- Email: [email protected]
Calibration and examination of piezoresistive Wheatstone bridge cantilevers for scanning probe microscopy
ARTICLE IN PRESS
Ultramicroscopy 97 (2003) 385–389
Calibration and examination of piezoresistive Wheatstone bridge cantilevers for scanning probe microscopy Teodor Gotszalka,*, Piotr Grabiecb, Ivo W. Rangelowc a
Faculty of Microsystem Electronics and Photonics, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50-372 Wroclaw, Poland b ! 11, 02-688 Warszawa, Poland Institute of Electron Technology, Al. Lotnikow c Institute of Technical Physics, University of Kassel, Heinrich-Plett-Str. 40, 34109 Kassel, Germany Received 20 September 2002; received in revised form 20 December 2002
Abstract This paper describes the method of determining the force constant and displacement sensitivity of piezoresistive Wheatstone bridge cantilevers applied in scanning probe microscopy (SPM). In the procedure presented here, the force constant for beams with various geometry is determined based on resonance frequency measurement. The displacement sensitivity is measured by the deflection of the cantilever with the calibrated piezoactuator stage. Preliminary results show that our method is capable of measuring the force constant of Wheatstone bridge cantilevers with an accuracy of better than 5% and this is used as feedback for improvement of sensor micromachining process. r 2003 Elsevier Science B.V. All rights reserved. Keywords: Scanning probe microscopy; Piezoresistive sensor; Piezoresistive effect
1. Introduction Scanning probe microscopy (SPM) is a very sensitive technique to determine various surface properties with nanometer resolution. Recent developments enable investigations of other microtribological sample properties like elasticity, friction coefficients between tip and sample and surface roughness. The quantitative measurements require, however, knowledge of the near-field interactions between the tip and the surface. In most of the AFMs working in air, optical methods are used to observe cantilever motion. From the *Corresponding author. Fax: +48-71-328-3504. E-mail address: [email protected] (T. Gotszalk).
demand for simplifying the mechanical set-up of the AFMs head came the concept for the development of a cantilever with an integrated piezoresistive deflection sensor. In contrast to previous works [1], [2] we integrated with the silicon beam the Wheatstone piezoresistive bridge [3] (Fig. 1). Applying the technology developed by our team we constructed piezoresistive cantilevers for electrostatic force microscopy (EFM) [4], lateral force microscopy (LFM) [5], scanning thermal microscopy (SThM) [6] and scanning nearfield optical microscopy (SNOM) [7]. The mechanical stress occurred by the bending is the cantilever and this changed the resistance of the piezoresistor. In commercial SPM microscopes the interaction force F is estimated by multiplying the deflection
0304-3991/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-3991(03)00065-2
ARTICLE IN PRESS 386
T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
of the cantilever by the beam force constant. The major source is the uncertainty in the value of the force constant of the cantilever. Cantilever fabrication process includes several lithographic and micromachining steps on both the wafer sides. We find that even though technological parameters are weakly close to the required tolerances, some essential sensor parameter deviations across the wafer and wafer-to-wafer are observed. The determined electromechanical parameters are used as a basis for improvement of the micromachining technology, especially lithographic misalignments and sensor calibration.
solution. In the second lithography step a p+ diffusion windows was opened and afterwards heavily doped p+ connections were created by high concentration boron diffusion, followed by high temperature drive-in. In the subsequent processing step piezoresistors were formed by photolithography followed by moderate boron diffusion or, alternatively, by implantation and annealing. Doping conditions as well as annealing parameters were optimized to obtain high sensitivity of the piezoresistors. In the fourth lithography step contact holes were defined and etched in the oxide, for connection of p+ diffusion regions with metal paths. Then, a 1 mm-Al film was deposited using magnetron sputtering and electrical connections were defined by next lithography and metal etching. In this way a basic electrical structure was formed in silicon. The sixth lithography was performed on the reverse of the wafers to define the membrane area. A deep, anisotropic silicon etching was done in hot 30% KOH solution, to create a 15 mm thick silicon membrane in the future beam area. In most simple experimental set-up, the front side of the wafer with electronic structure already formed, was protected by placing the wafer in a chuck. The etching was stopped when membrane thickness reached 15 mm. Finally, in the last step, a shape of the beam was cut in the membrane and whole microprobe structure was formed by front side lithography, followed by silicon etching in SF6 plasma and removing of photoresist in oxygen plasma.
