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Electron Microscopy Sciences

Technical Data Sheets

MAG*I*CAL™ Calibration Standard for TEM

EMS Catalog #80069

Aligning the Reference Standard

The MAG*I*CAL ™ Calibration Standard is made from a single crystal of silicon, and therefore has many very useful attributes as a TEM standard. To take advantage of these attributes, mount the standard in the TEM sample holder with the epoxy line of the standard parallel to the stem of the TEM sample holder (see Fig.2, next page). Translate the standard to bring into view the calibration marks close to the thin edge near the perforation in the center of the sample (arrows, Fig. 2), and focus. Put the TEM into diffraction mode, choose the smallest camera length, and adjust the intensity control (condenser control) back and forth to find the proper value of over-focus that forms the striking pattern called a Kikuchi pattern, similar to Fig. 1 below, but perhaps rotated. These Kikuchi bands are formed by elastic Bragg scattering of previously inelastically scattered electrons.

The intensity control can be adjusted so that either a diffraction spot pattern or a Kikuchi pattern can be observed. The standard should be tilted to move the Kikuchi pattern so that the central “intersection” in this diagram (where the largest number of bands intersect) is centered on the brightest (zero order) diffraction spot in the electron diffraction pattern (adjust the intensity control back and forth). It may be necessary to translate the standard to slightly thicker or thinner regions to get a clear Kikuchi pattern.

kikuchi pattern

Fig. 1: Kikuchi pattern of single crystal silicon viewed down the <011> zone axis. The broad horizontal band in the center of this figure is between the {200} Kikuchi lines.

Image Magnification Calibration

The MAG*I*CAL calibration reference standard for transmission electron microscopy (TEM) consists of an ion-milled cross-section of a silicon wafer on which a series of calibration marks were deposited. The spacings between these calibration marks are very accurately known, and are included on the accompanying sheet entitled “LAYER THICKNESS VALUES”. There are four regions on the standard that contain the calibration marks. These four areas are marked by arrows on both the drawing and the photograph in Fig.2, two on either side of the thin epoxy line which joins two pieces of the silicon wafer which are mounted face-to-face. The central perforation in the standard is small, as shown in the drawing (approximately 0.1 mm in diameter - see the color image). Note that the epoxy line is very thin.

scale

Fig. 2: Diagram, photograph and color/thickness scale of the MAG*I*CAL® reference standard. The arrows on the drawing and photograph indicate the four regions on the standard where the calibration marks may be found.

The magnification calibration is the most common calibration, since it’s important to know if the magnification value on the microscope console or on the image is accurate, and if not, how to correct the value. This calibration procedure is simple in concept. A TEM image is taken of a calibration reference standard with a known (true) feature size. The calibrated (true) magnification is then calculated by dividing the measured feature size on the image by the known feature size. This calibrated magnification value is then used for accurate calculations of feature size whenever this magnification range is used in the future (see example below).

STEP 1: Mount the MAG*I*CAL® in the TEM sample holder so that the MAG*I*CAL® epoxy line is parallel to the stem of the TEM sample holder.

STEP 2: Find one of the regions of interest (marked by arrows in Fig. 2) by translating the standard in the microscope, and focus on the layered structure (Fig. 3).

STEP 3: The sample height should be adjusted so that the MAG*I*CAL® is at the eucentric position (see TEM manual). On microscopes with no sample height adjustment, the objective lens current must be monitored and kept constant at each magnification value.

figure 3

Fig. 3: TEM micrograph of the MAG*I*CAL®. Inset shows a higher magnification image of one of the layered structures. Four identical structures are found at each of the four locations shown by arrows in Fig. 2.

STEP 4: Switching to diffraction mode, tilt the MAG*I*CAL® so that the electron diffraction pattern or the Kikuchi pattern is exactly centered. The earlier page, “Aligning the Reference Standard) gives more detail on how to do this. The TEM electron beam should be exactly perpendicular to the MAG*I*CAL® reference standard (the TEM beam being parallel to the crystal zone axis of the silicon crystal material which forms the MAG*I*CAL®). If using the Kikuchi pattern, the image should look similar to Fig. 4.

