Fox, M..D., Frizzell, L.A., Franks, L.A., Darken, L.S., James, R.B. “Medical Imaging”
The Electrical Engineering Handbook
Ed. Richard C. Dorf
Boca Raton: CRC Press LLC, 2000
116
Medical Imaging
116.1 Tomography
Computerized Tomography ? Positron Emission
Tomography ? Single Photon Emission Computed
Tomography ? Magnetic Resonance Imaging ? Imaging
116.2 Ultrasound
Fundamentals of Acoustics ? Principles of Pulse-Echo
Ultrasound ? Future Developments
116.3 Semiconductor Detectors for Radiation Measurements
Cryogenic Detectors ? True Room-Temperature Detectors ?
Silicon Detectors ? Prices and Availability
116.1 Tomography
M. D. Fox
The term tomography derives from the Greek tomos (cutting) and grapho (to write). Originally the term was
applied to sectional radiography achieved by a synchronous motion of the x-ray source and detector in order
to blur undesired data while creating a sharp image of the selected plane. The term tomography was used to
distinguish between such slices and the more conventional plain film radiograph, which represents a two-
dimensional shadowgraphic superposition of all x-ray absorbing structures within a volumetric body.
Computerized tomography, also known as computerized axial tomography, was introduced by EMI, Ltd.
in 1973 and transformed medical imaging by obviating the superposition of intervening structures present in
conventional radiographic images. Initially, the clinical application was for imaging the head, but soon the
technique found wide application in body imaging.
As medical imaging has evolved into a multimodality field, the meaning of tomography has broadened to
include any images of thin cross-sectional slices, regardless of the modality utilized to produce them. Thus,
tomographic images can be generated by magnetic resonance imaging (MRI), ultrasound (US), computerized
tomography (CT), or such nuclear medicine techniques as positron emission tomography (PET) or single
photon emission computerized tomography (SPECT). For the purposes of this discussion we will cover all of
the foregoing modalities with the exception of ultrasound, which will be treated separately.
Since the power of such computerized techniques was recognized, the practice of radiology has been revo-
lutionized by making possible much more precise diagnosis of a wide range of conditions. In this necessarily
brief discussion we will describe the basic physical principles of the major tomographic modalities as well as
their key clinical applications.
Computerized Tomography
The basic concept of computerized tomography can be described by consideration of Fig. 116.1. An x-ray source
is passed through an aperture to produce a fan-shaped beam that passes through the body of interest with
absorption along approximately parallel lines. The natural logarithm of the detected intensity will be the integral
of the linear attenuation coefficient of the object along the ray directed from the source to the detector element.
If the source and the detector array are synchronously rotated about a point within the object, a number of
M. D. Fox
University of Connecticut
Leon A. Frizzell
University of Illinois
Larry A. Franks
Sandia National Laboratories
Larry S. Darken
Oxford Instruments
Ralph B. James
Sandia National Laboratories
? 2000 by CRC Press LLC
? 2000 by CRC Press LLC
APPARATUS AND METHOD FOR
DETECTING CANCER IN TISSUE
Raymond V. Damadian
Patented February 5, 1974
#3,789,832
Excerpts from Raymond Damadian’s patent application:
...It has now been found that, by measuring the degree of organization of these selected molecules in cells
being studied and comparing this with the degree of organization in a known cancerous cell, cancer cells can
be detected. Furthermore, it has now been found that the less the organization the greater the malignancy,
therefore a scale can be made to provide a standard for basing a decision on the degree of malignancy...
...Further apparatus is provided for scanning throughout the entire body during which time the relaxation
times are measured for selected nuclei and compared with standards. In this way a determination can be
made of the existence of cancer together with the location and degree of malignancy of the cancerous cells
present....
This patent describes a device that uses very powerful magnetic fields to resonate the nuclei in cells
in a body. Collapsing the field and measuring the relaxation times gave a comparison to healthy cells.
Later advances in digital signal processing have resulted in magnetic resonance imaging (MRI) equipment
with color-coded image viewing of living tissue and its chemical composition. (Copyright ? 1995, DewRay
Products, Inc. Used with permission.)
lines of data can be collected, each representing the projected density of the object as a function of lateral
position and angle.
A number of mathematical techniques can and have been used to recover the two-dimensional distribution
of the linear attenuation coefficient from this array of measurements. These include iterative solution of a set
of simultaneous linear equations, Fourier transform approaches, and techniques utilizing back-projection
followed by deconvolution [Macovski, 1983]. Conceptually, the Fourier transform approach is perhaps the most
straightforward, so we will describe it in some detail.
Using the coordinate system of Fig. 116.1(A) and assuming parallel rays, the intensity picked up by the
detector array can be expressed as
I
d
(y) = I
0
exp[–òa(x,y)dx]
where a(x,y) represents the linear attenuation coefficient to x-ray photons within the body as a function of x,y
position, and I
0
is the source intensity. Rearranging, we see that
where a
p
(y) is the projected attenuation function. Taking a one-dimensional Fourier transform of this projected
density function we see that
where A
p
(f
y
) is the Fourier transform of a single line of detected data. But this can also be written
FIGURE 116.1 Comparison of three photon-based tomographic imaging modalities.
ay axydx IyI
pd
() (, ) ln[ ()/ ]
–
==
￥
￥
ò
0
F a y A f a x y dx e dy
ppy
jfy
y
[ ( )] ( ) ( , )
–
––
==
￥
￥
￥
￥
òò
2 p
? 2000 by CRC Press LLC
Thus, the one-dimensional Fourier transform of the projection of the linear attenuation function, a
p
(y), is equal
to the two-dimensional Fourier transform of the original attenuation function evaluated along a line in the
frequency domain (in this case the f
x
= 0 line).
It can readily be demonstrated that if we rotate a function a(x,y) through an angle f in the x,y plane, its
transform will be similarly rotated through an angle f [Castleman, 1979]. Thus as we rotate the source and
detector around the object, each projected density function detected a
p
(r,f
i
) can be Fourier transformed to
provide one radial line of the two-dimensional Fourier transform of the desired reconstructed image, A(r,f
i
),
where r is a radial spatial frequency. The set of all A(r,f
i
) for small angular displacements f
i
form a set of
spokes in the transform domain which can be interpolated to estimate A(f
x
,f
y
), the two-dimensional Fourier
transform of the image in rectangular coordinates. The image can then be recovered by inverse transformation
of A(f
x
,f
y
), which can readily be carried out digitally using fast Fourier transform algorithms, i.e,
a(x,y) = F
–1
[A(f
x
,f
y
)]
While the Fourier transform approach is mathematically straightforward, many commercial scanners utilize
the equivalent but more easily implemented back-projection/deconvolution approach, where each ray is traced
back along its propagation axis. When all rays have been back-projected and the result summed, one obtains
an approximate (blurred) image of that plane. This image can then be sharpened (deblurred) through the use
of an appropriate filter, which is usually implemented by convolving with an appropriate two-dimensional
deblurring function. Refer to Macovski [1983] for the details of this process.
Clinically, the impact of computerized tomography was dramatic due to the vastly increased density resolu-
tion, coupled with the elimination of the superposition of overlying structures, allowing enhanced differenti-
ation of tissues with similar x-ray transmittance, such as blood, muscle, and organ parenchyma. CT scans of
the head are useful for evaluation of head injury and detection of tumor, stroke, or infection. In the body, CT
is also excellent in detecting and characterizing focal lesions, such as tumors and abscesses, and for the evaluation
of the skeletal system. [Axel et al., 1983]. In recent years the advent of magnetic resonance systems has provided
even greater soft tissue contrast, and thus the role of CT has been constrained by this at times competing
modality.
Positron Emission Tomography
Unlike computerized tomography, which relies on photons produced by an external source, in the modalities
of positron emission tomography (PET) and single photon emission computed tomography (SPECT), the
source of radiation is a radioisotope that is distributed within the body, and thus these modalities are sometimes
referred to as forms of emission computed tomography (ECT). While conventional CT can produce images
based upon anatomy of organs, emission CT techniques can quantitate the distribution of tracer materials that
can potentially elucidate physiologic function.
The positron or positive electron is a positively charged particle that can be emitted from the nucleus of a
radionuclide. The positron travels at most a few millimeters before being annihilated by interaction with a
negative electron from the surrounding tissue. The product of this event is the emission of 511-keV gamma
ray photons which travel in almost exactly opposite directions. The detectors themselves can be either discrete
detectors or a modified Anger camera like those used in conventional nuclear imaging. A coincidence detector
is employed to limit recorded outputs to cases in which events are detected simultaneously in both detector
arrays, thus reducing the pickup of noise or scattering.
A possible detection scheme is illustrated in Fig. 116.1(B). The detector arrays shown can be made energy
selective to eliminate lower energy scattered gamma rays. While the distribution of radioactivity can be recon-
structed using the reconstruction from projection techniques described in the section on CT [Hurculak, 1987],
Af axydxe dy
py
jxfy
y
(, ) (, )
–( )
––
0
20
=
+
￥
￥
￥
￥
òò
p
? 2000 by CRC Press LLC
the x,y source position of an event can be determined directly from the detection geometry as follows [Macovski,
1983]:
x ? x
L
d
R
/(d
R
+ d
L
) + x
R
d
L
/(d
R
+ d
L
)
y ? y
L
d
R
/(d
R
+ d
L
) + y
R
d
L
/(d
R
+ d
L
)
Typically a single plane is studied, and no collimators are required. A drawback of PET has been that because
of the short half-lives of positron-producing radioisotopes, the use of this modality has required the presence
of an expensive cyclotron facility located near the hospital.
One important radionuclide commonly used in PET is oxygen 15 with a half-life of 2.07 minutes, which can
be bonded to water for measurement of cerebral blood flow or to O
2
/CO
2
to assess cerebral oxygen utilization.
