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Quantitative sub-surface and non-contact imaging using scanning microwave microscopy
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 135701 (http://iopscience.iop.org/0957-4484/26/13/135701) View the table of contents for this issue, or go to the journal homepage for more
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Nanotechnology Nanotechnology 26 (2015) 135701 (9pp)
doi:10.1088/0957-4484/26/13/135701
Quantitative sub-surface and non-contact imaging using scanning microwave microscopy Georg Gramse1,6, Enrico Brinciotti2,6, Andrea Lucibello3, Samadhan B. Patil4, Manuel Kasper1, Christian Rankl2, Rajiv Giridharagopal5, Peter Hinterdorfer1, Romolo Marcelli3 and Ferry Kienberger2 1
Johannes Kepler University of Linz, Institute for Biophysics, Gruberstrasse 40, A-4020 Linz, Austria Keysight Technologies Austria GmbH, Keysight Labs, Gruberstrasse 40, A-4020 Linz, Austria 3 CNR-IMM Roma, Via del Fosso del Cavaliere 100, I-00133 Rome, Italy 4 London Centre for Nanotechnology, 19 Gordon St, London WC1H 0AH, UK 5 Intel Corporation, Technology Manufacturing Group Labs, 2501 NW 229th Ave, Hillsboro, OR, USA 2
E-mail: [email protected] Received 11 December 2014, revised 12 January 2015 Accepted for publication 20 January 2015 Published 9 March 2015 Abstract
The capability of scanning microwave microscopy for calibrated sub-surface and non-contact capacitance imaging of silicon (Si) samples is quantitatively studied at broadband frequencies ranging from 1 to 20 GHz. Calibrated capacitance images of flat Si test samples with varying dopant density (1015–1019 atoms cm−3) and covered with dielectric thin films of SiO2 (100–400 nm thickness) are measured to demonstrate the sensitivity of scanning microwave microscopy (SMM) for sub-surface imaging. Using standard SMM imaging conditions the dopant areas could still be sensed under a 400 nm thick oxide layer. Non-contact SMM imaging in lift-mode and constant height mode is quantitatively demonstrated on a 50 nm thick SiO2 test pad. The differences between non-contact and contact mode capacitances are studied with respect to the main parameters influencing the imaging contrast, namely the probe tip diameter and the tip–sample distance. Finite element modelling was used to further analyse the influence of the tip radius and the tip–sample distance on the SMM sensitivity. The understanding of how the two key parameters determine the SMM sensitivity and quantitative capacitances represents an important step towards its routine application for non-contact and sub-surface imaging. Keywords: nanotechnology, calibration, complex impedance, capacitance, sub-surface imaging, scanning microwave microscopy (Some figures may appear in colour only in the online journal) 1. Introduction
Similarly, frequency dependent electrical measurements can be used to probe local electric properties at certain depth within the sample. For established electrical SPM techniques like scanning capacitance microscopy and electrostatic force microscopy that operate at a single frequency or in a limited frequency range below 1 GHz, sub-surface imaging has still not been reported. Scanning microwave microscopy (SMM) [1, 2], a quantitative nanoscale electrical characterization technique operating at broadband microwave frequencies [8],
Sub-surface imaging of complex structures using scanning probe microscopy (SPM) has recently attracted considerable interest. Information on sub-surface features can be obtained exploiting the mechanical heterogeneity within the sample by frequency dependent mechanical measurements [3–7]. 6
Equally contributing author.
0957-4484/15/135701+09$33.00
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© 2015 IOP Publishing Ltd Printed in the UK
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can be used to selectively sense the sub-surface of the samples under study [9, 10]. The SMM consists of an atomic force microscope (AFM) combined with a vector network analyser (VNA) operating between 1 and 20 GHz. It combines the nanoscale spatial resolution of the AFM with the broadband electrical measurement capabilities of the VNA [11]. In the SMM reflection mode, the VNA sends an incident microwave signal through a conductive tip of a platinum–iridium cantilever. Depending on the impedance of the tip/sample interface, part of the microwave signal is reflected and measured by the VNA as the scattering S11 reflection signal [12]. The SMM has been successfully used to obtain calibrated values of relevant physical quantities, such as complex impedance, capacitance, and resistance [13, 14] and surface localized physical sample properties (electric permittivity, dopant density, and resistivity) with nanoscale spatial resolution [13–17]. Most of the advances in the SMM community were achieved studying surface structures including semiconductor devices. To the best of our knowledge, to date only studies on metallic and insulating substrates were reported that took advantage of the penetration ability of microwaves through materials [9, 10]. In these works, qualitative SMM imaging was performed exploiting the long-range electromagnetic (EM) interaction between microwaves and matter. Electrical contrast was obtained for flat samples with dielectric variations [9], whereas for metallic samples the dependence of EM penetration depth on the applied frequency through the metallic skin effect was used as contrast mechanism [10]. Here, we extend subsurface SMM imaging to doped semiconductors samples. For the first time we show calibrated capacitance images of buried semiconductor structures. Also the sensitivity of SMM for the measurement of subsurface elements is quantitatively studied. To obtain quantitative capacitance from the raw S11 measurements we calibrate the SMM using a procedure recently reported [13]. Additionally, we took advantage of the long-range sensitivity of the GHz EM field [18–20] to study the capability of SMM for calibrated non-contact capacitance imaging. The sensitivity of the SMM for sub-surface imaging is studied experimentally and theoretically by finite element modelling (FEM) under different conditions as a function of the tip radius and the tip–sample distance [21]. Understanding the effects of the key parameters on the SMM sensitivity represents an important step for future studies in this field [22].
schematic of the SMM experimental setup is shown in figure 1(a). The AFM tip is used as a nanoscale imaging and microwave probe, enabling simultaneous topographic and EM characterization of the sample under test. The VNA measures the ratio of the incident and reflected signal at the tip, the so called scattering S11 parameter. To transform the high impedance of the tip–sample contact to the sensitive 50 Ω of the VNA, a half-wavelength coaxial resonator in conjunction with a 50 Ω shunt resistor is used [23]. A high signal-to-noise ratio with good matching conditions is typically obtained every ∼2 GHz with the exact value depending on the cable lengths. Since the admittance Y scales linearly with the frequency f (ω = 2πf) and the capacitance C, Y ∼ jωC, it is favourable to measure at high frequencies. All the measurements presented in this work were performed at frequencies between 18 and 20 GHz while the SMM works in the range of 1–20 GHz. An intermediate bandwidth frequency of 100 Hz and 500 Hz has been used during the measurements, leading to a scan speed of 0.26 and 0.81 lines s-1 at 256 points/line, respectively.