2. Fabrication process
3. Measurement technique
The SPM microprobe fabrication process is based on a double side micromachining concept [8]. The developed sequence is conceived to enable fabrication of different microprobe type devices by simple modification of the lithography masks, with general procedure remaining basically the same. 2–5 O cm n-type, /1 0 0S silicon wafers were used as a starting material. After initial cleaning, surface oxidation and 100 nm LPCVD silicon nitride deposition, first photolithography was performed to define a mask dot in the future tip area. The sharp tip was formed by anisotropic under-etching of silicon in hot TMAH or KOH
Several methods have been developed to determine the force constant of a cantilever. We have chosen the procedure based on measurements of the beam resonance frequency. The force constant for a cantilever with a uniform rectangular crosssection is given by
Fig. 1. Piezoresistive Wheatstone bridge cantilever (beam dimensions length 600 mm, width 135 mm, thickness 15 mm).
k¼
Ebd 3 ; 4l 3
ð1Þ
where E is the modulus of elasticity of the cantilever material, b is the width of the cantilever, d is the beam thickness and l is the length of the beam. The width and the length of the cantilever
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
where r is the density of the cantilever material. Combining formulae (1) and (2) we obtain sffiffiffiffiffi r3 : ð3Þ k ¼ 58:806bl 3 fr3 E The total error of evaluation of the force constant with respect to the beam geometry can be calculated with dk db dL dfr ¼ þ3 þ3 : k b L fr
ð4Þ
The resonance frequency is measured with an accuracy of 0.2%, and the length and the width of the cantilever are measured with an accuracy of 1% with an optical microscope. Therefore, based on formula (4), the total error in the determination of the force constant of the piezoresistive bridge cantilever is 3.6%. In Fig. 2, the dependence of the force constant and beam thickness on the resonance beam frequency is presented (calculations were performed for the beam geometry: length 600 mm, thickness 135 mm).
4. Experimental results We have observed the resonance curve of the Wheatstone bridge piezoresistive cantilever using a measurement system consisting of an amplifier with adjustable gain, a digital high resolution signal generator, and a high-speed signal rectifier. The result is shown in Fig. 3, where the resonance frequency of the beam is 43250 Hz and quality factor Q is 266. The calculated force constant,
40000
50000
60000
70000 22
Force constant [N/m]
Force constant [N/m]
250
20
Beam thickness [mm]
18 200
16
150
14 12
100
10 50
Beam thickness [m]
30000 300
8
0 30000
40000
50000
60000
6 70000
Resonance frequency [Hz]
Fig. 2. Beam resonance frequency vs. force constant and beam thickness.
50200
50400
50600
50800
6
Amplitude [rel.]
can be measured with an accurately calibrated optical microscope and the Young modulus of the beam is well-known because the beam is made from single crystal silicon. However, the beam thickness, which is several microns, is difficult to measure with sufficient certainty. In our procedure we determine the beam thickness based on resonance frequency. The resonance frequency fr of a cantilever vibrating in vacuum can be calculated in accordance with sffiffiffiffiffiffi 3:52d E fr ¼ ; ð2Þ 4pl 2 3r
387
6
fr =50450Hz ∆f =165Hz Q = 300 k=105N/m
∆f
4
4
2
2
50200
50400
50600
50800
Frequency [Hz] Fig. 3. Resonance curve of the piezoresistive Wheatstone bridge cantilever (calculated force constant k ¼ 64:7 N/m).
using formula (3) is 64.7 N/m. For the measurements of the displacement sensitivity of the Wheatstone bridge piezoresistive cantilevers, the special mechanical set-up has been developed. It consists of a calibrated piezoactuator tube and a cantilever holder adjustable in XYZ directions (Fig. 4). In our investigations we calibrated the deflection of the piezoactuator using the Fabry–Perot fibre interferometer (Fig. 5). In these experiments one of the fibre ends of the bidirectional coupler is directly pigtailed to the single mode laser diode, which includes the optical
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
388
Fig. 4. Wheatstone bridge cantilever calibration stage.
