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De-embedding techniques for nanoscale characterization of semiconductors by scanning microwave microscopy
Microelectronic Engineering 159 (2016) 64–69
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De-embedding techniques for nanoscale characterization of semiconductors by scanning microwave microscopy L. Michalas a,⁎, E. Brinciotti b, A. Lucibello a, G. Gramse c, C.H. Joseph a, F. Kienberger b, E. Proietti a, R. Marcelli a a b c
National Research Council, Institute for Microelectronics and Microsystems, (CNR-IMM), Via del Fosso del Cavaliere 100, 00133 Rome, Italy Keysight Technologies Austria GmbH, Gruberstrasse 40, 4020 Linz, Austria Johannes Kepler University, Biophysics Institute, Gruberstrasse 40, 4020 Linz, Austria
a r t i c l e
i n f o
Article history: Received 23 October 2015 Received in revised form 5 February 2016 Accepted 20 February 2016 Available online 26 February 2016 Keywords: SMM De-embedding Nanoscale Semiconductors
a b s t r a c t The paper presents a methodology for de-embedding scanning microwave microscopy (SMM) measurements, mainly for semiconductor characterization. Analytical modeling, a parametric study and experimental verification are presented. The proposed methodology is based on the analysis of system response in the linear scale, instead of the dB scale commonly utilized in RF measurements, and on expressing the standard calibration capacitances per unit area. In this way the total measured capacitance is determined by the tip area which is then obtained as a result of the model fitting on the experimental data. Additional evaluation is performed by a straightforward experimental comparison with the usually adopted technique that is based on the electrostatic force microscopy approach curve method. The results obtained by the application of both techniques on the same tip during the same experiment were found to be in good agreement and moreover allowed a detailed discussion on the features of each one of the two methodologies. The paper provides also in this way useful knowledge for the potential users in order to choose the most appropriate technique according to the corresponding SMM application. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Scanning microwave microscopy (SMM) is an experimental technique that aims to provide nanoscale level characterization and imaging offering simultaneously high resolution and high sensitivity measurements. This is achieved by applying a microwave signal, provided by a Vector Network Analyzer (VNA), to the device under investigation, through a tip [1–5]. In particular a relatively novel setup utilizes an Atomic Force Microscope (AFM) with a modified nosecone, using also a specially manufactured AFM/SMM tip, able to support microwave propagation up to its apex. The tip/sample system response on the incident microwave signal is also recorded by the VNA, providing in this way precise characterization arising from the combination of the VNA sensitivity with the AFM lateral resolution. The demand for high sensitivity in SMM measurements is obtained by the proper matching of the high impedance tip/sample system with the VNA instrumentation requirements [6]. This can be achieved either by using an interferometric setup [7] or more commonly, as in the case presented below, implementing a shunt resistor and a resonator [8]. Both techniques demonstrated their ability to provide sub-fF sensitivity [7,8].
⁎ Corresponding author. E-mail address: [email protected] (L. Michalas).
http://dx.doi.org/10.1016/j.mee.2016.02.039 0167-9317/© 2016 Elsevier B.V. All rights reserved.
Regarding the lateral resolution of SMM, this is determined by the AFM tip apex dimensions and therefore is considered to be in the nanoscale. However besides that it should be noted that the accurate determination of the experimental lateral resolution of SMM measurements is not a trivial task. This is because in SMM beyond the contact point, there is also a microwave signal propagated through the tip. Accordingly the local tip/sample interaction may be determined, apart from the geometrical tip dimension, also by the presence of fringing fields around the edge of the tip. Moreover in most solid-state applications the AFM tip works in contact mode, therefore it is expected to gradually be deformed from its nominal shape. For these reasons the application of de-embedding methodologies on the experimental data is a critical step towards the enhancement of the SMM accuracy. Up to date, SMM signals are mainly de-embedded based on the application of the electrostatic force microscopy (EFM) approach curve method [9]. Alternatively a new methodology recently demonstrated that, by using the dopant profile calibration procedure obtained by the correlation of the amplitude of S11 to the MOS system capacitance [10], de-embedding can also be achieved by modeling the SMM system response in the linear scale and implementing the concept of effective scanned area [11]; however beyond this preliminary study no further information is presently available in literature. The present paper aims to present in details this new approach including the analytical modeling of the experimental setup with a parametric study. Also for the first time a straightforward experimental
L. Michalas et al. / Microelectronic Engineering 159 (2016) 64–69
comparison between the two methodologies is presented. For this, both techniques have been applied within the same experiment, first on a new tip, and then on the same tip after purposely enlarged. Beyond these novel experimental data and based on the results extracted by the corresponding analysis, the features of each method are also discussed in details. 2. Background knowledge in brief 2.1. The EFM approach curve method Estimation of the tip apex radius by the electrostatic force microscopy approach curve method is obtained [9] by fitting the capacitance acquired as a function of the tip to sample distance at a certain point. The total capacitance is considered to consist of three terms corresponding to the various parts of the cantilever, therefore C ¼ Capex þ Ccone þ CStray :
ð1Þ
The first term, Capex, corresponds to the apex of the AFM tip and is given by Capex ¼ 2πε0 rln
h þ εr z : h þ εr ðr þ zÞ εr rsinθ
ð2Þ
The second comes from the contribution of the truncated cone part of the tip and is equal to 1 ! 2πε 0 h z ln H þ z þ r ð 1 sinθ Þ 2 εr ln tan 2θ h h þ r 1 sinθ1 ln εr þ z þ r ð1 sinθÞ : εr εr
ð
Ccone ¼
ð3Þ
Þ
CStray ¼ cStray z þ const