2.2. Calibration workflow
In order to convert measured reflection S11 values into capacitance values, a systematic calibration workflow has to be applied [24]. We applied the calibration procedure recently proposed by Gramse et al [13]. The measured reflection coefficient S11 is converted into the complex impedance Z using the one-port black-box calibration. The defined calibration standards to calculate three complex error parameters e00, e01, and e11 are provided by simultaneously acquiring electrostatic force microscopy (EFM) and S11 approach curves. For this the tip is approached towards the surface until it gets into contact and both the EFM and the S11 signals are recorded. No external capacitance calibration sample is required. The main advantages of this approach are that it works in situ on the sample under test and that the calibration plane is located directly before the cantilever chip. For calibration, topography and complex S11 (amplitude and phase) images of the sample under test are acquired and a combined EFM/S11 approach curve is performed. From the electrostatic force, Fes,2ω, measured at the second harmonic of the excitation voltage v (t ) = V0 sin(ωt ), the gradient of the capacitance with respect to the tip–sample distance is obtained by dC /dz = 2Fes,2ω /V02 . The capacitance C (z ) can be calculated by integration. Assuming that the change in impedance Z in (z ) is only capacitive (strictly true only for nonlossy materials like dielectrics or highly conductive materials), three error parameters (e00, e01 and e11) can be calculated using where S11 = e00 + e01 S11, a /(1 − e11 S11, a ), S11,a = (Z in − Z ref )/(Z in + Z ref ), and Z ref is the characteristic impedance of the VNA (i.e. 50 Ω). Using the three e-parameters, from the complex S11 (amplitude and phase) image the calibrated capacitance image can be obtained. As shown elsewhere [13, 28, 29], the tip radius R can be obtained from the capacitance approach curve using the
2. Materials and methods 2.1. SMM setup
A commercial transmission line SMM (Keysight Technologies, Santa Rosa, CA, USA) consisting of a standard 5600 AFM interfaced with a 20 GHz VNA both from Keysight Technologies, was used. Rocky Mountain Nanotechnology (RMN) solid platinum AFM tips were used. All measurements were carried out in dry atmosphere (RH < 5%). A 2
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Figure 1. Experimental setup for sub-surface imaging of a doped Si substrate partly covered with SiO2. (a) The scanning microwave microscope (SMM) consists of a vector network analyser (VNA) and an atomic force microscope (AFM). In reflection mode a GHz microwave signal is sent through a conductive platinum cantilever to electrically characterize the sample under investigation. One port of the VNA is used to measure the reflection coefficient S11. (b),(d) SMM images of a doped Si substrate partly covered with 120 nm and 200 nm. Panels (b),(d) show the topography images with a sketch of the sample (inset) and panels (c),(e) show the reflection S11 phase images with the subsurface dopant features.
wide bulk interface layers at 1 × 1014 atoms cm−3. The region with doping level of 1 × 1018 atoms cm−3 contains dopant sublevels with very fine variations of ∼1 × 1017 atoms cm−3. The doped Si surface to be imaged was covered side by side with a SiO2 layer, 120 nm and 200 nm thick, using a shadow metal mask. A thickness gradient region between 120 and 200 nm of SiO2 was micro-patterned and etched to yield SiO2 free region. This effectively produces buried doped Si surface with SiO2 spacer dielectric of 120 nm, 200 nm and no spacer region as control (shown in figure 1). A second sample with the same doped Si staircase structure (shown in figure 2) was covered with SiO2 layers having thickness of 100 nm, 200 nm and 400 nm. The dielectric thin films were deposited through a SiH4 based plasma enhanced chemical vapour deposition process. In order to achieve the goal of 400 nm of SiO2, three separate deposition steps have been necessary. The 50 nm thick SiO2 structures on the highly doped Si substrate shown in figures 3 and 4 (resistivity of 0.001–0.005 Ω cm) were purchased from AMO GmbH (Aachen, Germany).
approximation:
(
)
C R , θ, H , c , cstray , z , h , εr = Capex + Ccone + Cstray, (1)
Capex = 2πε0 R ln
Ccone =
h + εr z , h + εr (R + z) − εr R sin θ
(2)
2πε0 (ln (tan θ /2))2 ⎛ ⎛ ⎛ ⎞−1 ⎞ h × ⎜ z ln ⎜ H ⎜⎜ + z + R (1 − sin θ ) ⎟ ⎟ ⎜ ⎜ ⎠ ⎟⎠ ⎝ ⎝ εr ⎝ ⎛h ⎞ − ⎜ + R 1 − sin θ −1 ⎟ ⎝ εr ⎠
(
)
⎛ ⎛h ⎞⎞⎞ × ln ⎜ εr ⎜ + z + R (1 − sin θ ) ⎟ ⎟ ⎟⎟ , ⎠⎠⎠ ⎝ ⎝ εr Cstray = cstray z + c,
(3) (4)
where, H is the cone height (nominally 80 μm), θ the cone angle (nominally 15°), z the tip–sample distance, h the thickness of the dielectric thin film, and εr its dielectric constant.
2.4. Finite element modelling 2.3. Samples preparation
FEM was carried out with Comsol Multiphysics 4.3 (2D axisymmetric, ac/dc module, electric currents, frequency domain). The simulations resemble the experimental conditions of the experiments in figure 3 (50 nm thick oxide of 6 μm diameter on a metallic substrate; 80 μm high AFM tip with cone angle of 15°; cantilever excelling the cone end by 10 μm) with variable tip substrate distance and tip radius. The tip bias is set to 1 V and the metallic substrate is set to ground. Similar models have been used in [13, 27].
The topographically flat doped silicon (Si) samples [15, 25, 26], were provided by Professor Smoliner from Technical University of Vienna. They consist of 20 μm wide n-type doped regions with the doping density arranged in a staircase like structure in epitaxially grown multilayer Si. The doping concentrations are, from the edge to the bulk of the sample, 4 × 1019 atoms cm−3, 1 × 1018 atoms cm−3, 8 × 1017 atoms cm−3 and 1 × 1016 atoms cm−3, separated by 5 μm 3
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Figure 2. Comparison of doped Si non-contact imaging in air and sub-surface imaging on SiO2. (a) Calibrated and flattened capacitance images are shown of a doped Si sample measured at different heights in air from 0 to 400 nm (upper panel) and covered with oxide thicknesses ranging from 0 to 400 nm in contact mode (lower panel). Capacitance images were derived from complex S11 measurements including phase and amplitude. (b) Cross section profiles represent averages of the corresponding capacitance images (used AFM-tip: 25Pt400B-RMN, f = 19.81 GHz). Also, the cross-section profile at 1000 nm distance is shown where no dopant signal was detected anymore.
3. Results and discussion
A quantitative evaluation of the S11 images was done in order to extract calibrated capacitance values of the buried doping profiles. For this we applied a recently published calibration procedure ([13]; see section 2). Figure 2 shows calibrated capacitance images for the flat doped Si sample covered with three different layers of Si oxide at 100 nm, 200 nm, and 400 nm thickness, respectively. Also, for comparison, the bare Si dopant sample with only the native oxide layer (i.e. 1–2 nm thick) is shown. The uncovered part of the Si sample was first measured in contact mode, and then in non-contact at three different heights above the sample (100 nm, 200 nm, 400 nm) (figure 2(a)). The oxide covered sample was measured in contact mode on each oxide layer (figure 2(a) below). Even though the fine dopant substructures are lost in both the non-contact mode and in the oxide sub-surface imaging mode, the overall dopant stripes and bulk interface layers can still be observed at 400 nm distance in air and on the 400 nm thick oxide, respectively. The highly doped areas show capacitances of up to 400 aF when the tip is in contact and around 15 aF when the tip is lifted 400 nm in air. Figure 2(b) shows averaged cross section profiles from each measured region in the capacitance image. The dielectric thickness variation is the same for both samples including an air and oxide thickness of 100 nm, 200 nm and 400 nm. The only discriminating factor is the dielectric constant of the insulator being air in the first case (εr,air = 1) and SiO2 (εr,SiO2 = 4) in the second case. Comparing the capacitance of the uncovered and the covered test samples at the same insulator thickness (figure 2(b)) it can be noticed that the capacitance values differ by approximately a factor of 4 being the permittivity ratio of the two dielectric materials εr,SiO2 /εr,air = 4. For instance, in figure 2(b), it can
3.1. Sub-surface imaging of a SiO2 covered doped Si sample
To explore the sub-surface imaging capabilities of the SMM we used a topographically flat Si test sample exhibiting various dopant stripes with increasing dopant density, from 1 × 1016 atoms cm−3 to 4 × 1019 atoms cm−3, intersected with bulk interface layers (1 × 1014 atoms cm−3). The dopant sample was partially covered with a layer of SiO2 having two different oxide thicknesses, 120 nm and 200 nm (figure 1). The partial SiO2 coverage was obtained by CVD oxide growth and subsequent focused ion beam milling and is clearly visible in the topographical images (figures 1(b) and (d)). The oxide thickness was verified using topography cross-section analysis. The surface of the doped Si sample is flat according to the topographical image (surface roughness less than 3 nm) and the doping pattern is only visible in the S11 images (figures 1(c) and (e)). Therefore, no cross-talk of the S11 image with the topography is obtained on those flat Si samples. The areas that are not covered with oxide show a strong S11 signal generated from the differently doped stripes. Even though the S11 signal is smaller on the oxide-covered areas, it can be noticed that the different dopant densities can still be detected both at 120 nm and 200 nm oxide coverage. In particular, the bulk interface layers that separate the individually doped areas can be clearly observed. However, very fine dopant differences within the second dopant stripe can only observed on the bare sample. These results confirm that the SMM can be used to electrically probe oxide buried structures as also shown by Plassard et al [10] for metallic samples and by Lai et al [9] on insulators. 4
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Figure 3. Calibrated SMM images of a 50 nm high SiO2 pad on a highly doped Si substrate measured in constant height mode (upper row) and lift mode (lower row). (a),(d) topographic 3D view of the oxide pad and the sketch of the measurement mode. (b),(e) Calibrated capacitance images measured in contact and at different distances as indicated in the images. Images have been flattened such that the bare Si substrate is ΔC = 0 aF. (c),(f) Average cross-section profiles extracted from the capacitance images showing the capacitance variation, ΔC. Topographic cross-talk was removed from lift-mode measurements. Images in lift mode were acquired with a smaller tip diameter (R ∼ 270 nm) compared to constant height images (R ∼ 1000 nm).
