Scanning Electron Microscopy and X-Ray Microanalysis

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5

Elevation (Take-Off ) Angle, ψ, and Azimuthal

Angle, ζ

The effective position of a detector is specified by two angles.

The elevation (“take-off”) angle, designated ψ, is the angle

above a horizontal plane perpendicular to the beam axis and

the vector that joins the center of the detector to the beam

impact position on the specimen, as shown in. Fig. 5.19a.

(Alternatively, the take-off angle can be measured as the

complement of the angle between the beam axis and a line

perpendicular to the detector face extended to the beam optic

axis.) The “azimuthal angle,” ζ, of the detector is the rotational

angle around the beam to the detector line, measured relative

to some arbitrary but fixed reference, such as the front face

of the specimen chamber, as shown in. Fig. 5.19b. When an

SEM image is created, it is critical for the user to understand

the relative position of the detector in the scanned image, as

given by the azimuthal angle, since the illumination of the

image will apparently come from the detector. Note that the

“scan rotation” function, which permits the user to arbi-

trarily choose the angular orientation for the presentation

of the image on the display, also varies the apparent angular

location of the detector. It is therefore critical for the user to

establish what setting of scan rotation corresponds to the cor-

rect known value of the detector azimuthal angle.

kGood Practice

Make a drawing (top view and side view) of the SEM cham-

ber showing the physical locations of all detectors (electron,

X-ray, and cathodoluminescence) and mark the values of the

elevation angle, ψ, and azimuthal angle, ζ.

Solid Angle, Ω

As shown in. Fig. 5.20, the effective size of the detector with

an active area A placed at a distance r from the beam impact

point on the specimen is given by the solid angle, Ω (Greek

omega, upper case), which is defined as

Ω=Ar/,^2 ()steradianssr

(5.13)

Note the strong dependence of Ω upon the distance of the

detector from the beam impact on the specimen.

As an estimate of the overall geometric efficiency, ε, the

solid angle of the detector can be compared to the solid angle

of the hemisphere (2π sr) into which all electrons leaving a

thick target are emitted:

εΩ= /2π (5.14)

ε provides only an estimate of efficiency because the simple

definition in Eq. (5.14) does not consider the non- uniform dis-

tribution in the emission of electrons from the specimen, for

example, the cosine distribution of BSE at normal incidence.

Elevation angle, ψ

ab

Side view Top view

Azimuthal angle, ζ

Arbitrary fixed

reference line

within specimen

chamber, e.g.,

parallel to front

face

. Fig. 5.19 a Detector take-off angle, ψ. b Detector azimuthal angle around beam, ζ

Solid angle,

Ω = A/r^2

Ω

A

r

. Fig. 5.20 Detector solid angle, Ω

Chapter 5 · Scanning Electron Microscope (SEM) Instrumentation