysis of light elements in ultra thin films being thinner than 10 nm is still a nontrivial task. This paper will summarise the prospects of high resolution elastic recoil detection (ERD) using a Q3D magnetic spectrograph. It has been shown that subnanometer resolution can be achieved in ultra thin films and even monolayer resolution is possible close to the surface. ERD has best quantification possibilities compared to any other method. Sensitivity is sufficient to analyse main elements and impurities as e.g. being necessary for the characterisation of microelectronic materials. In addition, high resolution channeling ERD can be performed in order to get information on lattice location of light elements in crystalline ultra thin layers. The potential of high resolution ERD will be demonstrated by several applications where it is the most valuable tool for elemental profiling. 2004 Elsevier B.V. All rights reserved.
1. Introduction Ultra thin films having thicknesses smaller than 10 nm are now widely used in the fields of microand nano-electronics, magnetics, hard coatings and for X-ray as well as neutron optics and there is ongoing research to develop smart films for these applications. The physical properties depend on film stoichiometry, film structure and stacking, on impurity content and on surface and interface properties of the ultra thin film structures. Therefore, there is a strong need to measure the elemental profiles with high accuracy and optimum depth
*
Corresponding author. Tel.: +49-89-2891-2431; fax: +4989-2891-2297. E-mail address: [email protected] (G. Dollinger).
resolution. Light element detection with high depth resolution, good sensitivity and reliable quantification of the measured profiles is still tough. The detection of hydrogen isotopes is difficult using X-ray techniques and also electron microscopy is essentially insensitive to hydrogen. But also other light elements like lithium, boron, carbon, nitrogen, oxygen and fluorine – any of these elements is nearly in any material in nonnegligible amount – is difficult to be detected by non-ion beam techniques. This paper is intended to summarise the unique possibilities of elastic recoil detection using a magnetic spectrograph with respect to profile light element distributions in ultra thin films. 2. Alternative methods To analyse light elements in ultra thin layers one has available electron microscopy techniques,
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.01.079
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XPS (X-ray induced photoelectron spectroscopy), AES (Auger electron spectroscopy) and SIMS (secondary ion mass spectrometry) beside ion beam analysis techniques. Because XPS and AES systems can easily be installed in any laboratory and there is no need for sample preparation these techniques are widely-used as a working horse in surface and sub-surface analysis. Using multiple angle analysis of emitted electrons, some kind of depth profiling in ultra thin layers is possible where even nanometer resolution is possible [1]. Combined with sputtering these techniques can also be used for depth profiling of thicker layers. An advantage of AES and XPS is that they give insight into chemical bonding. But sensitivity for light elements is in the 1% range, depth resolution is limited and quantification remains sometimes a problem. Electron microscopic techniques have for sure the best possible resolution, as there is not only 0.1 nm depth resolution but 2D or even 3D information in atomic dimensions. By using energy filtering light element detection is possible [2,3] but sensitivity is in the percentage range. Moreover it requires sophisticated sample preparation by ion beam milling, which is not only a time consuming and costly procedure but may also alter stoichiometry and materials structure by sputtering effects. Therefore, quantification of elemental concentration is limited and light elements are still not easy to be analysed. Hydrogen is the most severe problem to be detected by electron microscopy. One of the most commonly used technique for high resolution elemental profiling is SIMS (secondary ion mass spectrometry) which normally has very good sensitivity (down to the ppb level or even lower) for nearly any element. However there are some problems with background of elements which are common in the residual gas of vacuum chambers like hydrogen, carbon, nitrogen and oxygen [4]. The analyses of ultra thin films require slow sputtering which enhances the deposition of the residual gas species on the sample surface even under UHV conditions which therefore mask the true elemental content. There is also limited depth resolution due to the ion beam bombardment, which always has a mixing effect beside the desired
sputtering. Although beam energies have been reduced as low as 100–500 eV mixing of about 1 nm is unavoidable. On the other hand this mixing is fairly constant such that the 1 nm depth resolution can be maintained over a large depth (>100–200 nm). But the most striking problem in SIMS is to get quantitative depth profiles. The success in semiconductor business of SIMS was that it is relative simple and routinely used. It was able to determine depth profiles quite accurate as long as only a small number of matrix elements, e.g. silicon and oxygen is present. If impurities or dopants are far off materials interfaces (>1–3 nm) one get steady state conditions during analysis which can be empirically calibrated with an accuracy in the percent level. The situation changes drastically when ultra thin layers/profiles in a variable matrix are analysed. For instance, high k dielectrics contain aluminum, nitrogen, oxygen, hafnium or other heavy metals, more and more structured by ultra thin multilayers. It is for sure that SIMS gives still some qualitative insight into depth profiles of such structures. But quantification of the profiles remains problematic as long as not well characterised structures are analysed for reproducibility. Any change in materials composition will lead to unforeseen changes in the profiles. These changes may be used to announce a materials variation but it will debar a concise profiling.
3. Rutherford backscattering spectrometry versus elastic recoil detection The inherent advantage of ion beam analysis is its potential for quantitative analysis of elemental contents. It results from the fact that the ion–atom scattering processes being relevant for elemental detection are to good approximation described as two body reactions where many body contributions are week and can be corrected for. The simplest of all reactions, the elastic scattering at high ion energies and towards large scattering angles, can be analytically described by point-like, may be screened, Coulomb interaction as long as energy is significantly lower than the Coulomb threshold for nuclear reactions. Elastic scattering has the advantage over nuclear reactions for ele-
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mental analysis that any element can be addressed simultaneously in one measurement because any element will scatter with ions from the beam. This advantage has also a drawback: because any element gains a signal in the detector it normally limits sensitivity for trace element detection because all signals of the other elements may have to be counted and probably make background in the region of interest. This problem is essential in the commonly used Rutherford backscattering spectrometry (RBS) analysis where the backscattered ions from the incoming beam are analysed for their energy [5]. Since the energy spectrum contains two informations, namely the mass information from kinematics and the depth information from the ions energy loss on their way in and out off the sample, high sensitivity is obtained only for the heaviest elements in a sample. The lighter elements may be masked by events from ion scattering on heavy elements at larger depth or even by plural scattering effects. Due to this ambiguity there is limited sensitivity being in the percent range for light element detection by RBS analysis, hydrogen is not detectable at all. Under certain circumstances sensitivity for light elements can be improved about 10 times compared to standard RBS when amorphous layers on crystalline substrates are analysed as it is a common case for oxides or nitrides on silicon [6,7]. The silicon signal from the silicon wafer is reduced under channeling conditions while the elements from the amorphous cover layer give the full signal. A problem may arise if elements from the amorphous layer are embedded into the crystalline substrate or if there is some crystalline orientation of the top layer being assumed to be pure amorphous. Specific nuclear reactions are used in order to get reduced background and, therefore, better sensitivity for light element detection [8]. However, beam conditions and detectors have to be adapted for each element. Nuclear resonances can be used to get high depth resolution like the p(15 N,ac)12 C reaction for hydrogen detection, but it is a time consuming analysis and it is specific for only one element. The situation changes dramatically when elastic recoil detection (ERD) is used. In ERD analysis
170 MeV127 I
α 10˚
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Z, M, E-Analyse für H, ....., Ga 5˚-20˚
β
Fig. 1. Geometrical arrangement for ERD experiments.
