Chapter 8 Hyper-Pure Germanium Detector€¦ · Chapter 8 Hyper-Pure Germanium Detector 8.1. Introduction Silicon semiconductor detectors described in the previous chapter have depletion

Med Phys 4RA3, 4RB3/6R03 Radioisotopes and Radiation Methodology 8-1

Chapter 8 Hyper-Pure Germanium Detector 8.1. Introduction

Silicon semiconductor detectors described in the previous chapter have depletion depths less than 1 mm, which are sufficient for charged particle spectroscopy or soft X-ray detection. For photon spectroscopy in the energy region of hundred keV or several MeV, much thicker semiconductor detectors are required. Fig. 8.1 shows the mean free path of a photon in silicon and germanium. It is obvious that a depletion depth of at least several cm is required. Due to its higher atomic number, Ge has a much lager linear attenuation coefficient, which leads to a shorter mean free path. Thus, Ge is preferred for hard X-ray or gamma-ray detection to achieve higher detection efficiency.

101 102 103 10410-3

10-2

10-1

100

101

Ge

Si

Photon energy [keV]

Mea

n f

ree

pat

h [

cm]

Fig. 8.1. Photon mean free paths in Si and Ge.

For a semiconductor detector, the depletion depth is given by

2/10 )2

(eN

Vd

where, V0 is the reverse bias voltage and N represents the net impurity concentration in the initial semiconductor material. If silicon or germanium of normal semiconductor purity is employed, the maximum achievable depletion depth is a few mm even at bias voltages close to the breakdown level. Thus, the impurity concentration should be much reduced down to 1010 atoms/cm3 in order to realize intended depletion depths of cm order. At this impurity concentration, a reverse bias voltage of 1 kV can produce a depletion depth of 1 cm. The required impurity concentration corresponds to levels less than 1 part in 1012, which is quite challenging. One way to further improve the net impurity concentration is to compensate the residual impurities with an opposite type impurity material. In both Si and Ge, the material with highest available purity tends to be p-type, which requires addition of donor atoms for compensation. The alkali metals like Li, Na tend to form interstitial donors in Si and Ge. When one of these donor materials (practically Li) is introduced into Si or Ge, the donor atoms are easily ionized and are mobile enough to drift at elevated temperatures under the influence of a strong electric field. This process is so-called “lithium ion drifting” and has been applied in both Si and Ge. For convenience, Ge(Li) represents lithium drifted Ge and Si(Li) means lithium drifted Si. The


lithium mobility is much greater in germanium and remains high enough at room temperature, which leads to an undesirable redistribution of the lithium. Therefore, the lithium profile of Ge(Li) detectors must always be preserved at LN2 temperature while Si(Li) detectors can be stored at room temperature for a short period due to low mobility of the Li ion in silicon. The other way to improve the net impurity concentration is to add additional refining processes so that the intended purity of the crystal can be met. Techniques have been developed to achieve high purity Ge crystals in this approach and HyperPure Ge (HPGe) detectors are commercially available. However, no equivalent technique is available for Si yet. Ge(Li) detectors were popular in the past and served as the common type of large-volume germanium detector for a long time. Although there is little difference in detector performance between HPGe and Ge(Li), the maintenance of Ge(Li) is pretty inconvenient, which has made manufacturers stop producing them. 8.2. Configurations

A. Hyper-Pure Germanium (HPGe) detector fabrication [4]

HPGe crystal were first developed in the mid 1970s. The starting material is bulk germanium intended for the semiconductor industry. Although already of very high purity, the material is further purified with the zone refining technique. The germanium is melted in a crucible using radio-frequency (RF) heating coils. The underlying principle is that impurities concentrate in the liquid phase leaving the solid purer than the original melt as a liquid freezes and solid appears.

Fig. 8.2. Three coil zone refine.

Fig. 8.3. Growing Ge crystal.

