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Use of Genetic Algorithms to Determine Carriers Mobilities and Lifetimes in Semiconductor Detectors a
Noha SHAABAN & Hiroyuki TAKAHASHI
b
a
The National Center for Nuclear Safety and Radiation Control, The Egyptian Atomic Energy Authority , 3 Ahmed El Zomor Str., Nacr City, 11762 , Cairo , Egypt b
Department of Nuclear Engineering and Management , Graduate School of Engineering, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo , 113-8656 , Japan Published online: 05 Jan 2012.
To cite this article: Noha SHAABAN & Hiroyuki TAKAHASHI (2006) Use of Genetic Algorithms to Determine Carriers Mobilities and Lifetimes in Semiconductor Detectors, Journal of Nuclear Science and Technology, 43:7, 816-818 To link to this article: http://dx.doi.org/10.1080/18811248.2006.9711165
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Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 43, No. 7, p. 816–818 (2006)
SHORT NOTE Normalized Amplitude
1
Use of Genetic Algorithms to Determine Carriers Mobilities and Lifetimes in Semiconductor Detectors Noha SHAABAN
1; ,y
and Hiroyuki TAKAHASHI2
1
The National Center for Nuclear Safety and Radiation Control, The Egyptian Atomic Energy Authority, 3 Ahmed El Zomor Str., Nacr City, 11762 Cairo, Egypt 2 Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
µeτe/µhτh
0.8 50./5.
0.6
5./0.5 25/2.5 2.5/0.25
0.4
10./1. 1./0.1
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0.5/0.05
0 0
0.2 0.4 0.6 0.8 1 Normalized Interaction Location from Cathode
Fig. 1 Relative position dependent charge collection efficiency
(Received February 6, 2006 and accepted April 10, 2006)
semiconductor detector for single-point charge generation is given by the following equation,7)
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KEYWORDS: compound semiconductor detectors, genetic algorithms, mobility, lifetimes, signal waveform, digital signal processing
Qðx; tÞ ¼
1. Introduction Due to their intrinsic physical properties compound semiconductor detectors have many advantages for a variety of applications. However, their performance is very sensitive to the transport parameters of both electrons and holes. These charge carriers, generated in semiconductor detectors provide all types of information about incident radiation. Hence charge transport parameters are important properties for radiation detector materials. Poor hole mobilities of semiconductor materials results in non-uniform response to photons interacting in different regions of a detector. Although several methods to evaluate the transport parameters for both carriers introduced, however, the result often depend on the experimental method used; i.e. time of flight measurements,1) measurements of charge signals produced by -rays,2) direct measurements of the electron mobility and mean free drift time using positive sensitive single polarity charge sensing detectors.3) Another approach, which extracts realistic values of the transport properties of both electrons and holes in the semiconductor materials, compares the experimental gamma-ray spectra recorded with the detectors and a Monte Carlo code simulating the spectrum.4) Literature results of previous calculations of these transport parameters are shown in Ref. 5). In this study, we adopted genetic algorithms6) in order to extract realistic values of the transport parameters of both electrons and holes in semiconductor materials. A theoretical signal shape model was fitted to the real digitized signal shape taking into account the realistic transport parameters. 2. Signal Shape Analysis Assuming a single-point ionization process for the signal generation, the signal waveform Qðx; tÞ from an ideal planar y
Corresponding author, E-mail: n
[email protected] Present address: Computer Software Development Co., Ltd., 16-5, Konan 2-chome, Minato-ku Tokyo 108-0075, Japan
Qo fe ð1 expðe tÞg e d Qo þ fh ð1 expðh tÞg; h d
ð1Þ
where x is the initial charge carrier generation position, d is the distance between the anode and the cathode, e and h are the electron and hole velocities, Qo ¼qN is the deposited charge (q is the individual carrier charge, N is the number of carriers), and e and h are the electron and hole trapping coefficients, respectively. The first term on the right side of Eq. (1) is an electron component that becomes constant after time te ¼ðdxÞ=e . The second term is a hole component that similarly becomes constant after time th ¼x=h . The collection efficiency for a single event, Q=Qo becomes a function of the interaction location and e e =h h values as shown in Fig. 1. Model-simulated values were fitted with measured values in order to extract the value of the unknowns for each signal, which are the interaction position, mobility, , and lifetime, , for both electrons and holes, respectively. The fitting process was divided into two steps. Selected signals, which come from the interactions near the cathode, were used to determine the interaction position, mobility and lifetime of electrons. Selected signals, which come from interactions deeper in the detector, were used to determine the interaction position, mobility and lifetime of holes. During the second fitting step, the electron parameters are kept constant. Each signal waveform was divided from 10 to 90% of the maximum amplitude with a 5% interval. The time span of adjacent levels was used as a waveform vector; therefore, one signal waveform consisted of 16 elements. In this domain the major factors that affect the signal waveform vector are the shape (position dependent), the mobility and the lifetime values. 3. Genetic Algorithms The genetic algorithm has been applied to determine the charge generation positions inside the detector, the mobility and lifetime of both carriers individually. An objective function has to be selected to obtain an aggregate measure of deviation between the observed and simulated system. Here the
Atomic Energy Society of Japan 816
817
Use of Genetic Algorithms to Determine Carriers Mobilities and Lifetimes in Semiconductor Detectors
4. Results and Discussion The present algorithm was firstly approved using data performed using the EGS4 code. The interaction of 662 keV photons in a CdZnTe detector of 2 mm thickness was analyzed using known transport parameters e ¼1;350 cm2 /Vs, e ¼2:0 s, h ¼80 cm2 /Vs, and h ¼2:0 s respectively. The results agreed very well with the pre-known values. The calculations were repeated but for actual meas-
200 160
80
0 0
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Fig. 2 Selected signals under full energy peak versus relative area
80
25 20 15 10
HOLE
70
Number of Signals
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60 50 40 30 20 10
0
0 0
1046
1173
1270
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1489
0
Mobility (cm2/sec)
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94
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Mobility (cm2/sec)
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Electron
100 80 60 40
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Number of Signals
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20 15 10 5
20 0
0 0
0.108
0.129
Life-time (sec)
0.16
0.202
0
0.27 0.44 0.67 0.83 1.04 1.16
Life-time (sec)
Fig. 3 Transport parameters for electrons and holes
VOL. 43, NO. 7, JULY 2006
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Relative Area
Electron
35
Number of Signals
120
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Number of Signals
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where x denotes the distance from the cathode. For each genetic algorithm generation, the value of the objective function for each solution is evaluated; the new solution is then obtained by manipulating the old solution in order to arrive at a new one hopefully characterized by a better fitness according to the tournament selection rule.6) This is done by repeatedly performing four genetic operations of reproduction, crossover, replacement and mutation, all based on random sampling. This sequence continues until a termination criterion is reached.