be noticed that the capacitance at 100 nm height in air overlaps with the capacitance at 400 nm SiO2. The factor of 4 resulting from εr,SiO2 /εr,air indicates that the measured capacitance depends on the ratio C ∼ εr h−1 and the higher is the tip–substrate distance the lower is the capacitance. Additionally, a scan in air was performed at 1000 nm distance from the substrate (purple dashed line in figure 2(b)) resulting in a flat capacitance signal, indicating that the SMM sensitivity limit was reached and the S11 signal was below the noise level of ∼1 aF. It can be noticed that the plateaus on the different dopant levels are not always perfectly horizontal due to a flattening artefact.
oxide topography contributes to the capacitance signal, we measured the capacitance both in constant distance from the plane Si substrate (constant-height mode) and constant distance from the overall oxide pad (lift-mode) as schematically shown in figures 3(a) and (d), respectively. Figure 3(b) shows the calibrated constant height capacitance image obtained after calibration of the measured S11 data. The upper part of the SiO2 pad is measured in contact (blue colour), then the tip is lifted to z = 500 nm from the substrate and scans a few lines. It is successively lowered as indicated in the image until it touches the sample again and returns into contact in the lower part of the oxide pad. To emphasize the effect of the scan height on the contrast, the image has been flattened setting the capacitance of the substrate to ΔC = 0 aF. Figure 3(c) shows the cross-section profiles taken from the capacitance image. The oxide shows positive contrast with respect to the substrate, because it has a higher dielectric constant and thus a higher capacitance than air. At the closest distance of z = 50 nm a signal difference of ΔC = 50 aF was measured. When the tip–sample distance is increased, the measured capacitance difference gets smaller, until it finally disappears at z = 500 nm reaching a value of 1 aF which is the current SMM noise level.
3.2. SMM lift-mode and constant-height imaging
While in the previous section a flat semiconductor substrate was studied, here we investigate how the capacitance changes at increasing distance in air above a fully dielectric sample with a topographic pattern. The dielectric material has an additional height above the substrate therefore lift-mode imaging is compared quantitatively to constant-height imaging. The sample is a thin dielectric pattern of SiO2 pads on a highly doped Si2+ substrate (see figure 3(a)). The oxide pads are 50 nm in height with a lateral size of 8 × 8 μm2. Since the 5
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(150 aF in figure 3(c)). It should be noted that the non-local topography-cross talk in figure 3(e) was removed by taking the topography image into account. The image has been also flattened setting the capacitance on the Si substrate to ΔC = 0 aF. With increasing lift height the contrast disappears rapidly and is almost completely lost at z = 100 nm. The liftmode capacitance images and cross-section profiles show that the SiO2 pad has inverted contrast with respect to the constant-height measurements. To understand this better, it is instructive to look at quantitative capacitance versus distance curves when approaching the tip to the Si2+ and to the SiO2 pad. 3.3. Quantitative approach curve analysis
Figure 4 shows calibrated capacitance approach curves on the oxide pad and the bare Si (Si2+) substrate from the sample shown in figure 3. For constant-height mode (figure 4(a)) the distance is denoted with respect to the flat Si2+ substrate and for lift-mode (figure 4(b)) with respect to the overall sample topography. This results essentially in a shift of the SiO2 approach curve of h = 50 nm along the z-axis, z’ = z + h. The approach curves are plotted for the smaller tip (R ∼ 270 nm) and the bigger tip (R ∼ 1000 nm). The bigger tip gives a higher signal difference between Si and SiO2, especially close to contact as observed also in the images in figure 3. Also the inversion of the contrast between constantheight mode and lift mode observed in figure 3 is obtained in the approach curves with the SiO2 curve in figure 4(a) above and in figure 4(b) below the Si curve. This again is an effect of the shift along the z-axis. On top of the contrast inversion, two practical differences between lift-mode and constantheight mode can be found when looking at the capacitance difference between the approach curves on the Si and the SiO2 as shown in figure 4(c). Firstly, in lift mode there is a constant offset in the difference signal (marked by the blue scattered line), because the capacitance from the non-local parts of the AFM tip (e.g. upper cone, cantilever) change nearly linearly when the tip– substrate distance is changed. This so-called topography cross-talk is an undesired artefact but plays only a significant role for small AFM tips and can also be subtracted from the measurements as done in figure 3 [13, 28]. In constant-height mode there is no topography cross-talk. Secondly, a capacitance contrast in lift mode can be only observed when the tip is relatively close to the surface and the contrast decreases for higher dielectric constants of the dielectric layer as shown in the inset of figure 4(c). In constant height mode a contrast can be observed also at higher distances, and it increases with higher dielectric constant. This is because the capacitance is a function of C(h ε−1 r ) in lift mode and C(h/εr−h) in constant height mode as described in [13] and also discussed in [28, 29]. Independently of acquiring an image in lift mode or constant height mode, in principle the same result for εr is expected. In summary, acquisition of capacitance images in constant height mode is experimentally more demanding than in lift mode, especially if the substrate is not completely flat.
Figure 4. Calibrated capacitance approach curves on the oxide pad
(black) and the bare silicon substrate (Si2+, red). (a) Constant height mode taking the Si substrate as reference distance; (b) lift mode taking the sample surface as reference distance. Curves are shown for small tips (Rapex ∼ 270 nm) and big tips (Rapex ∼ 1000 nm). (c) Difference of approach curves on Si and SiO2 (small tip) for lift and constant-height mode. Inset shows the theoretical difference curves for three dielectric constants, εr = 3,4,5. Calculations were done with equation (1) using the parameters Rapex = 270 nm, θ = 15° and h = 50 nm.