As shown in Fig. 8.2, each zone refiner coil melts a small section of the germanium in the crucible. As the RF coils are slowly moved along the length of the crucible, the molten zone moves with them. Thus, the germanium melts as the coil approaches and freezes as the coil moves away. The impurities tend to remain in the molten section, which leads to a higher concentration of impurities in the liquid than the solid. In this way, the impurities are swept to one end. This sweeping operation is repeated many times, until the impurities are concentrated at one end of the ingot. This end is then removed, leaving the remaining portion much purer than


the original starting material. The improvement or reduction in impurity concentration actually realized is about a factor of 100 or more at the completion of this process. Large single crystals of germanium are grown using the Czochralski technique. A precisely cut seed crystal is dipped into the molten germanium and then withdrawn slowly, while maintaining the temperature of the melt just above the freezing point as shown in Fig. 8.3. The rate of crystal withdrawal and temperature of the melt are adjusted to control the growth of the crystal. If the remaining extremely low-level impurities are acceptors, the property of the crystal is mildly p-type while high purity n-type is the result in the other case. B. Planar configuration

An example of a planar HPGe detector using a p-type crystal is shown in Fig. 8.4. In this configuration, the electric contacts are provided on the two flat surfaces of a germanium crystal.

0.25 mm thick Be

n+ contact (0.7 mm Li)

Photons

e hp-type

p+ (0.3 m B)

p-n junction

Fig. 8.4. Planar HPGe detector (p-type).

A lithium evaporation and diffusion to form the n+ contact is performed over one of the surface. This lithium-diffused layer is about several hundred µm thick. The depletion region is formed by reverse biasing n+-p junction. The surface of the opposite side is modified to the p+ layer by ion implantation of boron acceptor atoms to increase the conductivity near the surface. Since both materials are p-type, no semiconductor junction exists at this side. Instead, the p+ layer provides the electric contact to collect the charge carriers created by the radiation. The thickness of the implanted boron layer is so thin (a few tenths of µm) that it is a suitable entrance window for low energy photons. To make a reverse bias, a positive high voltage is applied to the n+ contact with respect to the p+

surface. The depletion region is formed at the region close to the n+ contact and then expanded deeply into the p-side as the bias voltage is raised. Once the detector is fully depleted, further increase of the bias (overvoltage) does not make any effect on the sensitive volume, however, it makes the electric field stronger, which subsequently shortens carrier collection times and reduces the risk of carrier losses (recombination and trapping).


Planar HPGe detectors can also be fabricated starting with high-purity n-type crystals. Similarly, n+ and p+ contacts are provided on both sides. Reverse biasing also requires the application of a positive voltage to the n+ side. In this case, the depletion region is expanded from the p+ contact. When fully depleted and operated with a sufficient overvoltage, the electric field inside the crystal is almost uniform and charge carriers drift under a constant electric field. C. Coaxial configuration

From the photon mean free path in germanium, a detector thickness of the order of 5 cm is required for efficient detection of MeV photons. The maximum depletion depth for the planar detectors is limited to less than 1 or 2 cm. To produce a detector with a thicker depletion depth, a different electrode configuration must be employed. HPGe detectors dedicated for MeV photons are constructed in coaxial geometry as shown Fig. 8.5. In this configuration, one electrode is fabricated at the outer surface of a cylindrical crystal and the other electrode is located at the inner surface of the central hole. In this way, much larger active volumes can be achieved.

True coaxial Closed-ended coaxial

Fig. 8.5. Large volume coaxial HPGe detectors. A closed-ended configuration is one in which only part of the central core is removed and the outer electrode is extended over one flat side surface. This configuration is the most common type of commercial HPGe detector.

p-n junction p-n junction

depleted

Fig. 8.6. Extension of the depletion region for a coaxial detector.