Figure 4

Fig. 4: Kikuchi pattern of the [011] crystal zone axis of Si. The arrows show the location of the broad band between the {200} Kikuchi lines. When the electron diffraction pattern is centered anywhere along this band, the electron beam will be parallel to the layered structure, and result in accurate layer thickness values.

STEP 5: Focus the microscope on the region shown in fig. 3 at the highest magnification range available. A series of micrographs or digital images at all magnification ranges should be taken starting at the highest magnification range and working down to the lowest. The measured length on the micrograph or digital image can then be compared to the calibrated values on the attached sheet labeled “Layer Thickness Values”.

STEP 6: The most accurate calibrations at the highest magnification ranges (>400,000) can be accomplished by forming a lattice image of the Si material below the layered structure (Fig. 5).

Measure the perpendicular distance across a large number of (111) lattice fringes, then divide this length by the number of fringes. This gives the measurement on the micrograph or digital image that corresponds to the (111) lattice spacing of Si (0.3135428 nm.).

Fig 5

Fig. 5: Lattice image of Si viewed down the [011] zone axis, recognizable by the central diamond shape formed by the rows and columns of Si atoms. The lines marked parallel to the upper two sides of the diamond shape indicate (111) planes, with an interplanar spacing of 0.3135428 nm. Note that measurements must be made perpendicular to the (111) planes, since the planes viewed from this zone do not meet at right angles.

STEP 7: Make up a table of calibration values similar to Table 1 below, recording the Nominal Magnification (the magnification given on the TEM) with the Calibrated Magnification (the actual magnification determined by comparing the measured feature size from your micrograph or digital image, and the actual feature size, as taken from the attached sheet labeled “Layer Thickness Values”).

 

Nominal Calibrated Correction Nominal Calibrated Correction
650,000 647,000 .995 42,500 44,500 1.047
550,000 508,000 .923 30,600 30,500 .997
420,000 378,000 .900 21,200 21,800 1.028
340,000 347,000 1.021 17,100 17,500 1.023
260,000 267,500 1.023 13,600 14,000 1.029
160,000 161,000 1.006 10,300 10,700 1.039
122,000 124,600 1.021 7400 7750 1.047
88,600 91,200 1.029 5550 5900 1.063
69,000 71,000 1.029 4450 5170 1.162
52,100 54,000 1.036 3900 4200 1.077


Table 1: Magnification Calibration; 250 keV, Philips EM430 TEM, December, 2006.

Example: Suppose that a feature that is known to be 1.00 micrometer (1.00 *10-6 m) in length is imaged, and the Nominal (instrument) Magnification is given as 10,000X. If the image is measured digitally or on the film negative as being 1.10 cm (1.10*10-2 m), compute the calibrated magnification:

 

calibrated magnification
= measured size / known size
  = 1.10 *10-2 m / 1.00 *10-6
  = 11,000X

 

In the future, any time the 10,000X calibration range is used, the operator will know that the calibrated magnification value is actually 11,000X, and will correct the measurement accordingly.

Helpful Hints for Magnification Calibration:

• Sample alignment: the calibration reference standard must be perpendicular to the electron beam, or errors will result. A tilted MAG*I*CAL® reference standard will result in narrower light contrast material spacings, and broader dark contrast material spacings. Any tilt away from the correct zone axis will make crystal lattice spacings unobservable. Follow the procedure given in ‘Aligning the Reference Standard’.

• Eucentric height: the reference standard must be positioned at the eucentric height. This point in the microscope column is fixed and does not change. Positioning the standard at this reference point allows the standard to be tilted without changing its height on the optic axis, so it stays in focus. In addition, the objective lens and the intermediate 1 lens (the first lens in the projector system) are then always set to the same value for every sample, so all measurements remain consistent. If there is some difficulty using the eucentric height (top entry STEMs), then standardize on a particular objective lens current, which is another way to provide the same benefits.