In figure 3(e) the same sample was measured in lift mode at increasing lift-height from the sample. Compared to the previous constant height measurement, a smaller tip size was used to achieve lower capacitance values that are closer to the SMM noise level. The tip–radius was determined using a quantitative approach-curve analysis as described in equation (1) of the section 2. A tip apex radius of R = 1000 nm and R = 270 nm for figures 3(b) and (d) was calculated, respectively. In figure 3(e) at z = 0 nm (i.e. contact mode) the smaller tip gives a capacitance contrast of 6 aF which is significantly lower than for the larger tip measurement 6
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Figure 5. Simulated lift-mode capacitance difference between 50 nm thick SiO2 (εr = 4) and the highly conductive Si2+ substrate (metallic
behaviour assumed). (a) ΔC as a function of the tip sample distance shown for two different tip radii (20 nm—blue and 1000 nm—red). The SMM noise level region (below 1 aF) is highlighted with a dark grey colour. Note the logarithmical scale in the vertical axis. The 2D colour map in the inset shows the dependence of ΔC on the tip radius and the tip sample distance. (b) Simulated model with obtained potential distribution with zoom of the tip/sample region.
However, capacitance images from constant height mode are easier to handle for quantification, since crosstalk does not have to be removed and thus the extraction of dielectric properties is straight forward.
selected such that the S11 signal is above the noise level at a given imaging speed and lift height. This guarantees that local capacitive and dielectric properties are measured and not just topography cross-talk. For example, a noise level of 4 aF can be achieved with a scan speed slower than 1 ms/pixel; under these conditions a lift height lower than 30 nm is required to still resolve a signal on the sample with a tip as small as R = 60 nm.
3.4. Sensitivity analysis by FEM
For an extended sensitivity analysis we used FEM to study how the capacitance and dielectric contrast depends on the two parameters tip radius and tip–sample distance (figure 5). The electric potential and capacitance were calculated for the specific tip sample geometry shown in figure 5(b) (see section 2). The modelled capacitance differences in figure 5(a) represent the difference between the capacitance above the oxide and the bare conductive substrate, similar to the experiments. The capacitance difference decays thereby monotonically with increasing distance similar to the experimental approach curves in figure 4. Note the logarithmical scale in the vertical axis. For a big tip of 1000 nm apex radius the signal difference even at large distances (e.g. 1000 nm) is well above the SMM noise level of 1 aF. For very small tips with e.g. 20 nm tip radius the difference in the contrast disappears at 300 nm distance. The experimental SMM noise level of 1 aF that is indicated here is for measuring at relatively low speed of 10 ms/pixel (0.4 line s−1, 256 pixels per line, 100 Hz intermediate frequency bandwidth filter of the VNA). For normal speed imaging the noise level is typically around 2 aF (2 ms/pixel) or 3 aF (1 ms/pixel). Based on the capacitance modelling, this means that very small tips do not provide enough electrical contrast to differentiate the SiO2 from the bare substrate when measuring at normal speed. The inset shows this dependency for a wider range of tip radii indicating also the different noise levels at different imaging speeds. In general the tip-size has to be
4. Conclusions and perspectives Sub-surface and non-contact SMM imaging of doped Si samples and nanoscale SiO2 structures has been presented in this work. Reflection S11 SMM images have been calibrated and converted to quantitative capacitance images. The sensitivity of the SMM capacitance images has been studied with respect to sub-surface material changes under different conditions including lift-mode and constant-height mode. An ntype doping staircase (1014–1019 atoms cm−3) Si sample covered with SiO2 (100–400 nm thick) resulted in capacitance images with differences of 10–75 aF depending on the oxide thickness. The same doping staircase Si structure was measured without SiO2 in constant height mode (100–400 nm tip– sample distance). The latter sample resulted in capacitance differences of up to 25 aF. With the current SMM noise level of 1 aF and the corresponding tip diameter the electrical sample properties could be clearly measured on oxides with more than 400 nm thickness at reduced lateral resolution though. A pattern of SiO2 pads has been measured in contact, lift and constant height mode. The best capacitance contrast due to local material differences can be obtained in contact or at low lift heights and with big AFM tips. With ∼1 μm tip diameter the local capacitance signal was lost when scanned 7
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applications in the field of semiconductor failure analysis studies including process optimizations for integrated chip fabrication. Figure 6 shows an example of sub-surface imaging on a semiconductor device using differential capacitance imaging. Backside wafer imaging was done on a thin wafer of Si in order to demonstrate non-invasive and non-destructive through-Si imaging of SRAM structures. The backside of a Si wafer was mechanically polished down to a thickness ranging from 50 nm to 450 nm and imaged with the SMM in differential dC/dV capacitance mode [17] as shown in the sketch in figure 6(a). The active device region is thus beneath 50 nm– 450 nm of doped Si. The SRAM structure, which is on the opposite side of the tip–sample contact, could be imaged through the wafer with a thickness of 50 nm (figure 6(b)), 200 nm (figure 6(c)), and up to 450 nm (figure 6(d)). On a wafer thickness of more than 450 nm no dC/dV signal was detected anymore due to the noise limit of the SMM. In the future, the calibration and workflow procedures presented in this paper will be applied to more advanced sample designs in semiconductor failure analysis as well as for the imaging of bio-cell interiors.
Acknowledgments The authors would like to thank J Smoliner from TU Vienna (Austria); L Fumagalli and G Gomila from IBEC (Spain); M Moertelmaier, M Richter and H Tanbakuchi from Keysight Technologies for helpful technical discussions. This work has been supported by the EU-FP7 (NMP-2011-280516, VSMMART-Nano, and PEOPLE-2012-ITN-317116, Nanomicrowave).
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Figure 6. Sub-surface imaging applied to semiconductor wafer
devices. (a) Semiconductor device structures (SRAM) were imaged at the backside of the silicon wafer at three different thicknesses including (b) 50 nm, (c) 200 nm and (d) 450 nm. The left panel shows the topographical images and the right panel shows the differential capacitance images (dS11/dV amplitude).
