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Effect of differential bias on the transport of electrons in coplanar grid CdZnTe detectors
Nuclear Instruments and Methods in Physics Research A 476 (2002) 658–664
Effect of differential bias on the transport of electrons in coplanar grid CdZnTe detectors T.H. Prettymana,*, K.D. Ianakieva, S.A. Soldnerb, Cs. Szelesb a
Los Alamos National Laboratory, Safeguards Science and Technology Group, NIS-5, Mail Stop E540, Los Alamos, NM 87545, USA b eV PRODUCTS, a division of II-VI Inc., Saxonburg, PA 16056, USA
Abstract Segmented and pixilated electrode structures are used to compensate for poor hole transport in CdZnTe devices used for gamma-ray spectrometry and imaging. Efforts to model these structures have focused primarily on geometric effects; however, device performance also depends on the physical properties of the bulk and surface material, as well as the electrodes. In this paper, we describe experiments to characterize the electric field near the anode of a coplanar grid detector. The experiment is contrasted with a calculation that is based on an assumption commonly used to reduce the computational effort required to determine internal electric fields. Explanations for differences between the calculation and the experiment are proposed. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Cadmium zinc telluride; Modeling; Coplanar grid; Hemispheric detector; Resistivity; Surface; Passivation
1. Introduction For CdZnTe, the mobility-lifetime product of holes is significantly less than that of electrons (mp tp o104 cm2/V and mn tn B5 103 cm2/V). Devices that operate in sweep-out mode (planar detectors) are limited in thickness to omp tp E; approximately 1 mm under typical bias conditions (EB100 V/mm). Planar devices thicker than 1 mm perform poorly for gamma-ray spectroscopy. Since there is a need for large-volume gamma-ray spectrometers, much effort has gone into the development of devices that can make spatially uniform measurements of charge using signals induced by the motion of electrons. Coplanar grid *Corresponding author. Tel.: +1-505-667-6449; fax: +1505-665-5910. E-mail address: [email protected] (T.H. Prettyman).
detectors, hemispheric detectors, pixilated devices, and several three-terminal device structures have been developed for this purpose and have demonstrated improved pulse-height resolution and peak shape in comparison to planar devices [1–4]. The performance of these electron-sensing devices is such that the practical size of CdZnTe-based spectrometers is now limited by the ability to routinely manufacture material with uniform charge transport properties. The goal of our research is to develop modeling tools that can be used to optimize the design of CdZnTe detectors used for gamma-ray imaging and spectroscopy. While the equations describing the response of planar devices have a closed-form analytical solution [5], modeling of devices with complicated geometric structures, such as coplanar grids, requires the use of numerical methods. We are developing computationally efficient numerical
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methods that can be used for device design and analysis. A general-geometry version of the Hecht relation has been derived (as a partial differential equation) that can be used to efficiently model charge pulses produced by CdZnTe detectors with pixel- or strip-electrodes [6,7]. The model is based on single-carrier continuity equations that treat transport by drift and diffusion along with trapping and detrapping. Quasi-stationary conditions are assumed during signal formation and the steady state (DC) electric field must be known. We use a commercially available semiconductor device simulator (ATLAS) to model the DC electric field, which enables us to treat a wide variety of semiconductor phenomena [8]. While the framework exists for computationally efficient modeling of charge transport and signal formation, input parameters for the DC electric field calculation (e.g., trap levels, contact and surface parameters, etc.) are still being investigated. In the literature, it is generally assumed that the electrostatic potential within CdZnTe detectors is given by the solution of Poisson’s equation with the space charge set to zero throughout the device [9–12]. A notable exception is a study carried out by Bolotnikov et al. [13] on the effect of surface resistance on internal fields in pixel detectors. The assumption that there is no space charge within the device is convenient, because the calculation of the electric field is computationally inexpensive and does not require detailed knowledge of the physical parameters of CdZnTe. This approach, however, ignores physical effects that may be significant, particularly for non-planar electrode structures. The purpose of this paper is to show how charge is collected by coplanar grid detectors, particularly in the near-grid region where conventional assumptions regarding internal electric fields may be invalid.