Another is carbon 11 with a half-life of 20.4 minutes, which can be bonded to glucose to trace glucose utilization.
F-18 fluorodeoxyglucose (FDG) has been used to demonstrate the degree of malignancy of primary brain
tumors, to distinguish necrosis from tumor, and to predict outcome [Coleman, 1991]. Perhaps the most unusual
feature of this modality is the ability to quantitate the regional metabolism of the human heart [Schelbert, 1990].
Single Photon Emission Computed Tomography
In contrast to PET, SPECT can be utilized with any radioisotope that emits gamma rays, including such common
radioisotopes as Tc-99m, I-125, and I-131 which have been utilized in conventional nuclear imaging for the
last 30–35 years and which due to their relatively long half-lives are available at reasonable cost at nearly every
modern hospital. Due to the need for direction sensitivity of the detector, a collimator must be used to eliminate
gamma rays from other than the prescribed direction, thus resulting in a 1–2 order of magnitude decrease in
quantum efficiency as compared with PET scanning [Knoll, 1983].
The basic concept of SPECT is illustrated in Fig. 116.1(C). A gamma ray photon from a radionuclide with
energy above 100 keV will typically escape from the body without further interaction, and thus the body can
be regarded as a transparent object with luminosity proportional to the concentration of the radionuclide at
each point. The reconstruction mathematics are similar to those derived for absorption CT, with the exception
that the variable reconstructed is a source distribution rather than an attenuation coefficient. Some errors can
be introduced in the reconstruction because of the inevitable interaction of gamma rays with overlying tissue,
even at energies above 100 keV, although this can be compensated for to some extent. Detection of scattered
radiation can be reduced through the use of an energy acceptance window in the detector.
Technetium 99m can be used to tag red blood cells for blood pool measurements, human serum albumin
for blood pool and protein distribution, or monoclonal antibodies for potential detection of individual tumors
or blood cells. Emission computed tomography techniques such as PET and SPECT follow the recent trend
toward imaging techniques that image physiologic processes as opposed to anatomic imaging of organ systems.
The relatively low cost of SPECT systems has led to a recent resurgence of interest in this modality.
Magnetic Resonance Imaging
The basic magnetic resonance concept has been used as a tool in
chemistry and physics since its discovery by Bloch in 1946, but its use
expanded tremendously in the 1980s with the development of means
to represent magnetic resonance signals in the form of tomographic
images. Magnetic resonance imaging is based on the magnetic prop-
erties of atomic nuclei with odd numbers of protons or neutrons,
which exhibit magnetic properties because of their spin. The predom-
inant source of magnetic resonance signals in the human body is
hydrogen nuclei or protons. In the presence of an external magnetic
field, these hydrogen nuclei align along the axis of the field and can
precess or wobble around that field direction at a definite frequency
known as the Larmour frequency. This can be expressed:
FIGURE 116.2 Geometry of precessing
proton in a static magnetic field oriented
in the z direction.
? 2000 by CRC Press LLC
f
0
= gH
where f
0
is the Larmour frequency, g is the gyromagnetic ratio which is a property of the atomic element, and
H is the magnitude of the external magnetic field. For example, given a gyromagnetic ratio of 42.7 MHz/tesla
for hydrogen and a field strength of 1 tesla (10 kilogauss), the Larmour frequency would be 42.7 MHz, which
falls into the radio frequency range.
The magnetic resonance effect occurs when nuclei in a static magnetic field H are excited by a rotating
magnetic field H
1
in the x,y plane, resulting in a total vector field M given by
M = H z + H
1
(x cos w
0
t + y sin w
0
t)
Upon cessation of excitation, the magnetic field decays back to its original alignment with the static field H,
emitting electromagnetic radiation at the Larmour frequency, which can be detected by the same coil that
produced the excitation [Macovski, 1983].
Imaging
As shown in Fig. 116.3, one method for imaging utilizes a transmit/receive coil to emit a magnetic field at
frequency f
0
which is the Larmour frequency of plane P. Subsequently, magnetic gradients are applied in the y
and x directions. The detected signal during the data collection window can be expressed as
where s(x,y) represents the magnetic resonance signal at position (x,y) (G
x
,G
y
) are the x and y gradients, t
x
is
time within the data collection window, t
yi
is the y direction gradient application times, and g is the gyromagnetic
ratio. The two-dimensional spatial integration is obtained by appropriate geometry of the detection coil.
Collecting a number of such signals for a range of t
yi
, we can obtain the two-dimensional function S(t
x
,t
y
).
Comparing this to the two-dimensional Fourier transform relation
FIGURE 116.3Concept of magnetic resonance imaging. The static magnetic field H
0
has a gradient such that excitation
at frequency f
0
excites only the plane P. Gradient G
y
in the y direction is applied for time t
yi
, causing a phase shift along the
y direction. Gradient G
x
in the x direction is applied for time t
x
, causing a frequency shift along the x direction. Repetition
of this process for different t
yi
allows the receive coil to pick up a signal which is the two-dimensional Fourier transform of
the magnetic resonance effect within the slice.
Stt sxy iGxt Gyt dxdy
xyi xx yyi
(,) (,)exp[–( )]
––
=+
￥
￥
￥
￥
òò
g
Fuv fxy i uxvydxdy(,) (,)exp[– ( )]
––
=+
￥
￥
￥
￥
òò
2p
? 2000 by CRC Press LLC
we see that the detected signal S(t
x
,t
y
) is the two-dimensional Fourier transform of the magnetic resonance
signal s(x,y) with u = gG
x
t
x
/2p, v = gG
y
t
y
/2p. The magnetic resonance signal s(x,y) depends on the precise
sequence of pulses of magnetic energy used to perturb the nuclei. For a typical sequence known as spin-echo
consisting of a 90-degree pulse followed by a 180-degree pulse spaced at time t with the data collection at t
e
=
2t, and t
r
being the repetition time between 90-degree pulses, the detected magnetic resonance signal can be
expressed
s(x,y) = r(1 – e
–tr
/T
1
)(e
–te
/T
2
)
where r is the proton density, and T
1
(the spin-lattice decay time) and T
2
(the spin-spin decay time) are constants
of the material related to the bonding of water in cells [Wolf and Popp, 1984]. Typically T
1
ranges from 0.2 to
1.2 seconds, while T
2
ranges from 0.05 to 0.15 seconds.
By modification of the repetition and orientation of excitation pulses, an image can be made T
1
, T
2
, or proton
density dominated. A proton density image shows static blood and fat as white and bone as black, while a T
1
weighted image shows fat as white, blood as gray, and cerebrospinal fluid as black. T
2
weighted images tend to
highlight pathology since pathologic tissue tends to have longer T
2
than normal.
In general, magnetic resonance imaging has greater intrinsic ability to distinguish between soft tissues than
computerized tomography. It also has some ability to visualize moving blood. As the preceding discussion
indicates, magnetic resonance is a richer and more complex modality than CT. Typically MRI has been more
expensive than CT. Both MRI and CT have been used primarily for anatomic imaging, but MRI has the potential
through spectroscopy (visualization of other nuclei than hydrogen) to become a factor in physiologic imaging.
Thus, it can be anticipated that magnetic resonance imaging will continue to increase and become an even
more important modality in the next decade.
Defining Terms
Computerized axial tomography (CATscan, CT): A form of medical imaging based upon the linear attenu-
ation coefficient of x-rays in which a tomographic image is reconstructed from computer-based analysis
of a multiplicity of x-ray projections taken at different angles around the body.
Magnetic resonance imaging (MRI, NMR): Aform of medical imaging with tomographic display which
represents the density and bonding of protons (primarily in water) in the tissues of the body, based upon
the ability of certain atomic nuclei in a magnetic field to absorb and reemit electromagnetic radiation
at specific frequencies.
Positron emission tomography (PET scan): A form of tomographic medical imaging based upon the density
of positron-emitting radionuclides in an object.
Single photon emission computed tomography (SPECT): A form of tomographic medical imaging based
upon the density of gamma ray-emitting radionuclides in the body.
Tomography: A method of image presentation in which the data is displayed in the form of individual slices
that represent planar sections of the object.
Related Topic
35.1 Maxwell Equations
References
L. Axel, P.H. Arger, and R. Zimmerman, “Applications of computerized tomography to diagnostic radiology,”
Proceedings of the IEEE, vol. 71, no. 3, p. 293, March 1983.
K.R. Castleman, Digital Image Processing, Englewood Cliffs, N.J.: Prentice-Hall, 1979.
R.E. Coleman, “Single photon emission computed tomography and positron emission tomography,” Cancer,
vol. 67 (4 Suppl.), pp. 1261–1270, Feb. 1991.
? 2000 by CRC Press LLC
P.M. Hurculak, “Positron emission tomography,” Canadian Journal of Medical Radiation Technology, vol. 18,
no. 1, March 1987.
G.F. Knoll, “Single-photon emission computed tomography,” Proceedings of the IEEE, vol. 71, no. 3, p. 320,
March 1983.
A. Macovski, Medical Imaging Systems, Englewood Cliffs, N.J.: Prentice-Hall, 1983.
H.R. Schelbert, “Future perspectives: Diagnostic possibilities with positron emission tomography,” Roentgen
Blaetter, vol. 43, no. 9, pp. 384–390, Sept. 1990.
G.L. Wolf and C. Popp, NMR, A Primer for Medical Imaging, Thorofare, N.J.: Slack, Inc., 1984.
Further Information
The journal IEEE Transactions on Medical Imaging describes advances in imaging techniques and image pro-
cessing. Investigative Radiology, published by the Association of University Radiologists, emphasizes research
carried out by hospital-based physicists and engineers. Radiology, published by the North American Society of
Radiologists, contains articles which emphasize clinical applications of imaging technology. Diagnostic Imaging,
publishing by Miller Freeman, Inc., is a good source of review articles and information on the imaging
marketplace.
