Fermi level pinning characterisation on ammonium fluoride-treated surfaces of silicon by energy-filtered doping contrast in the scanning electron microscope

Two-dimensional dopant profiling using the secondary electron (SE) signal in the scanning electron microscope (SEM) is a technique gaining impulse for its ability to enable rapid and contactless low-cost diagnostics for integrated device manufacturing. The basis is doping contrast from electrical p-n junctions, which can be influenced by wet-chemical processing methods typically adopted in ULSI technology. This paper describes the results of doping contrast studies by energy-filtering in the SEM from silicon p-n junction specimens that were etched in ammonium fluoride solution. Experimental SE micro-spectroscopy and numerical simulations indicate that Fermi level pinning occurred on the surface of the treated-specimen, and that the doping contrast can be explained in terms of the ionisation energy integral for SEs, which is a function of the dopant concentration, and surface band-bending effects that prevail in the mechanism for doping contrast as patch fields from the specimen are suppressed.

can be strongly modified by any wet-chemical or electrochemical processing methods routinely employed for oxidation, etching or passivation, etc. during ULSI microfabrication. Doping contrast may also be produced due to ad-layer-semiconductor contacts that alter the surface band-bending depending on the doped region 14 . Hence, sufficient sensitivity and quantification accuracy cannot be reliably achieved unless the near-surface effects, including that of surface band-bending 2,3,15 and patch fields 4,16 on doping contrast are understood and well-controlled 7,9 . For example, to avoid surface-geometry influence from a non-homogeneous semiconductor sample that may hamper quantification via patch fields 7,8 , one approach may be to induce Fermi level pinning on the surface 9 , thereby resulting in surface band-bending and a surface junction potential that reduces from that in the bulk. Therefore the aim of this study is to examine and demonstrate for the first time, a uniquely innovative, rapid and facile route based on doping contrast to determine a nearly-equipotential surface of a semiconductor after wet-chemical etching, characterised by Fermi level pinning due to a high density of surface states that traps charges and removes patch fields with essentially no surface charge variation across the p-n junction.
We report herein results from silicon specimens that were surface-treated reproducibly using semiconductor-grade ammonium fluoride (NH 4 F) solution. Not only is it now commonly accepted that simple chemical etching in 40% NH 4 F is able to remove oxide layers and organic contamination, and produce atomically flat, hydrogen-terminated surfaces resulting in high quality substrates for micro-and nano-technology; it is widely believed that the resulting doping contrast change is due to an increase in patch fields owing to the hydrogen atom-passivation of dangling bonds that removes surface states and thus reduces surface band-bending 4,5,[17][18][19] . However, regarding the latter we will show by specialised energy-filtering and SE micro-spectroscopy measurements in the SEM, that theoretical calculations and computer simulations actually provide a converse explanation for this doping contrast change. In those studies cited above, besides a change in the charge states, the surface state density and surface band-bending have essentially increased, leading to doping contrast commensurate with dopant concentration.

Results
Doping contrast changes after NH 4 F-treatment. Figure 1 draws a comparison between the doping contrast from a freshly-cleaved and NH 4 F-treated silicon p-n junction specimen. Initially, doping contrast is typical under standard imaging conditions ( Fig. 1(a)) but contrast inversion (n-region bright and p-region dark) occurred under energy-filtering with a deflection voltage (V def ) below 10 V (e.g. Fig. 1(b)). The freshly-cleaved specimen will have a surface layer of native oxide, about 5 to 10 Å thick, which forms rapidly after cleaving in air. Treatment with 40% NH 4 F is believed to remove this oxide layer and passivate the surface so that the oxide layer does not reform rapidly. After this surface-treatment, the specimen was immediately placed into the SEM, and the SE intensities in Fig. 1(c) were acquired within ~10 min., so the specimen almost certainly does not have an oxide layer for this image under clean, high vacuum conditions, e.g according to ref. 20. Line profiles across the regions of interest were row-averaged over at least 100 pixels perpendicular to the scan direction, and using the formalism detailed in ref. 9, the standard imaging doping contrast reduced from 15.7 ± 2.4% ( Fig. 1(a)) to 14.3 ± 0.4% ( Fig. 1(c)) after surface-treatment. The contrast magnitude is enhanced only from p-regions that are sufficiently highly doped (e.g. > 10 19 acceptors cm −3 ) 7 , or from n-regions so that they can be distinguished from intrinsic regions 4 . The surface states on the silicon in Fig. 1(a) compared with Fig. 1(c) are very different because of the surface-treatment, and it is this difference that must be responsible for the change in doping contrast. Energy-filtered doping contrast from NH 4 F-treated silicon p-n junction specimens has not been characterised until now. Incontrovertible differences in terms of contrast inversion or lack thereof were established under lowpass energy-filtering at low V def . SE micro-spectroscopy characterisation. Unlike that on the as-cleaved specimen, no inversion occurred in energy-filtered doping contrast on the treated-surface, as reflected by the experimental