2. Theory We use the well-known Shockley–Ramo theorem [14–17] for the qualitative analysis of charge induced on electrodes by electrons moving within a coplanar grid detector. In the experiments, the electrons are generated by alpha particles incident
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on the cathode. Since free electrons and holes are generated near the cathode, we will assume that the charge induced by the drift of holes to the cathode is negligible compared to the charge induced by electrons as they drift across the detector. The change in charge on an electrode, induced by the motion of a test charge between two points in the volume of the detector, is given by h , , , , Qð r 0 - r Þ ¼ q jw ð r Þ jw ð r 0 Þ ð1Þ where q is the elementary charge and jw is the weighting potential. The weighting potential is given by the solution of Poisson’s equation with the space charge set to zero, the electrode of interest set to unit potential and all other electrodes grounded. The Shockley–Ramo theorem describes experiments in which the moving charge does not significantly perturb the electric field within the device. In analyzing charge pulses, we assume that the electric field near the cathode is sufficient to separate electrons and holes before significant recombination can occur and that electric field is not perturbed significantly by the charge liberated by the alpha particle interaction.
3. Experiment A 10 10 5 mm3 coplanar grid detector designated H15-08 was manufactured by eV PRODUCTS using high-pressure Bridgman-grown CdZnTe material. The grid pattern used with this detector follows the ‘‘third generation’’ pattern described by He [18]. This design includes bus bars to inter-connect grid electrodes, which form interlocking parallel strips. The grid electrodes are extended to wrap around each other to compensate for edge effects in the direction parallel to the strips. A guard ring was included in the pattern to eliminate surface leakage between the cathode and the grid electrodes. The width of the strips was 203 mm. The width of the gaps between the strips was 305 mm. To reduce intergrid leakage, the width of the strips was selected smaller than the width of the gaps. The width of
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the guard ring was, approximately, 276 mm. With these dimensions, nine strips are needed per grid electrode to fill an area of 10 10 mm2. Electrical connection to the device was made in a probe station developed for mapping charge pulses, which are observed as waveforms on an oscilloscope. The apparatus is described in detail elsewhere [19]. The detector was placed on a gold pad (for connection to the cathode) with an opening to allow exposure of a large portion of the cathode surface to alpha particles. Connections were made to the guard ring and grid electrodes using precision probes. The two grid electrodes and the cathode were connected to separate charge-sensitive preamplifiers. The guard ring was connected to the ground. Experiments carried out in this configuration included the measurement of gamma ray and alpha particle pulse-height spectra, and the measurement of alpha particle-induced waveforms. 3.1. Pulse-height spectra Gamma-ray spectra were measured using the coplanar grid technique under typical bias conditions. The inter-grid voltage was 30 V and the bulk bias was 500 V. Under these conditions, the pulse height resolution was found to be 23 keV fullwidth at half-maximum (FWHM) at 662 keV for an amplifier shaping time of 1 ms. Pulse-height spectra were also taken for full-area (flood-view) exposures of the cathode to alpha particles emitted by a 241Am source with the probe chamber under vacuum. Pulse-height spectra formed from the output of the cathode preamplifier showed a single, well-defined peak (o4% FWHM) with essentially no continuum, which indicated that the bulk material had relatively uniform electronic properties. Infrared transmission images of the detector showed no visible grain- or twin-boundaries; however, randomly distributed tellurium inclusions were observed.
electrodes was exposed to alpha particles from an uncollimated 241Am source. 241Am emits alpha particles with an average energy of 5.5 MeV, which have a range of, approximately, 20 mm in CdZnTe. Most of the ionization occurs near the end of the range. The electrodes consisted of sputtered platinum followed by a layer of gold for bonding. The total thickness of the electrode was, approximately, 150 nm [20]. Consequently, most of the ionization produced by alpha particles was expected to occur in the bulk material and charge production was not expected to be affected significantly by variations in electrode thickness. Also, the applied electric field (on the order of 100 V/mm) separates the electrons and holes before significant recombination can occur in the highly ionized region formed by the alpha particle. Under these circumstances, electron production near the cathode is sufficiently uniform to warrant use of alpha particles as a diagnostic tool. A typical set of waveforms for an alpha particle event is shown in Fig. 1. In order to interpret the waveforms, the weighting potential was calculated for the grid electrodes and the cathode. The weighting potential along chords connecting the cathode and arbitrary strips is shown in Fig. 2.
3.2. Charge measurements To measure charge pulses, a section of the cathode, approximately, 4 mm wide and running the length of the detector transverse to the grid
Fig. 1. Waveforms produced by an alpha particle event. Regions used to determine the final waveform values plotted in Fig. 2 are shown.