the recoil ions scattered off into forward directions are detected (see Fig. 1). Originally helium beams have been used for hydrogen analysis [9]. But the usage of heavy ions opens widespread application for light element detection [8,10]. The usage of heavy ions has two advantages: the momentum transfer from heavy ions to any light element is sufficient to detect all light elements and to identify them by either time of flight or energy loss versus energy or by magnetic or electrostatic analysis. Secondly, the number of projectiles scattered into the detector is significantly reduced. He-ions scattered off the substrate are several orders of magnitude more than the recoil hydrogen atoms in helium ERD. Therefore, a foil in front of the detector has to be used in order to get rid of this overwhelming signal. Such a foil can be avoided if ion beams much heavier than the matrix atoms are used because no heavy ion is scattered beyond a kinematic cutoff angle. Even if the mass of the ions is in the same range as the matrix atoms, the number of scattered projectiles is in the same order of magnitude as the scattered recoil ions and can therefore be accepted in the detector. Silicon detectors or gas ionisation chambers are normally used as energy dispersive particle detectors. These are multipurpose detectors and straight forward to be used. However, the drawback of these detectors is that energy resolution is limited by detector effects as long as the depth of origin of the analysed is low enough that energy straggling or small angle scattering effects are small. In order to improve depth resolution to the physical limit, several groups have used magnetic or electrostatic spectrometers [11,12]. Even monolayer resolution has been obtained, both in RBS [13] and ERD
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geometry [14]. In order to overcome the limits of RBS in analysing light elements we have introduced high resolution ERD by using a Q3D magnetic spectrograph at the Munich tandem accelerator. Since high resolution ERD requires much more effort with respect to ion beams, spectrometer and detectors, there are still only a few groups performing high resolution ERD. The characteristics of high resolution ERD will be summarised in this paper. First a short overview will be given on standard ERD using energetic heavy ion beams. Then the requirements for high resolution ERD will be discussed along with the setup in Munich and with respect to some applications in thin film analysis.
example of a measurement using such a hybrid detector is shown in Fig. 2(a), where an about 200 nm thick Alx Ga1x N layer deposited on Al2 O3 has been analysed using a 170 MeV 127 I beam, a scattering angle of 40.2 and an incident angle a of 15. The energy loss DE is plotted versus the total energy Etot which is the sum of DE and Eres . All light and medium heavy elements are well separated and even hydrogen at the surface and in the layer can be identified.
4. Elastic recoil detection The essential feature of ERD is, that the recoil target atoms are detected. Therefore the nuclear charge or the mass of the recoil ion can be analysed unambigiuously if a second signal is generated beside the energy signal of the ions. Although for hydrogen analyses a passive absorber is sometimes used as a simple possibility to get rid of scattered primary ions, a two stage detector approach has much more power in order to get the elemental and energy information independently. There are different possibilities for a two stage approach: (1) A time of flight (TOF) measurement along a certain distance together with an energy determination by an ionisation chamber or a silicon detector for mass and energy determination [15,16]. (2) An energy loss signal DE from a thin transmission detector and the residual energy Eres from a second detector. Such detectors often consist of an ionisation chamber divided into two or more separated anodes to get the energy loss and residual energy signals [17–19]. For a simultaneous measurement of hydrogen isotopes and heavier elements in one measurement, however, one may prefer a hybrid detector consisting of an ionisation chamber for DE and a silicon detector for Eres [20]. An
Fig. 2. (a) DE–E spectrum of recoil ions scattered by 170 MeV 127 I ions from a 200 nm thick Gax Al1x N on Al2 O3 substrate. (b) Depth profiles calculated from the data of (a) by generating an energy spectrum for each element and using the computer code KONZERD.
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(3) Any kind of magnetic spectrograph allows for some recoil ion identification. However such spectrographs mean additional experimental effort which is only accepted if e.g. both, elemental and mass information are required or redundant elemental information is needed. This may be the case to avoid background for sub ppm sensitivity in difficult cases where normally background is hard to be avoided, e.g. the determination of ppm concentrations of nitrogen in diamond [21]. However, in most cases such spectrographs are used to enhance energy resolution and therefore depth resolution (see Section 5). A drawback of heavy ion ERD is – as it is for any kind of ion beam analysis – that irradiation damage is the most severe physical limit. Several reports show that damage in several materials, mainly insulators and some kind of semiconductors and glasses, increases more than linearly with nuclear or electronic stopping power which is mainly due to Coulomb explosion [22,23] or thermal spike effects [24–26] or any kind of energy spike [27]. However, since ERD scattering crosssection rERD scales as 2 Z1 ðM1 þ M2 Þ rERD ; M 2 E1 E1 , Z1 , M1 are the energy, nuclear charge and mass of the projectiles, respectively, M2 the recoil ions mass – the damage is on a similar level as for light ions if damage is normalised to the number of detected ions. With respect to the analysis we assume the sample to be destroyed when the depth profile of any element is altered by the impinging beam. Therefore, the main goal is to measure the sample before the depth profiles under investigation are altered. Since this alteration is reached after a certain fluence until which you have achieved a certain sensitivity, at the end, irradiation damage limits sensitivity. In order to keep sensitivity as good as possible large solid angles of detection are required. Several msr of solid angle of detection are commonly used in standard ERD experiments. However, this means a broadening of the energy spectra due to the required large opening angle d/ within the scattering plane be-
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cause recoil energy depends on scattering angle which is the so-called kinematic shift (dE=E ¼ 2 tan / d/ + (higher orders in d/)). In order to overcome the kinematic effects the scattering angle is measured by a position sensitive setup in addition to the other signals for particle identification and energy measurement [19,20]. The energy spectrum in Fig. 2(a) is already corrected for the kinematical shift. The analysis of the depth profiles from heavy ion ERD experiments is straight forward. An energy profile can be generated from the DE–Etot spectrum (Fig. 2(a)) for any element by separately projecting the corresponding area of every element to the energy axis. From these energy spectra the depth profile is calculated by an iterative algorithm, e.g. using the computer code KONZERD [28], which follows layer by layer the elemental concentrations starting from the very surface where the energy is given for every element. As an example the depth profiles calculated from the data of Fig. 2(a) are plotted in Fig. 2(b). The figure shows the fractions of the main elements in the Alx Ga1x N and the Al2 O3 substrate including the impurity concentration of oxygen in the layer.