In principle, the p-n junction of a coaxial detector can be located either at the inner or outer surface of the crystal as shown in Fig. 8.6. If the junction is on the outer surface, the depletion region extends inward as the high voltage bias is increased until the crystal is fully depleted. In the opposite case, the depletion region grows outward. The p-n junction at the outer surface requires a much lower full depletion bias and therefore, is preferred. The practical electrode configurations of coaxial Ge detectors are shown in Fig. 8.7. To make the p-n junction at the outer surface, the n+ contact is performed over the outer surface for a p-type detector while the p+ contact is applied in case of an n-type crystal. The n-type coaxial detectors are often called reverse electrode detectors. The reverse bias requires a positive outside potential for a p-type and a negative potential for an n-type relative to the central electric potential.

n+ contact

p-type

p+

p+ contact

n-type

n+

Fig. 8.7. Electrode configurations for coaxial detectors.

Regardless of the crystal type, a coaxial detector can be used for general gamma-ray spectroscopy purposes. For low energy gamma-rays below 100 keV, a significant portion of the incident photons is attenuated for p-type detectors due to the relatively thick surface dead layer, i.e. lithium n+ contact. Thus, p-type coaxial detectors are normally limited down to 50 keV. Since the dead layer thickness of n-type detectors is much thinner, n-type detectors are still effective for low energy photons (down to several keV) when coupled to a thin Be entrance window. Therefore, n-type detectors cover quite a wide spectral region compared to p-type coaxial and planer detectors. D. Electric field and capacitance

The electric field in HPGe detectors governs the charge carrier collection process. The signal pulse shape and the timing behavior are consequently dependent on the variation of the electric field strength. As discussed in the general properties of semiconductor detectors, the governing equation is Poisson’s equation:

V2

The charge density is given as = -eNA for p-type crystals and as = eND for n-type crystals. For convenience, p-type crystals are assumed in the following derivation.


Planar detectors From the solution derived in the semiconductor detector chapter, the depletion depth corresponding to a reverse bias V0 is

2/102/10 )2

()2

(AeN

V

eN

Vd

where, N represents the impurity concentration in the initial semiconductor material. If the crystal thickness is T, the high voltage bias corresponding to the depletion depth T is

2

2TeNV A

d

In this case, the detector is fully depleted and Vd is defined as the depletion voltage. In one-dimensional slab geometry as shown in Fig. 8.8, Poisson’s equation becomes

AeN

dx

xVd

2

2 )( (0 x d)

For a partially depleted voltage, the equation is valid for the depleted region. The boundary condition of the electric potential becomes

0)()0( VdxVxV where x = 0 represents the n+ contact position. The electric field is obtained by integrating the Poisson’s equation:

)2

()( 0 xdeN

d

VxE A

(0 x d)

For a given bias voltage (if V0 < Vd), this solution is limited in the depleted region and the electric field outside the depleted region is zero. The variation of the electric field strength for a planar HPGe detector is shown in Fig. 8.9. The depletion voltage for NA = 1010 cm-3 and T = 1 cm is 565 V. The capacitance per unit area is

2/1

0

)2

(Vd

C

for partial depletion conditions. Once the bias V0 exceeds Vd, the detector capacitance becomes constant and independent of the bias voltage.

0.0 0.2 0.4 0.6 0.8 1.00

500

1000

1500

NA=1010 cm-3, T=1 cm

565 V

400 V

200 V100 V

1000 V

X [cm]

E(x

) [V

/cm

]

Fig. 8.9. Electric field variation of a planar detector.

p+n+

x=0

T

x=d

p-type

Fig. 8.8. Partial depletion of a planar detector.


Coaxial detectors For the true coaxial geometry, Poisson’s equation becomes

AeN

dr

dV

rdr

Vd

12

2

For partial depletion conditions, solving for the depletion depth is a little complicated, so that the bias voltage is assumed to be larger than the depletion voltage. Then the boundary condition can be set as

012 )()( VrVrV where r1 and r2 represent inner and outer radii.

0.0 0.5 1.0 1.5 2.0 2.50

1000

2000

3000

4000

2000 V

NA=1010 cm-3, r

1=4 mm, r

2=2.5 cm

Vd=1556 V

3000 V

r [cm]

E(x

) [V

/cm

]

Fig. 8.10. Electric field variation of a true coaxial detector.