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Fig. 2. Weighting potential for the grid electrodes and the cathode along a line connecting the cathode to the center of an arbitrary strip. The depth is measured from the anode. Note that the weighting potential for the non-collecting grid peaks at about 0.45 cm from the cathode.
The curve labeled ‘‘collecting electrode’’ corresponds to a strip for which the potential was set to 1 in the calculation. The curve labeled ‘‘noncollecting electrode’’ corresponds to a strip for which the weighting potential was set to 0. Note that the waveform (shown in Fig. 1) for one of the anode electrodes drops precipitously before collection, indicating that the electrode did not collect the electrons. Based on Eq. (1) and Fig. 2, the waveform for the non-collecting electrode should return to the baseline. However, Eq. (1) is only valid for a test charge. The fact that the waveform did not return to the baseline reflects that some of the electrons were trapped. The effect of differential bias on electron collection was examined using waveforms acquired for flood exposures with the cathode voltage set to 500 V. The final values of the signal amplitudes for the grounded electrode are plotted against the final values for the biased electrode for several values of differential bias, in Fig. 3. When no differential bias was applied, the pattern of final amplitude values was symmetric, indicating that both the grid electrodes collected charge. Note that
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the distribution contained events for which charge was shared between the two electrodes as well as events for which charge was fully collected by one electrode or the other. As the differential bias was increased, the distribution shifted towards the biased electrode. The distribution saturated at very low values of differential bias, and at 7.5 V, the electrons were collected exclusively by the biased electrode. Two types of waveforms were observed at 7.5 V. They are shown in Fig. 4. Eighty percent of all events acquired had waveforms shaped like those shown on the left of Fig. 4. The remaining 20% had waveforms shaped like those shown on the right. Based on the weighting potential, the waveforms on the right correspond to electrons that initially moved towards the grounded electrode and then veered away to be collected by the biased electrode. Note that the waveform for the biased electrode on the right has an inflection, which indicates that the electrons came very close to the grounded electrode prior to changing the direction. The inflection occurred at nearly the same time that the maximum amplitude was achieved for the grounded electrode. If the electrons were heading directly towards the grounded electrode, they must have veered near the peak in the weighting potential for non-collecting electrodes, which is roughly 450 mm from the anode (Fig. 2).
4. Calculation The electric field was computed on a slice through the center of the detector transverse to the grid electrodes. A finite element code was used to solve Poisson’s equation [rðerjÞ ¼ 0; where e is the dielectric constant] for a grid bias of 7.5 V and a bulk bias of –500 V. The boundary condition at free surfaces was n# erj ¼ 0; where n# is the unit outward surface normal vector. Contours of constant electrostatic potential and electric field lines are shown in Fig. 5 near four of the grid electrodes. Note that a large number of field lines contact the grounded electrodes. The acceptance channel for the grounded electrode is much wider than the electrode.
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Fig. 3. Scatter plots displaying the final value of the waveforms for the biased and grounded grid electrodes as a function of applied differential bias: (a) 0; (b) 2.5; (c) 5; and (d) 7.5 V. The bulk bias was 500 V in these experiments.
5. Discussion The calculation fails to predict how electrons are transported near the anode. In the experiment, the biased electrode always collected the electrons. The calculation predicts that for almost half of the time, the grounded electrode will collect the electrons. Diffusion of electrons is not significant; however, even if diffusion were treated, a large number of events would show significant charge sharing. Charge sharing was not observed in the experiment at 7.5 V. There are a number of phenomena that could account for the differences between the experiment and the calculation. For example, the barrier height for gold or platinum contacts on CdZnTe
is expected to be between 0.7 and 0.9 eV (based on barrier heights quoted by Brinkman [21] for various metals on CdTe). The results of studies with thermoelectric effect spectroscopy indicate that commercially available, high-pressure Bridgman-grown, semi-insulating CdZnTe for gammaray spectrometers is n-type [22,23]. Platinum and gold electrodes form back-to-back Schottky barriers on n-type CdZnTe devices leading to depletion of layers at the electrodes. When external bias is applied, band-bending at the cathode increases and decreases at the anode leading to a high-field region near the cathode and a reduction of the electric field in the bulk. An inversion layer is formed at the cathode and an accumulation layer is formed at the anode. Simulations of this effect
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Fig. 4. Waveforms collected at 7.5 V differential bias. Waveforms measured for the biased and grounded electrodes are indicated. Construction lines are provided to show the relative scale of common features.