SE yield curves (Fig. 2). The SE micro-spectroscopy acquisition was through measurements of the average pixel intensity as a function of the bias on the through-the-lens detector (TLD) deflector electrode that was swept through a specified range at fixed, but short time intervals (e.g. 500 ms), as documented in ref. 7 and detailed in Methods. Since contrast inversion is attributed to the presence of patch fields -which diminishes as surface bend-bending increases with the surface state density 9 -the above result is at variance with reports in the literature of a reduced number of surface states after NH 4 F-treatment 4,5,18,19 . Concretely, our numerical simulations of the cumulative energy distributions of the SEs (Fig. 3) demonstrate an underpinning increase in surface state density as a factor accounting for the lack of contrast inversion. On freshly-cleaved samples with a native oxide layer, typical surface states are of the order of 10 12 cm −2 21-24 having amphoteric energy levels localised in the bandgap at 0.38 eV from the respective band edges 25 , and the electron-and hole-capture cross-sections for the surface traps are 10 −15 and 10 cm −2 respectively. Where ε Si and ε SiO 2 are the electric permittivities of the semiconductor and native oxide respectively, and n is the unit vector normal to the surface, surface band-bending was computed according to a boundary condition at the semiconductor-oxide interface as in eq. 1.
Si Si SiO SiO s 2 2 The difference between the normal components of the electric fields at the respective regions across the surface boundary must be equal to the sheet charge density ρ s (Gauss' Law). This charge term incorporates both the mobile and fixed charges. On silicon (110) surfaces etched in 40% NH 4 F, amphoteric surface states based on Koyanagi et al. 26 have a density of 2 × 10 13 cm −2 , and their discrete energy levels are localised in the bandgap 0.43 eV below the conduction band edge for the donor-and acceptor-like states. This general model of monoenergetic states is consistent with the discrete-like states normally found on atomically clean surfaces 27 , as would be expected after NH 4 F-treatment of silicon. (c) after NH 4 F-treatment under standard imaging conditions (the white specks represent residual ammonium salts on the surface). Also included is a schematic showing the dopant concentrations in the specimen (measured using SIMS). The extraction potential was 250 V and working distance was 3 mm. Appropriate brightness and contrast settings were used for the respective images to demonstrate strong doping contrast.
Good agreement is observed between the experimental and numerical SE yield curves from the p-and n-regions in terms of their relative energy displacements before and after surface-treatment. The low-energy characteristics from the treated-sample signify surfaces virtually at equipotential 9 , and may confer evidence for semiconductor surface metallisation induced by atomic hydrogen 28 . Furthermore, the removal of the multiple kinks at relatively high kinetic energies after NH 4 F-treatment (see Fig. 2(b)) is striking, which a posteriori indicates that, far from being correctly imputed to tertiary SE3 signals originating from the pole piece or objects other than the sample as claimed in refs 29 and 30, the former are most likely associated with plasmon contributions from: oxides which form rapidly on the surface 31 ; or the Si-SiO 2 interface and/or oxide surface 32 ; or beam-induced contamination on the sample. The disappearance of these effects may correspond to the dissolution of the native oxide layer or any other organic contamination, followed by passivation of the surface. The spectra in Fig. 2(a) are "kink-free" in the low kinetic energy regime (below the cross-over V def ,) and this is a priori expected because the slowest SEs stem from deeper below the surface 7,33 . This means that by low-pass energy-filtering at an appropriate cut-off energy, it is possible to block out extraneous contributions directly from surface oxides, surface states and contamination, and thus, enhance dopant profiling quantification from as-cleaved surfaces. In fact, the treated-sample gives rise to a wider window of SE energies for superior quantification accuracy because of the removal of spurious contributions inherent in the specimen due to ambient air exposure of a previously reactive surface.

Discussion
In our studies, we used energy-filtering and SE micro-spectroscopy measurements to elucidate the doping contrast mechanism in the SEM after etching the silicon specimens in 40% NH 4 F solution. The SE yield characterisation revealed two major features: on one hand, Fermi level pinning by a high density of extrinsic surface states on the H-terminated surface, and on the other, a contamination-free surface. Ha 12 posited that the results of X-ray After specimen was (a) freshly-cleaved, and (b) surface-treated. Baseline spline fits (indicated by the dash-dotted lines) are applied to highlight kinks in the yield characteristics. The error in each intensity point ranges from 2.6 to 3.4% and 0.5 to 0.6% of the intensity value for the freshly-cleaved and surface-treated sample respectively. The same brightness and contrast settings were used to allow measureable SE intensities for the entire range of deflection voltages and enable direct comparison. photoelectron spectroscopy support evidence for Fermi level pinning on the surface. We validated this assumption by leveraging our Monte Carlo method to compute the SE yields, which integrates a semiconductor-based finite-element model for calculating electric potential distributions inside and outside the specimen, plus a ray-tracing algorithm, as described in refs 7 and 9.