5. High resolution ERD The energy resolution of energy dispersive detectors for analysing recoil ions like silicon detectors or ionisation chambers is limited by the statistics of creating electron hole pairs or ionisation in the detectors and by the electronic noise. In real ERD experiments the relative energy resolution is in most cases not better than 1% of the total energy [20]. As a consequence depth resolution is limited to about 10 nm in any solid material even if low incident angles a are used in order to spread the depth profiles. There are several possibilities to overcome this limit: (1) TOF detectors have the possibility to deliver better energy resolution. If the particle is already identified by the TOF-E method the energy scale can be generated from TOF. However, because timing resolution is limited to 100–200 ps in usual TOF-setups, long flight
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paths have to be used to significantly enhance the depth resolution of standard energy dispersive detectors. There is also a limit due to the energy spread in the carbon foil which is normally used for generating a start signal from secondary electrons. (2) At small energies, where the rigidity of the ions is not too large, electrostatic spectrometers can be used for ERD-analysis [31]. All electrostatic spectrometers used up to now for high resolution ERD have small angular acceptance making long measuring times necessary and running into limit of ion beam induced damage which gets much more important for high resolution work than in low resolution. (3) Magnetic spectrographs are the largest but most flexible instruments for high resolution ERD experiments. They can bend also higher energy recoil ions. There have been several instruments used up to now for high resolution ERD work [29–32]. Although there have been special developments of magnetic spectrographs for ion beam analysis we believe that the Q3D magnetic spectrographs (Fig. 3) like the Munich one [33] originally designed for nuclear physics experiments in the 1970s by H. Enge are the most powerful spectrographs for ERD analysis. Therefore, most of high resolution ERD work which has been done up to now used the Q3D
multipole
dipole 2
dipole 1
quadrupole
1m
dipole 3
target focal plane
ion beam
ionisation chamber Au 40 MeV
Fig. 3. Schematical drawing of the ERD setup at the Munich Q3D magnetic spectrograph. The multipole element is adjusted that recoil ions emitted from a certain depth are focused to one point in the focal plane although different scattering angles mean different energies due to kinematics and due to path length effects.
magnetic spectrograph at the Munich tandem accelerator. The main features of a Q3D are its large dispersion (dE=ðE dxÞ 2 104 /mm), the high intrinsic resolution (DE=E ¼ 2 104 ), the large solid angle of detection (up to 14.3 msr) and, most important, the possibility to optically correct for the kinematical shift, which is the dependence of recoil energy with scattering angle, by a magnetic multipole element up to the fourth-order. Routinely the kinematic shift is corrected up to the third-order at the Munich Q3D which makes possible an overall energy resolution of 7 · 104 even if a large solid angle of detection of 5 msr (6.3 · 2.5) is used [34]. Without correction the kinematical shift would be larger than 6% energy spread at the standardly used mean scattering angle of 15. At the end the multipole element is adjusted in such a way that the recoil ions scattered from a certain depth are focused as good as possible to a certain position of the focal plane of the Q3D where the ions are identified and there position is measured (Fig. 3). Even the changing correlation between recoil energy and scattering angle due to the path length effect [35] is corrected for by the ion optical behaviour of the higher order multipole elements if the correct incidence angle is used [34]. As a consequence the depth profile of an elemental distribution is directly imaged into the focal plane at a magnification of 107 –108 . Therefore this kind of imaging can be called ‘‘depth microscopy’’. The high energy resolution at a large solid angle of detection is the most important requirement for a depth resolution better than 1 nm in ERD experiments. The energy resolution and therefore depth resolution is only limited by energy loss straggling and small angle scattering effects which has a kinematic and a path length effect [35]. The kinematic effect introduced by multiple scattering is much larger than in normal RBS measurements. Therefore the energy cannot be reduced as much as in MEIS (medium energy ion scattering), where e.g. 0.05–0.1 MeV/nucl ions are used. An optimum energy is at about 0.5 MeV/nucl for heavy ion ERD with optimised depth resolution in order to keep multiple scattering effects low enough [36]. We have shown that even single monolayer resolution can be obtained when we analysed graphite
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6. Applications
100
atomic fraction [ at% ]
using 60 MeV 127 I ions [36]. However, in order to enhance scattering cross-section and to keep irradiation damage low, we often use 0.2 MeV/nucl ions (e.g. 40 MeV 197Au) at the expense of slightly reduced depth resolution mainly suffering from small angle scattering effects.
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H C N O
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6.1. High k dielectric ultra thin films 0.01 -5
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There is a wide field open for analysing ultra thin films by high resolution ERD. One field lies within the development of new ultra thin film structures for future microelectronic applications. For instance, there are strong activities to develop new high k dielectric materials as gate material of field effect transistors for sub 100 nm microelectronic generations. One of the materials which was thought as a first substitute of the commonly used SiO2 or SiON films is Al2 O3 . As an example of light element profiles we show the hydrogen, carbon, nitrogen and oxygen profiles of an Al2 O3 ultra thin film deposited onto a SiON-interfacial layer on crystalline silicon (Fig. 4). The total oxide thickness is about 5 nm while the oxynitride layer has a thickness of about 1 nm. The figure shows that these light elements can be analysed with a sensitivity down to the 100 ppm level and the surface, interface and bulk region of the thin film can clearly be separated. Depth resolution at the surface is about 0.5 nm fwhm and limited by contamination layers and by an undefined surface topology of the amorphous layer. Depth resolution at the interface is better than 1 nm. Therefore, it can be recognised that the maximum of the hydrogen and carbon peak is 0.5 nm in front of the maximum of the nitrogen peak (marked by a line) in the untreated sample (Fig. 4(a)), which indicates the carbon and hydrogen contamination between the Al2 O3 and the SiON layer. The changes of the elemental profiles can be followed quantitatively when the original sample is heat treated (Fig. 4(b)). The changes at the interfaces (marked line) are most prominent: the hydrogen agglomeration is reduced by nearly two orders of magnitude while carbon remains constant. It can also be seen that
H C N O
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0.01 -5
(b)
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15
depth [1016 at/cm2, nm]
Fig. 4. Ultra thin high k dielectric layer of Al2O3 deposited by atomic layer deposition onto about 1 nm thick SiON on crystalline silicon analysed by high resolution ERD using 40 MeV Au ions for the light elements. The line indicates the maximum of the nitrogen content which is at the same position for the two investigated films, (a) film as prepared, (b) film heat-treated by rapid thermal annealing. Nanometer scale is a rough estimate from the exact at./cm2 scale.
some oxidation takes place in the silicon substrate enlarging the oxide thickness due to the temperature treatment in an oxygen containing atmosphere. 6.2. Ultra shallow junctions The advantage of ion beam analysis using energetic ion beams compared to secondary ion mass spectrometry is that the high energy profiles are inherently quantitative while the SIMS profiles are subject to matrix effects from changing sputter
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atomic density [1/cm3]
velocities and ion yields and there are also mixing effects disturbing the profiles of ultra thin layers. An example of the different approaches is plotted in Fig. 5 [37]. This figure shows boron profiles of test structures for ultra shallow junctions obtained from SIMS and from high resolution ERD. The structures have been produced by implanting 1 keV boron at three different doses through 1.8 nm SiO2 on crystalline silicon followed by a thermal treatment. The SIMS and ERD profiles show substantial differences: The boron concentration is the highest at the surface from the SIMS measurement while it is peaked at the SiO2 /Si interface from ERD measurements. There was independent proof that the boron is peaked at the interface and that the SIMS profiles are wrong. Deeper in the crystalline substrate both measurements coincide where it is well known that SIMS can be calibrated to give quantitative results and where SIMS has better sensitivity. The results show that the SIMS profiles are not reliable at surfaces and interfaces even for well characterised and simple structures as the SiO2 /c–Si structures while ERD is free from artifacts. Recently [38], it has been established that the distortion of the SIMS B-profile at this oxide– silicon interface is closely linked to the experimental SIMS conditions i.e. normal incidence oxygen bombardment in combination with boron. SIMS-analysis under nonoxidizing conditions in combination with more refined data treatments
1E+22 SIMS
ERD 1E15
1E+21
4E14
1E+20 1E14 1E+19 -2
0
2
4
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depth [nm] Fig. 5. SIMS and ERD boron profiles of crystalline silicon samples were implanted by 1 keV boron ions through a 1.8 nm thick SiO2 layer at different fluences and heat-treated after implantation by rapid thermal annealing. Recognise the differences of the profiles close to the surface.