116.2 Ultrasound
Leon A. Frizzell
Ultrasound, acoustic waves at frequencies higher than those audible by humans, has developed over the past
35 years into an indispensable clinical diagnostic tool. Currently, ultrasound is used to image most parts of the
body. More than half of all pregnant women in the United States are examined with ultrasound. This widespread
utilization has resulted from ultrasound’s proven clinical utility for imaging soft tissues compared to more
expensive imaging techniques. The development of ultrasound, particularly for fetal examinations, has also
been fostered by its safety record; no case of an adverse biological effect induced by diagnostic ultrasound has
ever been reported in humans [AIUM, 1988].
Diagnostic ultrasound systems are used primarily for soft tissue imaging, motion detection, and flow mea-
surement. Except for some Doppler instruments, these systems operate in a pulse-echo mode. A brief summary
of some of the fundamentals of acoustic wave propagation and the principles of ultrasound imaging follows.
Fundamentals of Acoustics
Unlike electromagnetic waves, acoustic waves require a medium for propagation. The acoustic wave phenom-
enon causes displacement of particles (consisting of many molecules), which results in pressure and density
changes within the medium. For a traveling sinusoidal wave, the variation in acoustic pressure (the difference
between the total and ambient pressure), excess density, particle displacement, particle velocity, and particle
acceleration can all be represented by the form
p = P e
–ax
cos(wt – kx) (116.1)
for a wave propagating in the positive x direction, where p is the pressure (or one of the other parameters listed
above), P is its amplitude, w is the angular frequency, and w = 2pf where f is the frequency in hertz, k is the
propagation constant and k = w/c where c is the propagation speed, a is the attenuation coefficient, and t is
the time. The wave can experience significant attenuation, as represented by the exponential decay of amplitude
with distance, during propagation in tissues. The attenuation coefficient varies greatly among tissues [Goss
et al., 1978, 1980; Haney and O’Brien, 1986] but is low for most body fluids, much higher for solid tissues, and
very high for bone and lung (see Table 116.1). The skin depth is the distance that the wave can propagate before
being attenuated to e
–1
of its original amplitude and is thus simply the inverse of the attenuation coefficient.
? 2000 by CRC Press LLC
Ultrasound is typically used to image soft body tissues such as liver, but the sound beam often travels through
fluids, for example, through amniotic fluid when imaging the fetus. Generally, bone and lung are not imaged
with ultrasound. The attenuation processes include absorption, which is the conversion of acoustic energy to
heat, and scattering, which will be addressed later. The attenuation increases roughly linearly with frequency
in the 2- to 10-MHz range typically used for medical imaging. This range represents a compromise between
increased penetration at lower frequencies (because of decreased attenuation) and improved resolution asso-
ciated with higher frequencies as discussed below. Thus, the lower frequencies are used when greater penetration
is required, such as for fetal imaging in the obese patient, and higher frequencies for lesser penetration, such
as the examination of peripheral vascular flow.
When an acoustic wave impinges on an interface between two media of different specific acoustic impedance,
a portion of the incident energy is reflected. For normal incidence on an infinite plane interface, the pressure
reflection coefficient is given by [Kinsler et al., 1982]
(116.2)
where z
1
and z
2
are the specific acoustic impedance of the incident and transmitting media, respectively. For a
plane wave the specific acoustic impedance is equal to the characteristic impedance which is the product of the
density and acoustic speed in the medium (see Table 116.1). The speed is dependent upon the density and the
elastic properties of the medium. Thus, at an interface between media exhibiting different densities or elastic
properties, i.e., compressibility, some acoustic energy will be reflected. Although the reflection coefficient at an
interface between muscle and bone is large (approximately 0.54) the reflection coefficient between two soft
tissues such as liver and muscle is quite small (approximately 0.006). Reflection at oblique incidence obeys
Snell’s law in the same way it applies to electromagnetic waves.
In addition to the specular reflection that occurs at an interface between two media of different specific
acoustic impedance as described above (where any curvature along the interface is negligible over distances
comparable to a wavelength), energy may also be scattered in all directions by inhomogeneities in the medium.
An acoustic image is formed by using this scattered energy as well as specular reflections. The fraction of the
incident energy reflected or scattered is very small for soft tissues.
Although it is convenient to consider plane waves of infinite lateral extent, as was done above, real sources
generate finite beams of ultrasound. These sources may be unfocused, but for the typical diagnostic system
they are focused. Figure 116.4 shows the acoustic field from a typical focused source. The source consists of a
piezoelectric transducer which converts electrical to acoustic energy and vice versa. Most transducers for medical
applications are made from ceramic materials such as a lead zirconate titanate (PZT) mixture. For a circular
aperture these may be circular disks with a plano-concave lens mounted in front to produce spherical focusing.
Alternatively, the transducer itself may be a spherical segment that produces a focused field without a lens.
Some probes utilize electronic focusing methods. Such a phased array probe consists of many individual
elements which can be excited with signals having a controlled delay with respect to one another such that the
TABLE 116.1Approximate Ultrasonic Attenuation Coefficient, Speed, and
Characteristic Impedance for Water and Selected Tissues at 3.5 MHz
Attenuation Coefficient Speed Characteristic Impedance
Tissue (m
–1
) (m/s) (10
6
Pa s/m)
Water 0.2 1520 1.50
Amniotic fluid 0.7 1510 1.51
Blood 7 1550 1.60
Liver 35 1580 1.74
Muscle 50 1560 1.72
Bone 800 3360 5.70
Lung 1000 340 0.25
R
zz
zz
=
-
+
21
21
? 2000 by CRC Press LLC
signals constructively interfere at the desired focal region. At a receiver the signals are combined with delays
associated with various elements to provide reinforcement of the signals from a receiving focal region.
The 3 db lateral beam width D
L
is directly dependent upon the wavelength l and focal length F and inversely
related to the aperture diameter (diameter of the transducer) D [Kino, 1987]:
(116.3)
Because fl = c, the higher the frequency the smaller is l and D
L
. The smaller D
L
, the better the lateral resolution
near the focus, but the beam spread is greater with distance from the focus. Thus, the strength of the focusing
varies among transducers so that the user may choose very good resolution over a short region or somewhat
poorer resolution that is maintained over a greater depth. With phased array transducers, the focal region can
be varied dynamically to optimize lateral resolution at all distances.
Principles of Pulse-Echo Ultrasound
Ultrasound imaging usually employs frequencies in the 2- to 10-MHz range, though some of the new intra-
vascular probes use higher frequencies. Images are formed by using a transducer within a probe to generate a
short pulse (typically on the order of 1 ms in duration) of ultrasound which is propagated through the tissue.
A portion of the energy in this pulse is reflected back toward the transducer from specular reflectors and from
scatterers in the tissue. These acoustic echoes, with amplitudes much lower than the transmitted pulse, are
converted by the transducer to electrical signals which are converted to a (rectified) video signal, amplified by
a time gain controlled amplifier, and displayed. The A-mode display is rarely used but simply involves display
of the received echoes as amplitude versus time of arrival. The time of arrival is related by the wave speed to
the tissue depth from which the echo returns, i.e., d = ct/2. Figure 116.5 provides a very simple representation
of this process where the A-mode display associated with specular reflection from three different interfaces is
illustrated. For clinical imaging the interfaces would not necessarily be perpendicular to the axis of the sound
beam, and there would be a continuum of echoes, a continuous received signal, due to energy backscattered
from within the tissues. Since the ultrasound pulse is attenuated as it propagates, all ultrasonic imaging systems
use a logarithmic variation of amplifier gain with time to compensate the exponential attenuation of the tissue.
Thus, echoes from structures reflecting or backscattering the same fraction of the incident signal will have the
same amplitude after passing through the time gain controlled amplifier.
A B-mode display is typically used for ultrasound imaging. It involves display of the echoes at various
brightness or gray levels corresponding to their amplitude. A two-dimensional B-mode display involves
movement of the transducer (manually or automatically), movement of a mirror to change the direction of
the field (automatically), or movement of the ultrasound beam directly (electrically) such that it scans a plane
through the body. Figure 116.6 provides a simplified representation (again, echoes are shown as arising from
interfaces only) of the formation of a B-mode image. The direction of the beam is monitored so that the received
signals along each path are placed in their correct location on the display. Typically, the orientation information
and echoes are processed by a digital scan converter for appropriate display of the two-dimensional image on
FIGURE 116.4Cross section of a typical focused circular ultrasound source of aperture diameter D and focal length F,
showing the focused beam of lateral beam width at the focus D
L
.
D
F
D
L
=102.
l
? 2000 by CRC Press LLC
a cathode ray tube in the standard format used for television picture display. Most B-mode systems in use today
create an image in 0.1 s or less, so that the image is displayed in real-time for viewing of moving structures,
such as structures in the heart or the fetus moving within the womb. This is not possible with the typical
magnetic resonance or computed tomography system.
FIGURE 116.5 (a) The transmitted pulse (heavy wave) and echoes from reflecting structures; (b) the resulting A-mode
display.
FIGURE 116.6 (a) The transmitted pulse paths for a rotating transducer probe; (b) the resulting two-dimensional B-mode
display of echoes from the interfaces only.
? 2000 by CRC Press LLC
Many systems now use digital processing to enhance portions of the image. For example, it is possible to
emphasize the large amplitude, small amplitude, or midrange signals. It is also possible to perform a more
sophisticated analysis to enhance edges.
Many specialty probes have been designed for intracavitary examination. Examples include examination of
the fetus with a vaginal probe, the prostate with a rectal probe, and blood vessel walls with intravascular probes.