constant, T the absolute temperature, q the fundamental charge quantity and ND and ni the doping level and the intrinsic carrier concentration, respectively. Based on this the total capacitance can be defined as C = (area) × CMOS. 3. The proposed methodology The major features of the proposed methodology are two: expressing the standard capacitances per unit area and modeling the SMM setup using a circuital approach to analyze the system response in the linear scale, instead of the dB scale, commonly utilized in RF measurements. The total measured capacitance has been determined by the tip area. This is obtained by fitting the experimental results and therefore consists in an experimental estimation. The implementation of the linear scale for the assessment of S11 amplitude allows the straightforward extraction of important parameters from the experimental results as presented below, therefore it is an important step towards deembedding. In contact mode, the SMM setup can be modeled using a circuital approach, in particular, for semiconductor samples, and for thin tips, where the tip/sample impedance is determined mainly by capacitive contribution. Under this condition the system is usually modeled as a properly terminated shunt capacitor (Fig. 1) [13,14]. Considering the quasi-static and localized nature of the dominant effects in the frequency range of 1–20 GHz, but also the design of the SMM setup, this aims to maintain the traveling of the waves through the different components by means of transmission lines, such an assumption can be adopted for our experimental procedure especially working at frequencies very close to the resonance frequencies (matched condition) provided by the λ/2 resonator, utilized to increase sensitivity. Under these conditions, which represent the actual SMM operation, the reflection coefficient (expressed in the linear scale) measured by the VNA is Γ ¼ S11 ¼
The last term, CStray, from the cantilever can be defined as
65
ZL Z0 iωCZ 0 2iωCZ 0 þ ðωCZ 0 Þ2 ¼ ¼ : Z L þ Z 0 2 þ iωCZ 0 4 þ ðωCZ 0 Þ2
ð7Þ
ð4Þ So the reflection coefficient amplitude is expressed as
In the above equation r is the apex radius, H is the cone height, θ is the cone angle, z the tip to sample distance, h the dielectric thickness and ε0 and εr the vacuum and dielectric permittivity respectively. 2.2. The MOS system capacitance The methodology presented in the following section is based on the recording of the reflection coefficient for the microwave propagation, S11 on a silicon calibration sample with dopant profile. Such a sample is covered by native oxide and in contact with the metallic SMM tip on top, forms a Metal Oxide Semiconductor (MOS) capacitor. Therefore the standard capacitances used for the calibration procedure are based on the MOS system capacitance versus doping. For a MOS capacitor, working in the inversion regime the capacitance per unit area for the different doping levels can be quite accurately calculated by the following equation [12]. CMOS ¼
εox εox W εsem
dox þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2 u u ðωCZ 0 Þ2 2ωCZ 0 t : þ jS11 j ¼ 4 þ ðωCZ 0 Þ2 4 þ ðωCZ 0 Þ2
In the above equation ZL and Z0 are the load and characteristic impedance, in our case Z0 is 50 Ω, C is the reflected capacitance and ω = 2πf with f being the SMM operation frequency. The SMM capacitances formed by the nanometer scale tip and the semiconducting samples are in the order of fF or even less. Moreover SMM operates between 1 and 20 GHz, where the second order terms are expected to have minor contribution. Therefore, the amplitude of S11 is determined by the second term inside the square root of Eq. (8). In this case a linear relation between the measured amplitude and the reflective capacitance is expected. A parametric study presenting the relation between │S11│and C at different frequencies (under matched
ð5Þ
where W is the depletion layer width in inversion condition defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ND u u4εsem KTln t ni : W¼ q2 ND
ð6Þ
In the above equations εox and εsem are the oxide and silicon dielectric permittivity respectively, dox the oxide thickness, K the Boltzmann
ð8Þ
Fig. 1. Simplified schematic of the resistor/resonator SMM setup.
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condition) is presented below in Fig. 2(a). Fig. 2(b) presents in more details about the obtained relation at 20 GHz i.e. near the frequency of our experiment, while the inset graph is a close look on the region of linear behavior of the amplitude of S11, presenting excellent fitting results. Finally, Fig. 2(c) draws the limits of the validity of the linear relation between │S11│and C as a function of the operating frequency. From Fig. 2, two are the major features that should be noted. There is always a regime where a linear relation between those two parameters holds, i.e. the first term in Eq. (8) is negligible, and the sensitivity increases with the operation frequency.
In the region of linear behavior, │S11│can be written in more details as jS11 j ¼
ωCZ 0 : 2
ð9Þ
In the above equation C is the total capacitance that is detected by the cantilever. Therefore C ¼ C Tip þ C Stray C Top :
ð10Þ
The first term in the above equation, CTip, is the capacitance formed by the tip apex and the sample under investigation. In our case, the calibration sample has a silicon substrate with dopant staircase structure, covered by native oxide. The tip/sample system forms a MOS capacitor for which the total capacitance is C Tip ¼ ðeffective areaÞ CMOS :
ð11Þ
The effective area is the equivalent area of interaction, thus the experimental resolution and is related to the tip effective radius reff as (effective area) = πr2eff. The second term, CStray, represents the contribution of the parallel stray capacitances generated by the parasitic couplings of the cantilever chip with the surroundings. Finally, the term, CTop, is an additional term that includes the local contribution of the topography on the total detected capacitance. The term should be assessed point-wise and can be considered as negligible when working with flat samples, as in our case. Note that SMM provides this capability because may acquire simultaneously point-wise topography and microwave parameters measurements. The last term should be included when the equation proposed below is used as a calibration line to assess an unknown sample. In this case the last term will match the topography differences between the flat calibration sample and the unknown device. Incorporating Eqs. (10) and (11) into Eq. (9) the final form is obtained as
jS11 j ¼ ðÞ
ωZ 0 πr 2eff 2
CMOS þ
ωZ 0 C Stray : 2
ð12Þ
This means that working in the regime presented in Fig. 2(c), and by recording the amplitude of S11 at areas with different doping, a linear relation of the form Eq. (12) is expected between the |S11| measured in the linear scale and CMOS, expressed as F/cm2. In such a plot the slope may provide the effective area/radius of the tip and the intercept the stay capacitances. The term (±) is included to express the fact that depending on the relative position of the chosen frequency with respect to the resonance the obtained slope may be positive or negative. As already discussed the last term can be neglected in our case. 4. Experimental
Fig. 2. (a) Parametric study versus operation frequency for dependence between │S11│and the reflective capacitance. (b) Detailed presentation at f = 20 GHz. (c) Region of linear behavior of the amplitude of S11.