[39] does lead to an B-interfacial peak in much closer agreement with the ERD-data. However the present results show, as known for a very long time, that at multilayer interfaces SIMS profiles can be distorted by sputter yield and ionisation yield variations while ERD is free from artifacts. With increasing complexity of the ultra thin layer structure (such as for instance ultra thin high k film with complex stoichiometry) the problem of SIMS-analysis increases [40]. ERD offers complementary method for the analysis of these layers and to help quantify the SIMS data interpretation. 6.3. Range profiles of low energy carbon ions Another interesting application is the analysis of range and mixing profiles of low energy (22– 700 eV) carbon ions implanted into amorphous carbon. These profiles are measured in order to give the base for modelling the growth of tetrahedral amorphous carbon, an amorphous carbon modification containing up to 80% sp3-bonds [41]. The evolution of the structure of this amorphous carbon with properties close to diamond is not yet understood. A crucial base for any model is the initial interaction of the low energy carbon ions by which the carbon structure is formed. The results will be presented and discussed in a forthcoming paper. Here, we show one range profile of 5 · 1014 /cm2 , 47 eV 13 C-ions which have been implanted into a freshly prepared ta-C sample where 12 C-ions have been deposited by separated mass ion implantation (Fig. 6). The dots in Fig. 6 represent the data measured by high resolution ERD utilising 40 MeV Au ions. Inspite of the low concentration the statistics is sufficient to get a detailed information on the range profile which can be compared with range distributions calculated from different theories. The natural depth scale is shown in 1016 at./cm2 which is the same scale in nm if a density of 2 g/cm3 is assumed. However the density increases from the surface into the bulk within 1–2 nm from less than 2 g/cm3 to nearly 3 g/cm3 where the scale has than to be multiplied by about 2/3 in order to get the nanometer scale.
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13C
content [at%]
10 data deconvolution with confidence interval TRIM.SP MD calculation
8 6 4 2
47 eV
0 -1
0
1
2
3
4
depth [1016at/cm2, nm] Fig. 6. Range profiles (dots) of 47 eV 13 C-ions implanted into tetrahedral amorphous carbon layer consisting of 12 C isotope. The full line shows the deconvolution determined using Bayesian probability theory. The shaded area gives the 1 r error for all functions describing the data under the constraint of the possible informational content in agreement with the statistics of the data. Range profiles calculated from TRIDYN [46] and molecular dynamics calculations [47] are plotted for comparison.
7. Bayesian data analysis Because we want to compare calculations with the range profile we want to get as close as possible the real profile from the measured data. The best suited procedure to extract the best estimate of the real profile according to the data is one within the framework of Bayesian probability theory. The profile obtained from such an unfolding procedure is plotted as a solid line in Fig. 6. The procedure relies on an apparatus function which contains the zero of depth scale and the depth dependent depth resolution which is taken from calculations [42] and proofed and slightly corrected from independent measurements on multilayered samples. The data evaluation has been described in detail in [43]. The main advantages of this Bayesian framework is the following: (1) Get an optimum form free fit of the data using maximum likelihood methods. (2) Use probability theory with constraints which takes care of additional knowledge, e.g. the instrumental response function or the information on calibration measurements or other previous knowledge, e.g. that the calculated function has to be positive at any depth. (3) Use entropy methods and adaptive kernels in order to look for the best data reconstruction
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from the deconvoluted spectrum under the constraint of minimum informational content within the obtained statistics. Such methods are useful to suppress artificial oscillations in the reconstructed function. (4) The strength of the method is that the error of the deconvoluted function can be calculated using Monte Carlo methods. The 1 r confidence interval of the deconvolution of Fig. 6 is the shaded area around the average which shows the error within the limit of the informational content. Having this error available the differences between measured and calculated implantation profile can be quantified. In the case shown in Fig. 6 a significant deviation of the depth distribution from TRIM.SP or molecular dynamics calculations is found. This example shows that even range profiles with a medium range of less than 1 nm can be measured by high resolution ERD and that the data can directly be compared with theory.
8. High resolution channeling ERD In order to get information on the position of light elements in a crystalline lattice, it is desired to use channeling ERD [44]. In connection with high resolution analysis we are able to determine lattice positions of light elements in ultra thin films. The problem of performing channeling using the scattering geometry being necessary for high resolution ERD is the small scattering angle of about 15. In order to find an accessible axis we sometimes enlarge our scattering angle by several degrees. The details of heavy ion channeling ERD will also be presented in a forthcoming paper. Here, we present one example to demonstrate the potential of high resolution channeling ERD. Fig. 7 shows boron (Fig. 7(a)) and silicon (Fig. 7(b)) spectra of two ultra shallow boron doped structures which were deposited onto 1 1 1-oriented silicon [45]. One sample has been heat-treated after deposition at 700 C while the other was measured as deposited. The data were taken when the silicon substrate was aligned to the 3 1 1 – axis using a scattering angle of 18. In addition a
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3
(a)
random
B-Channeling Yield [a.U.]
channeling
2
1
9. Conclusion
0
(b)
si-channeling Yield [norm.]
crystallisation of the layer. However, the boron signal at the interface does not significantly change between as-deposited and heat-treated sample. It demonstrates that the delta boron profiles remain localised but not substituionally incorporated into the structure. Heat treatment at higher temperatures leads to substitutional incorporation as proofed also by channeling ERD but the sharp profile is lost due to a diffusion of the boron into the silicon substrate.
'Random'
1.0
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0.2
0.0
0
5
10
15
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25
depth [nm] Fig. 7. Channeling and random profiles of a boron-delta doped 1 1 1-silicon heat-treated at 700 C under 3 1 1 orientation of the substrate, (a) boron profiles, (b) silicon profiles. For comparison also the profile of the non-treated sample (RT) is shown having an amorphous silicon layer of about 15 nm on top of the crystalline substrate.
silicon profile of a randomly oriented sample is shown in Fig. 7(b). The as-deposited sample shows the silicon signal at the same height as the random profile for the amorphous cap layer while a reduced signal is obtained from the silicon substrate under aligned conditions. The heat-treated sample shows already a similar reduction of the silicon signal in the cover layer signalling a reasonable
The examples of application of high resolution ERD profiles show that we are able to measure profiles of light elements in ultra thin films with high depth resolution. The method is open for any analysis of ultra thin layers as they are investigated for microelectronics, optics, magnetics or tribological applications using a large variety of elemental compositions. Sensitivity is sufficient to measure concentrations down to 100–1000 ppm. High resolution ERD serves as a primary standard for high resolution analysis on ultra thin films since quantification is inherent as it is for any high energy ion beam analysis technique. It is not yet expected that high resolution ERD will be installed in any lab exploring new ultra thin film materials in the near future due to the costs involved running a high energy accelerator and the necessary detectors. But we expect that there will be various additional applications to analyse new materials within research and development.