The intracavitary probe offers the advantage of decreasing the distance from the transducer to the tissue of
interest and thus decreasing attenuation such that higher frequencies can be used for greater resolution. The
lateral resolution of a focused probe is improved with frequency as discussed in the preceding subsection, but
the axial (along the ultrasound beam) resolution also improves with frequency. The shorter the transmitted
pulse, the better the axial resolution. Shorter pulses are generated by sources with a larger bandwidth, which
corresponds to a higher center frequency when the sources have bandwidths which are approximately the same
fraction of the center frequency.
The use of ultrasound for motion detection and measurement has increased tremendously in recent years.
Most of these systems use the Doppler principle, but some use time domain detection. In Doppler detection,
if the ultrasound is reflected from a target moving at some speed v
t
toward (away from) the source at an angle
q with respect to the beam axis, the frequency of the transmitted signal f is shifted up (down) by an amount
f
D
, the Doppler shift, according to the following relation:
(116.4)
In principle a measurement of f
D
, when f, c, and q are known, will yield the speed of the target v
t
. However, it
is often difficult to determine q because the angle the transducer axis makes with a blood vessel, for example,
is often unknown. Even when that angle is known, the flow is not necessarily along the direction of the vessel
at every location and for all times. Time domain detection of motion, by measuring the movement of specific
echoes from one pulse to another, is a recently developed alternative to Doppler detection that is not currently
widely used.
For many years duplex systems, which provide both a two-dimensional image and a Doppler signal, showing
the change of target speed with time, from a particular selected target area, have been in wide use. More recently,
color flow imaging has been employed, which provides a two-dimensional color (typically red or blue) image
of flow toward and away from the transducer superimposed on the gray scale image of stationary tissue
structures. For these systems the speed, whether from Doppler or time domain detection schemes, is indicated
by color saturation, hue, or luminance. These systems have proven very valuable for detecting the existence of
flow in a region, detecting obstructions to flow and the turbulence associated with this, detecting reduced flow,
and so on. Some other systems add to the color flow image a display of speed versus time for a region that is
defined by a user-movable box.
Future Developments
It seems clear that the continuing development of intracavitary transducers, particularly for intravascular
imaging, and the use of ultrasound intraoperatively will lead to more high-frequency commercially available
probes that will produce better resolution images for these applications. The development of useful three-
dimensional ultrasonic imaging is progressing rapidly and should immediately improve the measurement of
tissue volumes [Gilja et al., 1995].
Defining Terms
A-mode display: Returned ultrasound echoes displayed as amplitude versus depth into the body.
B-mode display: Returned ultrasound echoes displayed as brightness or gray scale levels corresponding to
the amplitude versus depth into the body.
f
fv
c
D
t
=
2 cosq
? 2000 by CRC Press LLC
Color flow imaging or color Doppler: Two-dimensional image showing color-coded flow toward and away
from the transducer displayed with the two-dimensional gray scale image of stationary targets.
Duplex ultrasound: Simultaneous display of speed versus time for a chosen region and the two-dimensional
B-mode image.
Pulse-echo ultrasound: Using a probe containing a transducer to generate a short ultrasound pulse and
receive echoes of that pulse, associated with specular reflection from interfaces between tissues or scat-
tering from inhomogeneities within the tissue, to form a display of the tissue backscatter properties.
Two-dimensional B-mode display: Echoes from a transducer, or beam, scanned in one plane displayed as
brightness (or gray scale) versus location for the returned echo to produce a two-dimensional image.
Related Topic
48.1 Introduction
References
American Institute of Ultrasound in Medicine, “Bioeffects considerations for the safety of diagnostic ultra-
sound,” J. Ultrasound Med., vol. 7, no. 9 (supplement), 1988.
O.H. Gilja, A.I. Smievoll, N. Thune, K. Matre, T. Hausken, S. Odegaard, and A. Berstad, “In vivo comparison
of 3D ultrasonography and magnetic resonance imaging in volume estimation of human kidneys,”
Ultrasound Med. Biol., vol. 21, pp. 25–32, 1995.
S.A. Goss, R.L. Johnston, and F. Dunn, “Comprehensive compilation of empirical ultrasonic properties of
mammalian tissues,” J. Acoust. Soc. Am., vol. 64, pp. 423–457, 1978.
S.A. Goss, R.L. Johnston, and F. Dunn, “Compilation of empirical ultrasonic properties of mammalian tissues.
II,” J. Acoust. Soc. Am., vol. 68, pp. 93–108, 1980.
M.J. Haney, and W.D. O’Brien, Jr., “Temperature dependency of ultrasonic propagation properties in biological
materials,” in Tissue Characterization with Ultrasound, vol. 1, J. Greenleaf, Ed., Boca Raton, Fla.: CRC
Press, 1986, pp. 15–55.
G. Kino, Acoustic Waves, Englewood Cliffs, N.J.: Prentice-Hall, 1987, p. 185.
L.E. Kinsler, A.R. Frey, A.B. Coppens, and J.V. Sanders, Fundamentals of Acoustics, 3rd ed., New York: John
Wiley, 1982.
Further Information
The American Institute of Ultrasound in Medicine publishes monthly the Journal of Ultrasound in Medicine,
which contains largely clinically oriented articles, and many clinically oriented ultrasound texts are available
covering almost any medical discipline. However, there are only a few books that provide more than a cursory
treatment of the basic physics and instrumentation of ultrasound imaging.
One text that has been regularly updated since the first volume appeared in 1980 is Diagnostic Sonography:
Principles and Instruments, 4th edition, by F.W. Kremkau (W.B. Saunders, Philadelphia, 1993). Though this text
is designed primarily to train sonographers who do not have a technical background, it provides the funda-
mentals of ultrasound imaging in a format that is very easy to read and understand.
Other texts that provide a more technical background (though some are a bit dated) include:
Biomedical Ultrasonics, by P. N. T. Wells (Academic Press, New York, 1977).
New Techniques and Instrumentation in Ultrasonography, edited by P.N.T. Wells and M.C. Ziskin (Churchill
Livingstone, New York, 1980).
Medical Physics of CT and Ultrasound, edited by G.D. Fullerton and J.A. Zagzebski (American Institute of
Physics, New York, 1980).
Physical Principles of Medical Ultrasonics, edited by C. R. Hill (John Wiley, New York, 1986).
Ultrasonic Bioinstrumentation, by D.A. Christensen (John Wiley, New York, 1988).
The Physics of Medical Imaging, edited by S. Webb (IOP Publishing, New York, 1988).
Principles of Medical Imaging, by B. Tsui, M. Smith, and K.K. Shung (Academic Press, New York, 1992).
? 2000 by CRC Press LLC
116.3 Semiconductor Detectors For Radiation Measurements
Larry A. Franks, Larry S. Darken, and Ralph B. James
Since their introduction in the early 1960s, semiconductor radiation detectors have become the devices of choice
for numerous X-ray, gamma-ray, and charged particle measurements. They are essential in applications where
maximum energy resolution (i.e., the ability to record the energy of the incident photon or particle) is required.
In this characteristic, their performance greatly exceeds that of gaseous sensors (proportional counters, for
example) or scintillator/photocell-based spectrometers. Their superior energy resolution stems, in the main,
from the greater number of information carriers generated in semiconductors per unit of absorbed energy than
in, for example, scintillator/photocell combinations, which are widely used as low-resolution spectrometers. In
scintillator-based spectrometers, approximately 100 eV of absorbed energy is required to generate a single
information carrier. In a typical semiconductor, only 3 to 5 eV are required to create one electron-hole pair —
the information carrier in semiconductor detectors. The statistical variation of the number of carriers produced
per ionizing event is thus substantially greater in the case of the scintillator and is reflected in reduced energy
resolution. Similar arguments apply to gaseous detectors, where the relatively small number of information
carriers is due to the combination of the low density of the absorbing gas and the significant energy required
to produce ion-pairs (≈30 eV per ion-pair, [1]), the information carrier in the gas detector.
It is convenient to divide semiconductor detectors into two groups: those requiring cooling (normally to
77K) and those capable of room temperature (or near room temperature) operation. The former group is
dominated by high-purity germanium (HPGe) and lithium drifted silicon (Si:Li) — a group characterized by
particularly high energy resolution. The latter group includes detectors based on cadmium telluride, cadmium
zinc telluride, and mercuric iodide, as well as a number of silicon-based devices. This group finds application
in portable X-ray and gamma-ray spectrometers and counters and imaging systems where the freedom from
the weight and maintenance of a cryogenic cooler is particularly valued. This chapter section is divided into
sections on cryogenic detectors and room-temperature devices. Details of the physics of semiconductor detectors
as well as their performance characteristics can be found in several texts [1–7].
Cryogenic Detectors
Detectors in this group are limited principally to high-purity germanium (HPGe) and lithium drifted silicon
(Si:Li). HPGe detectors are available in a number of configurations for operation in the X-ray and gamma-ray
regions. Si:Li detectors are primarily for the X-ray region. Cryogenic detectors provide the ultimate in energy
resolution, as well as good detection efficiency. Common to the group is the requirement that they be operated
in the region of 77K. In most cases, the detector temperature is maintained by liquid nitrogen (LN
2
) contained
in an attached cryogenic vessel (dewar). Dewars are available in capacities ranging from a few liters to several
tens of liters, depending on the service interval that is acceptable and the degree of portability required.
Alternatively, electromechanical coolers are also available.
Germanium Detectors
High-purity germanium (HPGe) detectors are widely used for gamma-ray spectroscopy due to their combina-
tion of efficient absorption and high energy resolution. Figure 116.7 shows the cross sections for photoelectric
absorption, Compton scattering, and absorption by electron-positron pair production in several materials used
for solid-state nuclear radiation detectors. Attenuation is significantly stronger in germanium than in silicon.