The electric field can be set as )(ˆ)( rErrE

and is solved as

)/ln(

))(4/(

2)(

12

21

220

rrr

rreNVr

eNrE AA

)/ln(

))(4/(

2)(

12

21

220

rrr

rreNVr

eNrE AA

The depletion voltage Vd can be calculated from the condition

0)( 1 rE

)/ln(

22 122

1

21

22 rrr

rreNV A

d

Fig. 8.10 shows the variation of the electric field for a true coaxial HPGe detector. The capacitance per unit length of a fully depleted true coaxial detector is

)/ln(

2

12 rrC

To make the capacitance as low as possible, the radius of the center core r1 is kept to a minimum. For the closed-ended coaxial detectors, the Poisson’s equation is hard to solve analytically and therefore a numerical method like the Finite Difference Method must be employed. An example of the potential variation and the electric field direction is shown in Fig. 8.11.

Fig. 8.11. Potential and electric field distribution of a

closed-ended coaxial detector [5].


8.3. Operational characteristics

A. Cryostat and dewar Although silicon detectors can be operated at room temperature in principle, operating germanium detectors at room temperature is impossible due to the small bandgap energy, which generates an intolerable leakage current. Therefore, germanium crystals must be cooled to reduce the leakage current. HPGe detectors are allowed to warm to room temperature when they are not in operation, however, they are always maintained at LN2 temperature practically.

Fig. 8.12. Modern arrangement of HPGe detector and preamp within the cryostat housing. The Ge crystal is encased in a vacuum tight container (cryostat) to reduce thermal conduction between the crystal and the air. The basic function of a cryostat is to cool the germanium detector to LN2 temperature. The germanium detector preamp is normally included as part of the cryostat package. Since the preamp should be located as close as possible so that the overall capacitance can be minimized, the preamp is installed together. The input stages of the preamp are also cooled. The entire cold assembly is maintained by the cryostat under high vacuum for both thermal insulation and protection of the internal components from contamination.


All of the cryostat materials around the detector should be as low Z as possible to reduce photon scatter. Hence, aluminum, magnesium, beryllium, Teflon, and Mylar are used whenever possible. There are various types of dewars so that the detection geometry can be selected depending on the application. For general radioactive or neutron-activated samples, the vertical type is widely used. For in-beam spectroscopic purposes, either the horizontal or side-looking type is more convenient. Portable dewars are also available for outside field measurements.

Vertical Horizontal Side-looking

Fig. 8.13. Various configurations of LN2 dewars and cryostats. B. Energy resolution The most important characteristic of HPGe detectors is their excellent energy resolution. In Fig. 8.14, two spectra from an HPGe and a NaI(Tl) are compared for a 60Co source. The great superiority of the HPGe detector allows the separation of many closely spaced gamma lines, which is very beneficial for measuring multi-gamma emitting radioactive sources.

0 500 1000 1500 20000

1x102

2x102

3x102

4x102

5x102

1332 keV

1173 keV

NaI (75 keV FWHM) HPGe (2.35 keV FWHM)

Photon energy [keV]

Co

un

ts/c

ha

nn

el

Fig. 8.14. Comparison of NaI(Tl) and HPGe spectra for 60Co.


The energy resolution of the HPGe photon spectroscopy system is governed by the variation in the number of charge carriers, variation in the charge carrier collection, and the contribution of electronic noise. Hence, the FWHM of a peak in the spectrum can be represented as

2222EXDT WWWW

where W values on the right-hand side are peak widths expected due to carrier statistics, carrier collection and electronic noise. The variation in the number of the charge carriers is given by

N

F

N

NF

E

WD 355.2355.2

FwE

N

EFWD

22

22 )355.2()355.2(

where E is the photon energy, N is the number of e-h pairs, F is the Fano factor, and w is the energy required for creating a electron-hole pair. If the Fano factor is assumed to be 0.1, the equation predicts the WD value of 1.3 keV at 1.33 MeV when the w value of 3 eV is used. The contribution of the second term is due to incomplete charge collection and becomes important for large volume or low electric field detectors. The last term represents the broadening effects of all electronics following the detector. This component can be measured with a precision pulser as discussed in the pulse processing chapter. The pulser output is fed to the test input of the preamp and it undergoes exactly the same path as that of the actual signal from the detector. Fig. 8.15 shows the contribution of each component as a function of the photon energy. At low energies, electronic noise and charge collection are relatively important while the additional broadening due to carrier statistics becomes significant at higher energies.