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A second and more plausible reason for the difference relates to surfaces. Semiconductor surfaces are usually more conductive than the bulk due to the presence of electronic levels that are introduced in the band gap at the surface. These states cause band-bending at the surface, resulting in the formation of inversion or accumulation layers. Measurements of surface and bulk resistivity can be carried out using CdZnTe devices with guard rings (such as the coplanar grid detector described in this paper). The dependence of surface resistance and bulk resistivity on temperature is shown in Fig. 6. The theoretical values for bulk resistivity were determined by a Fermi-level calculation using a three-level model that we developed for high-pressure Bridgman CdZnTe. At room temperature, the surface resistance is several hundred GO. The resistivity of the surface layer is just the thickness of the surface layer times the resistance. Simulations of the surface layer have been carried out by introducing a single level at the surface. By varying the energy of the level and its type (donor or acceptor), inversion and accumulation layers can be simulated. Results of these simulations show that the conductive layer is thick, typically of the order of 100 nm. Consequently, the resistivity of the surface material at room temperature must be of the order of 106 O cm, which is many orders of magnitude less than the resistivity of the bulk material. Note that the temperature coefficient for the bulk material is essentially the same as the surface
Fig. 5. Lines of constant electrostatic potential and electric field lines near four of the anode electrodes. The biased electrodes are labeled B. The grounded electrodes are labeled G.
show that it leads to preferential collection of charge by the biased electrode. The magnitude of the effect depends on the barrier height and the electronic structure of the bulk material. Measurements of internal electric fields using Pockels effect sometimes show an enhanced field region near the cathode [24]; however, if such a region exists in practical devices, it must be quite thin: waveforms generated by alpha-particles show no evidence of a high-field region near the cathode.
Fig. 6. Bulk resistivity and surface resistance as a function of temperature.
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layer. This can occur only if the effective energy of the surface states is near the mid-gap. To achieve the experimentally observed resistivity, the density of surface states must be quite large. The presence of a conductive layer at the surface will effect internal electric fields by introducing a layer of charge at the surface and by providing a path for charge to flow between the anode electrodes. Preliminary results of simulations show that a conductive surface layer can cause preferential collection by the biased electrode. These results also show that an inversion layer is most effective in producing electric fields near the anode that result in waveforms similar to those observed in the experiment. However, the magnitude of the observed effect (preferential collection by the biased electrode) has not been duplicated.
6. Conclusion We have demonstrated that assumptions typically used to simplify the calculation of internal electric fields for coplanar grid detectors are not valid near the anode. A complete treatment of semiconductor physics, including contact and surface effects, is needed to accurately model internal electric fields. The most likely cause for differences between the calculation and the experiment is the presence of a surface layer that is more conductive than the bulk material. A model of the electronic properties of the surface layer is under development.
Acknowledgements This work was supported by the Department of Energy Office of Nonproliferation Research and Engineering and the Office of Safeguards and Security under contract W-7405-ENG-36 and by