The surface-treatment is seen to have significantly increased the number of the slowest SEs emitted from the p-region, exceeding that from the n-region that is considerably reduced due to surface band-bending. The foregoing result is intuitively meaningful considering the following principle. If the surface potential energy at the p-region is higher (or ionisation energy is smaller), a larger proportion of the slowest SEs that arrive at the detector will originate from the n-region since they mostly have lower kinetic energies compared to that from the p-region 7,9 . Consequently, the yield curve from the p-region translates towards higher energies relative to that from the n-region (Figs 2(a) and 3(a)). Therefore the contrast inversion on the as-cleaved surface under appropriate energy-filtering is a corollary of this surface potential energy (or ionisation energy) difference and the attendant patch fields that influence the SE angular distributions. Further elaboration of this result is given in ref. 9. The observation that no contrast inversion occurs after surface-treatment strongly pleads for the case of a dramatically reduced ionisation energy difference at the surface. Had the surface state density been reduced, it would, in turn, have reduced the surface band-bending. This in turn would have increased the difference in ionisation potential energies at the surface between the two sides of the p-n junction according to e.g. ref. 4, thus resulting in contrast inversion upon passing through only the slowest SEs.
Our experimental results here and others' 13,26,34 are in concordance with our expectations that for the surface-treatment procedure used here, the silicon (110) surface had been etched, and any ammonium salt deposits on the hydrogen-terminated surface may contribute to an increase in the extrinsic surface state density due to the adsorbent-induced states. Ongoing work is currently focussed on experimentally calibrating the simulation model to reliably provide quantitative determination of the exact shapes and sizes of the SE spectra under all operating conditions of the SEM, including the low energy offset and the kinks in the relatively high energy range. Besides correcting for the solid collection angle, this may also necessitate taking into consideration a non-ideal modulation transfer function (MTF) and detective quantum efficiency (DQE) of the TLD scintillator. With the origin of kinetic energy estimated to be centred on V def ≈ 1.5 V, there is clearly no contrast over a small range of deflector biases up to about 5 V for the freshly-cleaved sample. This may be because of attenuation of the secondary emission signal (that stems from deeper below the surface) by any surface oxides that the Monte Carlo simulations do not account for since no appropriate scattering models for ultra-thin native oxide coverages are available at present. Nevertheless, the effect of the native oxide layer on the potential is essentially irrelevant in the calculations since the electron probe in the SEM during operation completely penetrates the thin (~0.2 to 1 nm) surface oxide layer of the freshly-cleaved silicon, modulating its conductivity such that the surface of the over-layer assumes the same potential as that of the semiconductor surface 35 . Any surface contamination or micro-roughness is also not modelled, and therefore as expected, the theoretical SE spectra exhibit no irregular kinks that are inimitable characteristics of the experimental yield curves from the as-cleaved specimen at the relatively high kinetic energies.
In summary, the application of a novel, highly sensitive and straightforward SEM doping contrast technique to directly determine Fermi level pinning on the surface was demonstrated. Whilst appropriate treatment with NH 4 F facilitates the preparation of contamination-free, hydrogen atom-passivated surfaces that may be desirable for device fabrication, this also benefits dopant profiling quantification accuracy in the SEM. Through specialised energy-filtering techniques and numerical simulations, we showed that doping contrast from silicon samples that were etched in 40% NH 4 F is primarily governed by surface band-bending effects whilst patch fields are diminished; a near equipotential surface is created after surface-treatment, with an increased density of trapped surface charges and Fermi level pinning. These findings also show that the enhanced doping contrast reported by Sealy et al. 4 , Elliot et al. 5,18 , Müllerová et al. 17 and Lin and Lee 19 , is not due to a reduction in surface state density and surface bend-bending, but rather, to the contrary.

Methods
Doping contrast from p-n junction specimens. The monocrystalline silicon specimens in this study comprise a symmetric p-n junction with a 2.5 μ m thick p-layer, chemical vapour deposition (CVD)-grown with dopant incorporation at 5 × 10 18 B atoms cm −3 onto an Sb-doped n-substrate (Fig. 1). This was along the [001] direction at a growth rate of ~0.15 μ m/min., at an operating temperature of ~1123 K and atmospheric pressure. SE doping contrast and micro-spectroscopy measurements were performed a) on silicon (110) cross-sections of the specimens after they were freshly-cleaved in air, and b) directly after NH 4 F etching of the specimens in a), when inserted into the vacuum chamber at a base pressure of ~3 × 10 −6 mbar using an oil-free turbo-pump system; at least five repeated measurements were made on each sample. Great care was taken to ensure that the cleaved specimen exhibited a mirror-like reflective surface with no evident steps in the regions of interest. The samples were dipped into freshly-prepared 40% NH 4 F (ARISTAR ™ ) for ~1 min, using PTFE tweezers, before they were rinsed thoroughly in semiconductor-grade deionised (DI) water for ~3 -4 min. The highly hydrophobic nature implies that the silicon surface was at least partially hydrogen-terminated.
