Calibration Gratings

1. Introduction

2. Data sheets

3.1 The Device Calibration

3.1.1 Z-axis Calibration

3.1.2 XY-plane Calibration

3.2 Determination of scanning nonlinearity

3.3 Determination the distortion of object shape caused by CREEP-effect

3.4 Full 3-D image of the cantilever tip observing, its curvature radius measurement

1. Introduction

This test structures is intended for scanning probe microscopes.
It will help you:

to calibrate your scanner in normal directions;
to calibrate your scanner in lateral directions;
to determine normal and lateral nonlinearity, degree of angular distortion;
to determine piezoceramics hysteresis value of your device;
to determine degree of creep-effect influence on the image;
to obtain full 3-D image of the cantilever tip, to measure its curvature radius.

Using these gratings you can get maximum metrological opportunities of your device and detect distortions caused by tip shape and piezoceramics behavior.

If you only begin to master methods of scanning probe microscopy we rec-ommend you to carry out a complete cycle of calibration studies. It will allow you to display both opportunities and limitations of your device.

All of the gratings passed metrological certification at Gosstandart.

2. Data sheets

2.1 HOPG

Highly oriented pyrolithic graphite has angle of crystal off-orientation less then 0,3°, 0,8° or 3°. It is intended for atomically calibration of STM.

2.2 TGZ (Fig.1)

Silicon calibration gratings of TGZ series provide the calibration value of the step height on the whole sample area. The accuracy of step height for heights up to 30 nm is 1.0 nm, for step heights more than 30 nm - 1.5 nm. It is intended for Z-axis calibration and nonlinearity measurements.

2.3 TGX01 (Fig.2)

Silicon calibration gratings of TGX series provide square pillars arranged like a chessboard cells with 3 mm step in X-Y- directions with good linear edges, formed by <110> silicon crystallographic directions. The accuracy for pitch is 5 nm. Radius of curvature of a pillar edge is less than 5 nm. These gratings are applied as test structures for:

lateral calibration of SPM scanners;
assessment of lateral nonlinearity;
determination of hysteresis and piezoceramics creep-effect.


Fig.1. SEM-foto of TGZ02.		Fig.2. SEM-foto of TGX01.

2.4 TGG01 (Fig.3)

Silicon calibration gratings of TGG series provide exact linear and angular stripe sizes, formed by (111) silicon crystallographic planes. It characterizes small curvature radius at top of sides (less than 10 nm) on the whole sample area. The ac-curacy of pitch is 5 nm. These gratings are applied as test structures for

lateral calibration of SPM scanners;
detection of nonlinearity of the scanner in lateral and normal direc-tions;
assessment of angular distortion.

2.5 TGT (Fig.4)

Silicon calibration gratings of TGT series are characterized by strict symmetry of tip sides, small tip angle (less than 20 degrees), small curvature radius of tip (less than 10 nm) over the whole sample area. They are intended

to obtain full 3-D image of the cantilever tip;
to determine cantilever tip angle and its curvature radius.


Fig.3. SEM-foto of TGG01.		Fig.4. SEM-foto of TGT-01.

3. Application notes

3.1 The Device Calibration

It is well known that piezoceramics suffer from nonlinearity, hysteresis and creep. Ceramics properties also change with time and depend on temperature. So scanning probe microscopes have to be regularly calibrated in both normal and lateral directions.

3.1.1 Z-axis Calibration

For Z-axis calibration use a grating set TGS01. It comprises TGZ01, TGZ02, TGZ03 gratings. These gratings have steps of various heights. Choose a grating with step height approximately equal to characteristic heights of your sample (20, 100 and 600 nm). Carry out scanning of a structure and get evidence, that your device cor-rectly measure height (fig.5). If necessary update into Z-axis calibration of your device.


Fig.5a. Image of TGZ02 taken by 20x20 um scanner.		Fig.5b. The step image of the grating TGZ02 taken with 20x20 um scanner (scanning probe microscope SOLVER model Solver-P4). For Z-axis calibration of the device you should determine distance between the top and bottom step planes. It should be equal to the size specified in the grating certificate.

Verify that your device is correctly calibrated for fast scanning both along and across stripes. Check up how speed of scanning and parameter of feedback influence image. Choose optimum modes bringing least distortions of object height.

Pay attention to distortions caused by such parasitic effects (fig.6), connected with piezoceramics, as nonlinearity, hysteresis, creep (check the appropriate items of the description for more detailed information).


Fig.6a. Image of TGZ02 with 18.5x18.5 um micron scanner. Pay attention to dis-tortions connected with creep and Z-axis nonlinearity.		Fig 6b. Cross section of TGZ02 scan with 18.5x18.5 um micron scanner in Y -direction. Pay attention to distortions connected with creep and Z-axis nonlinearity.