at 500 nm height above the sample. To generalize the experimental findings the tip radius and the tip–sample distance effects on the capacitance sensitivity have been studied by analytical and numerical FEM calculations. Understanding how the two key parameters determine the SMM sensitivity represents an important step towards its routine application for more complex sample geometries. The results also confirm that the SMM can be used to accurately perform quantitative nanoscale probing of dielectric materials and to perform calibrated capacitance characterization of buried structures. This can for example find 8
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[20] Vlahacos C P et al 2000 Non-contact imaging of dielectric constant with a near-field scanning microwave microscope Microsc. Anal. 2000 13–15 [21] Lai K et al 2008 Modeling and characterization of a cantileverbased near-field scanning microwave impedance microscope Rev. Sci. Instrum. 79 063703 [22] Imtiaz A et al 2006 Effect of tip geometry on contrast and spatial resolution of the near-field microwave microscope J. Appl. Phys. 100 044304 [23] Tanbakuchi H et al 2009 Nanoscale materials and device characterization via a scanning microwave microscope IEEE Int. Conf. on Microwaves, Communications, Antennas and Electronics Systems—COMCAS 2009 p 4 [24] Farina et al October 2011 Calibration protocol for broadband near-field microwave microscopy IEEE Trans. Microw. Theory Tech. 59 7–10 [25] Kundhikanjana W et al 2013 Unexpected surface implanted layer in static random access memory devices observed by microwave impedance microscope Semicond. Sci. Technol. 28 025010 [26] Imtiaz A et al 2007 Nanometer-scale material contrast imaging with a near-field microwave microscope Appl. Phys. Lett. 90 143106 [27] Gomila G, Gramse G and Fumagalli L 2014 Finite-size effects and analytical modeling of electrostatic force microscopy applied to dielectric films Nanotechnology 25 255702 [28] Gomila G, Toset J and Fumagalli L 2008 Nanoscale capacitance microscopy of thin dielectric films J. Appl. Phys. 104 024315 [29] Fumagalli L et al 2007 Dielectric-constant measurement of thin insulating films at low frequency by nanoscale capacitance microscopy Appl. Phys. Lett. 91 243110
[8] Tselev A et al 2007 Broadband dielectric microwave microscopy on micron length scales Rev. Sci. Instrum. 78 044701 [9] Lai K et al 2007 Atomic-force-microscope-compatible nearfield scanning microwave microscope with separated excitation and sensing probes Rev. Sci. Instrum. 78 063702 [10] Plassard C et al 2011 Detection of defects buried in metallic samples by scanning microwave microscopy Phys. Rev. B 83 121409 [11] Lee J et al 2010 Atomic resolution imaging at 2.5 GHz using nearfield microwave microscopy Appl. Phys. Lett. 97 183111 [12] Karbassi A et al 2008 Quantitative scanning near-field microwave microscopy for thin film dielectric constant measurement Rev. Sci. Instrum. 79 094706 [13] Gramse G et al 2014 Calibrated complex impedance and permittivity measurements with scanning microwave microscopy Nanotechnology 25 145703 [14] Hoffmann J et al 2012 A calibration algorithm for nearfield scanning microwave microscopes 12th IEEE Conf. on Nanotechnology 2012 (New York: IEEE) [15] Huber H P et al 2012 Calibrated nanoscale dopant profiling using a scanning microwave microscope J. Appl. Phys. 111 014301 [16] Huber H P et al 2010 Calibrated nanoscale capacitance measurements using a scanning microwave microscope Rev. Sci. Instrum. 81 113701 [17] Humer I et al 2012 Tip geometry effects in dopant profiling by scanning microwave microscopy J. Appl. Phys. 111 044314 [18] Talanov V V et al 2006 Noncontact dielectric constant metrology of low-k interconnect films using a near-field scanned microwave probe Appl. Phys. Lett. 88 192906 [19] Ohara K, Cho Y et al 2005 Non-contact scanning nonlinear dielectric microscopy Nanotechnology 16 S54–8
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Quantitative sub-surface and non-contact imaging using scanning microwave microscopy
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Nanotechnology 26 135701 (http://iopscience.iop.org/0957-4484/26/13/135701) View the table of contents for this issue, or go to the journal homepage for more
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Nanotechnology Nanotechnology 26 (2015) 135701 (9pp)
doi:10.1088/0957-4484/26/13/135701
Quantitative sub-surface and non-contact imaging using scanning microwave microscopy Georg Gramse1,6, Enrico Brinciotti2,6, Andrea Lucibello3, Samadhan B. Patil4, Manuel Kasper1, Christian Rankl2, Rajiv Giridharagopal5, Peter Hinterdorfer1, Romolo Marcelli3 and Ferry Kienberger2 1
Johannes Kepler University of Linz, Institute for Biophysics, Gruberstrasse 40, A-4020 Linz, Austria Keysight Technologies Austria GmbH, Keysight Labs, Gruberstrasse 40, A-4020 Linz, Austria 3 CNR-IMM Roma, Via del Fosso del Cavaliere 100, I-00133 Rome, Italy 4 London Centre for Nanotechnology, 19 Gordon St, London WC1H 0AH, UK 5 Intel Corporation, Technology Manufacturing Group Labs, 2501 NW 229th Ave, Hillsboro, OR, USA 2
E-mail: [email protected] Received 11 December 2014, revised 12 January 2015 Accepted for publication 20 January 2015 Published 9 March 2015 Abstract
The capability of scanning microwave microscopy for calibrated sub-surface and non-contact capacitance imaging of silicon (Si) samples is quantitatively studied at broadband frequencies ranging from 1 to 20 GHz. Calibrated capacitance images of flat Si test samples with varying dopant density (1015–1019 atoms cm−3) and covered with dielectric thin films of SiO2 (100–400 nm thickness) are measured to demonstrate the sensitivity of scanning microwave microscopy (SMM) for sub-surface imaging. Using standard SMM imaging conditions the dopant areas could still be sensed under a 400 nm thick oxide layer. Non-contact SMM imaging in lift-mode and constant height mode is quantitatively demonstrated on a 50 nm thick SiO2 test pad. The differences between non-contact and contact mode capacitances are studied with respect to the main parameters influencing the imaging contrast, namely the probe tip diameter and the tip–sample distance. Finite element modelling was used to further analyse the influence of the tip radius and the tip–sample distance on the SMM sensitivity. The understanding of how the two key parameters determine the SMM sensitivity and quantitative capacitances represents an important step towards its routine application for non-contact and sub-surface imaging. Keywords: nanotechnology, calibration, complex impedance, capacitance, sub-surface imaging, scanning microwave microscopy (Some figures may appear in colour only in the online journal) 1. Introduction
Similarly, frequency dependent electrical measurements can be used to probe local electric properties at certain depth within the sample. For established electrical SPM techniques like scanning capacitance microscopy and electrostatic force microscopy that operate at a single frequency or in a limited frequency range below 1 GHz, sub-surface imaging has still not been reported. Scanning microwave microscopy (SMM) [1, 2], a quantitative nanoscale electrical characterization technique operating at broadband microwave frequencies [8],
Sub-surface imaging of complex structures using scanning probe microscopy (SPM) has recently attracted considerable interest. Information on sub-surface features can be obtained exploiting the mechanical heterogeneity within the sample by frequency dependent mechanical measurements [3–7]. 6
Equally contributing author.
0957-4484/15/135701+09$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
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can be used to selectively sense the sub-surface of the samples under study [9, 10]. The SMM consists of an atomic force microscope (AFM) combined with a vector network analyser (VNA) operating between 1 and 20 GHz. It combines the nanoscale spatial resolution of the AFM with the broadband electrical measurement capabilities of the VNA [11]. In the SMM reflection mode, the VNA sends an incident microwave signal through a conductive tip of a platinum–iridium cantilever. Depending on the impedance of the tip/sample interface, part of the microwave signal is reflected and measured by the VNA as the scattering S11 reflection signal [12]. The SMM has been successfully used to obtain calibrated values of relevant physical quantities, such as complex impedance, capacitance, and resistance [13, 14] and surface localized physical sample properties (electric permittivity, dopant density, and resistivity) with nanoscale spatial resolution [13–17]. Most of the advances in the SMM community were achieved studying surface structures including semiconductor devices. To the best of our knowledge, to date only studies on metallic and insulating substrates were reported that took advantage of the penetration ability of microwaves through materials [9, 10]. In these works, qualitative SMM imaging was performed exploiting the long-range electromagnetic (EM) interaction between microwaves and matter. Electrical contrast was obtained for flat samples with dielectric variations [9], whereas for metallic samples the dependence of EM penetration depth on the applied frequency through the metallic skin effect was used as contrast mechanism [10]. Here, we extend subsurface SMM imaging to doped semiconductors samples. For the first time we show calibrated capacitance images of buried semiconductor structures. Also the sensitivity of SMM for the measurement of subsurface elements is quantitatively studied. To obtain quantitative capacitance from the raw S11 measurements we calibrate the SMM using a procedure recently reported [13]. Additionally, we took advantage of the long-range sensitivity of the GHz EM field [18–20] to study the capability of SMM for calibrated non-contact capacitance imaging. The sensitivity of the SMM for sub-surface imaging is studied experimentally and theoretically by finite element modelling (FEM) under different conditions as a function of the tip radius and the tip–sample distance [21]. Understanding the effects of the key parameters on the SMM sensitivity represents an important step for future studies in this field [22].
schematic of the SMM experimental setup is shown in figure 1(a). The AFM tip is used as a nanoscale imaging and microwave probe, enabling simultaneous topographic and EM characterization of the sample under test. The VNA measures the ratio of the incident and reflected signal at the tip, the so called scattering S11 parameter. To transform the high impedance of the tip–sample contact to the sensitive 50 Ω of the VNA, a half-wavelength coaxial resonator in conjunction with a 50 Ω shunt resistor is used [23]. A high signal-to-noise ratio with good matching conditions is typically obtained every ∼2 GHz with the exact value depending on the cable lengths. Since the admittance Y scales linearly with the frequency f (ω = 2πf) and the capacitance C, Y ∼ jωC, it is favourable to measure at high frequencies. All the measurements presented in this work were performed at frequencies between 18 and 20 GHz while the SMM works in the range of 1–20 GHz. An intermediate bandwidth frequency of 100 Hz and 500 Hz has been used during the measurements, leading to a scan speed of 0.26 and 0.81 lines s-1 at 256 points/line, respectively.