The SMM experimental setup consists of a Keysight 5600LS Atomic Force Microscope interfaced with a Keysight E8362B Vector Network Analyzer. Commercially available platinum tips especially designed for SMM measurements (i.e. Rocky Mountain Nanotechnology 25Pt300B) have been used. The nominal spring constant of the probes is 18 N/m, the cone height H is 80 μm and the cone angle θ is 15° [15]. A 50 Ω shunt resistor and a resonator are also integrated in the SMM system to match the high impedance of the tip/sample interface to the characteristic impedance of the microwave instrumentation, increasing in this way the sensitivity. Before scanning the sample, the SMM tip is in contact with the DUT, and a VNA frequency sweep is performed from 1 to 20 GHz. Multiple resonance frequencies are obtained by using a resonator. Then, although the method can be in principle applied at any
L. Michalas et al. / Microelectronic Engineering 159 (2016) 64–69
frequency, a notch close to the maximum frequency selected as depicted by the above presented parametric study in order obtained the maximum sensitivity. The exact frequency was chosen based on the best imaging and impedance responses for the measurements to be performed. The measurements have been performed twice. Both de-embedding workflows were applied first using a new tip. Then, the tip was purposely enlarged and both calibration techniques re-applied in order to check their ability to identify the change in the tip radius but also to better understand their features to be discussed later. For the proposed methodology, a calibration sample is required. An n-type silicon sample with native oxide on top that consists of four areas of accurately defined doping levels has been used. The calibration sample was fabricated and provided to us by Prof. J. Smoliner of the T.U. of Vienna and it is a sample already utilized successfully in previously published SMM studies. The doping levels in the four stripes are 1016 cm− 3, 8 × 1017 cm−3, 1.5 × 1018 cm−3 and 3 × 1019 cm− 3. At the left end of the calibration sample (Fig. 3) there is the area named as “bulk” having very low level of doping (5 × 1014 cm−3)) not implemented in the calibration study. Regarding the native oxide thickness on top, this has been reported to saturate around 1 nm (depending on Si material properties and environmental details [16]), and therefore, considering also that any variation in the order of 1–2 Å, may cause negligible changes in the inversion capacitance (Eq. 5), in the present study it is considered as 1 nm thick. 5. Results and discussion For the experimental application of the proposed methodology and for the comparative study to be performed, initially a new tip is placed in the nosecone. The SMM tip is then approached to contact with the sample. After having performed a sweep between 1 and 20 GHz, a notch and a frequency close to the resonance are selected for the following experimental procedure to take place. In our case the frequency was fixed at 19.06 GHz.
Fig. 3. (a) SMM imaging of the calibration sample presented in filtered color scale for enhanced relative contrast. The bulk area and the four stripes having doping levels 5 × 1014 cm−3 and 1016 cm−3, 8 × 1017 cm−3, 1.5 × 1018 cm−3 and 3 × 1019 cm−3 respectively are clearly visible. (b) SMM absolute measured amplitudes on the calibration sample. Presentation using the same color scale that allows the straightforward comparison between the new and the used tip.
67
Keeping the selected frequency fixed, the sample is scanned and the reflection coefficient, S11, is recorded point by point. In order for the proposed methodology to be applied the formed MOS capacitor should be in the inversion condition. Such a condition for a MOS system is defined by the type of metal tip, by the properties of semiconductor but also by the properties of the oxide/semiconductor interface as well as by possible charging of the native oxide. For this a DC bias may be required to be applied through the tip. In our case the system was found to be inverted at 0 V. This allowed extensive scanning of the sample without charging the native oxide. After the end of the first scan, an electrostatic approach curve is performed. The tip apex radius is then enlarged by letting the system scan the sample with a high setpoint (i.e. 2.5 V). After few hours, a new S11 image and a new EFM approach curve are then acquired. A typical SMM imaging obtained on the calibration sample is presented, using a filtered scale, relatively colored for enhanced contrast, in Fig. 3(a). In this way the four areas of different doping levels are clearly visible as well as the small not intentionally doped areas between them. At the left edge there is also the low level doping entitled “bulk” that is not involved in the following analysis. Moreover the obtained results for the two scans are presented using the absolute measured values of S11 amplitude, in a merge picture in Fig. 3(b). The same color scale is applied for both scans and so the changes between the new and the used tip to be clearly visible. The proposed methodology has been applied in both areas and the lines have been obtained by the linear fitting procedure, using Eq. (12) on the experimental data presented in Fig. 4. A clear increase in the slope (in absolute values) is obtained, denoting the enlargement of the area of interaction, and thus of the tip radius according to Eq. (12). In addition, it is worth to notice that the intercept remained practically unchanged, thus suggesting that during the experimental procedure no significant changes on the stray capacitance have occurred. This is an additional validation of the reliability of the experimental procedure. The tip radius values that have been calculated for the new and the used tip are 65 nm and 100 nm, respectively. The stray capacitance obtained from the intercept is 1.5 fF. These calculated values cross confirmed that the experiments are in the regime where the linear relation Eq. (9) according to Fig. 2(c) is valid, a fact also supported by the very good fitting results presented in Fig. 4. In the EFM approach curve method a nonlinear fitting procedure is applied, the results are presented in Fig. 5. For enhanced accuracy these measurements were performed on the heavily doped stripe [9]. Compared to the proposed methods, higher values for the capacitance in the case of the used tip are obtained with the EFM method. This is something aligned with respect to what was predicted by the corresponding Eqs. (1) to (4). The results in this case lead to values of 65 nm and 150 nm for the new and the used tip respectively.
Fig. 4. Fitting procedure of the proposed model on the experimental data.
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L. Michalas et al. / Microelectronic Engineering 159 (2016) 64–69
The proposed analysis is based on the assessment of the SMM system response in the linear scale and the use of the standard capacitances that arise by a dopant profiling sample, expressed per area. In this way by the implementation of the appropriate modeling the effective tip radius is experimentally estimated. Furthermore the methodology is experimentally evaluated by a straightforward comparison with an electrostatic force microscopy based calibration method. Both techniques have been applied during the same experimental procedure on the same tip that has been gradually deformed. In addition, based on the obtained results the features of each methodology are also discussed in details. The paper provides a full picture of the up to date available experimental techniques for de-embedding SMM measurements. Considering the broad area of SMM applications, the present study provides a very useful tool for the potential users in order to choose the most appropriate technique according to the application of interest. Acknowledgment Fig. 5. Fitting procedure of the approach curve method on the experimental data.
