- Email: [email protected]
Au detector under flux
Nuclear Instruments and Methods in Physics Research A 633 (2011) S100–S102
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Simulation of charge transport in semi-insulating Au/CdTe/Au detector under flux J. Franc n, R. Grill, J. Kuba´t, E. Belas, P. Hoschl, P. Moravec, P. Praus Faculty of Mathematics and Physics, Institute of Physics, Prague, CZ 121 16, Czech Republic
a r t i c l e in f o
a b s t r a c t
Available online 18 June 2010
We report our simulations on charge transport in semi-insulating CdTe and CdZnTe with Au contacts under radiation flux. The type of the space charge and electric field distribution in an Au/CdTe/Au structure is at high fluxes result of a combined influence of charge formed due to band bending at the electrodes and from photo generated carriers, which are trapped at deep levels. The profile of the electric field determines the collection times of electrons and holes. Simultaneous solution of driftdiffusion and Poisson equations is used for the simulations. We show that the space charge originating from trapped photo-carriers starts to dominate at fluxes 1015–1016 cm 2 s 1 (expressed in the number of generated electron–hole pairs), when the influence of contacts starts to be negligible. & 2010 Elsevier B.V. All rights reserved.
Keywords: CdTe Detectors Recombination
1. Introduction Charge collection efficiency in CdTe and CdZnTe X-ray and gamma ray detectors is influenced by a profile of the electric field in the detector and its time evolution. The Pockels electro-optic effect is frequently used to study the electric field distribution in the volume of the devices [1–3]. The profile of the electric field is governed by the space charge accumulated at deep levels. Accumulation of positive space charge resulting in an increased electric field near the cathode was observed in CdZnTe [1–3]. On the contrary, CdTe has a tendency to accumulate negative space charge (electric field is decreased near the cathode) [4].The type of the space charge and electric field distribution in the Metal/CdTe/ Metal structure is at low fluxes, mostly influenced by the charge present due to the band bending near the electrodes. Additional space charge originating from trapped photo-carriers is accumulated with an increasing photon flux at deep levels further modifying the profile of the electric field. The nature of polarization due to space charge built-in the X-ray detectors operating at high fluxes was recently described in Ref. [5]. Here the space charge formed below the electrodes due to the band bending was not included in the calculation. The purpose of the present paper is to calculate distribution of the electric field and its impact on charge transport in the metal/ CdTe/metal structure in dependence of the flux of incoming radiation, in order to estimate the potential influence of contacts on operation of CdTe and CZT detectors under high fluxes of X-ray photons. Gold was chosen for this simulation, because it n
Corresponding author. Tel.: +420 221911335. E-mail address: [email protected] (J. Franc).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.06.136
represents one of the most optimal materials for formation of non-injecting and non-blocking contacts on semi-insulating CdTe and CZT. The work function of Au FAu is 5.3 eV [6], while the work function in semi-insulating CdTe is in the range of 5.2–5.4 eV [7] depending on the position of the Fermi level in the near midgap region. In the case, that the CdTe is slightly n-type, the bends at the interface are bent upwards and positive space charge is present in the volume of CdTe. The opposite case occurs for slightly p-type semi-insulating CdTe. The voltage U ¼100 V and the band bending of 150 meV was chosen for the simulation set presented in this paper.
2. Results and discussion We work with a model including one deep level. Parameters of midgap level from Ref. [5], which represent situation in state-ofthe art detector-grade fully compensated semi-insulating material were used (N ¼2 1011 cm 3, se ¼5 10 13 cm2, sh ¼3 10 14 cm2). Simultaneous solution of drift-diffusion and Poisson equation was used to calculate profiles of the electric field. The case interesting for X-ray radiation detectors at high fluxes (low attenuation coefficient a ¼50 cm 1) will be discussed 4:2 FCdTe o FAu Bands are bent upwards in this case, positive space charge is formed at the electrodes. The distribution of an electric field for this case is presented in Fig. 1 The monotonous evolution of the slope can be seen up to the flux 1014 cm 2 s 1. Then a minimum in the field distribution starts to develop. This effect was for the case of flatband conditions at contacts in detail
0
0
-200
-200
-400
-400
-600
Electric field (V/cm)
Electric field (V/cm)
J. Franc et al. / Nuclear Instruments and Methods in Physics Research A 633 (2011) S100–S102
-800 -1000 -1200
no flux N=1012cm-2s-1 N=1013cm-2s-1
-1400 -1600
N=1014cm-2s-1 N=1015cm-2s-1 N=1016cm-2s-1
-1800 -2000 -2200 0.00 cathode
0.02
0.04 0.06 X (cm)
S101
-600 -800 -1000 -1200
no flux N=1014cm-2s-1 N=1015cm-2s-1 N=1016cm-2s-1
-1400 -1600 -1800
0.08
-2000 0.00 cathode
0.10 anode
Fig. 1. The distribution of electric field (positive space charge present due to bend bending at both contacts), for a ¼50 in dependence of the radiation flux.