NASA’s Planetary Instrument Definition and Development Program.
References [1] P.N. Luke, Appl. Phys. Lett. 65 (22) (1994) 2884. [2] R. Arlt, D.E. Rundquist, Nucl. Instr. and Meth. 380 (1–2) (1996) 455. [3] J.F. Butler, Nucl. Instr. and Meth. 396 (3) (1997) 427. [4] D.S. McGregor, Z. He, H.A. Seifert, et al., Appl. Phys. Lett. 72 (7) (1998) 792. [5] K. Hecht, Z. Phys. 77 (1932) 235. [6] T.H. Prettyman, Nucl. Instr. and Meth. 422 (1–3) (1999) 232. [7] T.H. Prettyman, Nucl. Instr. and Meth. 428 (1) (1999) 72. [8] Atlas, Silvaco International, Copyright, 1997. [9] T.H. Prettyman, C.S. Cooper, P.N. Luke, et al., J. Radioanal. Nucl. Chem. 233 (1998) 257. [10] J.A. Heanue, J.K. Brown, B.H. Hasegawa, IEEE Trans. Nucl. Sci. NS-44 (3) (1997) 701. [11] L.A. Hamel, J.R. Macri, C. Stahle, et al., IEEE Trans. Nucl. Sci. NS-43 (3) (1996) 1422. [12] E.Y. Lee, R.B. James, Nucl. Instr. and Meth. 428 (1) (1999) 66. [13] A.E. Bolotnikov, W.R. Cook, F.A. Harrison, A.-S. Wong, S.M. Schindler, A.C. Eichelberger, Nucl. Instr. and Meth. 432 (1999) 326. [14] W. Shockley, J. Appl. Phys. 9 (1938) 635. [15] S. Ramo, Proc. IRE 27 (1939) 584. [16] A.H.W. Beck, Thermionic Valves: Their Theory and Design, Cambridge University Press, Cambridge, 1953. [17] G. Cavalleri, G. Fabri, E. Gatti, V. Svelto, Nucl. Instr. and Meth. 21 (1963) 177. [18] Z. He, G.F. Knoll, D.K. Wehe, Y.F. Du, Nucl. Instr. and Meth. 411 (#1) (1998) 107. [19] T.H. Prettyman, M.K. Smith, P.N. Luke, M. Amman, J.S. Lee, Proc. SPIE 3768 (1999) 27. [20] S.A. Soldner, eV Products, Private communication. [21] A.W. Brinkman, Contacts to Cd/Zn/Te/Se compounds. In: P. Capper (Ed.), Properties of Narrow Gap Cadmium based Compounds, Emis Datareview Series No. 10, INSPEC Publication, London, 1994, p. 575. [22] Cs. Szeles, Y.Y. Shan, K.G. Lynn, A.R. Moodenbaugh, E.E. Eissler, Phys. Rev. B 55 (11) (1997) 6945. [23] Cs. Szeles, Y.Y. Shan, K.G. Lynn, E.E. Eissler, Nucl. Instr. and Meth. 380 (1996) 148. [24] H.W. Yao, R.B. James, J.C. Erickson, Proc. SPIE 3768 (1999) 330.
Effect of differential bias on the transport of electrons in coplanar grid CdZnTe detectors T.H. Prettymana,*, K.D. Ianakieva, S.A. Soldnerb, Cs. Szelesb a
Los Alamos National Laboratory, Safeguards Science and Technology Group, NIS-5, Mail Stop E540, Los Alamos, NM 87545, USA b eV PRODUCTS, a division of II-VI Inc., Saxonburg, PA 16056, USA
Abstract Segmented and pixilated electrode structures are used to compensate for poor hole transport in CdZnTe devices used for gamma-ray spectrometry and imaging. Efforts to model these structures have focused primarily on geometric effects; however, device performance also depends on the physical properties of the bulk and surface material, as well as the electrodes. In this paper, we describe experiments to characterize the electric field near the anode of a coplanar grid detector. The experiment is contrasted with a calculation that is based on an assumption commonly used to reduce the computational effort required to determine internal electric fields. Explanations for differences between the calculation and the experiment are proposed. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Cadmium zinc telluride; Modeling; Coplanar grid; Hemispheric detector; Resistivity; Surface; Passivation
1. Introduction For CdZnTe, the mobility-lifetime product of holes is significantly less than that of electrons (mp tp o104 cm2/V and mn tn B5 103 cm2/V). Devices that operate in sweep-out mode (planar detectors) are limited in thickness to omp tp E; approximately 1 mm under typical bias conditions (EB100 V/mm). Planar devices thicker than 1 mm perform poorly for gamma-ray spectroscopy. Since there is a need for large-volume gamma-ray spectrometers, much effort has gone into the development of devices that can make spatially uniform measurements of charge using signals induced by the motion of electrons. Coplanar grid *Corresponding author. Tel.: +1-505-667-6449; fax: +1505-665-5910. E-mail address: [email protected] (T.H. Prettyman).