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High resolution elastic recoil detection G. Dollinger a
a,* ,
A. Bergmaier a, L. Goergens a, P. Neumaier a, W. Vandervorst b, S. Jakschik c
Physik Department E12, Technische Universit€at M€unchen, D-85748 Garching, Germany b IMEC, Kapeldreef, Belgium c Infineon Technologies, Dresden, Germany
Abstract The quantitative analysis of light elements in ultra thin films being thinner than 10 nm is still a nontrivial task. This paper will summarise the prospects of high resolution elastic recoil detection (ERD) using a Q3D magnetic spectrograph. It has been shown that subnanometer resolution can be achieved in ultra thin films and even monolayer resolution is possible close to the surface. ERD has best quantification possibilities compared to any other method. Sensitivity is sufficient to analyse main elements and impurities as e.g. being necessary for the characterisation of microelectronic materials. In addition, high resolution channeling ERD can be performed in order to get information on lattice location of light elements in crystalline ultra thin layers. The potential of high resolution ERD will be demonstrated by several applications where it is the most valuable tool for elemental profiling. 2004 Elsevier B.V. All rights reserved.
1. Introduction Ultra thin films having thicknesses smaller than 10 nm are now widely used in the fields of microand nano-electronics, magnetics, hard coatings and for X-ray as well as neutron optics and there is ongoing research to develop smart films for these applications. The physical properties depend on film stoichiometry, film structure and stacking, on impurity content and on surface and interface properties of the ultra thin film structures. Therefore, there is a strong need to measure the elemental profiles with high accuracy and optimum depth
*
Corresponding author. Tel.: +49-89-2891-2431; fax: +4989-2891-2297. E-mail address: [email protected] (G. Dollinger).
resolution. Light element detection with high depth resolution, good sensitivity and reliable quantification of the measured profiles is still tough. The detection of hydrogen isotopes is difficult using X-ray techniques and also electron microscopy is essentially insensitive to hydrogen. But also other light elements like lithium, boron, carbon, nitrogen, oxygen and fluorine – any of these elements is nearly in any material in nonnegligible amount – is difficult to be detected by non-ion beam techniques. This paper is intended to summarise the unique possibilities of elastic recoil detection using a magnetic spectrograph with respect to profile light element distributions in ultra thin films. 2. Alternative methods To analyse light elements in ultra thin layers one has available electron microscopy techniques,
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.01.079
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XPS (X-ray induced photoelectron spectroscopy), AES (Auger electron spectroscopy) and SIMS (secondary ion mass spectrometry) beside ion beam analysis techniques. Because XPS and AES systems can easily be installed in any laboratory and there is no need for sample preparation these techniques are widely-used as a working horse in surface and sub-surface analysis. Using multiple angle analysis of emitted electrons, some kind of depth profiling in ultra thin layers is possible where even nanometer resolution is possible [1]. Combined with sputtering these techniques can also be used for depth profiling of thicker layers. An advantage of AES and XPS is that they give insight into chemical bonding. But sensitivity for light elements is in the 1% range, depth resolution is limited and quantification remains sometimes a problem. Electron microscopic techniques have for sure the best possible resolution, as there is not only 0.1 nm depth resolution but 2D or even 3D information in atomic dimensions. By using energy filtering light element detection is possible [2,3] but sensitivity is in the percentage range. Moreover it requires sophisticated sample preparation by ion beam milling, which is not only a time consuming and costly procedure but may also alter stoichiometry and materials structure by sputtering effects. Therefore, quantification of elemental concentration is limited and light elements are still not easy to be analysed. Hydrogen is the most severe problem to be detected by electron microscopy. One of the most commonly used technique for high resolution elemental profiling is SIMS (secondary ion mass spectrometry) which normally has very good sensitivity (down to the ppb level or even lower) for nearly any element. However there are some problems with background of elements which are common in the residual gas of vacuum chambers like hydrogen, carbon, nitrogen and oxygen [4]. The analyses of ultra thin films require slow sputtering which enhances the deposition of the residual gas species on the sample surface even under UHV conditions which therefore mask the true elemental content. There is also limited depth resolution due to the ion beam bombardment, which always has a mixing effect beside the desired
sputtering. Although beam energies have been reduced as low as 100–500 eV mixing of about 1 nm is unavoidable. On the other hand this mixing is fairly constant such that the 1 nm depth resolution can be maintained over a large depth (>100–200 nm). But the most striking problem in SIMS is to get quantitative depth profiles. The success in semiconductor business of SIMS was that it is relative simple and routinely used. It was able to determine depth profiles quite accurate as long as only a small number of matrix elements, e.g. silicon and oxygen is present. If impurities or dopants are far off materials interfaces (>1–3 nm) one get steady state conditions during analysis which can be empirically calibrated with an accuracy in the percent level. The situation changes drastically when ultra thin layers/profiles in a variable matrix are analysed. For instance, high k dielectrics contain aluminum, nitrogen, oxygen, hafnium or other heavy metals, more and more structured by ultra thin multilayers. It is for sure that SIMS gives still some qualitative insight into depth profiles of such structures. But quantification of the profiles remains problematic as long as not well characterised structures are analysed for reproducibility. Any change in materials composition will lead to unforeseen changes in the profiles. These changes may be used to announce a materials variation but it will debar a concise profiling.
3. Rutherford backscattering spectrometry versus elastic recoil detection The inherent advantage of ion beam analysis is its potential for quantitative analysis of elemental contents. It results from the fact that the ion–atom scattering processes being relevant for elemental detection are to good approximation described as two body reactions where many body contributions are week and can be corrected for. The simplest of all reactions, the elastic scattering at high ion energies and towards large scattering angles, can be analytically described by point-like, may be screened, Coulomb interaction as long as energy is significantly lower than the Coulomb threshold for nuclear reactions. Elastic scattering has the advantage over nuclear reactions for ele-
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mental analysis that any element can be addressed simultaneously in one measurement because any element will scatter with ions from the beam. This advantage has also a drawback: because any element gains a signal in the detector it normally limits sensitivity for trace element detection because all signals of the other elements may have to be counted and probably make background in the region of interest. This problem is essential in the commonly used Rutherford backscattering spectrometry (RBS) analysis where the backscattered ions from the incoming beam are analysed for their energy [5]. Since the energy spectrum contains two informations, namely the mass information from kinematics and the depth information from the ions energy loss on their way in and out off the sample, high sensitivity is obtained only for the heaviest elements in a sample. The lighter elements may be masked by events from ion scattering on heavy elements at larger depth or even by plural scattering effects. Due to this ambiguity there is limited sensitivity being in the percent range for light element detection by RBS analysis, hydrogen is not detectable at all. Under certain circumstances sensitivity for light elements can be improved about 10 times compared to standard RBS when amorphous layers on crystalline substrates are analysed as it is a common case for oxides or nitrides on silicon [6,7]. The silicon signal from the silicon wafer is reduced under channeling conditions while the elements from the amorphous cover layer give the full signal. A problem may arise if elements from the amorphous layer are embedded into the crystalline substrate or if there is some crystalline orientation of the top layer being assumed to be pure amorphous. Specific nuclear reactions are used in order to get reduced background and, therefore, better sensitivity for light element detection [8]. However, beam conditions and detectors have to be adapted for each element. Nuclear resonances can be used to get high depth resolution like the p(15 N,ac)12 C reaction for hydrogen detection, but it is a time consuming analysis and it is specific for only one element. The situation changes dramatically when elastic recoil detection (ERD) is used. In ERD analysis
170 MeV127 I
α 10˚
335
Z, M, E-Analyse für H, ....., Ga 5˚-20˚
β
Fig. 1. Geometrical arrangement for ERD experiments.