0.02
0.04
0.06 X (cm)
0.08
0.10 anode
Fig. 3. Profiles of the electric field for the case of injection of negative charge from electrodes (low absorption coefficient a ¼ 50 cm 1.
-200
-200
-400
-400 Electric field (V/cm)
Electric field (V/cm)
0
-600 -800 -1000 -1200 -1400
N=1014cm-2s-1 N=1015cm-2s-1
-1800
N=1015cm-2s-1, flatband
-2000 0.00 cathode
-800 -1000 -1200 -1400 -1600
N=1014cm-2s-1, flatband
-1600
-600
0.04
0.06
X (cm)
Flux=1014cm-2s-1, flatband Flux=1015cm-2s-1 Flux=1015cm-2s-1, flatband
-1800 -2000 0.00 cathode
0.02
Flux=1014cm-2s-1
0.08
0.10 anode
Fig. 2. Comparison of electric field profiles for the small band bending and for flatband conditions at both contact interfaces.
described in Ref. [5], where this extreme was named the ‘‘pinch point’’. Holes traveling from the generation point to the cathode are trapped left to the pinch point, while electrons are trapped in the region between the pinch point and the anode. Fig. 2 shows the comparison of electric field profiles for the small band bending and for flatband conditions at both contact interfaces. It is apparent, that even a small band bending influences the formation of pinch point and its position within the detector. 4:3 FCdTe 4 FAu In the next section, we will discuss the case of slightly p-type semi-insulated CdTe (FCdTe ¼5.5 eV4 FAu ¼5.35 eV). The bands at both interfaces are bent downwards; negative space charge is formed at the electrodes. Fig. 3 shows the evolution of the pinch point similar to Fig. 1. The profiles of the field at fluxes 1014 and 1015 cm 2 s 1 are compared to the ideal situation of flatband conditions at both interfaces in Fig. 4. A significant difference in the position and electric field of the pinch point minimum at flux 1015 cm 2 s 1 is
0.02
0.04
0.06
X (cm)
0.08
0.10 anode
Fig. 4. The profiles of the field at fluxes 1014 and 1015 cm 2 s 1 compared with the ideal situation of flatband conditions at both interfaces.
apparent. While under flatband conditions, the pinch point is clearly seen and is located deep in the sample, band bending effectively stops its formation. The negative space charge formed at the electrodes prevails over the positive charge from trapped photo holes at this flux.
3. Conclusions We conclude, that the electric field in a non-irradiated sample is strongly distorted by space charge even at very small bend bending at the interfaces ( o150 meV). The space charge originating from trapped photo-carriers starts to dominate at fluxes 1015–1016 cm 2 s 1, when the influence of contacts starts to be negligible. Formation and position of electric field minimum (pinch point) is also influenced by contacts. The minimum can completely disappear with an increasing band bending.
Acknowledgments This work is a part of the research plan MSM 0021620834 that is financed by the Ministry of Education of the Czech Republic. It
S102
J. Franc et al. / Nuclear Instruments and Methods in Physics Research A 633 (2011) S100–S102
was also supported by the Grant Agency of Charles University (No. 7692/2007). References ¨ szan, IEEE Trans. Nucl. Sci NS-49 (2002) 1960. [1] M.A. Hossain, E.J. Morton, M.E. O [2] H.W. Yao, R.B. James, E.C. Erikson, Proc. SPIE 3115 (1997) 62.
[3] A.E. Bolotnikov, G.S. Camarda, Y. Cui, A. Hossain, G. Yang, H.W. Yao, R.B. James, IEEE Trans. Nucl. Sci. NS-56 (2009) 791. [4] A. Cola, I. Farella, A.M. Mancini, A. Donati, IEEE Trans. Nucl. Sci. NS-54 (2007) 868. [5] D Bale, C Szeles, Phys. Rev. B. 77 (2008) 033205. [6] R.Lide David (Ed.), CRC Handbook on Chemistry and Physics, CRC Press, New York, 1999. [7] A.W. Brinkman, Properties of Narrow Gap Cadmium based Compounds, EMIS Datareviews Series no. 10, INSPEC, 1994, p. 575.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Simulation of charge transport in semi-insulating Au/CdTe/Au detector under flux J. Franc n, R. Grill, J. Kuba´t, E. Belas, P. Hoschl, P. Moravec, P. Praus Faculty of Mathematics and Physics, Institute of Physics, Prague, CZ 121 16, Czech Republic
a r t i c l e in f o
a b s t r a c t
Available online 18 June 2010
We report our simulations on charge transport in semi-insulating CdTe and CdZnTe with Au contacts under radiation flux. The type of the space charge and electric field distribution in an Au/CdTe/Au structure is at high fluxes result of a combined influence of charge formed due to band bending at the electrodes and from photo generated carriers, which are trapped at deep levels. The profile of the electric field determines the collection times of electrons and holes. Simultaneous solution of driftdiffusion and Poisson equations is used for the simulations. We show that the space charge originating from trapped photo-carriers starts to dominate at fluxes 1015–1016 cm 2 s 1 (expressed in the number of generated electron–hole pairs), when the influence of contacts starts to be negligible. & 2010 Elsevier B.V. All rights reserved.