Coupler
Detector
DFB Laser Diode
Isolator
Fig. 6. Optical spectrum of the single mode laser diode applied in fibre Fabry–Perot interferometer. Piezoactuator
Fig. 5. Fibre Fabry–Perot interferometer for measurements of Wheatstone Bridge cantilever force/displacement sensitivity.
Faraday isolator. In this way, the light reflected from the interferometer fibre end does not disturb the operation of the laser diode. The signal photodiode measures the interference of the light reflected from the fibre end and from the mirror mounted on the piezoactuator end. The bias current of the laser diode was stabilized with an accuracy of 10 ppm and the laser temperature was controlled with a resolution of 10 mK. The optical spectrum of the light that was emitted from the laser was measured with the optical analyser ANDO 1847 (Fig. 6). We determined that the light wavelength of the applied single mode semiconductor laser was 1313 nm. The recorded interferometric fringes are presented in Fig. 7. We applied to the tube electrodes a voltage of 107.6 V and observed displacement of the piezoactuator was 1:4l; which corresponds with the actuator sensitivity of 16.2 nm/V. In our experiments, the piezoresistive Wheatstone bridge cantilever was deflected with the calibrated piezoactuator (the contact point between the beam and the piezotube was on the opposite side of the microtip location) and the electrical detector output was recorded using the DSP I/O card and the PC computer. The
Fig. 7. Fabry–Perot fibre interferometer calibration of the piezoactuator for testing of the piezoresistive cantilever displacement/force sensitivity.
static load force, acting on the cantilever, was maintained using the PI controller with time constant of 0.1 s. The frequency of piezoactuator deflection was adjusted over the frequency of the PI controller, so that the influence of piezoexcitation on the static force stabilization was minimized. Based on these measurements (Fig. 8), the piezoresistive detector displacement sensitivity of 0.8 mV/1 nm (7)5% and force sensitivity of 80 mV/nN (7)5% were determined.
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389 0 140
100
200
Piezoactuator deflection [nm]
1.0
120
0.5
110 100
0.0
90 -0.5
80 70 Detector output [µV]
60 0
100
z Displacement [nm]
Detector output [µV]
130
-1.0
389
The presented complete cantilever characterization enables improvement of the sensor fabrication technology and determination of the cantilever force and displacement sensitivity is independent of the scanning probe microscope and mechanical and electronical set-up.
References
200
Samples
Fig. 8. Piezoresistive detector output vs. deflection of the piezoactuator (detector supply voltage 71 V).
5. Summary In this article we described a method for testing and calibrating Wheatstone piezoresistive cantilevers applied in SPM. We developed a technique allowing measurements of beam force constant and displacement sensitivity of the piezoresistive detector with an accuracy of 5%. For the purpose of calibration of the piezoresistive sensor we constructed the fibre Fabry–Perot interferometer. The resolution of the constructed instrument is 0.01 nm in the measurement bandwidth of 100 Hz.
[1] M. Tortonese, R.C. Barett, C.F. Quate, Appl. Phys. Lett. 62 (1993) 834. [2] Xiaomeio Yu, J. Thaysen, O. Hansen, A. Boisen, J. Appl. Phys. 92 (2002) 6292. [3] T. Gotszalk, I.W. Rangelow, P. Dumania, P. Grabiec, Micromachinig and microfabrication process technology II, Proc. SPIE 2880 (1996) 256. [4] T. Gotszalk, F. Shi, P. Grabiec, P. Dumania, P. Hudek, I.W. Rangelow, J. Vac. Sci. Technol. B 16 (6) (1998) 3948. [5] P.B. Grabiec, R. Sunyk, F. Shi, G. Popovic, T. Gotszalk, P. Hudek, P. Dumania, I.W. Rangelow, Microectron. Eng. 46 (1999) 405. [6] K. Edinger, T. Gotszalk, I.W. Rangelow, J. Vac. Sci. Technol. B 19 (6) (2001) 2344. [7] P. Grabiec, T. Gotszalk, J. Radojewski, I.W. Rangelow, Microelectron. Eng. 61 and 62 (2002) 981. [8] T. Gotszalk, P. Grabiec, I.W. Rangelow, Ultramicroscopy 82 (2000) 39.