Interestingly, both techniques provide the same value for the new tip, while a small variation is observed in the case of the used tip. This is because the techniques are based on two different approximations. The approach curve method relies on the preservation of a specific shape of the SMM tip, while the new methodology is based on an equivalent area. For a new tip the approximations are found to be in agreement. Based on the presented analysis as well as on the experimentally obtained results it is thus possible to draw some conclusion on the major features of each one of the two methodologies. The EFM approach curve method may be in principle applied on different types of samples under investigation and allows an estimation of the tip radius without the use of a calibration standard. Therefore, it may provide useful for SMM studies on applications beyond semiconductors e.g. on biological samples [17]. The accuracy of the technique is even more valuable in case of non-contact SMM measurements where the tip shape remain unchanged and is practically the nominal one. The methodology introduced in the present paper has the big advantage of being accurate for contact-mode measurements even when the tip shape is modified during the scan. For semiconductor materials and device characterization, this is extremely important. By taking into account the tip/sample interactions, it allows a straightforward estimation of the effective tip radius, which is the actual SMM experimental resolution. This means that effective areas may be different than the geometrical ones, since they incorporate also the interaction that arises by the contribution of fringing fields around the tip edge. Such fringing fields are determined by several experimental parameters and elements, (i) the tip detailed shape, if it is conic or pyramidal, (ii) possibly the tip to sample inclination angle [18], (iii) the nature of the material under investigation, (iv) the presence of water meniscus due to humidity around the tip edge [19] and/or (v) the presence of DC bias on the tip [20]. It should be noted that the calculation of the effective area is coming out from the analysis of the experimental results and does not require the knowledge of geometrical details of the tip. Therefore, it properly works even in cases where the tip shape is not any more strictly cylinder or conic or anything else easily defined. Note that in cases of deformed tip shape [21] and of not easily defined dimensions, it is very difficult to apply any modeling to calculate accurately the area of interaction. Finally, it is worth to point out that the methodology allows the calibration and de-embedding of SMM data on the exact frequency of the experimental procedure and therefore can incorporate any frequency dependent behavior of the material or device under investigation. 6. Conclusions A methodology for de-embedding scanning microwave microscopy measurements, mainly for semiconductor characterization, is presented.
The authors wish to acknowledge the support from EC by means of “Marie Curie” fellowship in the framework of PEOPLE-2012-ITN project: Microwave Nanotechnology for Semiconductor and Life Science -NANOMICROWAVE, under GA:317116. The authors wish also to acknowledge Prof. J. Smoliner from TU Vienna who fabricated and provided us the calibration standard for the experimental procedure. References [1] D.E. Steinhauer, C.P. Vlahacos, S.K. Dutta, F.C. Wellstood, Steven M. Anlage, Surface resistance imaging with a scanning near-field microwave microscope, Appl. Phys. Lett. 71 (1997) 1736, http://dx.doi.org/10.1063/1.120020. [2] M. Tabib-Azar, D.-P. Su, A. Pohar, S.R. LeClair, G. Ponchak, 0.4 μm spatial resolution with 1 GHz (λ = 30 cm) evanescent microwave probe, Rev. Sci. Instrum. 70 (1999) 1725, http://dx.doi.org/10.1063/1.1149658. [3] C. Gao, B. Hu, P. Zhang, M. Huang, W. Liu, I. Takeuchi, Quantitative microwave evanescent microscopy of dielectric thin films using a recursive image charge approach, Appl. Phys. Lett. 84 (2004) 4647, http://dx.doi.org/10.1063/1.1759389. [4] A. Tselev, S.M. Anlage, Z. Ma, J. Melngailis, Broadband dielectric microwave microscopy on micron length scales, Rev. Sci. Instrum. 78 (2007) 044701, http://dx.doi.org/ 10.1063/1.2719613. [5] M. Farina, D. Mencarelli, A. Di Donato, G. Venanzoni, A. Morini, Calibration Protocol for broadband near-field microwave microscopy, IEEE Trans. Microwave Theory Tech. 59 (2011) 2769, http://dx.doi.org/10.1109/TMTT.2011.2161328. [6] H. Happy, K. Haddadi, D. Theron, T. Larsi, G. Dambrine, Measurement techniques for RF nanoelectronics devices, IEEE Microw. Mag. 15 (2014) 30–39, http://dx.doi.org/ 10.1109/MMM.2013.2288710. [7] T. Dargent, K. Haddadi, T. Lasri, N. Clément, D. Ducatteau, B. Legrand, H. Tanbakuchi, D. Theron, An intereforemtric scanning microwave microscope and calibration method for sub-fF microwave measurements, Rev. Sci. Instrum. 84 (2013) 123705, http://dx.doi.org/10.1063/1.4848995. [8] H.P. Huber, M. Moertelmeier, T.M. Wallis, C.J. Chiang, M. Hochleitner, A. Imtiaz, Y.J. Oh, K. Schilcher, M. Dieudonne, J. Smoliner, P. Hinterdorfer, S.J. Rosner, H. Tanbakuchi, P. Kabos, F. Kienberger, Calibrated nanoscale capacitance measurements using scanning microwave microscopy, Rev. Sci. Instrum. 81 (2010) 113701, http://dx.doi.org/10.1063/1.3491926. [9] G. Gramse, M. Kasper, L. Fumagalli, G. Gomila, P. Hinterdorfer, F. Kienberger, Calibrated complex impendance and permittivity measurements with scanning microwave microscopy, Nanotechnology 25 (2014) 145703, http://dx.doi.org/10.1088/ 0957-4484/25/14/145703. [10] L. Michalas, A. Lucibello, C.H. Joseph, E. Brinciotti, F. Kienberger, E. Proietti, R. Marcelli, Nanoscale characterization of MOS systems by microwaves: Dopant profiling calibration, in: IEEE (Ed.), Proceedings of EUROSOI-ULIS 2015, Joint International EUROSOI Workshop and International Conference of Ultimate Integration in Silicon, Bologna, Italy, 26–28 January 2015 2015, pp. 269–272, http://dx.doi.org/10.1109/ ULIS.2015.7063825. [11] L. Michalas, A. Lucibello, G. Badino, C.H. Joseph, E. Brinciotti, F. Kienberger, E. Proietti, R. Marcelli, Scanning microwave microscopy for nanoscale characterization of semiconductors: de-embedding reflection contact mode measurements, in: IEEE-EuMA (Ed.), Proceedings of 45th EuMW, European Microwave Conference, Paris, France 5–11 September 2015 2015, pp. 159–162, http://dx.doi.org/10.13140/RG.2.1.2050. 3520. [12] S.M. Sze, Physics of Semiconductor Device, John Wiley & Sons, NY, 1981. [13] J. Smoliner, H.P. Huber, M. Hochleitner, M. Moertelmaier, F. Kienberger, Scanning microwave microscopy/spectroscopy for metal-oxide-semiconductor systems, J. Appl. Phys. 108 (2010) 064315, http://dx.doi.org/10.1063/1.3482065. [14] K. Torigoe, M. Arita, T. Motooka, Sensitivity analysis of microwave microscopy for nano scale dopant measurements in Si, J. Appl. Phys. 112 (2012) 104325, http:// dx.doi.org/10.1063/1.4765730.