• Hysteresis: electronic and mechanical devices sometimes overshoot or undershoot when a range is changed, and usually repeat this behavior consistently. When calibrating, start at the highest magnification range and work down to lower ranges, generating consistent hysteresis effects. When acquiring an important image, initially set the TEM to a higher magnification range, and then lower the range to the desired magnification

• Overfocus first, and then focus. This provides fine-tuning of lens hysteresis effects, and will help standardize the lens currents for important measurements.

• Measure directly on the film negative if using film. Do not measure from a print. Make several measurements on the negative and average them, and avoid using the edges of the negative where
there can be distortions from lenses, especially at lower magnifications.

• Digital images: there are a wide variety of digital techniques for making measurements. Choose one procedure for all measurements of both reference standards and test samples, so that all measurements are made in a consistent manner.

• Verify: Measure the same feature at 2 or more magnifications and compare the results to avoid errors.

Camera Constant Calibration

The camera constant calibration is the most common calibration used in electron diffraction. It allows the microscopist to identify the crystal lattice spacings of the material being observed, which helps to identify the material. This identification is accomplished by measuring distances between spots on a single crystal (spot) diffraction pattern, or ring diameters on a polycrystalline diffraction pattern. This calibration makes use of the Camera Constant equation (derived from Bragg’s law with the small angle approximation):

λL
= dhkl R
where:  
λ
= wavelength of the TEM accelerating voltage (nm)
L
= camera length (mm)
dhkl
= lattice spacing (nm)
R =
measured distance between two adjacent diffraction spots on a single crystal diffraction pattern 7 or half the diameter on a polycrystalline diffraction pattern (mm)

 

Note that this definition is set up for nm-mm, but there are many choices for units. With digitized images, Angstrom-pixel or nm-pixel are good options.

The product λL is called the Camera Constant. While the exact values for ‘λ’ ‘L’ are difficult to measure accurately, values for both ‘dhkl’ and ‘R’ are easily acquired by making careful measurements of ‘R’ and using a reference standard with a known value of ‘dhkl’. A table similar to Table 2 should be assembled of Camera Constant values for each combination of TEM accelerating voltage and each nominal camera length ‘’ (the camera length as given on the console). This can be quite time consuming, since we need a complete series of diffraction patterns at all camera lengths for each accelerating voltage. Some microscopists perform all of their diffraction measurements at a favorite accelerating voltage, to cut down on the number of tables needed.

Once this table is complete, the microscopists know that any time they choose a particular camera length ‘L’, they can divide that Camera Constant value by the measured diffraction spot spacing of their sample, and accurately determine the crystal lattice spacing of that material. An example may make this more understandable.

Table 2: Camera Constants for a Philips EM430T TEM, operating at 250 kV, December, 2006).

Camera Length (mm) λL (nm*mm) Camera Length (mm) λL (nm*mm)
270 0.493 1650 3.45
350 0.664 2200 4.63
500 0.986 2900 6.13
700 1.414 3600 7.63
950 1.950 5000 10.63
1200 2.49 6300 13.41

Example:

Fig. 6 shows a positive image of an electron diffraction pattern taken of single crystal silicon (the MAG*I*CAL® reference standard) with the beam parallel to the [011] crystal zone axis (defined as the [011] beam direction). The diffraction pattern was taken at a nominal camera length of 1650 mm. Fig. 7 shows a set of indexed (identified) diffraction spots of silicon calculated for the [011] beam direction, which we can use as a map for identifying the spots on the diffraction pattern. By examining the patterns carefully (notice this is not a ‘square’ pattern), we can identify the unknown spots in Fig. 6 as lying along one of the {111} systematic rows, as indicated by the double-arrowed line in both images. The double-arrowed line in Fig. 6 indicates a distance ‘x’ that is four times the distance between two adjacent {111} spots, so R = x/4. Our measurement of Fig. 6 gave a value of 44.0 mm, so ‘R’ = 11.0 mm. We know that the (111) lattice spacing of silicon is nominally equal to 0.314 nm (available in Handbook of Chemistry and Physics [1], as well as many other references).