Fig. 8.15. Dependence of resolution on photon energy.

C. Pulse shape and timing properties

The detailed shape of the signal pulse is important for determining the shaping time of the pulse height spectroscopy and for applications requiring timing information. The ultimate time resolution obtainable from HPGe detectors depends on both the average rise time and the variation in the pulse shape from event to event. Two factors limit the ultimate time resolution of HPGe detectors. The first factor is the slow process of the charge carrier collection. If the electric field is strong enough, the drift velocities of electron and hole are saturated. The electron saturation drift velocity is ~ 105 m/s, which


makes a travel time of 100 ns/cm. Typical pulse rise times will be of this order and are much longer than those of organic scintillation detectors. The second factor is the large variation in the shape of the output pulses. The leading edge of the pulse changes substantially from event to event depending on the position of electron-hole creation. The pulse shape of planar detectors can be described from the energy balance as follows. The infinitesimal induced charge is given by

dQVdW 0

where, dW is the work done on the charge carriers, V0 is the applied voltage and dQ is the induced charge. The work done on the charge carriers with charge q0 is

)(0 xdVqdW T

VqxEq

dx

dW 000 )(

where, E(x) is the electric field and T is the detector thickness. The energy absorbed by the motion from x0 to x is

)( 00000

00

xxT

Vqdx

T

VqdWW

x

x

x

x

which induces charge Q as

T

vtq

T

xxq

V

WdQQ 0

00

0

The corresponding signal voltage VR can be represented as

T

vt

C

q

C

QVR

0

There are two components of the induced charge: one from the motion of electrons, the other from holes. Let’s suppose charge carriers were produced at a distance x from the n+ layer after a photon interaction as shown in Fig. 8.16. In the initial stage of the charge carrier collection, both electrons and holes are drifting, thus,

)()( 0 tT

vt

T

vqtQ he

If electrons have been collected, but holes are still drifting,

)()( 0 tT

v

T

lqtQ he

In the opposite case (holes have been collected),

)()( 0 T

lTt

T

vqtQ ee

After both holes and electrons are collected

0)( qtQ

Fig. 8.16 shows typical patterns of pulse shapes depending on the production positions of e-h pairs.

h

xe


Fig. 8.16. Shape of the leading edge of the output pulse Q(t) for a planar HPGe detector.

8.4. Photon spectroscopy with HPGe detectors

A. Detector response [6]

Fig. 8.17. Pulse height spectrum of 54Mn single gamma emitter.

The response of a HPGe detector for a single gamma emitter is shown in Fig. 8.17. Interaction events contributing the full-energy peak are more likely to consist of multiple interactions, such as Compton scattering followed by photoelectric absorption of the scattered photon. Absorption of the full photon energy in a single photoelectric effect is pretty rare. The table below summarizes a Monte Carlo simulation result.

Number of interactions contributing to the 1332 keV peak for a coaxial HPGe detector

1 2 3 4 5 6

4.2 % 17.8 % 27.0 % 25.1 % 15.4 % 7.0 %


As the photon energy increases above 2mec2, the pair production interaction becomes dominant

and the escape peaks are quite important. The spectra in Fig. 8.18 show different patterns of the full-energy, single escape, double escape peaks depending on the photon energy.

Fig. 8.18. The relative intensity of the full-energy, single escape and double escape peaks for a coaxial detector.

Fig. 8.19. Pulse height spectrum of a HPGe detector for 56Mn multi-gamma emitter.


Fig. 8.19 is an example of the response for a multi-gamma emitter. Thanks to the excellent resolution, each peak is well identified, which is pretty important for analyzing a complicated spectrum. B. Compton suppression system

Fig. 8.20. Guard detector arrangements for Compton suppression.