L. Michalas et al. / Microelectronic Engineering 159 (2016) 64–69 [15] See Rmnano.com for information about AFM/SMM tips. [16] N. Morita, T. Ohmi, E. Hasegawa, M. Kawakami, M. Ohwada, Growth of native oxide on a silicon surface, J. Appl. Phys. 68 (1990) 1272, http://dx.doi.org/10.1063/1. 347181. [17] Y.J. Oh, H.P. Huber, M. Hochleitner, M. Duman, B. Bozna, M. Kastner, F. Kienberger, P. Hinterdorfer, High-frequency electromagnetic dynamics properties of THP1 cell using scanning microwave microscopy, Ultramicroscopy 111 (2011) 1625–1629, http://dx.doi.org/10.1016/j.ultramic.2011.09.005. [18] A.O. Oladipo, M. Kasper, S. Lavdas, G. Gramse, F. Kienberger, N.C. Panoiu, Threedimensional finite-element simulations of scanning microwave microscope cantilever for imaging at the nanoscale, Appl. Phys. Lett. 103 (2013) 213106, http://dx.doi. org/10.1063/1.4832456.
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Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
De-embedding techniques for nanoscale characterization of semiconductors by scanning microwave microscopy L. Michalas a,⁎, E. Brinciotti b, A. Lucibello a, G. Gramse c, C.H. Joseph a, F. Kienberger b, E. Proietti a, R. Marcelli a a b c
National Research Council, Institute for Microelectronics and Microsystems, (CNR-IMM), Via del Fosso del Cavaliere 100, 00133 Rome, Italy Keysight Technologies Austria GmbH, Gruberstrasse 40, 4020 Linz, Austria Johannes Kepler University, Biophysics Institute, Gruberstrasse 40, 4020 Linz, Austria
a r t i c l e
i n f o
Article history: Received 23 October 2015 Received in revised form 5 February 2016 Accepted 20 February 2016 Available online 26 February 2016 Keywords: SMM De-embedding Nanoscale Semiconductors
a b s t r a c t The paper presents a methodology for de-embedding scanning microwave microscopy (SMM) measurements, mainly for semiconductor characterization. Analytical modeling, a parametric study and experimental verification are presented. The proposed methodology is based on the analysis of system response in the linear scale, instead of the dB scale commonly utilized in RF measurements, and on expressing the standard calibration capacitances per unit area. In this way the total measured capacitance is determined by the tip area which is then obtained as a result of the model fitting on the experimental data. Additional evaluation is performed by a straightforward experimental comparison with the usually adopted technique that is based on the electrostatic force microscopy approach curve method. The results obtained by the application of both techniques on the same tip during the same experiment were found to be in good agreement and moreover allowed a detailed discussion on the features of each one of the two methodologies. The paper provides also in this way useful knowledge for the potential users in order to choose the most appropriate technique according to the corresponding SMM application. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Scanning microwave microscopy (SMM) is an experimental technique that aims to provide nanoscale level characterization and imaging offering simultaneously high resolution and high sensitivity measurements. This is achieved by applying a microwave signal, provided by a Vector Network Analyzer (VNA), to the device under investigation, through a tip [1–5]. In particular a relatively novel setup utilizes an Atomic Force Microscope (AFM) with a modified nosecone, using also a specially manufactured AFM/SMM tip, able to support microwave propagation up to its apex. The tip/sample system response on the incident microwave signal is also recorded by the VNA, providing in this way precise characterization arising from the combination of the VNA sensitivity with the AFM lateral resolution. The demand for high sensitivity in SMM measurements is obtained by the proper matching of the high impedance tip/sample system with the VNA instrumentation requirements [6]. This can be achieved either by using an interferometric setup [7] or more commonly, as in the case presented below, implementing a shunt resistor and a resonator [8]. Both techniques demonstrated their ability to provide sub-fF sensitivity [7,8].
⁎ Corresponding author. E-mail address: [email protected] (L. Michalas).
http://dx.doi.org/10.1016/j.mee.2016.02.039 0167-9317/© 2016 Elsevier B.V. All rights reserved.
Regarding the lateral resolution of SMM, this is determined by the AFM tip apex dimensions and therefore is considered to be in the nanoscale. However besides that it should be noted that the accurate determination of the experimental lateral resolution of SMM measurements is not a trivial task. This is because in SMM beyond the contact point, there is also a microwave signal propagated through the tip. Accordingly the local tip/sample interaction may be determined, apart from the geometrical tip dimension, also by the presence of fringing fields around the edge of the tip. Moreover in most solid-state applications the AFM tip works in contact mode, therefore it is expected to gradually be deformed from its nominal shape. For these reasons the application of de-embedding methodologies on the experimental data is a critical step towards the enhancement of the SMM accuracy. Up to date, SMM signals are mainly de-embedded based on the application of the electrostatic force microscopy (EFM) approach curve method [9]. Alternatively a new methodology recently demonstrated that, by using the dopant profile calibration procedure obtained by the correlation of the amplitude of S11 to the MOS system capacitance [10], de-embedding can also be achieved by modeling the SMM system response in the linear scale and implementing the concept of effective scanned area [11]; however beyond this preliminary study no further information is presently available in literature. The present paper aims to present in details this new approach including the analytical modeling of the experimental setup with a parametric study. Also for the first time a straightforward experimental
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comparison between the two methodologies is presented. For this, both techniques have been applied within the same experiment, first on a new tip, and then on the same tip after purposely enlarged. Beyond these novel experimental data and based on the results extracted by the corresponding analysis, the features of each method are also discussed in details. 2. Background knowledge in brief 2.1. The EFM approach curve method Estimation of the tip apex radius by the electrostatic force microscopy approach curve method is obtained [9] by fitting the capacitance acquired as a function of the tip to sample distance at a certain point. The total capacitance is considered to consist of three terms corresponding to the various parts of the cantilever, therefore C ¼ Capex þ Ccone þ CStray :
ð1Þ
The first term, Capex, corresponds to the apex of the AFM tip and is given by Capex ¼ 2πε0 rln
h þ εr z : h þ εr ðr þ zÞ εr rsinθ
ð2Þ
The second comes from the contribution of the truncated cone part of the tip and is equal to 1 ! 2πε 0 h z ln H þ z þ r ð 1 sinθ Þ 2 εr ln tan 2θ h h þ r 1 sinθ1 ln εr þ z þ r ð1 sinθÞ : εr εr
ð
Ccone ¼
ð3Þ
Þ
CStray ¼ cStray z þ const