Therefore, to find the Camera Constant for L = 1650 mm:

λL
= d111 R
  = 0.314 nm X 11.0 mm
  = 3.45 nm-mm

 

This value was entered into Table 2, along with the same calculation for the other camera lengths available with this instrument. These values can also be graphed, and the results will be linear if the manufacturers’ values for the camera lengths are accurate.

figure 6 7

Fig. 6: Electron diffraction pattern from single crystal silicon, with the beam parallel to the [011] zone axis.

Fig. 7: Indexing of single crystal silicon diffraction pattern, with the beam parallel to the [011] zone axis.

Helpful Hints; Camera Constant Calibration:

• Eucentric height: the standard must be positioned at the TEM’s eucentric height. If that is not possible, then standardize on a particular objective lens current so all images are taken with the sample at the same height in the microscope column.

• Alignment: For the MAG*I*CAL® and single crystal TEM samples, ensure that the sample is aligned so that the beam is parallel to the zone axis of the crystal.

• Hysteresis: Start at highest camera length and work down to provide consistency and to avoid hysteresis effects. When taking an important diffraction pattern, initially set at a higher camera length, and then lower the setting to the desired camera length.

• (S)TEM: If your instrument is a true (S)TEM, the Camera Constant calibrations may vary depending on whether you are in STEM or TEM mode. Check this.

• For diffraction patterns: the intermediate 1 lens needs to be focused properly on the diffraction pattern.

There are several methods to do this and both the standard and unknown must be focused in the same way. In the first way, the condenser is set fully clockwise and then the diffraction spots are focused to the smallest size. In the second way, the objective aperture is inserted into the diffraction pattern and its edge is set to be as sharp as possible. In the third way, a focused convergent beam pattern is formed and the shadow edge of the condenser aperture is focused.

Image / Diffraction Pattern Rotation Calibration

The image / diffraction pattern rotation calibration is used to identify the orientation of crystalline material relative to other crystals, features or interfaces in your sample. For this calibration, it is necessary to take double exposures of the reference standard image plus the reference standard diffraction pattern, at each magnification range and at each camera length for every accelerating voltage of interest. This is a lot of images!

 

Fig. 8 shows an example of a double exposure of the MAG*I*CAL® reference standard (plus an inset image showing the detail of one of the layered structures). In Fig. 8, the [100] direction is‘up’ in the image, but at an angle of about 67° to the (200) reflection (spot) shown on the diffraction pattern (see Figs. 6 and7). To measure the rotation calibration values, draw a line from the zero order diffraction spot up through the (200) spot. Also draw a line from the zero order spot in a direction perpendicular to the layered structure. The angle θ between these two lines is the rotation calibration value for this magnification/camera length condition, and can now be used to identify crystal direction in unknown samples, when the images and diffraction patterns of the unknown material are taken at the same magnification/camera length condition.

figure 8

Fig. 8: Double exposure of the image and the electron diffraction pattern from a single crystal silicon region of the MAG*I*CAL® reference standard.

A table is made of all magnification ranges (for the images) versus all camera constants (for the electron diffraction patterns) to display this data. Choose a standard way of presenting the measurements, such as: “Angle θ measured counter-clockwise from diffraction spot to image direction”, and include this information with your chart. This will help avoid symmetry errors. See Table 3 for an example. As mentioned, this is a lot of measurements - this table is for only a single accelerating voltage!

Table 3: Image / diffraction pattern rotation calibration - 250 keV, Philips EM430T, December, 2006.