And you can find the calibration standards at these companies:

VLSI

3.1.2 XY-plane Calibration

There is a number of different calibration standards now[VLSI, Moxtex]. The most widely used one is a diffraction grating with submicron pitch. But manufacturing technology for those structures can not usually ensure edge roughness better than about tens of nanometers. Therefore rather big number of grooves is to be taken to get reasonable accuracy, that complicates the calibration procedure and needs additional mathematical calculations.

We have developed structures with edge shape determined by silicon crystal structure. That ensures the edge roughness value of few nanometers (fig.2) and right geometrical square shape. This value of edge roughness is well below typical tip radius (10 to 40 nm) and single scan is enough for lateral calibration of a scanner (fig.7). A test grating of square pillars are arranged like a chessboard cells with 3 mkm step (fig.2). Such arrangement permits to calibrate scanners with lateral scanning range of about 3 mkm or more.

For calibration in a X-Y plane use calibration grating a TGX01. Get evidence that your device correctly measures period of grating (fig.7). If necessary update calibration factors.

For lateral SPM calibration you can use TGG01 too.

Fig.7.

Image of TGX01 taken with the 20x20 um scanner (scanning probe microscope SOLVER model Solver-P4). For X and Y - axes calibration of the device you should measure period of a grating in X(Y)-direction. It should be equal 3 microns, as specified in DATA SHEETS of a lattice.

Verify that your device is correctly calibrated on fast, and on a slow direction of scanning. Check up how speed of scanning and feedback parameters influence the image.

Pay attention to distortions caused by such parasitic effects connected with piezoceramics, as nonlinearity, hysteresis, creep (check the appropriate items of the description for more detailed information).

3.2 Determination of scanning nonlinearity

Scanned image distortion results from nonlinearity, hysteresis and creep of piezoceramics response to applied voltage.

To measure this distortion you can use TGX01 grating. It is structure with edge shape determined by silicon crystal structure. That ensures the edge roughness value of few nanometers (fig.8) and provides right geometrical shape of square.

Fig.8 shows the characteristic images of that grating scanned without and with correction of nonlinearity. Compare the images to photo of the grating in fig.2. Changing the size and position of a scanning area you can determine degree of dis-tortion for various operation parameters.


Fig.8a. Image of TGX01 with 20x20um image without correction of nonlinearity.		Fig.8b. Image of TGX01 with 20x20um image with software correction of non-linearity.

Due to its precise geometry, the structure can be used to measure distortions caused by scanner nonlinearity aver the total scanning range. 40x40 um scan image and nonlinerity dependence versus the distance from the center of the scan are show in fig.9.

Fig. 9. Nonlinearity dependence versus the distance from the center of the scan.

To check Z-axis nonlinearity of your device you should scan the whole set of heights (TGS01, it consists of TGZ01,TGZ02,TGZ03).

To check up nonlinearity of the scanner in lateral and normal directions and angular distortion use TGG01 grating (fig.3 and fig.10). Grating sides formed by silicon planes (111). Top angle between sides is formed by planes (111) and is equal 70°.

Fig.10.

Image of TGG01 taken with 20x20 mm scanner (scanning probe microscope SOLVER model Solver-P4) with Mi-crolever PSI cantilever. On cross section of a grating it is possible to check up nonlinearity of the scanner in lateral and normal direc-tions and angular distortion (top angle is formed by planes (111) and is equal 70°). Curvature radius of edge in the image is equal to the sum of curvature radii of cantilever tip and grating edge.

3.3	Determination the distortion of object shape caused by CREEP-effect

To avoid distortion connected with lateral creep-effect the scanning speed should be decreased and the scanning of object should be repeated in 1-2 minuets after first scanning. However, distortion of object edges with large slope caused by normal creep effect could be only evaluated. Carry out the scanning TGX for deter-mination the value of this effect in your device. The grating edge distortion image permits to estimate and minimize CREEP-effect value of your device (fig.11). Pay attention to how the image in fast and slow directions is formed, how the scanning directions effect on edge form distortion.


Fig.11a. Image of TGX01 taken with 20x20 mm scanner (scanning probe microscope SOLVER model Solver-P4). There is not grating edge distortion on cross section of a grating (Y-direction scan-ning).		Fig.11b. The same image of TGX01, as in fig.11a. On cross section of a grating the grating edge is distorted. The scanner moves over grating edge when tip climbing grating side.

Fig.11c.

The same image of TGX01 as in fig.11b. There is not grating edge dis-tortion on cross section of a grating due to scanning direction was changed.