2.2. Calibration workflow
In order to convert measured reflection S11 values into capacitance values, a systematic calibration workflow has to be applied [24]. We applied the calibration procedure recently proposed by Gramse et al [13]. The measured reflection coefficient S11 is converted into the complex impedance Z using the one-port black-box calibration. The defined calibration standards to calculate three complex error parameters e00, e01, and e11 are provided by simultaneously acquiring electrostatic force microscopy (EFM) and S11 approach curves. For this the tip is approached towards the surface until it gets into contact and both the EFM and the S11 signals are recorded. No external capacitance calibration sample is required. The main advantages of this approach are that it works in situ on the sample under test and that the calibration plane is located directly before the cantilever chip. For calibration, topography and complex S11 (amplitude and phase) images of the sample under test are acquired and a combined EFM/S11 approach curve is performed. From the electrostatic force, Fes,2ω, measured at the second harmonic of the excitation voltage v (t ) = V0 sin(ωt ), the gradient of the capacitance with respect to the tip–sample distance is obtained by dC /dz = 2Fes,2ω /V02 . The capacitance C (z ) can be calculated by integration. Assuming that the change in impedance Z in (z ) is only capacitive (strictly true only for nonlossy materials like dielectrics or highly conductive materials), three error parameters (e00, e01 and e11) can be calculated using where S11 = e00 + e01 S11, a /(1 − e11 S11, a ), S11,a = (Z in − Z ref )/(Z in + Z ref ), and Z ref is the characteristic impedance of the VNA (i.e. 50 Ω). Using the three e-parameters, from the complex S11 (amplitude and phase) image the calibrated capacitance image can be obtained. As shown elsewhere [13, 28, 29], the tip radius R can be obtained from the capacitance approach curve using the
2. Materials and methods 2.1. SMM setup
A commercial transmission line SMM (Keysight Technologies, Santa Rosa, CA, USA) consisting of a standard 5600 AFM interfaced with a 20 GHz VNA both from Keysight Technologies, was used. Rocky Mountain Nanotechnology (RMN) solid platinum AFM tips were used. All measurements were carried out in dry atmosphere (RH < 5%). A 2
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Figure 1. Experimental setup for sub-surface imaging of a doped Si substrate partly covered with SiO2. (a) The scanning microwave microscope (SMM) consists of a vector network analyser (VNA) and an atomic force microscope (AFM). In reflection mode a GHz microwave signal is sent through a conductive platinum cantilever to electrically characterize the sample under investigation. One port of the VNA is used to measure the reflection coefficient S11. (b),(d) SMM images of a doped Si substrate partly covered with 120 nm and 200 nm. Panels (b),(d) show the topography images with a sketch of the sample (inset) and panels (c),(e) show the reflection S11 phase images with the subsurface dopant features.
wide bulk interface layers at 1 × 1014 atoms cm−3. The region with doping level of 1 × 1018 atoms cm−3 contains dopant sublevels with very fine variations of ∼1 × 1017 atoms cm−3. The doped Si surface to be imaged was covered side by side with a SiO2 layer, 120 nm and 200 nm thick, using a shadow metal mask. A thickness gradient region between 120 and 200 nm of SiO2 was micro-patterned and etched to yield SiO2 free region. This effectively produces buried doped Si surface with SiO2 spacer dielectric of 120 nm, 200 nm and no spacer region as control (shown in figure 1). A second sample with the same doped Si staircase structure (shown in figure 2) was covered with SiO2 layers having thickness of 100 nm, 200 nm and 400 nm. The dielectric thin films were deposited through a SiH4 based plasma enhanced chemical vapour deposition process. In order to achieve the goal of 400 nm of SiO2, three separate deposition steps have been necessary. The 50 nm thick SiO2 structures on the highly doped Si substrate shown in figures 3 and 4 (resistivity of 0.001–0.005 Ω cm) were purchased from AMO GmbH (Aachen, Germany).
approximation:
(
)
C R , θ, H , c , cstray , z , h , εr = Capex + Ccone + Cstray, (1)
Capex = 2πε0 R ln
Ccone =
h + εr z , h + εr (R + z) − εr R sin θ
(2)
2πε0 (ln (tan θ /2))2 ⎛ ⎛ ⎛ ⎞−1 ⎞ h × ⎜ z ln ⎜ H ⎜⎜ + z + R (1 − sin θ ) ⎟ ⎟ ⎜ ⎜ ⎠ ⎟⎠ ⎝ ⎝ εr ⎝ ⎛h ⎞ − ⎜ + R 1 − sin θ −1 ⎟ ⎝ εr ⎠
(
)
⎛ ⎛h ⎞⎞⎞ × ln ⎜ εr ⎜ + z + R (1 − sin θ ) ⎟ ⎟ ⎟⎟ , ⎠⎠⎠ ⎝ ⎝ εr Cstray = cstray z + c,
(3) (4)
where, H is the cone height (nominally 80 μm), θ the cone angle (nominally 15°), z the tip–sample distance, h the thickness of the dielectric thin film, and εr its dielectric constant.
2.4. Finite element modelling 2.3. Samples preparation
FEM was carried out with Comsol Multiphysics 4.3 (2D axisymmetric, ac/dc module, electric currents, frequency domain). The simulations resemble the experimental conditions of the experiments in figure 3 (50 nm thick oxide of 6 μm diameter on a metallic substrate; 80 μm high AFM tip with cone angle of 15°; cantilever excelling the cone end by 10 μm) with variable tip substrate distance and tip radius. The tip bias is set to 1 V and the metallic substrate is set to ground. Similar models have been used in [13, 27].
The topographically flat doped silicon (Si) samples [15, 25, 26], were provided by Professor Smoliner from Technical University of Vienna. They consist of 20 μm wide n-type doped regions with the doping density arranged in a staircase like structure in epitaxially grown multilayer Si. The doping concentrations are, from the edge to the bulk of the sample, 4 × 1019 atoms cm−3, 1 × 1018 atoms cm−3, 8 × 1017 atoms cm−3 and 1 × 1016 atoms cm−3, separated by 5 μm 3
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Figure 2. Comparison of doped Si non-contact imaging in air and sub-surface imaging on SiO2. (a) Calibrated and flattened capacitance images are shown of a doped Si sample measured at different heights in air from 0 to 400 nm (upper panel) and covered with oxide thicknesses ranging from 0 to 400 nm in contact mode (lower panel). Capacitance images were derived from complex S11 measurements including phase and amplitude. (b) Cross section profiles represent averages of the corresponding capacitance images (used AFM-tip: 25Pt400B-RMN, f = 19.81 GHz). Also, the cross-section profile at 1000 nm distance is shown where no dopant signal was detected anymore.