the recoil ions scattered off into forward directions are detected (see Fig. 1). Originally helium beams have been used for hydrogen analysis [9]. But the usage of heavy ions opens widespread application for light element detection [8,10]. The usage of heavy ions has two advantages: the momentum transfer from heavy ions to any light element is sufficient to detect all light elements and to identify them by either time of flight or energy loss versus energy or by magnetic or electrostatic analysis. Secondly, the number of projectiles scattered into the detector is significantly reduced. He-ions scattered off the substrate are several orders of magnitude more than the recoil hydrogen atoms in helium ERD. Therefore, a foil in front of the detector has to be used in order to get rid of this overwhelming signal. Such a foil can be avoided if ion beams much heavier than the matrix atoms are used because no heavy ion is scattered beyond a kinematic cutoff angle. Even if the mass of the ions is in the same range as the matrix atoms, the number of scattered projectiles is in the same order of magnitude as the scattered recoil ions and can therefore be accepted in the detector. Silicon detectors or gas ionisation chambers are normally used as energy dispersive particle detectors. These are multipurpose detectors and straight forward to be used. However, the drawback of these detectors is that energy resolution is limited by detector effects as long as the depth of origin of the analysed is low enough that energy straggling or small angle scattering effects are small. In order to improve depth resolution to the physical limit, several groups have used magnetic or electrostatic spectrometers [11,12]. Even monolayer resolution has been obtained, both in RBS [13] and ERD
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geometry [14]. In order to overcome the limits of RBS in analysing light elements we have introduced high resolution ERD by using a Q3D magnetic spectrograph at the Munich tandem accelerator. Since high resolution ERD requires much more effort with respect to ion beams, spectrometer and detectors, there are still only a few groups performing high resolution ERD. The characteristics of high resolution ERD will be summarised in this paper. First a short overview will be given on standard ERD using energetic heavy ion beams. Then the requirements for high resolution ERD will be discussed along with the setup in Munich and with respect to some applications in thin film analysis.
example of a measurement using such a hybrid detector is shown in Fig. 2(a), where an about 200 nm thick Alx Ga1x N layer deposited on Al2 O3 has been analysed using a 170 MeV 127 I beam, a scattering angle of 40.2 and an incident angle a of 15. The energy loss DE is plotted versus the total energy Etot which is the sum of DE and Eres . All light and medium heavy elements are well separated and even hydrogen at the surface and in the layer can be identified.
4. Elastic recoil detection The essential feature of ERD is, that the recoil target atoms are detected. Therefore the nuclear charge or the mass of the recoil ion can be analysed unambigiuously if a second signal is generated beside the energy signal of the ions. Although for hydrogen analyses a passive absorber is sometimes used as a simple possibility to get rid of scattered primary ions, a two stage detector approach has much more power in order to get the elemental and energy information independently. There are different possibilities for a two stage approach: (1) A time of flight (TOF) measurement along a certain distance together with an energy determination by an ionisation chamber or a silicon detector for mass and energy determination [15,16]. (2) An energy loss signal DE from a thin transmission detector and the residual energy Eres from a second detector. Such detectors often consist of an ionisation chamber divided into two or more separated anodes to get the energy loss and residual energy signals [17–19]. For a simultaneous measurement of hydrogen isotopes and heavier elements in one measurement, however, one may prefer a hybrid detector consisting of an ionisation chamber for DE and a silicon detector for Eres [20]. An
Fig. 2. (a) DE–E spectrum of recoil ions scattered by 170 MeV 127 I ions from a 200 nm thick Gax Al1x N on Al2 O3 substrate. (b) Depth profiles calculated from the data of (a) by generating an energy spectrum for each element and using the computer code KONZERD.
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(3) Any kind of magnetic spectrograph allows for some recoil ion identification. However such spectrographs mean additional experimental effort which is only accepted if e.g. both, elemental and mass information are required or redundant elemental information is needed. This may be the case to avoid background for sub ppm sensitivity in difficult cases where normally background is hard to be avoided, e.g. the determination of ppm concentrations of nitrogen in diamond [21]. However, in most cases such spectrographs are used to enhance energy resolution and therefore depth resolution (see Section 5). A drawback of heavy ion ERD is – as it is for any kind of ion beam analysis – that irradiation damage is the most severe physical limit. Several reports show that damage in several materials, mainly insulators and some kind of semiconductors and glasses, increases more than linearly with nuclear or electronic stopping power which is mainly due to Coulomb explosion [22,23] or thermal spike effects [24–26] or any kind of energy spike [27]. However, since ERD scattering crosssection rERD scales as 2 Z1 ðM1 þ M2 Þ rERD ; M 2 E1 E1 , Z1 , M1 are the energy, nuclear charge and mass of the projectiles, respectively, M2 the recoil ions mass – the damage is on a similar level as for light ions if damage is normalised to the number of detected ions. With respect to the analysis we assume the sample to be destroyed when the depth profile of any element is altered by the impinging beam. Therefore, the main goal is to measure the sample before the depth profiles under investigation are altered. Since this alteration is reached after a certain fluence until which you have achieved a certain sensitivity, at the end, irradiation damage limits sensitivity. In order to keep sensitivity as good as possible large solid angles of detection are required. Several msr of solid angle of detection are commonly used in standard ERD experiments. However, this means a broadening of the energy spectra due to the required large opening angle d/ within the scattering plane be-
337
cause recoil energy depends on scattering angle which is the so-called kinematic shift (dE=E ¼ 2 tan / d/ + (higher orders in d/)). In order to overcome the kinematic effects the scattering angle is measured by a position sensitive setup in addition to the other signals for particle identification and energy measurement [19,20]. The energy spectrum in Fig. 2(a) is already corrected for the kinematical shift. The analysis of the depth profiles from heavy ion ERD experiments is straight forward. An energy profile can be generated from the DE–Etot spectrum (Fig. 2(a)) for any element by separately projecting the corresponding area of every element to the energy axis. From these energy spectra the depth profile is calculated by an iterative algorithm, e.g. using the computer code KONZERD [28], which follows layer by layer the elemental concentrations starting from the very surface where the energy is given for every element. As an example the depth profiles calculated from the data of Fig. 2(a) are plotted in Fig. 2(b). The figure shows the fractions of the main elements in the Alx Ga1x N and the Al2 O3 substrate including the impurity concentration of oxygen in the layer.