constant, T the absolute temperature, q the fundamental charge quantity and ND and ni the doping level and the intrinsic carrier concentration, respectively. Based on this the total capacitance can be defined as C = (area) × CMOS. 3. The proposed methodology The major features of the proposed methodology are two: expressing the standard capacitances per unit area and modeling the SMM setup using a circuital approach to analyze the system response in the linear scale, instead of the dB scale, commonly utilized in RF measurements. The total measured capacitance has been determined by the tip area. This is obtained by fitting the experimental results and therefore consists in an experimental estimation. The implementation of the linear scale for the assessment of S11 amplitude allows the straightforward extraction of important parameters from the experimental results as presented below, therefore it is an important step towards deembedding. In contact mode, the SMM setup can be modeled using a circuital approach, in particular, for semiconductor samples, and for thin tips, where the tip/sample impedance is determined mainly by capacitive contribution. Under this condition the system is usually modeled as a properly terminated shunt capacitor (Fig. 1) [13,14]. Considering the quasi-static and localized nature of the dominant effects in the frequency range of 1–20 GHz, but also the design of the SMM setup, this aims to maintain the traveling of the waves through the different components by means of transmission lines, such an assumption can be adopted for our experimental procedure especially working at frequencies very close to the resonance frequencies (matched condition) provided by the λ/2 resonator, utilized to increase sensitivity. Under these conditions, which represent the actual SMM operation, the reflection coefficient (expressed in the linear scale) measured by the VNA is Γ ¼ S11 ¼
The last term, CStray, from the cantilever can be defined as
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ZL Z0 iωCZ 0 2iωCZ 0 þ ðωCZ 0 Þ2 ¼ ¼ : Z L þ Z 0 2 þ iωCZ 0 4 þ ðωCZ 0 Þ2
ð7Þ
ð4Þ So the reflection coefficient amplitude is expressed as
In the above equation r is the apex radius, H is the cone height, θ is the cone angle, z the tip to sample distance, h the dielectric thickness and ε0 and εr the vacuum and dielectric permittivity respectively. 2.2. The MOS system capacitance The methodology presented in the following section is based on the recording of the reflection coefficient for the microwave propagation, S11 on a silicon calibration sample with dopant profile. Such a sample is covered by native oxide and in contact with the metallic SMM tip on top, forms a Metal Oxide Semiconductor (MOS) capacitor. Therefore the standard capacitances used for the calibration procedure are based on the MOS system capacitance versus doping. For a MOS capacitor, working in the inversion regime the capacitance per unit area for the different doping levels can be quite accurately calculated by the following equation [12]. CMOS ¼
εox εox W εsem
dox þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2 u u ðωCZ 0 Þ2 2ωCZ 0 t : þ jS11 j ¼ 4 þ ðωCZ 0 Þ2 4 þ ðωCZ 0 Þ2
In the above equation ZL and Z0 are the load and characteristic impedance, in our case Z0 is 50 Ω, C is the reflected capacitance and ω = 2πf with f being the SMM operation frequency. The SMM capacitances formed by the nanometer scale tip and the semiconducting samples are in the order of fF or even less. Moreover SMM operates between 1 and 20 GHz, where the second order terms are expected to have minor contribution. Therefore, the amplitude of S11 is determined by the second term inside the square root of Eq. (8). In this case a linear relation between the measured amplitude and the reflective capacitance is expected. A parametric study presenting the relation between │S11│and C at different frequencies (under matched
ð5Þ
where W is the depletion layer width in inversion condition defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ND u u4εsem KTln t ni : W¼ q2 ND
ð6Þ
In the above equations εox and εsem are the oxide and silicon dielectric permittivity respectively, dox the oxide thickness, K the Boltzmann
ð8Þ
Fig. 1. Simplified schematic of the resistor/resonator SMM setup.
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condition) is presented below in Fig. 2(a). Fig. 2(b) presents in more details about the obtained relation at 20 GHz i.e. near the frequency of our experiment, while the inset graph is a close look on the region of linear behavior of the amplitude of S11, presenting excellent fitting results. Finally, Fig. 2(c) draws the limits of the validity of the linear relation between │S11│and C as a function of the operating frequency. From Fig. 2, two are the major features that should be noted. There is always a regime where a linear relation between those two parameters holds, i.e. the first term in Eq. (8) is negligible, and the sensitivity increases with the operation frequency.
In the region of linear behavior, │S11│can be written in more details as jS11 j ¼
ωCZ 0 : 2
ð9Þ
In the above equation C is the total capacitance that is detected by the cantilever. Therefore C ¼ C Tip þ C Stray C Top :
ð10Þ
The first term in the above equation, CTip, is the capacitance formed by the tip apex and the sample under investigation. In our case, the calibration sample has a silicon substrate with dopant staircase structure, covered by native oxide. The tip/sample system forms a MOS capacitor for which the total capacitance is C Tip ¼ ðeffective areaÞ CMOS :
ð11Þ
The effective area is the equivalent area of interaction, thus the experimental resolution and is related to the tip effective radius reff as (effective area) = πr2eff. The second term, CStray, represents the contribution of the parallel stray capacitances generated by the parasitic couplings of the cantilever chip with the surroundings. Finally, the term, CTop, is an additional term that includes the local contribution of the topography on the total detected capacitance. The term should be assessed point-wise and can be considered as negligible when working with flat samples, as in our case. Note that SMM provides this capability because may acquire simultaneously point-wise topography and microwave parameters measurements. The last term should be included when the equation proposed below is used as a calibration line to assess an unknown sample. In this case the last term will match the topography differences between the flat calibration sample and the unknown device. Incorporating Eqs. (10) and (11) into Eq. (9) the final form is obtained as
jS11 j ¼ ðÞ
ωZ 0 πr 2eff 2
CMOS þ
ωZ 0 C Stray : 2
ð12Þ
This means that working in the regime presented in Fig. 2(c), and by recording the amplitude of S11 at areas with different doping, a linear relation of the form Eq. (12) is expected between the |S11| measured in the linear scale and CMOS, expressed as F/cm2. In such a plot the slope may provide the effective area/radius of the tip and the intercept the stay capacitances. The term (±) is included to express the fact that depending on the relative position of the chosen frequency with respect to the resonance the obtained slope may be positive or negative. As already discussed the last term can be neglected in our case. 4. Experimental
Fig. 2. (a) Parametric study versus operation frequency for dependence between │S11│and the reflective capacitance. (b) Detailed presentation at f = 20 GHz. (c) Region of linear behavior of the amplitude of S11.