Over much of the gamma spectrum, the dominant interaction is Compton scattering. However, it is principally
the stronger photoelectric absorption in germanium that makes it more suitable than silicon for gamma-ray
spectroscopy. In the typical germanium detector, a gamma-ray can be scattered several times before it is
photoelectrically absorbed. Thus, the energy of the gamma-ray is primarily transmitted directly to a small
number of electrons. These energetic electrons, in turn, interact with electrons in the valence bands to create
mobile pairs of electrons and holes. The average number of electron-hole pairs N produced by a completely
absorbed gamma-ray of energy E becomes independent of the details of the initial reaction path and varies
linearly with E:
? 2000 by CRC Press LLC
N = E/ε (116.5)
This relationship is more broadly valid and is the foundation of energy spectroscopy of gamma-rays using
semiconductors, gases, and cryogenic liquids (ε depending on the material). While ε is independent of the
gamma-ray energy (and is also virtually the same for energy deposited by charged particles), ε in germanium
does increase slightly with decreasing temperature, as does the energy gap. At 77K, ε is 2.96 eV and the energy
gap is 0.72 eV.
Practical exploitation of Eq. (116.5) depends on electronically detecting the motion of the ionized charge in
an electric field. The signal-to-noise ratio is improved by reducing current flow in the detector from other
mechanisms. In germanium, this is achieved by producing a rectifying and a blocking contact and by cooling
to about 100K. For a planar detector, a slice of high-purity germanium is diffused with the donor lithium on
one side, forming a strongly n-type layer. The opposite side is implanted with the acceptor boron, forming a
p
+
layer. When voltage is properly applied, the electric field direction prevents the majority carriers in the
contact regions from being injected across the device. As the voltage is applied, a region depleted of holes will
advance into the slice from the n
+
contact if the slice is p-type. If the slice is n-type, the a region depleted of
electrons will advance from the p
+
contact. At the depletion voltage V
d
, the depletion region reaches the opposite
contact. For germanium:
(116.6)
FIGURE 116.7 Attenuation coefficients vs. energy common semiconductor materials. (T. E. Schlesinger and R. B. James,
Semiconductors for Room Temperature Detector Applications.)
V V N N dm d cm
dAD
=?? ?
?
565 10
10 3 2 2
? 2000 by CRC Press LLC
Here, N
A
– N
D
is the net charge density in the depleted or active region of the detector and d is the thickness
of this region. This is a key relationship in high-purity germanium technology as it quantifies the effect of the
residual impurity concentration on device size and depletion voltage. Techniques to grow germanium pure
enough for gamma detectors were pioneered by Hall [8] and the detector group at Lawrence Berkeley Laboratory
[Haller, Hansen, and Goulding [9], based on purification methods of Pfann [10] and crystal-growing techniques
developed by Teal and Little [11] to produce crystals for germanium transistors.
Leakage Current
Germanium detectors need to be cooled to reduce leakage current. There are several potential sources of leakage
current, including diffusion of minority carriers from either doped contact into the depletion region, thermal
generation of carriers at either bulk or surface defects in the depletion region, and electrical breakdown at
points where the electrical field is concentrated due to irregularities in the contact geometry, large-scale
inhomogeneities in the bulk, or surface states. Current will also be generated if the detector is not shielded
from room-temperature infrared radiation. Background nuclear radiation from materials near the detector and
cosmic radiation also generate current.
Germanium detectors are typically liquid-nitrogen cooled and operated between 85K and 100K. In this
temperature range, leakage current is typically less than 40 pA in “good” detectors, and is not a significant
contributor to system noise (400–900 eV). Leakage current increases with temperature and eventually becomes
the predominate noise component. Pehl, Haller, and Cordi [12] reported a leakage current-driven system noise
of 2 KeV at 150K and 7 KeV at 170K for an 8 cm
3
planar detector. These authors also reported that above about
120K, the leakage current had an activation energy of approximately one-half the bandgap, and attributed this
to generation at mid-gap surface states. Below 120K, the temperature dependence was milder.
A typical detector/cryostat configuration is shown in Fig. 116.8. The detector resides in an evacuated cryostat
and is cooled by means of a copper rod inserted into a liquid nitrogen dewar. The first stage of amplification
is an FET, also cooled, positioned nearby the detector. Mechanical fixturing is designed to stabilize the detector
and the mechanisms for contacting it, to provide a cooling path from the detector to liquid nitrogen, and to
electrically insulate the high-voltage contact.
A variety of detector geometries is shown in Fig. 116.9. These different electrode configurations allow the
detectors’ efficiency and energy resolution to be optimized for different gamma-ray energies and applications. For
example, the detector in Fig. 116.9(c) minimizes noise by the lower capacitance of its electrode configuration at the
expense of the reduced stopping power. Thus, this detector would be more suitable for lower-energy gamma-rays.
Coaxial Detectors
The detector type shown in Fig. 116.8 and in Fig. 116.9(e) has a closed-end coaxial geometry. Nearly all the
largest volume (active volumes of 100 cm
3
to 800 cm
3
) HPGe detectors are of this type. This electrode geometry
reduces both capacitance and depletion voltage with respect to a planar detector of the same volume. This latter
benefit relaxes the constraint on material purity. In addition, charge collection distances are shortened, and the
uncontacted surface area, frequently troublesome in processing, is reduced. Also, the HPGe is grown by the
Czochralski technique, and is therefore nearly cylindrical even before machining. It is important, however, to
note that the reduction in depletion voltage is realized only when the device is contacted so that it depletes
from the outer contact to the inner contact. Thus, p-type HPGe to be fabricated into a coaxial detector is
lithium diffused on the outer diameter; and in the case of n-type HPGe, the outer diameter is boron implanted.
The boron-implanted contact (depth approximately 0.2 μ) is thinner than the lithium-diffused contact (depth
approximately 750 μ), so the n-type coaxial detector can detect lower-energy radiation and is usually built with
a beryllium window in the aluminum end-cap to take full advantage of this feature. The difference in the range
of use is illustrated in Fig. 116.10. The geometric asymmetry of the contacting electrodes in the coaxial detector
makes charge collection more dependent on the carriers (electrons or holes) traversing to the inner contact.
As more gamma-rays are absorbed near the outer contact, the carriers traversing to the inner contact must
travel on average a longer distance. Also, charge traversal near the inner contact is particularly effective in
inducing current in the external circuit [13]. Thus, the p-type coaxial detector with positive bias on the outer
electrode is more sensitive to hole collection, and the n-type coaxial detector with negative bias on the outer
electrode is more sensitive to electron collection. This is a crucial consideration in applications where hole
collection is going to be degraded during use by exposure to fast neutrons or other damaging radiation. The
? 2000 by CRC Press LLC
superior neutron damage resistance of the electrode biasing polarity on n-type coaxial detectors was demon-
strated by Pehl et al. [14].
A typical gamma-ray spectrum of a
60
Co source taken with a coaxial HPGe detector is shown in Fig. 116.11.
The salient features are the full-energy peaks at 1.17 MeV and 1.33 MeV, and the lower-energy plateaus due to
incomplete energy absorption of Compton scattered gamma-rays. The peak-to-Compton ratio [15] is generally
40 to 100, depending on the size and quality of the detector. The 1.33-MeV peak is shown separately in
Fig. 116.12. The energy resolution measured as the full width at half the peak maximum (FWHM) for typical
coaxial germanium detectors is between 1.6 KeV and 2.1 KeV for 1.33-MeV gamma-rays, again depending on
the size and quality of the detector. The variance in the peak L
2
(FWHM = 2.35 × L, L being the standard
deviation for a Gaussian distribution) can be divided into three additive components: the electronic noise
component L
N
2
, a component reflecting the variance in the number of electron-hole pairs created L
F
2
, and a
component due to incomplete charge collection L
T
2
:
FIGURE 116.8 Schematic cross section of a dipstick cryostat. (Darken and Cox, 1993; reprinted with permission of Oxford
Instruments, Inc.)
? 2000 by CRC Press LLC
(116.7)
F is called the Fano factor and has been experimentally determined to be no greater than 0.08 for germanium
[16]. F < 1 implies that electron-hole pair creation events are not uncorrelated. L
T
2
is usually dominated by the
trapping of electrons and holes at defect sites. However, shorter electronic shaping times, lower electric fields,
and larger detectors accentuate ballistic deficit (loss of collected charge in the external electronics due to the
finite traversal time of the electrons and holes across the detector). L
N
2
is independent of gamma-ray E and is
FIGURE 116.9 Schematic cross section and electrostatic field distribution in high-purity germanium detectors. The dark
line represents the p-n junction: (a) true planar, (b) grooved planar, (c) low-capacity planar, (d) truncated coaxial, (e) closed
end coaxial, (f) well geometry.
FIGURE 116.10 Relative absorption efficiencies for typical n- and p-type detectors. (Darken and Cox, 1993; reprinted with
permission of Oxford Instruments, Inc.)
LL L L
LEF
NF T
F
2222
2
=++
=ε
? 2000 by CRC Press LLC
the dominant resolution limiting factor at low energies. L
F
2
depends linearly on E, and for a coaxial detector
usually dominates L
N
2
for E over a few hundred KeV. The energy dependence of L
T
2
is not given simply from
first principles for an arbitrary trap distribution, but an E
2
dependence seems to fit under many circumstances.
Thus, at high enough E, L
T
2
is expected to be the largest component. For “good” detectors at 1.33 MeV though,
L
T
2
is always smaller than L
F
2
. However, the magnitude of L
T
2
is variable enough between detectors that it distin-
guishes between acceptable, very good, and excellent detectors. L
T
2
is usually also the only component of
resolution drawn from a nongaussian distribution and is thus responsible for any low-energy tailing of the peak.
X-ray Detection
Both silicon and germanium detectors are used in low noise systems for the detection of fluorescent X-rays
produced by electron beams (usually in an electron microscope) or X-rays (XRF). For both materials, the
detector is liquid-nitrogen cooled to reduce leakage current, and small volume devices (Fig. 116.9, typically
FIGURE 116.11 A
60
Co spectrum collected with a 15% p-type detector showing typical features of the germanium detector
spectrum.