  Angle θ counterclockwise from diffraction spot to image direction
MAGNIFICATION > 5550 9400 10300 13600 17100 21200 30600 42500 52100
CAMERA LENGTH                  
270 61.0 62.0 67.0 64.5 68.0 63.0 95.5 328.5 330.0
350 49.5 50.5 55.5 53.0 56.5 51.5 84.0 317.0 318.5
500 15.0 16.0 21.0 18.5 22.0 17.0 49.5 282.5 284.0
700 142.0 143.0 148.0 145.5 149.0 144.0 176.5 49.5 51.0
950 139.5 140.5 145.5 143.0 146.5 141.5 174.0 47.0 48.5
1200 135.5 136.5 141.5 135.0 142.5 137.5 170.0 43.0 44.5
1650 130.5 131.5 136.5 134.0 137.5 132.5 165.0 38.0 35.5
2200 123.0 124.0 125.0 126.5 130.0 125.0 157.5 30.5 32.0
2900 115.0 116.0 121.0 118.5 122.0 117.0 149.5 22.5 24.0
3600 105.5 106.5 111.5 107.0 112.5 107.5 140.0 13.0 14.5
5000 86.0 87.0 92.0 89.5 93.0 88.0 120.5 353.5 355.0
6300 64.0 65.0 70.0 67.5 71.0 66.0 98.5 331.5 333.0
                   
MAGNIFICATION > 69000 88600 132000 160000 260000 340000 420000 550000 650000
CAMERA LENGTH                  
270 331.5 338.5 339.5 337.0 18.0 41.0 65.0 49.5 85.5
350 320.0 327.0 328.0 325.5 6.5 29.5 53.5 38.0 72.0
500 285.5 292.5 293.5 291.0 332.0 355.0 19.0 3.5 37.5
700 52.5 59.5 60.5 58.0 99.0 122.0 146.0 130.5 164.2
950 50.0 57.0 58.0 55.5 96.5 119.5 143.5 128.0 162.0
1200 46.0 53.0 54.0 51.5 92.5 115.5 139.5 124.0 158.0
1650 41.0 48.0 49.0 46.5 87.5 110.5 134.5 115.0 153.0
2200 33.5 40.5 41.5 39.0 80.0 103.0 127.0 111.5 145.5
2900 25.5 32.5 33.5 31.0 22.0 45.0 113.0 103.5 137.5
3600 16.0 23.0 24.0 21.5 62.5 85.5 109.5 94.0 128.0
5000 356.5 3.5 4.5 2.0 43.0 66.0 90.0 74.5 105.5
6300 334.5 341.5 342.5 340.0 21.0 44.0 68.0 52.5 86.5

 

Symmetries can cause errors of 180° and/or other angles – see Fig. 7. Two techniques that eliminate this ambiguity can be used with the MAG*I*CAL® reference standard. First, to confirm the identity of the (200) diffraction spot, slowly translate the standard ‘up’ through the layered structure and past the top surface while viewing the diffraction pattern. As the standard is translated past the top surface into empty space, the diffraction pattern will fade and finally disappear first from the direction corresponding to the (200) diffraction spot. Second, if a convergent beam pattern of the standard is obtained and the condenser is then underfocused (crossover below the standard), a shadow image of the standard will appear in the central (bright field) spot, and the orientation of the standard relative to the diffraction pattern can be recorded.

Helpful Hints; Image / diffraction pattern rotation calibration:

• All of the ‘Helpful Hints’ for both images and diffraction patterns apply.

• Choose the single most useful accelerating voltage and only the most useful magnification ranges and camera lengths, to keep the amount of measurements down to a manageable level. When measuring an unknown sample, make sure to set the instrument to the same parameters that were used for the calibration.

Layer Thickness Values

layer thickness

To improve accuracy when making measurements, always measure the largest distance clearly visible on the micrograph. For example, at the highest magnification ranges, measure the distance across the entire set of five dark layers and four light layers, instead of trying to measure an individual dark layer.

Online Ordering

MAG*I*CAL™ is available online from the EMS Catalog. For ordering or product information, click here.

Additional Documents

MAG*I*CAL Technical Reference PDF
MAG*I*CAL™ Standard Certificate Examples
MAG*I*CAL™ Standard Quality Check and Handling