ured data obtained using 137 Cs source. A CdZnTe detector (3 mm3 mm2 mm) was used and 400 V bias voltages was applied to this detector. Preamplifier (ORTEC. 142A) output pulses from this detector were digitized by a Tektronix TDS640 DSO with a sampling frequency of 500 MHz. Two thousand data points with 2 ns time period (for a total of 4 ms) were used for testing each waveform. Signals that contribute to the full energy peak were selected. The selection process depends on the relative area integration under the signal shape, where a larger area corresponds to the interactions near the cathode while the smaller area corresponds to interactions deeper in the detector as shown in Fig. 2. After the fitting calculation of the parameters performed for individual signal events, histograms for each estimated
Amplitude
objective function is the performance criterion to be minimized and it is equal the difference between observed, and model-simulated state variables, this difference reflects the residual of errors in the domain available. Fitness of an individual, f1 , is judged according to how well the simulated waveform vectors M can approximate the measured waveform vectors P: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 16 uX P j Mx;; 2 f1 ¼ t ; ð2Þ Pj j¼1
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N. SHAABAN and H. TAKAHASHI
and hole transport properties for semiconductor detectors was introduced. The algorithm is based on an analysis of the signal shape using genetic algorithms. The fitting between theoretical and experimental results was quite satisfactory. The future of this algorithm lies in the possibility to perform transport parameter estimation from the signal shape with no need for additional experiments. The algorithm can be applied for detectors having any electrode configuration. References
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Fig. 4 Comparison between measured and simulated waveforms
parameter were obtained. Figure 3 shows the results for the determination of the 4 transport parameters. For this detector, the estimated transport parameters were as following e ¼1;200 cm2 /Vs, e ¼0:1 s, h ¼80 cm2 /Vs, and h ¼ 0:4 s. The lifetimes of holes are widely distributed compared to the lifetimes of electrons due to irregularities of the signal shapes in the low energy tail, which come from noise and multiple scattering interactions. The ratio between the electron mobility to hole mobility is 15 which is consistent with known properties of commercially available CdZnTe detectors. Figure 4 shows some examples of the measured waveforms and the simulated signal waveforms using the estimated transport parameters at different interaction positions. It is shown that both signal waveforms are in a good agreement, which verifies the capability of the genetic algorithm for the estimation of the transport parameters. 5. Conclusion A new developed algorithm to determine both electron,
1) O. Tousignant, L. A. Hamel, J. F. Courville, J. R. Marci, M. Mayer, M. L. McConnell, J. M. Ryan, ‘‘Transport properties and performance of CdZnTe strip detectors,’’ IEEE Trans. Nucl. Sci., 45[3], 413 (1998). 2) Z. Burshtein, H. N. Jayatirtha, A. Burger, J. F. Butler, B. Apotosovsky, F. P. Doty, ‘‘Charge-carrier mobilities in Cd ZnTe single crystals used as nuclear radiation detectors,’’ Appl. Phys. Lett., 63[1], 102 (1993). 3) Z. He, G. F. Knoll, D. K. Wehe, ‘‘Direct measurement of product of the electron mobility and mean free drift time of CdZnTe semiconductors using position sensitive single polarity charge sensing detectors,’’ J. Appl. Phys., 84[10], 5566 (1998). 4) E. Muller, M. Jung, P. Fougeres, M. Hage-Ali, P. Siffert, ‘‘Use of a Monte-Carlo code to determine in high Z semi-conductor CdTe and CZT, both carriers lifetimes and mobilities,’’ Mater. Res. Soc. Symp. Proc., 487, 301 (1998). 5) Semiconductors for room temperature radiation detector applications II, Mater. Res. Soc. Symp. Proc., R. B. James, et al., Boston, MA, USA, Dec. 1–5, 1997, 487 (1998). 6) D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, (1989). 7) N. Shaaban, H. Takahashi, S. Hasegawa, A. Suzuki, ‘‘Application of genetic algorithms to the charge loss correction in CdZnTe semiconductor detectors,’’ Jpn. J. Appl. Phys., 41[2A], 908 (2002).
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