FIGURE 116.12 A
60
Co spectrum collected with a 22% relative efficiency p-type detector. (Darken and Cox, 1993; reprinted
with permission of Oxford Instruments, Inc.)
? 2000 by CRC Press LLC
10 mm
2
active area, and 3 mm depth) are used in order to decrease capacitance and therefore further reduce
electronic noise. Lithium-drifted silicon (Si:Li) detectors were used first for these applications. Early germanium
detectors displayed poor peak shape for X-ray energies just above the L absorption edges (attributed to diffusion
against the field to the front contact by some electrons and their resulting loss to the photopeak [17]). However,
as was first demonstrated by Cox et al. [18], this is not a fundamental problem, but can be solved by the
contacting technology. An X-ray spectrum taken with an HPGe detector is shown in Fig. 116.13. Germanium
has the advantages with respect to silicon of a smaller ε (2.96 eV/pair vs. 3.96 eV/pair at 77K) for better energy
resolution, and a higher Z (32 vs. 14) for better photoelectric absorption of higher-energy X-rays.
Current Status of HPGe Detector Technology
High-purity germanium detectors are a mature commercial technology. Process development in crystal growing
and diode fabrication have been conducted in private industry where significant advances are proprietary.
However, the results of technological advances in these areas are quite evident in the continual improvement
in the size, performance, and availability of HPGe detectors. Maximum photopeak efficiency for HPGe gamma-
ray detectors is doubling every 6 to 8 years. Concurrently, energy resolutions are moving toward the theoretical
limits of Eq. (116.7) as the concentrations of trapping centers are reduced.
The reliability as well as the performance of germanium gamma-ray detectors has also continued to improve,
although this is harder to quantify. Cryostats have been redesigned to reduce virtual and direct leaks, reduce
microphonics, implement modular design, and improve ruggedness. Detector makers are also making more
serious attempts to offer models with reduced backgrounds by judicious design changes and careful selection
of materials.
FIGURE 116.13 Manganese X-ray spectrum from an
55
Fe source collected with an HPGe detector. (Darken and Cox, 1993;
reprinted with permission of Oxford Instruments, Inc.)
? 2000 by CRC Press LLC
New applications for gamma-ray spectroscopy have emerged. The HPGe detector industry has recently
supplied over 100 detectors each to two different experimental facilities (GAMMASPHERE in the U.S., and
EUROBALL in Europe), where they were arranged spherically in a modular fashion around the target of an
ion accelerator to study the decay of nuclei from excited states of high angular momentum.
For users of single detector systems, developments in the pulse processing electronics necessary for data
acquisition and in the hardware and software for data analysis have resulted in both more compact and more
flexible systems. Plug-in cards for a personal computer are available now that not only contain the functions
of the ADC and multichannel analyzer, but also the high voltage power supply and amplifier as well. Software
developments also allow for control of many pulse processing parameters that were previously set manually.
Si:Li Type Silicon Detectors
As with germanium for gamma-ray spectroscopy, the impurity requirements on silicon for nuclear radiation
detectors are also stringently low and difficult to obtain. Such silicon must be grown by the float zone technique
to eliminate contamination from a crucible. Unlike germanium, little dedicated effort has been expended trying
to improve silicon growth techniques to achieve superior detector characteristics. Most progress in material
quality has come from technology improvements aimed at other applications. The purest silicon commercially
available typically has a net electrically active impurity concentration of a few times 10
11
cm
–3
(compared to
10
10
cm
–3
for HPGe), which usually limits device thicknesses to less than a millimeter. When thicker silicon
devices are required, as in X-ray spectroscopy, silicon of higher net purity can be obtained by lithium drifting
[19], but such material cannot be subsequently processed above room temperature.
In X-ray spectroscopy for microanalysis, liquid-nitrogen cooled Si:Li detectors are being challenged by
similarly sized HPGe detectors, but Si:Li detectors are still more widely used. Recent developments in specialized
low-noise silicon drift detectors and CCD-based detector (see Room Temperature Semiconductor section)
designs that have yielded promising results at room temperature may find future application in liquid nitrogen-
cooled systems for microanalysis using X-ray spectroscopy.
Room-Temperature Semiconductors
Applications arise that require energy resolution beyond the capability of scintillator systems and where cryo-
genically cooled semiconductors are not suitable. Examples include detector probes for monitoring restricted
areas, monitoring at remote sites where replenishing the coolant is impractical, spectral imaging, and many
portable instrument applications. There is available a class of semiconductor detectors that satisfy many such
needs by providing energy resolution substantially better than the best scintillators (although inferior to
cryogenic semiconductors) while operating at ambient temperature. In addition to spectroscopy, these devices
are also useful for counting applications where high detection efficiency per unit volume is required. In these
applications, the devices are operated in pulse mode wherein the charge associated with single photon absorp-
tion events is recorded. They also can be operated in a current mode in the manner of a solid-state ion chamber.
In their current stage of development, room-temperature detectors are limited in size and best suited for the
energy region below 1 MeV.
There are numerous detector types in the general category of room-temperature detectors: those capable of
ambient temperature operation (true room-temperature devices) and those requiring cooling to the region of
–30°C. The former group includes wide bandgap materials such as cadmium zinc telluride, mercuric iodide,
cadmium telluride, and a number of silicon structures. The latter group consist primarily of p-intrinsic-n (PIN)
silicon devices. As a group, room-temperature detectors are employed mainly in X-ray and gamma-ray spectros-
copy, although silicon surface barrier and ion-implanted devices are highly valued for charge particle spectroscopy.
True Room-Temperature Detectors
True room-temperature detectors are distinguished from cryogenic semiconductors by the magnitude of the
energy gap that separates the normally vacant conduction band from the highest filled band. If this energy gap
is small, as in the case of germanium (0.67 eV), electrons can be thermally stimulated across the bandgap at
room temperature. The resultant current competes with the gamma-ray generated signal, precluding room-
temperature operation of germanium (and many high-resolution applications of silicon). Thermally induced
? 2000 by CRC Press LLC
current is reduced to acceptable levels at bandgap energies of about 1.4 eV and above. This phenomenon has
been successfully exploited in the development of room-temperature detector materials, including cadmium
zinc telluride (acronym CZT), cadmium telluride (CdTe), and mercuric iodide (HgI
2
).
Theory of Operation
Operating principles of room-temperature detectors are similar to those governing the more familiar cryogenic
semiconductor devices. Gamma-radiation is absorbed in the material and generates electron-hole pairs that
move under the influence of an applied electric field to contacts and external electronics for processing and
production of the familiar pulse height spectrum. The process is shown schematically in Fig. 116.14. Funda-
mental to the charge-transfer process is the carrier mobility (μ) and the carrier life time (τ). The product μτE
defines a drift length (λ), which should be long compared to the inter-contact dimensions. Owing to the
substantially higher average atomic number of the room-temperature detector materials, the probability of
gamma-ray absorption is much higher than in silicon or germanium (see Fig. 116.7). As a result, room-
temperature detectors provide greater detection efficiency per unit volume.
The energy required to produce an electron-hole pair (ε) is typically a few times the energy bandgap of the
material. In silicon where the bandgap is 1.14 eV, the energy to produce an electron-hole pair (ε) is 3.62 eV. In
HgI
2
, where the bandgap is 2.13 eV, about 4.2 eV is required to create an electron-hole pair. The absorption of
a 1 MeV photon thus produces about 276,000 e-h pairs in silicon and 240,000 e-h pairs in HgI
2.
Values of ε
for room-temperature materials are in the region of 4.2 to 5.0 eV/e-h pair (see Table 116.2) and consequently
fewer electron-hole pairs are generated per unit of absorbed energy. Complete collection of the charge is desired
although charge trapping, which may not affect the two carrier types equally, prevents this in most cases. The
drift length for holes (λ
h
) in these materials is often less than the inter-contact dimensions and creates a
condition where the collection efficiency depends on the photon interaction depth. This phenomenon is
illustrated in Fig. 116.15 where induced charge from single gamma absorption events originating at various
FIGURE 116.14 Schematic illustration of charge generation in a planar detector.
TABLE 116.2 Physical Parameters of Common Room-Temperature Semiconductor Materials
Material E
g
, eV Z ε, eV ρ, ? (μτ)
e
cm
2
/V (μτ)
h
cm
2
/V
Cadmium zinc telluride 1.65 48 5.0 10
11
1 × 10
–3
6 × 10
–6
Cadmium telluride 1.5 50 4.4 10
9
3.5 × 10
–3
2.3 × 10
–4
Mercuric iodide 2.13 62 4.2 10
13
1 × 10
–4
4 × 10
–5
Note: E
g
= bandgap energy; Z = average atomic number; ε = energy to create an electron-hole
pair; ρ = resistivity.
Source: Semiconductors for Room-Temperature Radiation Detector Applications, R. B. James, T. E.
Schlesinger, P. Siffert, and L. A. Franks (Eds.), Materials Research Society, Vol. 32, Pittsburgh, PA, 1993.
? 2000 by CRC Press LLC
depths in the material is plotted as a function of time. The initial fast-rising segment is due to the more mobile
electrons; the slower component is due to holes. In this example, hole trapping is assumed and manifests itself
in the curvature of the hole segment. The charge collection efficiency (η) can be derived from the Hecht relation
[20]. For a photon absorbed at a distance X from the cathode of a planar detector of thickness L operated with
a uniform electric, the relationship becomes
(116.8)
The dependence of the collection efficiency on interaction depth reduces energy resolution and without
mitigation would limit high resolution to thin devices. Fortunately, methods have been developed that permit
high-energy resolution to be achieved in relatively thick samples. As with cooled semiconductor detectors, the
energy resolution of the combined detector-electronics system is normally specified by the full width of a
monoenergetic spectral peak at its half amplitude points (?E). The FWHM is, in turn, related to the variance
in the peak L
2
(see Eq. 116.7). It is useful to note that the energy resolution is inversely related to the product μτ.