Ultramicroscopy 97 (2003) 385–389
Calibration and examination of piezoresistive Wheatstone bridge cantilevers for scanning probe microscopy Teodor Gotszalka,*, Piotr Grabiecb, Ivo W. Rangelowc a
Faculty of Microsystem Electronics and Photonics, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50-372 Wroclaw, Poland b ! 11, 02-688 Warszawa, Poland Institute of Electron Technology, Al. Lotnikow c Institute of Technical Physics, University of Kassel, Heinrich-Plett-Str. 40, 34109 Kassel, Germany Received 20 September 2002; received in revised form 20 December 2002
Abstract This paper describes the method of determining the force constant and displacement sensitivity of piezoresistive Wheatstone bridge cantilevers applied in scanning probe microscopy (SPM). In the procedure presented here, the force constant for beams with various geometry is determined based on resonance frequency measurement. The displacement sensitivity is measured by the deflection of the cantilever with the calibrated piezoactuator stage. Preliminary results show that our method is capable of measuring the force constant of Wheatstone bridge cantilevers with an accuracy of better than 5% and this is used as feedback for improvement of sensor micromachining process. r 2003 Elsevier Science B.V. All rights reserved. Keywords: Scanning probe microscopy; Piezoresistive sensor; Piezoresistive effect
1. Introduction Scanning probe microscopy (SPM) is a very sensitive technique to determine various surface properties with nanometer resolution. Recent developments enable investigations of other microtribological sample properties like elasticity, friction coefficients between tip and sample and surface roughness. The quantitative measurements require, however, knowledge of the near-field interactions between the tip and the surface. In most of the AFMs working in air, optical methods are used to observe cantilever motion. From the *Corresponding author. Fax: +48-71-328-3504. E-mail address: [email protected] (T. Gotszalk).
demand for simplifying the mechanical set-up of the AFMs head came the concept for the development of a cantilever with an integrated piezoresistive deflection sensor. In contrast to previous works [1], [2] we integrated with the silicon beam the Wheatstone piezoresistive bridge [3] (Fig. 1). Applying the technology developed by our team we constructed piezoresistive cantilevers for electrostatic force microscopy (EFM) [4], lateral force microscopy (LFM) [5], scanning thermal microscopy (SThM) [6] and scanning nearfield optical microscopy (SNOM) [7]. The mechanical stress occurred by the bending is the cantilever and this changed the resistance of the piezoresistor. In commercial SPM microscopes the interaction force F is estimated by multiplying the deflection
0304-3991/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-3991(03)00065-2
ARTICLE IN PRESS 386
T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
of the cantilever by the beam force constant. The major source is the uncertainty in the value of the force constant of the cantilever. Cantilever fabrication process includes several lithographic and micromachining steps on both the wafer sides. We find that even though technological parameters are weakly close to the required tolerances, some essential sensor parameter deviations across the wafer and wafer-to-wafer are observed. The determined electromechanical parameters are used as a basis for improvement of the micromachining technology, especially lithographic misalignments and sensor calibration.
solution. In the second lithography step a p+ diffusion windows was opened and afterwards heavily doped p+ connections were created by high concentration boron diffusion, followed by high temperature drive-in. In the subsequent processing step piezoresistors were formed by photolithography followed by moderate boron diffusion or, alternatively, by implantation and annealing. Doping conditions as well as annealing parameters were optimized to obtain high sensitivity of the piezoresistors. In the fourth lithography step contact holes were defined and etched in the oxide, for connection of p+ diffusion regions with metal paths. Then, a 1 mm-Al film was deposited using magnetron sputtering and electrical connections were defined by next lithography and metal etching. In this way a basic electrical structure was formed in silicon. The sixth lithography was performed on the reverse of the wafers to define the membrane area. A deep, anisotropic silicon etching was done in hot 30% KOH solution, to create a 15 mm thick silicon membrane in the future beam area. In most simple experimental set-up, the front side of the wafer with electronic structure already formed, was protected by placing the wafer in a chuck. The etching was stopped when membrane thickness reached 15 mm. Finally, in the last step, a shape of the beam was cut in the membrane and whole microprobe structure was formed by front side lithography, followed by silicon etching in SF6 plasma and removing of photoresist in oxygen plasma.