The SMM experimental setup consists of a Keysight 5600LS Atomic Force Microscope interfaced with a Keysight E8362B Vector Network Analyzer. Commercially available platinum tips especially designed for SMM measurements (i.e. Rocky Mountain Nanotechnology 25Pt300B) have been used. The nominal spring constant of the probes is 18 N/m, the cone height H is 80 μm and the cone angle θ is 15° [15]. A 50 Ω shunt resistor and a resonator are also integrated in the SMM system to match the high impedance of the tip/sample interface to the characteristic impedance of the microwave instrumentation, increasing in this way the sensitivity. Before scanning the sample, the SMM tip is in contact with the DUT, and a VNA frequency sweep is performed from 1 to 20 GHz. Multiple resonance frequencies are obtained by using a resonator. Then, although the method can be in principle applied at any
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frequency, a notch close to the maximum frequency selected as depicted by the above presented parametric study in order obtained the maximum sensitivity. The exact frequency was chosen based on the best imaging and impedance responses for the measurements to be performed. The measurements have been performed twice. Both de-embedding workflows were applied first using a new tip. Then, the tip was purposely enlarged and both calibration techniques re-applied in order to check their ability to identify the change in the tip radius but also to better understand their features to be discussed later. For the proposed methodology, a calibration sample is required. An n-type silicon sample with native oxide on top that consists of four areas of accurately defined doping levels has been used. The calibration sample was fabricated and provided to us by Prof. J. Smoliner of the T.U. of Vienna and it is a sample already utilized successfully in previously published SMM studies. The doping levels in the four stripes are 1016 cm− 3, 8 × 1017 cm−3, 1.5 × 1018 cm−3 and 3 × 1019 cm− 3. At the left end of the calibration sample (Fig. 3) there is the area named as “bulk” having very low level of doping (5 × 1014 cm−3)) not implemented in the calibration study. Regarding the native oxide thickness on top, this has been reported to saturate around 1 nm (depending on Si material properties and environmental details [16]), and therefore, considering also that any variation in the order of 1–2 Å, may cause negligible changes in the inversion capacitance (Eq. 5), in the present study it is considered as 1 nm thick. 5. Results and discussion For the experimental application of the proposed methodology and for the comparative study to be performed, initially a new tip is placed in the nosecone. The SMM tip is then approached to contact with the sample. After having performed a sweep between 1 and 20 GHz, a notch and a frequency close to the resonance are selected for the following experimental procedure to take place. In our case the frequency was fixed at 19.06 GHz.
Fig. 3. (a) SMM imaging of the calibration sample presented in filtered color scale for enhanced relative contrast. The bulk area and the four stripes having doping levels 5 × 1014 cm−3 and 1016 cm−3, 8 × 1017 cm−3, 1.5 × 1018 cm−3 and 3 × 1019 cm−3 respectively are clearly visible. (b) SMM absolute measured amplitudes on the calibration sample. Presentation using the same color scale that allows the straightforward comparison between the new and the used tip.
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Keeping the selected frequency fixed, the sample is scanned and the reflection coefficient, S11, is recorded point by point. In order for the proposed methodology to be applied the formed MOS capacitor should be in the inversion condition. Such a condition for a MOS system is defined by the type of metal tip, by the properties of semiconductor but also by the properties of the oxide/semiconductor interface as well as by possible charging of the native oxide. For this a DC bias may be required to be applied through the tip. In our case the system was found to be inverted at 0 V. This allowed extensive scanning of the sample without charging the native oxide. After the end of the first scan, an electrostatic approach curve is performed. The tip apex radius is then enlarged by letting the system scan the sample with a high setpoint (i.e. 2.5 V). After few hours, a new S11 image and a new EFM approach curve are then acquired. A typical SMM imaging obtained on the calibration sample is presented, using a filtered scale, relatively colored for enhanced contrast, in Fig. 3(a). In this way the four areas of different doping levels are clearly visible as well as the small not intentionally doped areas between them. At the left edge there is also the low level doping entitled “bulk” that is not involved in the following analysis. Moreover the obtained results for the two scans are presented using the absolute measured values of S11 amplitude, in a merge picture in Fig. 3(b). The same color scale is applied for both scans and so the changes between the new and the used tip to be clearly visible. The proposed methodology has been applied in both areas and the lines have been obtained by the linear fitting procedure, using Eq. (12) on the experimental data presented in Fig. 4. A clear increase in the slope (in absolute values) is obtained, denoting the enlargement of the area of interaction, and thus of the tip radius according to Eq. (12). In addition, it is worth to notice that the intercept remained practically unchanged, thus suggesting that during the experimental procedure no significant changes on the stray capacitance have occurred. This is an additional validation of the reliability of the experimental procedure. The tip radius values that have been calculated for the new and the used tip are 65 nm and 100 nm, respectively. The stray capacitance obtained from the intercept is 1.5 fF. These calculated values cross confirmed that the experiments are in the regime where the linear relation Eq. (9) according to Fig. 2(c) is valid, a fact also supported by the very good fitting results presented in Fig. 4. In the EFM approach curve method a nonlinear fitting procedure is applied, the results are presented in Fig. 5. For enhanced accuracy these measurements were performed on the heavily doped stripe [9]. Compared to the proposed methods, higher values for the capacitance in the case of the used tip are obtained with the EFM method. This is something aligned with respect to what was predicted by the corresponding Eqs. (1) to (4). The results in this case lead to values of 65 nm and 150 nm for the new and the used tip respectively.
Fig. 4. Fitting procedure of the proposed model on the experimental data.
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The proposed analysis is based on the assessment of the SMM system response in the linear scale and the use of the standard capacitances that arise by a dopant profiling sample, expressed per area. In this way by the implementation of the appropriate modeling the effective tip radius is experimentally estimated. Furthermore the methodology is experimentally evaluated by a straightforward comparison with an electrostatic force microscopy based calibration method. Both techniques have been applied during the same experimental procedure on the same tip that has been gradually deformed. In addition, based on the obtained results the features of each methodology are also discussed in details. The paper provides a full picture of the up to date available experimental techniques for de-embedding SMM measurements. Considering the broad area of SMM applications, the present study provides a very useful tool for the potential users in order to choose the most appropriate technique according to the application of interest. Acknowledgment Fig. 5. Fitting procedure of the approach curve method on the experimental data.