The Compton continuum in photon spectra from HPGe detectors is generated primarily by photons that undergo one or more scatterings in the detector followed by escape of the scattered photon from the active volume. If those events contributing to the continuum are rejected, the peak-to-continuum ratio is greatly improved and accordingly, the minimum detectable radioactivity can be reduced significantly. To realize a rejection process, the HPGe detector is surrounded with a Guard detector (inorganic scintillation type) as shown in Fig. 8.20. Then the pulse processing system can reject the escape events by the anticoincidence technique when proper timing electronics are implemented. In other words, the pulse processing system accepts each detection event from the HPGe only when there is no detection event from the guard detector in coincidence. Figs. 8.21 and 8.22 show a standard pulse processing system for Compton suppression and an example of the suppression effect.

Fig. 8.21. Standard pulse processing system for Compton suppression.

Ge Ge


Fig. 8.22. 137Cs spectrum with and without the Compton suppression.

C. Efficiency calibration Conventionally, the relative efficiency is conveniently used for quoting the peak efficiency of a HPGe detector. The relative efficiency is defined as Rel. eff. = HPGe peak effi/NaI(Tl) (33) peak effi at 1332 keV from 60Co. The source-detector distance of 25 cm is uniquely used for this definition. The absolute peak efficiency of a 33 NaI(Tl) is 1.210-3 in this geometry. A typical variation of the full-energy peak efficiencies for coaxial detectors is shown in Fig. 8.23. Due to the relatively thick dead layer, the p-type efficiency starts dropping at ~ 100 keV while the n-type efficiency is constant down to ~ 5 keV.

Fig. 8.23. Absolute efficiencies of n-type and p-type coaxial detectors.


A practical example of the efficiency calibration for a wide dynamic range is shown in Fig. 8.24. The experimental efficiency data points were obtained from standard calibration sources up to ~ 1.5 MeV and extended up to 12 MeV with both 14N(n,) and 35Cl(n,) prompt gamma-rays. The measured data points are converted into the log E versus the log of the efficiency and then fitted with a polynomial so that a wide energy region is covered.

Fig. 8.24. Fitting of a HPGe detector efficiency in a wide energy region.

8.5. Medical applications

A. In vivo X-ray spectrometry [7,8] In our department, planar HPGe and Si(Li) detectors have been used for in vivo X-ray spectrometry to analyze both trace (Pb, Hg, As etc.) and major (Sr) elements in the body quantitatively. The targeted elements are excited either with radiation from a radionuclide or an X-ray generator and then the characteristic X-rays are emitted and detected. Fig. 8.25 shows a system developed for Hg and an example phantom spectrum.

Fig. 8.25. In vivo X-ray spectrometry system for measuring mercury and a phantom spectrum [8].


B. Collimator-less Compton imaging

(a)

(b)

Fig. 8.26. Concept of collimator-less Compton imaging (a) and three projected cones intersecting at one point (b) [9,10]. Segmented (or position sensitive) semiconductor detector technology has been developing rapidly. For medical applications, this class of semiconductor detector makes possible collimator-less gamma-ray imaging. In principle, Compton imaging is effective even with a single segmented detector if the scattering process inside the detector can be tracked (gamma-ray tracking [11]) with sufficient spatial resolution. With a highly segmented structure of Ge or Si, accurate information on both interaction position and deposited energy can be analyzed. From this information, the interaction sequence of the photon inside the detector can be extracted with a proper tracking algorithm using the Compton scattering formula studied in the chapter 5. Then, the direction cone of the incident photon is obtained. Since the segmentation of the electrode is physically limited, the pulse shape analysis technique is employed to further improve the spatial resolution. Finally, the source position is constructed as shown in Fig. 8.26. Both planar and coaxial configurations have been developed.

Fig. 8.27. Two-dimensionally segmented closed-ended coaxial (40-fold) and planar detectors (239-fold).