2. Fabrication process
3. Measurement technique
The SPM microprobe fabrication process is based on a double side micromachining concept [8]. The developed sequence is conceived to enable fabrication of different microprobe type devices by simple modification of the lithography masks, with general procedure remaining basically the same. 2–5 O cm n-type, /1 0 0S silicon wafers were used as a starting material. After initial cleaning, surface oxidation and 100 nm LPCVD silicon nitride deposition, first photolithography was performed to define a mask dot in the future tip area. The sharp tip was formed by anisotropic under-etching of silicon in hot TMAH or KOH
Several methods have been developed to determine the force constant of a cantilever. We have chosen the procedure based on measurements of the beam resonance frequency. The force constant for a cantilever with a uniform rectangular crosssection is given by
Fig. 1. Piezoresistive Wheatstone bridge cantilever (beam dimensions length 600 mm, width 135 mm, thickness 15 mm).
k¼
Ebd 3 ; 4l 3
ð1Þ
where E is the modulus of elasticity of the cantilever material, b is the width of the cantilever, d is the beam thickness and l is the length of the beam. The width and the length of the cantilever
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
where r is the density of the cantilever material. Combining formulae (1) and (2) we obtain sffiffiffiffiffi r3 : ð3Þ k ¼ 58:806bl 3 fr3 E The total error of evaluation of the force constant with respect to the beam geometry can be calculated with dk db dL dfr ¼ þ3 þ3 : k b L fr
ð4Þ
The resonance frequency is measured with an accuracy of 0.2%, and the length and the width of the cantilever are measured with an accuracy of 1% with an optical microscope. Therefore, based on formula (4), the total error in the determination of the force constant of the piezoresistive bridge cantilever is 3.6%. In Fig. 2, the dependence of the force constant and beam thickness on the resonance beam frequency is presented (calculations were performed for the beam geometry: length 600 mm, thickness 135 mm).
4. Experimental results We have observed the resonance curve of the Wheatstone bridge piezoresistive cantilever using a measurement system consisting of an amplifier with adjustable gain, a digital high resolution signal generator, and a high-speed signal rectifier. The result is shown in Fig. 3, where the resonance frequency of the beam is 43250 Hz and quality factor Q is 266. The calculated force constant,
40000
50000
60000
70000 22
Force constant [N/m]
Force constant [N/m]
250
20
Beam thickness [mm]
18 200
16
150
14 12
100
10 50
Beam thickness [m]
30000 300
8
0 30000
40000
50000
60000
6 70000
Resonance frequency [Hz]
Fig. 2. Beam resonance frequency vs. force constant and beam thickness.
50200
50400
50600
50800
6
Amplitude [rel.]
can be measured with an accurately calibrated optical microscope and the Young modulus of the beam is well-known because the beam is made from single crystal silicon. However, the beam thickness, which is several microns, is difficult to measure with sufficient certainty. In our procedure we determine the beam thickness based on resonance frequency. The resonance frequency fr of a cantilever vibrating in vacuum can be calculated in accordance with sffiffiffiffiffiffi 3:52d E fr ¼ ; ð2Þ 4pl 2 3r
387
6
fr =50450Hz ∆f =165Hz Q = 300 k=105N/m
∆f
4
4
2
2
50200
50400
50600
50800
Frequency [Hz] Fig. 3. Resonance curve of the piezoresistive Wheatstone bridge cantilever (calculated force constant k ¼ 64:7 N/m).
using formula (3) is 64.7 N/m. For the measurements of the displacement sensitivity of the Wheatstone bridge piezoresistive cantilevers, the special mechanical set-up has been developed. It consists of a calibrated piezoactuator tube and a cantilever holder adjustable in XYZ directions (Fig. 4). In our investigations we calibrated the deflection of the piezoactuator using the Fabry–Perot fibre interferometer (Fig. 5). In these experiments one of the fibre ends of the bidirectional coupler is directly pigtailed to the single mode laser diode, which includes the optical
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389
388
Fig. 4. Wheatstone bridge cantilever calibration stage.