Operational Considerations
Important physical parameters for the leading room-temperature detectors are summarized in Table 116.2.
Detectors are available with surface areas of a few square centimeters and thicknesses up to about 1 cm. The
performance of detectors based on the different materials varies considerably, as can the performance for
detectors of the same material. The choice of specific detector material is normally dictated by the application.
The exceptionally high resistivity and high photoelectric cross section in mercuric iodide permit good resolution
and high efficiency in the X-ray region, particularly below 10 KeV. For example, ?E of 5% at 5.9 KeV has been
reported [21] with 1 cm
2
devices, with typical values in the region of 10%. For mercuric iodide applications in
the region of 0.5 MeV, trade-offs between efficient gamma absorption and resolution may be required.
FIGURE 116.15 Charge collection in a planar detector for single-photon interaction. Curves a to d depict the charge from
photon interactions at increasing depths below the cathode.
η
λ
λ
λ
λ
=?
?
( )
?
?
?
?
?
?
?
?
+?
?
?
?
?
?
?
?
e
e
h
h
L
L
L
11exp exp
X
X
? 2000 by CRC Press LLC
In gamma-ray applications where energy resolution is the primary concern, thinner devices that minimize
charge trapping are often utilized, although procedures have been developed to mitigate many of the thickness
and area limitations. Two general approaches have been developed to mitigate the effects of incomplete hole
collection. Those approaches are based on electronic pulse processing via ancillary circuitry or novel electrode
structures that achieve monopolar (electron transport only) operation. These methods have been particularly
successful with CZT and CT devices. CZT- and CT-based devices incorporating such technology are available
in commercial products. In CZT, for example, 1.5 × 1.5 × 0.8 cm
3
detectors (electron only collection) are
available with 3% resolution at 662 KeV. Somewhat better resolution can be obtained with smaller devices. For
example, 1 × 1 × 0.5 cm
3
detectors, operated in the electron-only mode, provide 2% at 662 KeV. Similarly,
cylindrical detectors 6 mm in diameter and 5 mm high provide about 1% resolution at 662 KeV. An energy
spectrum obtained with a typical CZT spectrometer obtained with a
137
Cs
source is shown in Fig. 116.16.
Improvements in material quality can be expected to further improve the performance of thick detectors.
While the area of single crystal detectors is limited currently to a few square centimeters, electronics have been
developed to facilitate the operation of large arrays of single-crystal detectors and thus achieve high detection
efficiency. Multiple CZT detector arrays 20 × 20 cm have been produced using such technology.
Further information concerning the performance of single charge collection and array structures as well as
electronic processing and design details are available in the literature [2, 3, 22, 23].
Silicon Detectors
In contrast to germanium detectors, silicon detectors can be operated at room temperature in applications
where some current noise can be tolerated. Compared to gas and scintillation detectors, silicon detectors have
good energy resolution and are reasonably compact. They are fabricated from slices of a silicon single crystal
and are available in a variety of areas (25 mm
2
to 3000 mm
2
), and the active thickness is usually a few hundred
microns. Specialized detectors have been developed for a wide variety of applications.
Charged Particle Detectors
Energetic heavy-charged particles lose kinetic energy continuously along a linear path in an absorbing material.
Energy is transferred primarily to the electrons in the absorbing material, but to a lesser extent to the nuclei
also via Rutherford scattering. Although only energy transferred directly to the electronic system generates
electron-hole pairs, Eq. (116.5) (with ε = 3.62/pair for silicon at 300K) is still a good approximation. Energy
loss is characterized by two parameters: specific ionization loss dE/dx, which depends on the incident particle,
its energy, and the absorbing material, and the range R (i.e., the penetration depth of the particle), which
FIGURE 116.16 Energy spectrum of a
137
Cs source obtained with a multi-electrode CZT spectrometer. (Courtesy AMPTEK
Inc. Bedford, MA.)
? 2000 by CRC Press LLC
determines the detector thickness required for complete energy absorption. The continuous nature of energy
loss leads to substantial window effects.
Diffused Junction Detector
Silicon detectors can be generically categorized by the type of rectifying contact employed. The diffused junction
detector is fabricated by diffusing phosphorus from the gas phase into p-type silicon. This is a high-temperature
(900°C to 1200°C) operation that is prone to introducing faster diffusing metals into the bulk that can act
either as generation centers increasing leakage current, or as trapping centers degrading charge collection. The
thickness of the diffused region, from 0.1 to 2.0 μ, also presents a dead layer to incident particles that is reduced
in alternate technologies. Nonetheless, these detectors find use due to their ruggedness and economy.
Surface Barrier Detector
Surface barrier junctions are fabricated by either evaporating gold onto n-type silicon or aluminum onto p-type
silicon. A typical entrance window is equivalent to 80 nm of silicon. The rectification properties depend on the
charge density of surface states of the silicon and of the thin oxide layer over the silicon, as well as on the
evaporated metal. The wafer is epoxied in an insulating ring before metallization. The finished detector is
encapsulated in a can that has a front window for particle entry and a single contact in the back for the combined
function of applying bias and for extracting the signal pulse. Devices can be operated either in the partially
depleted or totally depleted mode. As fabrication is entirely at room temperature, there is no opportunity for
metal contamination by diffusion. Generally, surface barrier detectors have lower leakage current, and less
system noise than a diffused junction detector of comparable area and depth. However, detectors currently
fabricated by ion implantation have still lower leakage current and electronic noise, together with a thinner
and more rugged front contact. On the other hand, implanted detectors are not available in the same range of
active thicknesses as surface barrier detectors. Below 100 μ and above 500 μ, only surface barrier detectors are
currently available. Surface barrier detectors can be made in small quantities with rather simple equipment.
Ion-Implanted Detector
A simplified representation of ion-implanted detector fabrication is shown in Fig. 116.17. The first successful
implementation of silicon planar processing to silicon detectors was reported by Kemmer [24]. The procedure
starts with the thermal growth of an oxide film on a high-purity, n-type silicon wafer. Windows are then opened
in the oxide by photolithographic techniques. The front contact area is implanted with boron to form the
rectifying contact, and arsenic is implanted into the backside. The wafer is then annealed to activate the implant,
and aluminum is evaporated on both sides to reduce sheet resistivity. Typical entrance windows are 50 nm
silicon equivalent. Electrical connections are made by wire bonding to the aluminum layers. Finished detectors
are canned in a manner similar to surface barrier detectors. More than one detector can be fabricated on the
same wafer using the appropriate masks during photolithography. In fact, quite elaborate detector geometries
can be achieved via photolithography. The detector in Fig. 116.17 is actually a strip type.
The ion implantation planar process technology is well suited for mass production of wafer sizes compatible
with the rest of the silicon industry. Minimum wafer diameters are now 4 in. or 5 in. At this diameter, breakage
during fabrication is an issue for thicknesses less than 150 μ. For thicknesses over 500 μ, the availability of
enough sufficiently pure material to justify the cost of photolithographic masks is an issue. Ion-implanted
detectors can be baked at 200°C to reduce outgassing. This is a significant improvement over surface barrier
detectors, which irreversibly degrade by device processing above room temperature. This is a useful feature as
most heavy charged particle spectroscopy is done in a vacuum.
Leakage currents are, at room temperature, typically 1 to 10 nA cm
–2
active area and per 100-μ depletion
depth. These values represent an order of magnitude reduction in leakage current with respect to surface barrier
detectors. Two factors are relevant. Passivation of silicon surfaces by thermal oxidation is extremely effective in
reducing leakage current around the rectifying contact. Also, the bulk generation current is reduced by the
gettering of metal impurities during the high-temperature oxidation. Float zone silicon for radiation detectors
usually has a minority carrier lifetime longer than 1 ms, and this can be increased an order of magnitude during
detector fabrication [25]. Thus, not only is leakage current reduced, but potential charge collection problems
are also eliminated.
? 2000 by CRC Press LLC
Energy Resolution
A typical spectrum of an
241
Am alpha-particle source taken with an ion-implanted detector is shown in
Fig. 116.18. While the factors considered in Eq. (116.7) for germanium gamma-ray spectrometers are still valid,
additional considerations also apply. In particular, if the source is moved closer to the detector to improve
collection efficiency, larger differences in the angle of incidence will produce peak broadening due to larger
variation in effective window thickness. Even when the source is sufficiently distanced from the detector, there
FIGURE 116.17 Steps in the fabrication of passivated planar silicon diode detectors. (Kemmer et al., 1982).
FIGURE 116.18 Spectrum of a
241
Am alpha-particle source (log scale) measured with an IP detector (25 mm
2
area, 300 μm
thick) at room temperature. Resolution at 5.486 MeV is 10.6 KeV (FWHM). (Kemmer et al., 1982.)
? 2000 by CRC Press LLC
will still be spatial variations in window thickness, as well as some variation in energy lost escaping from the
source and traversing to the detector.
Another source of peak broadening is the variation in the small amount of particle energy lost during
Rutherford scattering. This energy is transmitted directly to the scattering nuclei and does not generate electron-
hole pairs, and a small pulse deficit results. These events are relatively few but large, and therefore contribute
disproportionately to peak variance. The FWHM contribution of this effect on a 6-MeV alpha particle peak
has been estimated to be 3.5 KeV [26].