detectors, hemispheric detectors, pixilated devices, and several three-terminal device structures have been developed for this purpose and have demonstrated improved pulse-height resolution and peak shape in comparison to planar devices [1–4]. The performance of these electron-sensing devices is such that the practical size of CdZnTe-based spectrometers is now limited by the ability to routinely manufacture material with uniform charge transport properties. The goal of our research is to develop modeling tools that can be used to optimize the design of CdZnTe detectors used for gamma-ray imaging and spectroscopy. While the equations describing the response of planar devices have a closed-form analytical solution [5], modeling of devices with complicated geometric structures, such as coplanar grids, requires the use of numerical methods. We are developing computationally efficient numerical
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 6 6 0 - 6
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methods that can be used for device design and analysis. A general-geometry version of the Hecht relation has been derived (as a partial differential equation) that can be used to efficiently model charge pulses produced by CdZnTe detectors with pixel- or strip-electrodes [6,7]. The model is based on single-carrier continuity equations that treat transport by drift and diffusion along with trapping and detrapping. Quasi-stationary conditions are assumed during signal formation and the steady state (DC) electric field must be known. We use a commercially available semiconductor device simulator (ATLAS) to model the DC electric field, which enables us to treat a wide variety of semiconductor phenomena [8]. While the framework exists for computationally efficient modeling of charge transport and signal formation, input parameters for the DC electric field calculation (e.g., trap levels, contact and surface parameters, etc.) are still being investigated. In the literature, it is generally assumed that the electrostatic potential within CdZnTe detectors is given by the solution of Poisson’s equation with the space charge set to zero throughout the device [9–12]. A notable exception is a study carried out by Bolotnikov et al. [13] on the effect of surface resistance on internal fields in pixel detectors. The assumption that there is no space charge within the device is convenient, because the calculation of the electric field is computationally inexpensive and does not require detailed knowledge of the physical parameters of CdZnTe. This approach, however, ignores physical effects that may be significant, particularly for non-planar electrode structures. The purpose of this paper is to show how charge is collected by coplanar grid detectors, particularly in the near-grid region where conventional assumptions regarding internal electric fields may be invalid.
2. Theory We use the well-known Shockley–Ramo theorem [14–17] for the qualitative analysis of charge induced on electrodes by electrons moving within a coplanar grid detector. In the experiments, the electrons are generated by alpha particles incident
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on the cathode. Since free electrons and holes are generated near the cathode, we will assume that the charge induced by the drift of holes to the cathode is negligible compared to the charge induced by electrons as they drift across the detector. The change in charge on an electrode, induced by the motion of a test charge between two points in the volume of the detector, is given by h , , , , Qð r 0 - r Þ ¼ q jw ð r Þ jw ð r 0 Þ ð1Þ where q is the elementary charge and jw is the weighting potential. The weighting potential is given by the solution of Poisson’s equation with the space charge set to zero, the electrode of interest set to unit potential and all other electrodes grounded. The Shockley–Ramo theorem describes experiments in which the moving charge does not significantly perturb the electric field within the device. In analyzing charge pulses, we assume that the electric field near the cathode is sufficient to separate electrons and holes before significant recombination can occur and that electric field is not perturbed significantly by the charge liberated by the alpha particle interaction.
3. Experiment A 10 10 5 mm3 coplanar grid detector designated H15-08 was manufactured by eV PRODUCTS using high-pressure Bridgman-grown CdZnTe material. The grid pattern used with this detector follows the ‘‘third generation’’ pattern described by He [18]. This design includes bus bars to inter-connect grid electrodes, which form interlocking parallel strips. The grid electrodes are extended to wrap around each other to compensate for edge effects in the direction parallel to the strips. A guard ring was included in the pattern to eliminate surface leakage between the cathode and the grid electrodes. The width of the strips was 203 mm. The width of the gaps between the strips was 305 mm. To reduce intergrid leakage, the width of the strips was selected smaller than the width of the gaps. The width of
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the guard ring was, approximately, 276 mm. With these dimensions, nine strips are needed per grid electrode to fill an area of 10 10 mm2. Electrical connection to the device was made in a probe station developed for mapping charge pulses, which are observed as waveforms on an oscilloscope. The apparatus is described in detail elsewhere [19]. The detector was placed on a gold pad (for connection to the cathode) with an opening to allow exposure of a large portion of the cathode surface to alpha particles. Connections were made to the guard ring and grid electrodes using precision probes. The two grid electrodes and the cathode were connected to separate charge-sensitive preamplifiers. The guard ring was connected to the ground. Experiments carried out in this configuration included the measurement of gamma ray and alpha particle pulse-height spectra, and the measurement of alpha particle-induced waveforms. 3.1. Pulse-height spectra Gamma-ray spectra were measured using the coplanar grid technique under typical bias conditions. The inter-grid voltage was 30 V and the bulk bias was 500 V. Under these conditions, the pulse height resolution was found to be 23 keV fullwidth at half-maximum (FWHM) at 662 keV for an amplifier shaping time of 1 ms. Pulse-height spectra were also taken for full-area (flood-view) exposures of the cathode to alpha particles emitted by a 241Am source with the probe chamber under vacuum. Pulse-height spectra formed from the output of the cathode preamplifier showed a single, well-defined peak (o4% FWHM) with essentially no continuum, which indicated that the bulk material had relatively uniform electronic properties. Infrared transmission images of the detector showed no visible grain- or twin-boundaries; however, randomly distributed tellurium inclusions were observed.