Coupler
Detector
DFB Laser Diode
Isolator
Fig. 6. Optical spectrum of the single mode laser diode applied in fibre Fabry–Perot interferometer. Piezoactuator
Fig. 5. Fibre Fabry–Perot interferometer for measurements of Wheatstone Bridge cantilever force/displacement sensitivity.
Faraday isolator. In this way, the light reflected from the interferometer fibre end does not disturb the operation of the laser diode. The signal photodiode measures the interference of the light reflected from the fibre end and from the mirror mounted on the piezoactuator end. The bias current of the laser diode was stabilized with an accuracy of 10 ppm and the laser temperature was controlled with a resolution of 10 mK. The optical spectrum of the light that was emitted from the laser was measured with the optical analyser ANDO 1847 (Fig. 6). We determined that the light wavelength of the applied single mode semiconductor laser was 1313 nm. The recorded interferometric fringes are presented in Fig. 7. We applied to the tube electrodes a voltage of 107.6 V and observed displacement of the piezoactuator was 1:4l; which corresponds with the actuator sensitivity of 16.2 nm/V. In our experiments, the piezoresistive Wheatstone bridge cantilever was deflected with the calibrated piezoactuator (the contact point between the beam and the piezotube was on the opposite side of the microtip location) and the electrical detector output was recorded using the DSP I/O card and the PC computer. The
Fig. 7. Fabry–Perot fibre interferometer calibration of the piezoactuator for testing of the piezoresistive cantilever displacement/force sensitivity.
static load force, acting on the cantilever, was maintained using the PI controller with time constant of 0.1 s. The frequency of piezoactuator deflection was adjusted over the frequency of the PI controller, so that the influence of piezoexcitation on the static force stabilization was minimized. Based on these measurements (Fig. 8), the piezoresistive detector displacement sensitivity of 0.8 mV/1 nm (7)5% and force sensitivity of 80 mV/nN (7)5% were determined.
ARTICLE IN PRESS T. Gotszalk et al. / Ultramicroscopy 97 (2003) 385–389 0 140
100
200
Piezoactuator deflection [nm]
1.0
120
0.5
110 100
0.0
90 -0.5
80 70 Detector output [µV]
60 0
100
z Displacement [nm]
Detector output [µV]
130
-1.0
389
The presented complete cantilever characterization enables improvement of the sensor fabrication technology and determination of the cantilever force and displacement sensitivity is independent of the scanning probe microscope and mechanical and electronical set-up.
References
200
Samples
Fig. 8. Piezoresistive detector output vs. deflection of the piezoactuator (detector supply voltage 71 V).
5. Summary In this article we described a method for testing and calibrating Wheatstone piezoresistive cantilevers applied in SPM. We developed a technique allowing measurements of beam force constant and displacement sensitivity of the piezoresistive detector with an accuracy of 5%. For the purpose of calibration of the piezoresistive sensor we constructed the fibre Fabry–Perot interferometer. The resolution of the constructed instrument is 0.01 nm in the measurement bandwidth of 100 Hz.
[1] M. Tortonese, R.C. Barett, C.F. Quate, Appl. Phys. Lett. 62 (1993) 834. [2] Xiaomeio Yu, J. Thaysen, O. Hansen, A. Boisen, J. Appl. Phys. 92 (2002) 6292. [3] T. Gotszalk, I.W. Rangelow, P. Dumania, P. Grabiec, Micromachinig and microfabrication process technology II, Proc. SPIE 2880 (1996) 256. [4] T. Gotszalk, F. Shi, P. Grabiec, P. Dumania, P. Hudek, I.W. Rangelow, J. Vac. Sci. Technol. B 16 (6) (1998) 3948. [5] P.B. Grabiec, R. Sunyk, F. Shi, G. Popovic, T. Gotszalk, P. Hudek, P. Dumania, I.W. Rangelow, Microectron. Eng. 46 (1999) 405. [6] K. Edinger, T. Gotszalk, I.W. Rangelow, J. Vac. Sci. Technol. B 19 (6) (2001) 2344. [7] P. Grabiec, T. Gotszalk, J. Radojewski, I.W. Rangelow, Microelectron. Eng. 61 and 62 (2002) 981. [8] T. Gotszalk, P. Grabiec, I.W. Rangelow, Ultramicroscopy 82 (2000) 39.