3. Results and discussion
A quantitative evaluation of the S11 images was done in order to extract calibrated capacitance values of the buried doping profiles. For this we applied a recently published calibration procedure ([13]; see section 2). Figure 2 shows calibrated capacitance images for the flat doped Si sample covered with three different layers of Si oxide at 100 nm, 200 nm, and 400 nm thickness, respectively. Also, for comparison, the bare Si dopant sample with only the native oxide layer (i.e. 1–2 nm thick) is shown. The uncovered part of the Si sample was first measured in contact mode, and then in non-contact at three different heights above the sample (100 nm, 200 nm, 400 nm) (figure 2(a)). The oxide covered sample was measured in contact mode on each oxide layer (figure 2(a) below). Even though the fine dopant substructures are lost in both the non-contact mode and in the oxide sub-surface imaging mode, the overall dopant stripes and bulk interface layers can still be observed at 400 nm distance in air and on the 400 nm thick oxide, respectively. The highly doped areas show capacitances of up to 400 aF when the tip is in contact and around 15 aF when the tip is lifted 400 nm in air. Figure 2(b) shows averaged cross section profiles from each measured region in the capacitance image. The dielectric thickness variation is the same for both samples including an air and oxide thickness of 100 nm, 200 nm and 400 nm. The only discriminating factor is the dielectric constant of the insulator being air in the first case (εr,air = 1) and SiO2 (εr,SiO2 = 4) in the second case. Comparing the capacitance of the uncovered and the covered test samples at the same insulator thickness (figure 2(b)) it can be noticed that the capacitance values differ by approximately a factor of 4 being the permittivity ratio of the two dielectric materials εr,SiO2 /εr,air = 4. For instance, in figure 2(b), it can
3.1. Sub-surface imaging of a SiO2 covered doped Si sample
To explore the sub-surface imaging capabilities of the SMM we used a topographically flat Si test sample exhibiting various dopant stripes with increasing dopant density, from 1 × 1016 atoms cm−3 to 4 × 1019 atoms cm−3, intersected with bulk interface layers (1 × 1014 atoms cm−3). The dopant sample was partially covered with a layer of SiO2 having two different oxide thicknesses, 120 nm and 200 nm (figure 1). The partial SiO2 coverage was obtained by CVD oxide growth and subsequent focused ion beam milling and is clearly visible in the topographical images (figures 1(b) and (d)). The oxide thickness was verified using topography cross-section analysis. The surface of the doped Si sample is flat according to the topographical image (surface roughness less than 3 nm) and the doping pattern is only visible in the S11 images (figures 1(c) and (e)). Therefore, no cross-talk of the S11 image with the topography is obtained on those flat Si samples. The areas that are not covered with oxide show a strong S11 signal generated from the differently doped stripes. Even though the S11 signal is smaller on the oxide-covered areas, it can be noticed that the different dopant densities can still be detected both at 120 nm and 200 nm oxide coverage. In particular, the bulk interface layers that separate the individually doped areas can be clearly observed. However, very fine dopant differences within the second dopant stripe can only observed on the bare sample. These results confirm that the SMM can be used to electrically probe oxide buried structures as also shown by Plassard et al [10] for metallic samples and by Lai et al [9] on insulators. 4
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Figure 3. Calibrated SMM images of a 50 nm high SiO2 pad on a highly doped Si substrate measured in constant height mode (upper row) and lift mode (lower row). (a),(d) topographic 3D view of the oxide pad and the sketch of the measurement mode. (b),(e) Calibrated capacitance images measured in contact and at different distances as indicated in the images. Images have been flattened such that the bare Si substrate is ΔC = 0 aF. (c),(f) Average cross-section profiles extracted from the capacitance images showing the capacitance variation, ΔC. Topographic cross-talk was removed from lift-mode measurements. Images in lift mode were acquired with a smaller tip diameter (R ∼ 270 nm) compared to constant height images (R ∼ 1000 nm).
be noticed that the capacitance at 100 nm height in air overlaps with the capacitance at 400 nm SiO2. The factor of 4 resulting from εr,SiO2 /εr,air indicates that the measured capacitance depends on the ratio C ∼ εr h−1 and the higher is the tip–substrate distance the lower is the capacitance. Additionally, a scan in air was performed at 1000 nm distance from the substrate (purple dashed line in figure 2(b)) resulting in a flat capacitance signal, indicating that the SMM sensitivity limit was reached and the S11 signal was below the noise level of ∼1 aF. It can be noticed that the plateaus on the different dopant levels are not always perfectly horizontal due to a flattening artefact.
oxide topography contributes to the capacitance signal, we measured the capacitance both in constant distance from the plane Si substrate (constant-height mode) and constant distance from the overall oxide pad (lift-mode) as schematically shown in figures 3(a) and (d), respectively. Figure 3(b) shows the calibrated constant height capacitance image obtained after calibration of the measured S11 data. The upper part of the SiO2 pad is measured in contact (blue colour), then the tip is lifted to z = 500 nm from the substrate and scans a few lines. It is successively lowered as indicated in the image until it touches the sample again and returns into contact in the lower part of the oxide pad. To emphasize the effect of the scan height on the contrast, the image has been flattened setting the capacitance of the substrate to ΔC = 0 aF. Figure 3(c) shows the cross-section profiles taken from the capacitance image. The oxide shows positive contrast with respect to the substrate, because it has a higher dielectric constant and thus a higher capacitance than air. At the closest distance of z = 50 nm a signal difference of ΔC = 50 aF was measured. When the tip–sample distance is increased, the measured capacitance difference gets smaller, until it finally disappears at z = 500 nm reaching a value of 1 aF which is the current SMM noise level.
3.2. SMM lift-mode and constant-height imaging
While in the previous section a flat semiconductor substrate was studied, here we investigate how the capacitance changes at increasing distance in air above a fully dielectric sample with a topographic pattern. The dielectric material has an additional height above the substrate therefore lift-mode imaging is compared quantitatively to constant-height imaging. The sample is a thin dielectric pattern of SiO2 pads on a highly doped Si2+ substrate (see figure 3(a)). The oxide pads are 50 nm in height with a lateral size of 8 × 8 μm2. Since the 5
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(150 aF in figure 3(c)). It should be noted that the non-local topography-cross talk in figure 3(e) was removed by taking the topography image into account. The image has been also flattened setting the capacitance on the Si substrate to ΔC = 0 aF. With increasing lift height the contrast disappears rapidly and is almost completely lost at z = 100 nm. The liftmode capacitance images and cross-section profiles show that the SiO2 pad has inverted contrast with respect to the constant-height measurements. To understand this better, it is instructive to look at quantitative capacitance versus distance curves when approaching the tip to the Si2+ and to the SiO2 pad. 3.3. Quantitative approach curve analysis
Figure 4 shows calibrated capacitance approach curves on the oxide pad and the bare Si (Si2+) substrate from the sample shown in figure 3. For constant-height mode (figure 4(a)) the distance is denoted with respect to the flat Si2+ substrate and for lift-mode (figure 4(b)) with respect to the overall sample topography. This results essentially in a shift of the SiO2 approach curve of h = 50 nm along the z-axis, z’ = z + h. The approach curves are plotted for the smaller tip (R ∼ 270 nm) and the bigger tip (R ∼ 1000 nm). The bigger tip gives a higher signal difference between Si and SiO2, especially close to contact as observed also in the images in figure 3. Also the inversion of the contrast between constantheight mode and lift mode observed in figure 3 is obtained in the approach curves with the SiO2 curve in figure 4(a) above and in figure 4(b) below the Si curve. This again is an effect of the shift along the z-axis. On top of the contrast inversion, two practical differences between lift-mode and constantheight mode can be found when looking at the capacitance difference between the approach curves on the Si and the SiO2 as shown in figure 4(c). Firstly, in lift mode there is a constant offset in the difference signal (marked by the blue scattered line), because the capacitance from the non-local parts of the AFM tip (e.g. upper cone, cantilever) change nearly linearly when the tip– substrate distance is changed. This so-called topography cross-talk is an undesired artefact but plays only a significant role for small AFM tips and can also be subtracted from the measurements as done in figure 3 [13, 28]. In constant-height mode there is no topography cross-talk. Secondly, a capacitance contrast in lift mode can be only observed when the tip is relatively close to the surface and the contrast decreases for higher dielectric constants of the dielectric layer as shown in the inset of figure 4(c). In constant height mode a contrast can be observed also at higher distances, and it increases with higher dielectric constant. This is because the capacitance is a function of C(h ε−1 r ) in lift mode and C(h/εr−h) in constant height mode as described in [13] and also discussed in [28, 29]. Independently of acquiring an image in lift mode or constant height mode, in principle the same result for εr is expected. In summary, acquisition of capacitance images in constant height mode is experimentally more demanding than in lift mode, especially if the substrate is not completely flat.