3.4	Full 3-D image of the cantilever tip observing, its curvature radius measurement

Any SPM image represents not only the sample itself but also the shape of a cantilever tip used for getting that image [1,2]. Moreover, the shape of the tip can be changed during scanning [3], thus causing different distortions of the image. For the correct interpretation of the image data it is useful to determine the tip shape before scanning and check if it has been changed afterwards.

We produced especial tip characterizer TGT01. It is an array of tips with full cone angles less than 20 degrees and radii of curvature less than 10 nm (fig.4). The tips are arranged into a square grating with 2.12 um pitch (3 mkm diagonal length). Tip height is about 0.6-0.8 um. At the least one tip has to be found for scan size of about 3 um.

The main advantages of this characterizer are:

strict symmetry of tip sides;
small angle between tip sides (less than 20 degrees);
small curvature radius of tips (less than 10 nm).

We used this structure to inspect common SPM cantilever tips: Si₃N₄ pyramid, sharpened Si₃N₄ pyramid and Si cone tips. Corresponding scanned images are presented in fig.12-14. The scans have been got with scanning probe microscope Solver-P4 in semicontact mode. It should be noted that the scanning tip gives an inverted image of itself, and therefor it is a mirror transformation of the real tip shape (compare SPM images and SEM photos of the same tips in fig.12-14). But for the same reason the object distortion caused by the tip shape is also a mirror transformation of the tip features.

Fig.12. SPM and SEM images of Si₃N₄ pyramid tip.

An images of commercial Si₃N₄ cantilever with pyramid tip is presented in fig.12. The left one has been got by scanning over our tip characterizer and the right one with SEM. SFM image reveals the characteristic features if the tip: flat top area with size of about 0.1 mm and surface roughness. Tip shape is completely reproduced. Pyramids on the SPM image are inclined on 20 degrees. This is the angle between the cantilever plane and the sample (TGT01).

[Image]

Fig.13. SPM and SEM images of sharpened Si₃N₄ pyramid tip.

An images of commercial Si₃N₄ cantilever with Sharpened Microlever PSI cantilever is presented in fig.13. SPM images (cross section of SPM image) permits to measure the sum of cantilever tip curvature radius and that of charcterizer tip. It is equal to about 250 angstroms that corresponds to the nominal sharpened tip radius (200 angstroms) plus characterizer tip radius (less than 100 angstroms).

[Image]

Fig.14. SPM image and cross-section of ULTRASHARP Si cone tip (NT-MDT).

An image of silicon cone tip of ULTRASHARP cantilever produced by NT-MDT is presented in fig.14. The sum of cantilever and grating tips radii is equal to 150 angstroms, that corresponds to nominal radii of both tips less than 100 angstroms.

As mentioned above, the tip destruction and pollution are possible when the object is scanned. It will lead to some distortion of the obtained image. When studying some biological objects (E-coli) we observed dramatic decrease of image quality after scanning in contact mode. We used the test array to compare tip shape before and after the scanning of biological objects. Corresponding images are presented in fig.15-16.

Fig.15. An image of the cantilever tip before contact mode scanning the sample with deposit E-coli. Fig.16. An image of the cantilever tip after contact mode scanning the sample with deposit E-coli.

The image in fig.16 reveals strong contamination of the tip that can cause substantial distortion of the shape of scanned objects.

In case the obtained image has unsatisfactory parameters (large curvature radius of tip, wrong geometrical shape), repeat the measurement of another grating tip or part of grating.

When tip image features repeat while scanning different grating parts, turn the grating on any angle and repeat measurement. The image distortions caused by cantilever tip will keep their orientation. The image distortions caused by grating tips will turn round (fig.17).

Fig.17a. The image of Microlever Sharpened cantilever taken by scanning TGT01. The tip shape is completely reproduced. On the front side of image the fifth edge is observed. This edge belongs. Fig.17b. The image of the same Microlever Sharpened cantilever taken by scanning TGT01 after turning round of grating. The fifth edge is turned round at 450. The other features kept the orientation.

If the object sides are more vertical than cantilever tip sides it is possible to find out a number of object shape distortions when carrying out the scanning of TGX01. The images of TGX01 obtained by different types of cantilevers are given in fig.18. Pay attention to specific distortions of grating shape of these cantilevers types.

Fig.18a.The image of the TGX01 part taken by ULTRASHARP cantilever (angle between tip sides is less than 200). The step high is 1500 nm. The tip reaches the grating bottom. Fig.18b. The image of the same TGX01 part taken by Microlever Sharpened cantilever (angle between tip sides is about 700). The step high is 800 nm. The tip does not reach the grating bottom due to angle between sides is more larger.