The specimen stage was aligned so that the electron beam was incident normally on the semiconductor cross-section and the doping junction was orthogonal to the direction of the raster scan. An optimised set of beam parameters was used with an objective aperture of 30 μ m diameter: a 1 kV primary electron probe having a current of ~32 pA and a probe diameter of ~16 nm. These probe conditions are known to maximise doping contrast, at least from freshly-cleaved cross-sections 7,8 . All the images (712 × 484 pixels) were digitally acquired at a magnification of 6,500× and a scan frequency of ~0.1 frame s −1 (the doped regions of interest were scanned only once), and stored as 8-bit datasets. The doping contrast data were processed using a Java plug-in written for ImageJ TM36 .
The SEM was an FEI XL30 TM Schottky field emission gun (sFEG) equipped with an SE detection system that combines a TLD with an energy filter that is available in many modern instruments. The extraction potential was 250 V and working distance was 3 mm. Under standard ultra-high resolution (UHR) imaging conditions, image formation and doping contrast are derived from SEs of all energies (up to 50 eV), which are trapped on-axis by the strong objective lens magnetic fields and pass up through the lens bore at a rate depending on the extraction field. Under low-pass energy-filtering, V def sets the maximum kinetic energy for the SEs that are allowed to pass through to the scintillator to be collected and contribute to the image. SE micro-spectroscopy characterisation. Further elaboration of energy-filtering with the TLD can be found in ref. 29, which can be employed for micro-spectroscopy measurements by means of varying V def in definite steps at judiciously chosen, regular time intervals. Fine energy resolution is enabled by a custom-built DC power supply that can configure discrete steps as small as ±30 mV to bias the deflector electrode over a dynamic range from 0 to 20 V 7,29 . Automated control of V def was through the National Instruments (NI) LabVIEW 7 TM software, and a frame grabber card was used to feedback the generated image onto a separate display screen for measurements. For cumulative SE spectra measurements, the intensity value at each bias step is the energy integral of the yield spectrum up to the maximum kinetic energy limit set by V def . The data were processed from box-averaging over at least 40 × 40 pixels within the scanned field areas of interest at a TV scan frequency of 1 frame 8 × s −1 (frame 8 × refers to 8 averaged frames), and recorded in real-time against V def at fixed time intervals. Whilst V def was ramped from 20 to 0 V in − 0.5 V steps, beam-induced extraneous effects were kept minimal as data acquisition was performed rapidly, within a total timescale of 20 s; essentially the same spectra were obtained when sweeping V def in the reverse direction from 0 to 20 V, indicating that temporal control of the voltage steps was optimised to avoid statistical fluctuations in the measurements due to contamination and/or charging by the electron probe interaction. A delicate balance between accuracy and throughput is struck with a sweep rate of 2 Hz as a sensible maximum, limited by the signal-to-noise ratio, and system response time taking into account, e.g. the slew rate and settling time of the data converters and electronic amplifiers involved.
Scientific RepoRts | 6:32003 | DOI: 10.1038/srep32003 Numerical simulations. Solutions to the semiconductor Poisson (Laplace) equation for a semiconductor-(oxide-) vacuum system were self-consistently obtained by the finite-element method through an iterative procedure that satisfies a convergence criterion, thereby providing the equilibrium carrier and electrostatic field distributions. Surface band-bending was computed from the modified boundary condition between the semiconductor and the hydrogenated surface layer. In the foregoing calculations, the spatial distribution of the surface states before or after surface-treatment was assumed to be uniform in the semiconductor plane, and independent of doping. When computing the ratio and angular distribution of the SEs, a quantum-mechanical model for transmission, reflection or refraction was employed to describe electron scattering at the surface boundary of the solid. A generic, geometric finite-element model integrating the TLD (provided in private communication with FEI company) was incorporated in these simulations, including realistic descriptions of the immersion lens electromagnetic and electrostatic fields in the electron optical column and the specimen chamber of the SEM; hence e.g., embodying the working distance-and bias-dependent variables, etc. Extraction and deflection field conditions equivalent to that adopted in the experiments were accounted for and specified, and 100% internal detection efficiency was assumed for the TLD.