5. High resolution ERD The energy resolution of energy dispersive detectors for analysing recoil ions like silicon detectors or ionisation chambers is limited by the statistics of creating electron hole pairs or ionisation in the detectors and by the electronic noise. In real ERD experiments the relative energy resolution is in most cases not better than 1% of the total energy [20]. As a consequence depth resolution is limited to about 10 nm in any solid material even if low incident angles a are used in order to spread the depth profiles. There are several possibilities to overcome this limit: (1) TOF detectors have the possibility to deliver better energy resolution. If the particle is already identified by the TOF-E method the energy scale can be generated from TOF. However, because timing resolution is limited to 100–200 ps in usual TOF-setups, long flight
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paths have to be used to significantly enhance the depth resolution of standard energy dispersive detectors. There is also a limit due to the energy spread in the carbon foil which is normally used for generating a start signal from secondary electrons. (2) At small energies, where the rigidity of the ions is not too large, electrostatic spectrometers can be used for ERD-analysis [31]. All electrostatic spectrometers used up to now for high resolution ERD have small angular acceptance making long measuring times necessary and running into limit of ion beam induced damage which gets much more important for high resolution work than in low resolution. (3) Magnetic spectrographs are the largest but most flexible instruments for high resolution ERD experiments. They can bend also higher energy recoil ions. There have been several instruments used up to now for high resolution ERD work [29–32]. Although there have been special developments of magnetic spectrographs for ion beam analysis we believe that the Q3D magnetic spectrographs (Fig. 3) like the Munich one [33] originally designed for nuclear physics experiments in the 1970s by H. Enge are the most powerful spectrographs for ERD analysis. Therefore, most of high resolution ERD work which has been done up to now used the Q3D
multipole
dipole 2
dipole 1
quadrupole
1m
dipole 3
target focal plane
ion beam
ionisation chamber Au 40 MeV
Fig. 3. Schematical drawing of the ERD setup at the Munich Q3D magnetic spectrograph. The multipole element is adjusted that recoil ions emitted from a certain depth are focused to one point in the focal plane although different scattering angles mean different energies due to kinematics and due to path length effects.
magnetic spectrograph at the Munich tandem accelerator. The main features of a Q3D are its large dispersion (dE=ðE dxÞ 2 104 /mm), the high intrinsic resolution (DE=E ¼ 2 104 ), the large solid angle of detection (up to 14.3 msr) and, most important, the possibility to optically correct for the kinematical shift, which is the dependence of recoil energy with scattering angle, by a magnetic multipole element up to the fourth-order. Routinely the kinematic shift is corrected up to the third-order at the Munich Q3D which makes possible an overall energy resolution of 7 · 104 even if a large solid angle of detection of 5 msr (6.3 · 2.5) is used [34]. Without correction the kinematical shift would be larger than 6% energy spread at the standardly used mean scattering angle of 15. At the end the multipole element is adjusted in such a way that the recoil ions scattered from a certain depth are focused as good as possible to a certain position of the focal plane of the Q3D where the ions are identified and there position is measured (Fig. 3). Even the changing correlation between recoil energy and scattering angle due to the path length effect [35] is corrected for by the ion optical behaviour of the higher order multipole elements if the correct incidence angle is used [34]. As a consequence the depth profile of an elemental distribution is directly imaged into the focal plane at a magnification of 107 –108 . Therefore this kind of imaging can be called ‘‘depth microscopy’’. The high energy resolution at a large solid angle of detection is the most important requirement for a depth resolution better than 1 nm in ERD experiments. The energy resolution and therefore depth resolution is only limited by energy loss straggling and small angle scattering effects which has a kinematic and a path length effect [35]. The kinematic effect introduced by multiple scattering is much larger than in normal RBS measurements. Therefore the energy cannot be reduced as much as in MEIS (medium energy ion scattering), where e.g. 0.05–0.1 MeV/nucl ions are used. An optimum energy is at about 0.5 MeV/nucl for heavy ion ERD with optimised depth resolution in order to keep multiple scattering effects low enough [36]. We have shown that even single monolayer resolution can be obtained when we analysed graphite
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6. Applications
100
atomic fraction [ at% ]
using 60 MeV 127 I ions [36]. However, in order to enhance scattering cross-section and to keep irradiation damage low, we often use 0.2 MeV/nucl ions (e.g. 40 MeV 197Au) at the expense of slightly reduced depth resolution mainly suffering from small angle scattering effects.
339
H C N O
10
1
0.1
6.1. High k dielectric ultra thin films 0.01 -5
0
5
10
15
depth [1016 at/cm2, nm]
(a) 100
atomic fraction [ at% ]
There is a wide field open for analysing ultra thin films by high resolution ERD. One field lies within the development of new ultra thin film structures for future microelectronic applications. For instance, there are strong activities to develop new high k dielectric materials as gate material of field effect transistors for sub 100 nm microelectronic generations. One of the materials which was thought as a first substitute of the commonly used SiO2 or SiON films is Al2 O3 . As an example of light element profiles we show the hydrogen, carbon, nitrogen and oxygen profiles of an Al2 O3 ultra thin film deposited onto a SiON-interfacial layer on crystalline silicon (Fig. 4). The total oxide thickness is about 5 nm while the oxynitride layer has a thickness of about 1 nm. The figure shows that these light elements can be analysed with a sensitivity down to the 100 ppm level and the surface, interface and bulk region of the thin film can clearly be separated. Depth resolution at the surface is about 0.5 nm fwhm and limited by contamination layers and by an undefined surface topology of the amorphous layer. Depth resolution at the interface is better than 1 nm. Therefore, it can be recognised that the maximum of the hydrogen and carbon peak is 0.5 nm in front of the maximum of the nitrogen peak (marked by a line) in the untreated sample (Fig. 4(a)), which indicates the carbon and hydrogen contamination between the Al2 O3 and the SiON layer. The changes of the elemental profiles can be followed quantitatively when the original sample is heat treated (Fig. 4(b)). The changes at the interfaces (marked line) are most prominent: the hydrogen agglomeration is reduced by nearly two orders of magnitude while carbon remains constant. It can also be seen that
H C N O
10
1
0.1
0.01 -5
(b)
0
5
10
15
depth [1016 at/cm2, nm]
Fig. 4. Ultra thin high k dielectric layer of Al2O3 deposited by atomic layer deposition onto about 1 nm thick SiON on crystalline silicon analysed by high resolution ERD using 40 MeV Au ions for the light elements. The line indicates the maximum of the nitrogen content which is at the same position for the two investigated films, (a) film as prepared, (b) film heat-treated by rapid thermal annealing. Nanometer scale is a rough estimate from the exact at./cm2 scale.
some oxidation takes place in the silicon substrate enlarging the oxide thickness due to the temperature treatment in an oxygen containing atmosphere. 6.2. Ultra shallow junctions The advantage of ion beam analysis using energetic ion beams compared to secondary ion mass spectrometry is that the high energy profiles are inherently quantitative while the SIMS profiles are subject to matrix effects from changing sputter
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atomic density [1/cm3]
velocities and ion yields and there are also mixing effects disturbing the profiles of ultra thin layers. An example of the different approaches is plotted in Fig. 5 [37]. This figure shows boron profiles of test structures for ultra shallow junctions obtained from SIMS and from high resolution ERD. The structures have been produced by implanting 1 keV boron at three different doses through 1.8 nm SiO2 on crystalline silicon followed by a thermal treatment. The SIMS and ERD profiles show substantial differences: The boron concentration is the highest at the surface from the SIMS measurement while it is peaked at the SiO2 /Si interface from ERD measurements. There was independent proof that the boron is peaked at the interface and that the SIMS profiles are wrong. Deeper in the crystalline substrate both measurements coincide where it is well known that SIMS can be calibrated to give quantitative results and where SIMS has better sensitivity. The results show that the SIMS profiles are not reliable at surfaces and interfaces even for well characterised and simple structures as the SiO2 /c–Si structures while ERD is free from artifacts. Recently [38], it has been established that the distortion of the SIMS B-profile at this oxide– silicon interface is closely linked to the experimental SIMS conditions i.e. normal incidence oxygen bombardment in combination with boron. SIMS-analysis under nonoxidizing conditions in combination with more refined data treatments
1E+22 SIMS
ERD 1E15
1E+21
4E14
1E+20 1E14 1E+19 -2
0
2
4
6
8
10
depth [nm] Fig. 5. SIMS and ERD boron profiles of crystalline silicon samples were implanted by 1 keV boron ions through a 1.8 nm thick SiO2 layer at different fluences and heat-treated after implantation by rapid thermal annealing. Recognise the differences of the profiles close to the surface.