Interestingly, both techniques provide the same value for the new tip, while a small variation is observed in the case of the used tip. This is because the techniques are based on two different approximations. The approach curve method relies on the preservation of a specific shape of the SMM tip, while the new methodology is based on an equivalent area. For a new tip the approximations are found to be in agreement. Based on the presented analysis as well as on the experimentally obtained results it is thus possible to draw some conclusion on the major features of each one of the two methodologies. The EFM approach curve method may be in principle applied on different types of samples under investigation and allows an estimation of the tip radius without the use of a calibration standard. Therefore, it may provide useful for SMM studies on applications beyond semiconductors e.g. on biological samples [17]. The accuracy of the technique is even more valuable in case of non-contact SMM measurements where the tip shape remain unchanged and is practically the nominal one. The methodology introduced in the present paper has the big advantage of being accurate for contact-mode measurements even when the tip shape is modified during the scan. For semiconductor materials and device characterization, this is extremely important. By taking into account the tip/sample interactions, it allows a straightforward estimation of the effective tip radius, which is the actual SMM experimental resolution. This means that effective areas may be different than the geometrical ones, since they incorporate also the interaction that arises by the contribution of fringing fields around the tip edge. Such fringing fields are determined by several experimental parameters and elements, (i) the tip detailed shape, if it is conic or pyramidal, (ii) possibly the tip to sample inclination angle [18], (iii) the nature of the material under investigation, (iv) the presence of water meniscus due to humidity around the tip edge [19] and/or (v) the presence of DC bias on the tip [20]. It should be noted that the calculation of the effective area is coming out from the analysis of the experimental results and does not require the knowledge of geometrical details of the tip. Therefore, it properly works even in cases where the tip shape is not any more strictly cylinder or conic or anything else easily defined. Note that in cases of deformed tip shape [21] and of not easily defined dimensions, it is very difficult to apply any modeling to calculate accurately the area of interaction. Finally, it is worth to point out that the methodology allows the calibration and de-embedding of SMM data on the exact frequency of the experimental procedure and therefore can incorporate any frequency dependent behavior of the material or device under investigation. 6. Conclusions A methodology for de-embedding scanning microwave microscopy measurements, mainly for semiconductor characterization, is presented.
The authors wish to acknowledge the support from EC by means of “Marie Curie” fellowship in the framework of PEOPLE-2012-ITN project: Microwave Nanotechnology for Semiconductor and Life Science -NANOMICROWAVE, under GA:317116. The authors wish also to acknowledge Prof. J. Smoliner from TU Vienna who fabricated and provided us the calibration standard for the experimental procedure. References [1] D.E. Steinhauer, C.P. Vlahacos, S.K. Dutta, F.C. Wellstood, Steven M. Anlage, Surface resistance imaging with a scanning near-field microwave microscope, Appl. Phys. Lett. 71 (1997) 1736, http://dx.doi.org/10.1063/1.120020. [2] M. Tabib-Azar, D.-P. Su, A. Pohar, S.R. LeClair, G. Ponchak, 0.4 μm spatial resolution with 1 GHz (λ = 30 cm) evanescent microwave probe, Rev. Sci. Instrum. 70 (1999) 1725, http://dx.doi.org/10.1063/1.1149658. [3] C. Gao, B. Hu, P. Zhang, M. Huang, W. Liu, I. Takeuchi, Quantitative microwave evanescent microscopy of dielectric thin films using a recursive image charge approach, Appl. Phys. Lett. 84 (2004) 4647, http://dx.doi.org/10.1063/1.1759389. [4] A. Tselev, S.M. Anlage, Z. Ma, J. Melngailis, Broadband dielectric microwave microscopy on micron length scales, Rev. Sci. Instrum. 78 (2007) 044701, http://dx.doi.org/ 10.1063/1.2719613. [5] M. Farina, D. Mencarelli, A. Di Donato, G. Venanzoni, A. Morini, Calibration Protocol for broadband near-field microwave microscopy, IEEE Trans. Microwave Theory Tech. 59 (2011) 2769, http://dx.doi.org/10.1109/TMTT.2011.2161328. [6] H. Happy, K. Haddadi, D. Theron, T. Larsi, G. Dambrine, Measurement techniques for RF nanoelectronics devices, IEEE Microw. Mag. 15 (2014) 30–39, http://dx.doi.org/ 10.1109/MMM.2013.2288710. [7] T. Dargent, K. Haddadi, T. Lasri, N. Clément, D. Ducatteau, B. Legrand, H. Tanbakuchi, D. Theron, An intereforemtric scanning microwave microscope and calibration method for sub-fF microwave measurements, Rev. Sci. Instrum. 84 (2013) 123705, http://dx.doi.org/10.1063/1.4848995. [8] H.P. Huber, M. Moertelmeier, T.M. Wallis, C.J. Chiang, M. Hochleitner, A. Imtiaz, Y.J. Oh, K. Schilcher, M. Dieudonne, J. Smoliner, P. Hinterdorfer, S.J. Rosner, H. Tanbakuchi, P. Kabos, F. Kienberger, Calibrated nanoscale capacitance measurements using scanning microwave microscopy, Rev. Sci. Instrum. 81 (2010) 113701, http://dx.doi.org/10.1063/1.3491926. [9] G. Gramse, M. Kasper, L. Fumagalli, G. Gomila, P. Hinterdorfer, F. Kienberger, Calibrated complex impendance and permittivity measurements with scanning microwave microscopy, Nanotechnology 25 (2014) 145703, http://dx.doi.org/10.1088/ 0957-4484/25/14/145703. [10] L. Michalas, A. Lucibello, C.H. Joseph, E. Brinciotti, F. Kienberger, E. Proietti, R. Marcelli, Nanoscale characterization of MOS systems by microwaves: Dopant profiling calibration, in: IEEE (Ed.), Proceedings of EUROSOI-ULIS 2015, Joint International EUROSOI Workshop and International Conference of Ultimate Integration in Silicon, Bologna, Italy, 26–28 January 2015 2015, pp. 269–272, http://dx.doi.org/10.1109/ ULIS.2015.7063825. [11] L. Michalas, A. Lucibello, G. Badino, C.H. Joseph, E. Brinciotti, F. Kienberger, E. Proietti, R. Marcelli, Scanning microwave microscopy for nanoscale characterization of semiconductors: de-embedding reflection contact mode measurements, in: IEEE-EuMA (Ed.), Proceedings of 45th EuMW, European Microwave Conference, Paris, France 5–11 September 2015 2015, pp. 159–162, http://dx.doi.org/10.13140/RG.2.1.2050. 3520. [12] S.M. Sze, Physics of Semiconductor Device, John Wiley & Sons, NY, 1981. [13] J. Smoliner, H.P. Huber, M. Hochleitner, M. Moertelmaier, F. Kienberger, Scanning microwave microscopy/spectroscopy for metal-oxide-semiconductor systems, J. Appl. Phys. 108 (2010) 064315, http://dx.doi.org/10.1063/1.3482065. [14] K. Torigoe, M. Arita, T. Motooka, Sensitivity analysis of microwave microscopy for nano scale dopant measurements in Si, J. Appl. Phys. 112 (2012) 104325, http:// dx.doi.org/10.1063/1.4765730.
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