electrodes was exposed to alpha particles from an uncollimated 241Am source. 241Am emits alpha particles with an average energy of 5.5 MeV, which have a range of, approximately, 20 mm in CdZnTe. Most of the ionization occurs near the end of the range. The electrodes consisted of sputtered platinum followed by a layer of gold for bonding. The total thickness of the electrode was, approximately, 150 nm [20]. Consequently, most of the ionization produced by alpha particles was expected to occur in the bulk material and charge production was not expected to be affected significantly by variations in electrode thickness. Also, the applied electric field (on the order of 100 V/mm) separates the electrons and holes before significant recombination can occur in the highly ionized region formed by the alpha particle. Under these circumstances, electron production near the cathode is sufficiently uniform to warrant use of alpha particles as a diagnostic tool. A typical set of waveforms for an alpha particle event is shown in Fig. 1. In order to interpret the waveforms, the weighting potential was calculated for the grid electrodes and the cathode. The weighting potential along chords connecting the cathode and arbitrary strips is shown in Fig. 2.
3.2. Charge measurements To measure charge pulses, a section of the cathode, approximately, 4 mm wide and running the length of the detector transverse to the grid
Fig. 1. Waveforms produced by an alpha particle event. Regions used to determine the final waveform values plotted in Fig. 2 are shown.
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Fig. 2. Weighting potential for the grid electrodes and the cathode along a line connecting the cathode to the center of an arbitrary strip. The depth is measured from the anode. Note that the weighting potential for the non-collecting grid peaks at about 0.45 cm from the cathode.
The curve labeled ‘‘collecting electrode’’ corresponds to a strip for which the potential was set to 1 in the calculation. The curve labeled ‘‘noncollecting electrode’’ corresponds to a strip for which the weighting potential was set to 0. Note that the waveform (shown in Fig. 1) for one of the anode electrodes drops precipitously before collection, indicating that the electrode did not collect the electrons. Based on Eq. (1) and Fig. 2, the waveform for the non-collecting electrode should return to the baseline. However, Eq. (1) is only valid for a test charge. The fact that the waveform did not return to the baseline reflects that some of the electrons were trapped. The effect of differential bias on electron collection was examined using waveforms acquired for flood exposures with the cathode voltage set to 500 V. The final values of the signal amplitudes for the grounded electrode are plotted against the final values for the biased electrode for several values of differential bias, in Fig. 3. When no differential bias was applied, the pattern of final amplitude values was symmetric, indicating that both the grid electrodes collected charge. Note that
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the distribution contained events for which charge was shared between the two electrodes as well as events for which charge was fully collected by one electrode or the other. As the differential bias was increased, the distribution shifted towards the biased electrode. The distribution saturated at very low values of differential bias, and at 7.5 V, the electrons were collected exclusively by the biased electrode. Two types of waveforms were observed at 7.5 V. They are shown in Fig. 4. Eighty percent of all events acquired had waveforms shaped like those shown on the left of Fig. 4. The remaining 20% had waveforms shaped like those shown on the right. Based on the weighting potential, the waveforms on the right correspond to electrons that initially moved towards the grounded electrode and then veered away to be collected by the biased electrode. Note that the waveform for the biased electrode on the right has an inflection, which indicates that the electrons came very close to the grounded electrode prior to changing the direction. The inflection occurred at nearly the same time that the maximum amplitude was achieved for the grounded electrode. If the electrons were heading directly towards the grounded electrode, they must have veered near the peak in the weighting potential for non-collecting electrodes, which is roughly 450 mm from the anode (Fig. 2).
4. Calculation The electric field was computed on a slice through the center of the detector transverse to the grid electrodes. A finite element code was used to solve Poisson’s equation [rðerjÞ ¼ 0; where e is the dielectric constant] for a grid bias of 7.5 V and a bulk bias of –500 V. The boundary condition at free surfaces was n# erj ¼ 0; where n# is the unit outward surface normal vector. Contours of constant electrostatic potential and electric field lines are shown in Fig. 5 near four of the grid electrodes. Note that a large number of field lines contact the grounded electrodes. The acceptance channel for the grounded electrode is much wider than the electrode.
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Fig. 3. Scatter plots displaying the final value of the waveforms for the biased and grounded grid electrodes as a function of applied differential bias: (a) 0; (b) 2.5; (c) 5; and (d) 7.5 V. The bulk bias was 500 V in these experiments.