Silicon Detectors for Spatial Resolution
The uninterrupted progress of the semiconductor silicon industry in achieving both larger wafers and smaller
device features has allowed the development of larger and more complex silicon detectors that can provide
position information in addition to (or instead of) energy information. Spatial detection can be obtained by
fabricating detectors as pixels (two-dimensional) or strips (one-dimensional) on the same wafer. For penetrating
radiation, two strip detectors, one behind the other but with the strip pattern rotated 90°, provide two-
dimensional positioning. Frequently, such detectors are individually designed and fabricated for a particular
application. Strip detectors and CCD (charge-coupled device) detectors will be discussed here.
Strip Detectors
Silicon strip detectors are currently fabricated on silicon wafers (typically approximately 300 μ thick) using
photolithographic masking to implant the rectifying contact in strips [27]. The strips usually have a pitch on
the order of 100 μ and a width less than half of this to minimize strip-to-strip capacitance and hence electronic
noise [28]. The device is biased past depletion, and the back blocking contact is continuous. Each strip requires,
in principle, its own signal processing electronics; however, charge division readout (capacitive or resistive) can
reduce the number of amplifiers by a factor of 10. Detectors are fabricated in rectangular segments from a
single wafer, and can be ganged together if a larger area is needed.
Strip detectors are well established in high-energy physics experiments for reconstruction on the micron
scale of the tracks of ionizing particles. The particles being tracked result from the collision of accelerated
particles with a target and are highly energetic (>10
10
eV). Frequently, experimental interest is focused on short-
lived particles created in the collision but which decay before they can be directly detected. Spatial resolution
of the decay vertex from the original collision is necessary to detect such a particle and to determine its lifetime.
The requirements of new high-energy experiments and advances in silicon technology have produced much
evolution and innovation in the strip detector concept. For example, a double-sided microstrip detector with
an oxide-nitride-oxide capacitor dielectric film has been reported [29]. The use of intermediate strips to improve
spatial resolution has become common [30], and the biasing network has been integrated onto the detector [31].
Silicon Drift Detectors
Silicon drift detectors were first proposed by Gatti and Rehak [32] as an alternative to silicon strip detectors in
high-energy physics experiments. The primary motivation was to significantly reduce the number of readout
channels. Drift detectors have subsequently been adapted for X-ray spectroscopy. These detectors are usually
fabricated on n-type silicon wafers with holes collected to either a p
+
contact on the back side of the detector,
or to concentric annular p
+
contacts on the front side. The detector is depleted from both sides. The reverse
bias applied to the p
+
annular rings is varied in such a way that electrons are collected radially in a potential
energy trough to an n
+
anode at the center of the detector on the front side.
A cross section through a circular drift detector is shown in Fig. 116.19. The electron collecting anode ring
surrounds the integrated FET used for the first stage of signal amplification. Enough negative bias is applied
to the back contact (actually the entrance window) to deplete the wafer to the anode, which is near ground
potential. At the same time, negative bias progressively increasing in magnitude is applied from the ring next
to the anode (near ground potential) to the outermost ring, which is maintained at about two times the bias
of the back contact. These applied biases deplete the detector in such a way that there is an electrostatic potential
minimum for electrons that varies in depth across the detector from right under the front surface at the anode
to near the back contact at the last ring. Ionized electrons will drift first to this minimum, then drift radially
to the anode as shown in Fig. 116.19. A feature of this contacting arrangement is that the anode capacitance,
? 2000 by CRC Press LLC
and hence amplifier series noise, is low and nearly independent of the active area of the detector. Radial position
is deduced from the signal risetime.
CCD Detectors
The design of CCD (charge-coupled device) detectors has similarities to the silicon drift detector [32]. The
CCD detector is normally fabricated on an n-type silicon wafer depleted both from the backside with a
continuous p
+
contact on the back, and from p
+
CCD registers on the front. Reverse bias voltages are such that
the wafer is totally depleted and the electron potential minimum is about 10 μ below the CCD registers. After
an ionizing event, holes are collected to the p
+
contacts, and electrons are trapped under a nearby register, then
transported down a channel of registers by properly clocked voltage pulses to the registers. Each channel has
its own readout anode, which can be made small to minimize capacitance — a prerequisite for minimizing
noise. The first stage of amplification is frequently integrated onto the same wafer. Spatial resolution is limited
to the register (pixel) size. Brauniger et al. [33] described initial results on a 6 × 6 cm CCD array of 150 × 150 μ
pixels intended for satellite X-ray imaging. The system also had an energy resolution of 200 eV FWHM for
5.9 KeV X-rays at room temperature.
Silicon pixel detectors have also been designed using other highly integrated device structures to optimize
particular performance aspects such as timing resolution. Pixel detectors using MOS transistors [34] and using
reverse biased diodes with individual readout circuitry [35] have been described.
PIN Silicon X-ray Spectrometers
Detectors based on PIN silicon structures have found considerable success as X-ray spectrometers in the region
below 10 KeV. The devices consist of n and p layers on opposite sides of a high purity (10–20 K ohm-cm)
silicon wafer. Particularly good performance is obtained if the devices are operated in the region of –30°C as
can be provided by a thermoelectric cooler. On the order of 1 W is required to maintain a typical device at
–30°C. Energy resolution (FWHM) of 186 eV at 5.9 KeV can be obtained in 7-mm
2
devices (with 20 μs shaping
time). Spectrometers with areas up to about 25 mm
2
are also available, but with reduced resolution. The energy
spectrum of
55
Fe obtained with a 7-mm
2
detector is shown in Fig. 116.20(a), together with a schematic showing
construction details (Fig. 116.20(b)).
Status of Silicon Detector Technology
The simply structured silicon detectors fabricated with parallel contacts on a silicon wafer continue to serve a
well established need for charged particle spectroscopy. Where economies of scale can be applied, ion implanted
detectors have replaced surface barrier detectors. In projects of sufficient size to support their development,
specialized low-noise silicon drift detectors and CCD-based detectors have been designed and fabricated with
promising room-temperature energy resolution: 200 eV FWHM at 5.9 KeV. These highly structured detector
FIGURE 116.19 Cross section of a cylindrical silicon drift detector with integrated n-channel JFET. The gate of the
transistor is connected to the collecting mode. The radiation entrance window for the ionizing radiation is the non-structured
backside of the device. (P. Lechner, S. Eckbauer, R. Hartmann, S. Krisch, D. Hauff, R. Richter, H. Soltau, L. Struder, C. Fiorini,
E. Gatti, A. Longoni, M. Sampietro, Nuclear Instruments and Methods in Physics Research, A377, 346–351, 1996.)
? 2000 by CRC Press LLC
technologies may find future application in liquid nitrogen-cooled or room-temperature systems for microanal-
ysis using X-ray spectroscopy.
In high-energy physics, the use of various strip, drift, and pixellated detectors for tracking and vertex
determination has flourished. These efforts will intensify as experimental requirements for spatial resolution
increase. However, radiation damage to the detector is already an issue in this application, and higher luminosity
beams will only increase the problem. Nevertheless, it appears that the continuing need of the high-energy
physics community for a higher number and density of signal paths forecasts continued reliance on the ever-
improving integration technology of the semiconductor silicon industry.
Prices and Availability
The detectors described in this section are available commercially. Their prices vary widely, depending on type,
size, and performance. Room-temperature semiconductor detectors range from a few hundred dollars for small,
low-resolution devices to over $1000 for large, high-resolution devices. Because of the dynamic nature of wide
bandgap detector technology, buyer guides should be consulted for the latest price and availability information.
Pricing of coaxial HPGe detectors is based largely on their gamma-ray efficiency, which is specified relative
to a 3 in. × 3 in. sodium iodide scintillator at 1.33 MeV. Coaxial detectors are available with relative efficiencies
up to about 150% with cost in the area of several hundred dollars per percent efficiency. Planar HPGe detectors
are normally less expensive than coaxial designs. In either case, the price includes the cryostat, dewar, and
preamplifier. Cryogenic silicon detectors are available in areas up to several tens of square millimeters. Cost
ranges to over $10,000 depending on size, performance, and complexity of design.
Defining Terms
Ballistic deficit: The loss of signal amplitude that occurs when the charge collection time in a detector is a
significant fraction of the amplifier’s time constant.
Current mode: Measurement mode in which the detector signal provides information on the flux X-rays,
gamma-rays, or charged particles.
Dead layer: A layer (frequently associated with a contact region) in which no significant part of the energy
lost by photons or particles can contribute to the resulting signal.
Electrical junction: The metallurgical transition boundary between the semiconductor regions of different
electrical properties (for example, PIN or between a metal and a semiconductor).
Energy bandgap: The energy difference between the bottom of the conduction band and the top of the valence
band.
FIGURE 116.20 (a) Energy spectrum of
55
Fe source obtained with a 7-mm
2
PIN silicon detector using a shaping time of
20 μs. (b) Schematic diagram showing construction details of typical PIN-silicon detector with thermoelectric cooler.
(Courtesy AMTEK Inc. Bedford, MA.)
? 2000 by CRC Press LLC
Energy resolution: The full width of the half maximum of a peak in the energy spectrum, after subtraction
of the background under the peak; expressed in units of energy, usually KeV or as a percentage of the
energy of the peak.
Energy spectrum: A differential distribution of the intensity of the radiation as a function of the energy.
Leakage current: In the absence of external ionizing radiation and at the operating bias, the total current
flowing through or across the surface of the detector element.
Line of peak (in a spectrum): A sharply peaked portion of the spectrum that represents a specific feature of
the incident radiation, usually the full energy of a monoenergetic X-ray, gamma-ray, or charged particle.
Pulse mode: Measurement mode in which the detector signal provides information on a single X-ray, gamma-
ray, or charged particle.
Semiconductor: Material in which the conductivity is due to charge carriers of both signs (electrons and
holes) and is normally in the range between metals and insulators, and in which the charge carrier density
can be changed by external means.
Semiconductor radiation detector: A semiconductor device in which the production and motion of excess
free carriers is used for the detection and measurement of incident particles or photons.
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? 2000 by CRC Press LLC
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