References 1. G.F. Knoll, Radiation Detection and Measurement - 3rd edition (Chapters 12 and 13), John Wiley & Sons, 1999. 2. G. Gilmore, J.D. Hemingway, Practical Gamma-Ray Spectrometry, John Wiley & Sons, 1995. 3. K. Debertin, R.G. Helmer, Gamma- and X-ray Spectrometry with Semiconductor Detectors, North-Holland, 1988. 4. HPGe Detector Manufacturing, ORTEC, URL: http://www.ortec-online.com/. 5. Th. Kröll et al., Nucl. Intstr. and Meth. A 371 (1996) 489. 6. Online Ge(Li)-Si(Li) Gamma Spectrum Catalog, Gamma-ray Spectrometry Center, Idaho National Laboratory, Published 3-29-1999, URL: http://www.inl.gov/gammaray/catalogs/. 7. D.R. Chettle, X-Ray Spectrom. 34 (2005) 446. 8. J. Grinyer, M. Popovic, D.R. Chettle, X-Ray Spectrom. 36 (2007) 99. 9. L. Mihailescu et al., Nucl. Intstr. and Meth. A 570 (2007) 89. 10. K. Vetter, M. Burks, L. Mihailescu, Nucl. Intstr. and Meth. A 525 (2004) 322. 11. I.Y. Lee, Nucl. Intstr. and Meth. A 422 (1999) 195.


Problems 1. For a 2 cm thick planar HPGe detector given below: (a) In order to use as a radiation detector, which surface must be kept at zero voltage and which surface must be kept at a high voltage ? Which polarity of a high voltage must be applied ? Briefly explain the reason.

n+

p-type

p+

2 cm

0.5 cmA

(b) The E-field distribution for V0 = 200 V is shown. Find the depletion voltage. (c) Suppose a gamma interaction happened at the position A. Sketch the expected signal shape, i.e. Vout(t) as a function of time t. Indicate the contribution by holes and the contribution by electrons. Briefly explain the reason.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00

500

1000

X [cm]

E(x

) [V

/cm

]

2. An n-type HPGe coaxial detector has the following geometry: (a) To which surface, a p-type impurity must be added ? Briefly explain the reason. (b) Sketch equipotential lines for a full depletion condition. (c) Sketch the drift direction of electrons and holes created at the position A. Do the same work for the position B.

3. Suppose you aim to measure an unknown photon radiation field in the energy range of 20 keV to 5 MeV using a semiconductor detector. Write down i) a proper detector material, ii) type and iii) configuration. Briefly justify the reason. 4. For a p-type true coaxial HPGe detector, the electric field for an applied bias voltage V0 at the full depletion condition is given by

)(ˆ)( rErrE

, )/ln(

))(4/(

2)(

12

21

220

rrr

rreNVr

eNrE AA

Find the depletion voltage. 5. A p-type planar HPGe detector has a depletion voltage of 1,500 V. (a) Sketch the electric field E(x) as a function of the depth x for three bias voltages 500, 1,000 and 2,000 V. For convenience, x=0 is located on the n+ surface. (b) For the partial depletion condition, explain how the depletion depth changes as you increase the bias voltage.


(c) For a fixed position within the depleted region, explain how the E-field strength changes when the bias increases from 500 to 1,000 V ? How about in case of increasing from 1,500 to 2,000 V ?

6. Suppose one of your fingers is exposed to a collimated gamma-ray beam to measure the concentration

of an element in the finger bone as shown below. (a) When an atom of interest in the bone absorbs a gamma-ray photon by the photo electric effect, what kind of the photon radiation is emitted from the atom following the gamma-ray absorption ?

(b) Suppose the energy of the photon emitted from the element of interest is 45 keV. A Si detector is positioned to detect this radiation. Referring to the linear attenuation coeff. table below, find the thickness of Si that is equivalent to the mean free path of the photon. (c) Based on the result obtained in (b), what kind of Si detector do you think must be used for this measurement ? Briefly justify the reason.

Documents

Chapter 8 Hyper-Pure Germanium Detector€¦ · Chapter 8 Hyper-Pure Germanium Detector 8.1. Introduction Silicon semiconductor detectors described in the previous chapter have depletion