5. Discussion The calculation fails to predict how electrons are transported near the anode. In the experiment, the biased electrode always collected the electrons. The calculation predicts that for almost half of the time, the grounded electrode will collect the electrons. Diffusion of electrons is not significant; however, even if diffusion were treated, a large number of events would show significant charge sharing. Charge sharing was not observed in the experiment at 7.5 V. There are a number of phenomena that could account for the differences between the experiment and the calculation. For example, the barrier height for gold or platinum contacts on CdZnTe
is expected to be between 0.7 and 0.9 eV (based on barrier heights quoted by Brinkman [21] for various metals on CdTe). The results of studies with thermoelectric effect spectroscopy indicate that commercially available, high-pressure Bridgman-grown, semi-insulating CdZnTe for gammaray spectrometers is n-type [22,23]. Platinum and gold electrodes form back-to-back Schottky barriers on n-type CdZnTe devices leading to depletion of layers at the electrodes. When external bias is applied, band-bending at the cathode increases and decreases at the anode leading to a high-field region near the cathode and a reduction of the electric field in the bulk. An inversion layer is formed at the cathode and an accumulation layer is formed at the anode. Simulations of this effect
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Fig. 4. Waveforms collected at 7.5 V differential bias. Waveforms measured for the biased and grounded electrodes are indicated. Construction lines are provided to show the relative scale of common features.
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A second and more plausible reason for the difference relates to surfaces. Semiconductor surfaces are usually more conductive than the bulk due to the presence of electronic levels that are introduced in the band gap at the surface. These states cause band-bending at the surface, resulting in the formation of inversion or accumulation layers. Measurements of surface and bulk resistivity can be carried out using CdZnTe devices with guard rings (such as the coplanar grid detector described in this paper). The dependence of surface resistance and bulk resistivity on temperature is shown in Fig. 6. The theoretical values for bulk resistivity were determined by a Fermi-level calculation using a three-level model that we developed for high-pressure Bridgman CdZnTe. At room temperature, the surface resistance is several hundred GO. The resistivity of the surface layer is just the thickness of the surface layer times the resistance. Simulations of the surface layer have been carried out by introducing a single level at the surface. By varying the energy of the level and its type (donor or acceptor), inversion and accumulation layers can be simulated. Results of these simulations show that the conductive layer is thick, typically of the order of 100 nm. Consequently, the resistivity of the surface material at room temperature must be of the order of 106 O cm, which is many orders of magnitude less than the resistivity of the bulk material. Note that the temperature coefficient for the bulk material is essentially the same as the surface
Fig. 5. Lines of constant electrostatic potential and electric field lines near four of the anode electrodes. The biased electrodes are labeled B. The grounded electrodes are labeled G.
show that it leads to preferential collection of charge by the biased electrode. The magnitude of the effect depends on the barrier height and the electronic structure of the bulk material. Measurements of internal electric fields using Pockels effect sometimes show an enhanced field region near the cathode [24]; however, if such a region exists in practical devices, it must be quite thin: waveforms generated by alpha-particles show no evidence of a high-field region near the cathode.
Fig. 6. Bulk resistivity and surface resistance as a function of temperature.
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layer. This can occur only if the effective energy of the surface states is near the mid-gap. To achieve the experimentally observed resistivity, the density of surface states must be quite large. The presence of a conductive layer at the surface will effect internal electric fields by introducing a layer of charge at the surface and by providing a path for charge to flow between the anode electrodes. Preliminary results of simulations show that a conductive surface layer can cause preferential collection by the biased electrode. These results also show that an inversion layer is most effective in producing electric fields near the anode that result in waveforms similar to those observed in the experiment. However, the magnitude of the observed effect (preferential collection by the biased electrode) has not been duplicated.
6. Conclusion We have demonstrated that assumptions typically used to simplify the calculation of internal electric fields for coplanar grid detectors are not valid near the anode. A complete treatment of semiconductor physics, including contact and surface effects, is needed to accurately model internal electric fields. The most likely cause for differences between the calculation and the experiment is the presence of a surface layer that is more conductive than the bulk material. A model of the electronic properties of the surface layer is under development.
Acknowledgements This work was supported by the Department of Energy Office of Nonproliferation Research and Engineering and the Office of Safeguards and Security under contract W-7405-ENG-36 and by
NASA’s Planetary Instrument Definition and Development Program.
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