How the x-ray detector is specified by means of the graphical user interface (GUI) is described in Chapter 5. In this chapter it is only referred to the actual input files which are read by SESAME during program execution.
The x-ray detector is fully determined by the direction to the detector the detector efficiency, the solid angle of detection, the energy resolution, and the detector type (ED or WD). The direction to the detector determines the proportion of x-rays which is absorbed in the sample from the location of their generation to the sample surface. The detector efficiency describes the proportion of detected x-rays in relation to their energies. All variables needed to specify an x-ray detector are summarized in table 6.3.
Table 6.3: Variables needed for the specification of the x-ray detector
The absorption of x-rays in the sample is determined by the location of the detector which can be described simply by a direction. This direction is defined through the take-off angle - this is the angle between the target surface (x-axis of the coordinate system in which the target geometry is defined) and the direction to the detector - and the detector rotation angle - this is the angle between the simulation plane (x-z plane) and the direction to the detector (see Figure 6.2 and 6.3).
The take-off angle may be specified using the TAKOFF variable in the &MSETUP namelist - the default value is 30 degrees (see Chapter 9.6). The detector rotation angle can be specified by the XDEROT variable in the &MSETUP namelist - the default value is 0 (see Chapter 9.6).
Two options can be taken to specify an x-ray detector efficiency in the input deck. The first uses a linear combination of Beer's law taking into account all absorbing layers and the active layer of a semiconductor detector, for instance a Si(Li)-detector.
Generally, the detector efficiency of such a detector will be calculated by the following formula,
n being the total number of specified layers. E is the x-ray energy of
interest, the mass absorption
coefficient of x-rays with energy E in layer i in
,
the
density in
, and
the thickness of layer i. Note, that the last (n-th) layer specified in the
input deck is always an active layer represented by the first factor in the
above equation.
A typical energy dispersive x-ray detector system with a Be detector window and a Si(Li)-detector, for instance, shall be described in the following paragraphs.
The first absorbing layer is the detector window (see Figure 6.5). This window can be made from a variety of materials. Historically, a beryllium window, typically about 7.6 microns thick, has been used. During the last several years window materials with considerably less mass-thickness have been gaining wide popularity. These window materials are either boron, silicon nitride, diamond or are organic.
The second absorbing layer is a surface-barrier contact about 20 nm thick and usually made of gold. The third layer in front of the active region is an inactive layer of silicon extending 200nm or less into the detector. This layer is often called the silicon dead layer. The radiation then enters the active (intrinsic) region of the detector which has a thickness typically between 2 and 5 mm.
Modelling the transmission through these various layers can be achieved by applying the linear combination of the already mentioned Beer's law which can be written in the following form:
,
,
, and
are the thicknesses of the
Be detector window, the Au surface-barrier contact, the Si dead layer, and the
Si active layer, all in cm, respectively.
is the mass absorption coefficient of x-rays with energy E in
Material X in
.
The quantities of this equation may be specified in the input deck.
XLAYTH is an array containing the thicknesses in microns of all layers,
including the detector window and the active area. Note, that although the
layer thicknesses used in the formula are in cm, their specification in the
input deck must be in microns! The last entry in this array
which is greater than zero is considered to describe the active area.
Additionaly, it is necessary to specify the densities for each layer in the
XLAYDN array (in ).
The composition of these detector layers is specified by the array XLAYMAT. XLAYMAT is exactly defined according to ATMAT, the array for specifying the target composition, in the &TARGET namelist. XLAYMAT contains the chemical abbreviations of all elements of the detector layers and their relative fractions. The chemical abbreviations in one layer as well as the strings describing different layers must be separated by commas ( Note: strings must be enclosed by single quotes!). Relative fractions of elements in one layer must, if necessary at all, be specified right after the corresponding chemical abbreviation without a blank, comma or any other character inbetween. In this particular example, for instance, the first layer is composed of pure beryllium, the second layer is pure gold, the third and the forth region are pure silicon.
Additionaly, a detector type - either energy- or wavelength-dispersive - may be specified by means of the XDTYPE variable in the &DETECT namelist. Furthermore, the energy resolution of such a detector may be specified using the Full Width at Half Maximum (FWHM) definition. The FWHM is energy dependent and for an energy dispersive system the FWHM value for a certain x-ray energy may be calculated using the following formula:
This equation takes advantage of the fact that the noise is constant for
a given detector, operated under a fixed set of conditions. By specifying
only a reference energy ENFWHM () and a full width at half
maximum FWHM at this energy (
) it is possible to calculate
the detector resolution for any peak located at any place in a spectrum.
The specification of this detector (detector number 2) in the input deck would look like following:
&DETECT SOLIDA=0.0083 XDTYPE='ED' FWHM=150,ENFWHM=5899 XLAYMAT(2,1)='BE',XLAYTH(2,1)=7.6,XLAYDN(2,1)=1.86 XLAYMAT(2,2)='AU',XLAYTH(2,2)=0.02,XLAYDN(2,2)=19 XLAYMAT(2,3)='SI,O2',XLAYTH(2,3)=0.2,XLAYDN(2,3)=2.2 XLAYMAT(2,4)='SI',XLAYTH(2,4)=4000,XLAYDN(2,4)=2.33 &ENDThe second option is to specify the detector efficiency by stating a file name of an ASCII file containing the detector efficiency in the input file. This file must contain two columns, the first representing the energies and the second representing the corresponding detector efficiency values. Linear interpolation is used to find detector efficiency values between the discrete energies stored in the file. Comment lines may be written to the detector efficiency file using a ''#'' as the first character of a line. Specification of a detector efficiency file can be done by using the XEDEFF variable (see Chapter 9.8). An example of an x-ray detector efficiency file may be copied from:
VMS DISK$AXP_USER1:[SLED.NEW.SESAME.EXA]EXA1.EFFUnix
tcad/sesame/exam/EXA1.EFF
The full specification of an x-ray detector, describing the detector position, the detector efficiency (detector efficiency file), the solid angle of detection, and the energy resolution is given in the following example:
&MSETUP TAKOFF=37.5 XDEROT=0.0 &END &DETECT SOLIDA=0.0083 XDTYPE='ED' FWHM=150,ENFWHM=5899 XEDEFF='EXA1.EFF' &ENDThe location of the detector is defined in the &MSETUP namelist whereas other detector specific parameters like the detector efficiency are specified in the &DETECT record. In this case the detector efficiency shall be read from the file EXA1.EFF.
The file EXA1.EFF may contain the following lines:
# THIS IS AN X-RAY DETECTOR EFFICIENCY # ENERGY(KEV) DETECTOR EFFICIENCY 0 0 0.5 0.3 1 0.5 2 0.7 3 0.85 4 0.93 5 0.98 15 0.98 20 0.9 30 0.7 50 0.5