[39] does lead to an B-interfacial peak in much closer agreement with the ERD-data. However the present results show, as known for a very long time, that at multilayer interfaces SIMS profiles can be distorted by sputter yield and ionisation yield variations while ERD is free from artifacts. With increasing complexity of the ultra thin layer structure (such as for instance ultra thin high k film with complex stoichiometry) the problem of SIMS-analysis increases [40]. ERD offers complementary method for the analysis of these layers and to help quantify the SIMS data interpretation. 6.3. Range profiles of low energy carbon ions Another interesting application is the analysis of range and mixing profiles of low energy (22– 700 eV) carbon ions implanted into amorphous carbon. These profiles are measured in order to give the base for modelling the growth of tetrahedral amorphous carbon, an amorphous carbon modification containing up to 80% sp3-bonds [41]. The evolution of the structure of this amorphous carbon with properties close to diamond is not yet understood. A crucial base for any model is the initial interaction of the low energy carbon ions by which the carbon structure is formed. The results will be presented and discussed in a forthcoming paper. Here, we show one range profile of 5 · 1014 /cm2 , 47 eV 13 C-ions which have been implanted into a freshly prepared ta-C sample where 12 C-ions have been deposited by separated mass ion implantation (Fig. 6). The dots in Fig. 6 represent the data measured by high resolution ERD utilising 40 MeV Au ions. Inspite of the low concentration the statistics is sufficient to get a detailed information on the range profile which can be compared with range distributions calculated from different theories. The natural depth scale is shown in 1016 at./cm2 which is the same scale in nm if a density of 2 g/cm3 is assumed. However the density increases from the surface into the bulk within 1–2 nm from less than 2 g/cm3 to nearly 3 g/cm3 where the scale has than to be multiplied by about 2/3 in order to get the nanometer scale.
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13C
content [at%]
10 data deconvolution with confidence interval TRIM.SP MD calculation
8 6 4 2
47 eV
0 -1
0
1
2
3
4
depth [1016at/cm2, nm] Fig. 6. Range profiles (dots) of 47 eV 13 C-ions implanted into tetrahedral amorphous carbon layer consisting of 12 C isotope. The full line shows the deconvolution determined using Bayesian probability theory. The shaded area gives the 1 r error for all functions describing the data under the constraint of the possible informational content in agreement with the statistics of the data. Range profiles calculated from TRIDYN [46] and molecular dynamics calculations [47] are plotted for comparison.
7. Bayesian data analysis Because we want to compare calculations with the range profile we want to get as close as possible the real profile from the measured data. The best suited procedure to extract the best estimate of the real profile according to the data is one within the framework of Bayesian probability theory. The profile obtained from such an unfolding procedure is plotted as a solid line in Fig. 6. The procedure relies on an apparatus function which contains the zero of depth scale and the depth dependent depth resolution which is taken from calculations [42] and proofed and slightly corrected from independent measurements on multilayered samples. The data evaluation has been described in detail in [43]. The main advantages of this Bayesian framework is the following: (1) Get an optimum form free fit of the data using maximum likelihood methods. (2) Use probability theory with constraints which takes care of additional knowledge, e.g. the instrumental response function or the information on calibration measurements or other previous knowledge, e.g. that the calculated function has to be positive at any depth. (3) Use entropy methods and adaptive kernels in order to look for the best data reconstruction
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from the deconvoluted spectrum under the constraint of minimum informational content within the obtained statistics. Such methods are useful to suppress artificial oscillations in the reconstructed function. (4) The strength of the method is that the error of the deconvoluted function can be calculated using Monte Carlo methods. The 1 r confidence interval of the deconvolution of Fig. 6 is the shaded area around the average which shows the error within the limit of the informational content. Having this error available the differences between measured and calculated implantation profile can be quantified. In the case shown in Fig. 6 a significant deviation of the depth distribution from TRIM.SP or molecular dynamics calculations is found. This example shows that even range profiles with a medium range of less than 1 nm can be measured by high resolution ERD and that the data can directly be compared with theory.
8. High resolution channeling ERD In order to get information on the position of light elements in a crystalline lattice, it is desired to use channeling ERD [44]. In connection with high resolution analysis we are able to determine lattice positions of light elements in ultra thin films. The problem of performing channeling using the scattering geometry being necessary for high resolution ERD is the small scattering angle of about 15. In order to find an accessible axis we sometimes enlarge our scattering angle by several degrees. The details of heavy ion channeling ERD will also be presented in a forthcoming paper. Here, we present one example to demonstrate the potential of high resolution channeling ERD. Fig. 7 shows boron (Fig. 7(a)) and silicon (Fig. 7(b)) spectra of two ultra shallow boron doped structures which were deposited onto 1 1 1-oriented silicon [45]. One sample has been heat-treated after deposition at 700 C while the other was measured as deposited. The data were taken when the silicon substrate was aligned to the 3 1 1 – axis using a scattering angle of 18. In addition a
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3
(a)
random
B-Channeling Yield [a.U.]
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9. Conclusion
0
(b)
si-channeling Yield [norm.]
crystallisation of the layer. However, the boron signal at the interface does not significantly change between as-deposited and heat-treated sample. It demonstrates that the delta boron profiles remain localised but not substituionally incorporated into the structure. Heat treatment at higher temperatures leads to substitutional incorporation as proofed also by channeling ERD but the sharp profile is lost due to a diffusion of the boron into the silicon substrate.
'Random'
1.0
0.8
0.6
0.4
0.2
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0
5
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depth [nm] Fig. 7. Channeling and random profiles of a boron-delta doped 1 1 1-silicon heat-treated at 700 C under 3 1 1 orientation of the substrate, (a) boron profiles, (b) silicon profiles. For comparison also the profile of the non-treated sample (RT) is shown having an amorphous silicon layer of about 15 nm on top of the crystalline substrate.
silicon profile of a randomly oriented sample is shown in Fig. 7(b). The as-deposited sample shows the silicon signal at the same height as the random profile for the amorphous cap layer while a reduced signal is obtained from the silicon substrate under aligned conditions. The heat-treated sample shows already a similar reduction of the silicon signal in the cover layer signalling a reasonable
The examples of application of high resolution ERD profiles show that we are able to measure profiles of light elements in ultra thin films with high depth resolution. The method is open for any analysis of ultra thin layers as they are investigated for microelectronics, optics, magnetics or tribological applications using a large variety of elemental compositions. Sensitivity is sufficient to measure concentrations down to 100–1000 ppm. High resolution ERD serves as a primary standard for high resolution analysis on ultra thin films since quantification is inherent as it is for any high energy ion beam analysis technique. It is not yet expected that high resolution ERD will be installed in any lab exploring new ultra thin film materials in the near future due to the costs involved running a high energy accelerator and the necessary detectors. But we expect that there will be various additional applications to analyse new materials within research and development.
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