Figure 4. Calibrated capacitance approach curves on the oxide pad
(black) and the bare silicon substrate (Si2+, red). (a) Constant height mode taking the Si substrate as reference distance; (b) lift mode taking the sample surface as reference distance. Curves are shown for small tips (Rapex ∼ 270 nm) and big tips (Rapex ∼ 1000 nm). (c) Difference of approach curves on Si and SiO2 (small tip) for lift and constant-height mode. Inset shows the theoretical difference curves for three dielectric constants, εr = 3,4,5. Calculations were done with equation (1) using the parameters Rapex = 270 nm, θ = 15° and h = 50 nm.
In figure 3(e) the same sample was measured in lift mode at increasing lift-height from the sample. Compared to the previous constant height measurement, a smaller tip size was used to achieve lower capacitance values that are closer to the SMM noise level. The tip–radius was determined using a quantitative approach-curve analysis as described in equation (1) of the section 2. A tip apex radius of R = 1000 nm and R = 270 nm for figures 3(b) and (d) was calculated, respectively. In figure 3(e) at z = 0 nm (i.e. contact mode) the smaller tip gives a capacitance contrast of 6 aF which is significantly lower than for the larger tip measurement 6
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Figure 5. Simulated lift-mode capacitance difference between 50 nm thick SiO2 (εr = 4) and the highly conductive Si2+ substrate (metallic
behaviour assumed). (a) ΔC as a function of the tip sample distance shown for two different tip radii (20 nm—blue and 1000 nm—red). The SMM noise level region (below 1 aF) is highlighted with a dark grey colour. Note the logarithmical scale in the vertical axis. The 2D colour map in the inset shows the dependence of ΔC on the tip radius and the tip sample distance. (b) Simulated model with obtained potential distribution with zoom of the tip/sample region.
However, capacitance images from constant height mode are easier to handle for quantification, since crosstalk does not have to be removed and thus the extraction of dielectric properties is straight forward.
selected such that the S11 signal is above the noise level at a given imaging speed and lift height. This guarantees that local capacitive and dielectric properties are measured and not just topography cross-talk. For example, a noise level of 4 aF can be achieved with a scan speed slower than 1 ms/pixel; under these conditions a lift height lower than 30 nm is required to still resolve a signal on the sample with a tip as small as R = 60 nm.
3.4. Sensitivity analysis by FEM
For an extended sensitivity analysis we used FEM to study how the capacitance and dielectric contrast depends on the two parameters tip radius and tip–sample distance (figure 5). The electric potential and capacitance were calculated for the specific tip sample geometry shown in figure 5(b) (see section 2). The modelled capacitance differences in figure 5(a) represent the difference between the capacitance above the oxide and the bare conductive substrate, similar to the experiments. The capacitance difference decays thereby monotonically with increasing distance similar to the experimental approach curves in figure 4. Note the logarithmical scale in the vertical axis. For a big tip of 1000 nm apex radius the signal difference even at large distances (e.g. 1000 nm) is well above the SMM noise level of 1 aF. For very small tips with e.g. 20 nm tip radius the difference in the contrast disappears at 300 nm distance. The experimental SMM noise level of 1 aF that is indicated here is for measuring at relatively low speed of 10 ms/pixel (0.4 line s−1, 256 pixels per line, 100 Hz intermediate frequency bandwidth filter of the VNA). For normal speed imaging the noise level is typically around 2 aF (2 ms/pixel) or 3 aF (1 ms/pixel). Based on the capacitance modelling, this means that very small tips do not provide enough electrical contrast to differentiate the SiO2 from the bare substrate when measuring at normal speed. The inset shows this dependency for a wider range of tip radii indicating also the different noise levels at different imaging speeds. In general the tip-size has to be
4. Conclusions and perspectives Sub-surface and non-contact SMM imaging of doped Si samples and nanoscale SiO2 structures has been presented in this work. Reflection S11 SMM images have been calibrated and converted to quantitative capacitance images. The sensitivity of the SMM capacitance images has been studied with respect to sub-surface material changes under different conditions including lift-mode and constant-height mode. An ntype doping staircase (1014–1019 atoms cm−3) Si sample covered with SiO2 (100–400 nm thick) resulted in capacitance images with differences of 10–75 aF depending on the oxide thickness. The same doping staircase Si structure was measured without SiO2 in constant height mode (100–400 nm tip– sample distance). The latter sample resulted in capacitance differences of up to 25 aF. With the current SMM noise level of 1 aF and the corresponding tip diameter the electrical sample properties could be clearly measured on oxides with more than 400 nm thickness at reduced lateral resolution though. A pattern of SiO2 pads has been measured in contact, lift and constant height mode. The best capacitance contrast due to local material differences can be obtained in contact or at low lift heights and with big AFM tips. With ∼1 μm tip diameter the local capacitance signal was lost when scanned 7
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applications in the field of semiconductor failure analysis studies including process optimizations for integrated chip fabrication. Figure 6 shows an example of sub-surface imaging on a semiconductor device using differential capacitance imaging. Backside wafer imaging was done on a thin wafer of Si in order to demonstrate non-invasive and non-destructive through-Si imaging of SRAM structures. The backside of a Si wafer was mechanically polished down to a thickness ranging from 50 nm to 450 nm and imaged with the SMM in differential dC/dV capacitance mode [17] as shown in the sketch in figure 6(a). The active device region is thus beneath 50 nm– 450 nm of doped Si. The SRAM structure, which is on the opposite side of the tip–sample contact, could be imaged through the wafer with a thickness of 50 nm (figure 6(b)), 200 nm (figure 6(c)), and up to 450 nm (figure 6(d)). On a wafer thickness of more than 450 nm no dC/dV signal was detected anymore due to the noise limit of the SMM. In the future, the calibration and workflow procedures presented in this paper will be applied to more advanced sample designs in semiconductor failure analysis as well as for the imaging of bio-cell interiors.
Acknowledgments The authors would like to thank J Smoliner from TU Vienna (Austria); L Fumagalli and G Gomila from IBEC (Spain); M Moertelmaier, M Richter and H Tanbakuchi from Keysight Technologies for helpful technical discussions. This work has been supported by the EU-FP7 (NMP-2011-280516, VSMMART-Nano, and PEOPLE-2012-ITN-317116, Nanomicrowave).
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Figure 6. Sub-surface imaging applied to semiconductor wafer
devices. (a) Semiconductor device structures (SRAM) were imaged at the backside of the silicon wafer at three different thicknesses including (b) 50 nm, (c) 200 nm and (d) 450 nm. The left panel shows the topographical images and the right panel shows the differential capacitance images (dS11/dV amplitude).
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