Keywords: CdTe Detectors Recombination
1. Introduction Charge collection efficiency in CdTe and CdZnTe X-ray and gamma ray detectors is influenced by a profile of the electric field in the detector and its time evolution. The Pockels electro-optic effect is frequently used to study the electric field distribution in the volume of the devices [1–3]. The profile of the electric field is governed by the space charge accumulated at deep levels. Accumulation of positive space charge resulting in an increased electric field near the cathode was observed in CdZnTe [1–3]. On the contrary, CdTe has a tendency to accumulate negative space charge (electric field is decreased near the cathode) [4].The type of the space charge and electric field distribution in the Metal/CdTe/ Metal structure is at low fluxes, mostly influenced by the charge present due to the band bending near the electrodes. Additional space charge originating from trapped photo-carriers is accumulated with an increasing photon flux at deep levels further modifying the profile of the electric field. The nature of polarization due to space charge built-in the X-ray detectors operating at high fluxes was recently described in Ref. [5]. Here the space charge formed below the electrodes due to the band bending was not included in the calculation. The purpose of the present paper is to calculate distribution of the electric field and its impact on charge transport in the metal/ CdTe/metal structure in dependence of the flux of incoming radiation, in order to estimate the potential influence of contacts on operation of CdTe and CZT detectors under high fluxes of X-ray photons. Gold was chosen for this simulation, because it n
Corresponding author. Tel.: +420 221911335. E-mail address: [email protected] (J. Franc).
0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.06.136
represents one of the most optimal materials for formation of non-injecting and non-blocking contacts on semi-insulating CdTe and CZT. The work function of Au FAu is 5.3 eV [6], while the work function in semi-insulating CdTe is in the range of 5.2–5.4 eV [7] depending on the position of the Fermi level in the near midgap region. In the case, that the CdTe is slightly n-type, the bends at the interface are bent upwards and positive space charge is present in the volume of CdTe. The opposite case occurs for slightly p-type semi-insulating CdTe. The voltage U ¼100 V and the band bending of 150 meV was chosen for the simulation set presented in this paper.
2. Results and discussion We work with a model including one deep level. Parameters of midgap level from Ref. [5], which represent situation in state-ofthe art detector-grade fully compensated semi-insulating material were used (N ¼2 1011 cm 3, se ¼5 10 13 cm2, sh ¼3 10 14 cm2). Simultaneous solution of drift-diffusion and Poisson equation was used to calculate profiles of the electric field. The case interesting for X-ray radiation detectors at high fluxes (low attenuation coefficient a ¼50 cm 1) will be discussed 4:2 FCdTe o FAu Bands are bent upwards in this case, positive space charge is formed at the electrodes. The distribution of an electric field for this case is presented in Fig. 1 The monotonous evolution of the slope can be seen up to the flux 1014 cm 2 s 1. Then a minimum in the field distribution starts to develop. This effect was for the case of flatband conditions at contacts in detail
0
0
-200
-200
-400
-400
-600
Electric field (V/cm)
Electric field (V/cm)
J. Franc et al. / Nuclear Instruments and Methods in Physics Research A 633 (2011) S100–S102
-800 -1000 -1200
no flux N=1012cm-2s-1 N=1013cm-2s-1
-1400 -1600
N=1014cm-2s-1 N=1015cm-2s-1 N=1016cm-2s-1
-1800 -2000 -2200 0.00 cathode
0.02
0.04 0.06 X (cm)
S101
-600 -800 -1000 -1200
no flux N=1014cm-2s-1 N=1015cm-2s-1 N=1016cm-2s-1
-1400 -1600 -1800
0.08
-2000 0.00 cathode
0.10 anode
Fig. 1. The distribution of electric field (positive space charge present due to bend bending at both contacts), for a ¼50 in dependence of the radiation flux.
0.02
0.04
0.06 X (cm)
0.08
0.10 anode
Fig. 3. Profiles of the electric field for the case of injection of negative charge from electrodes (low absorption coefficient a ¼ 50 cm 1.
-200
-200
-400
-400 Electric field (V/cm)
Electric field (V/cm)
0
-600 -800 -1000 -1200 -1400
N=1014cm-2s-1 N=1015cm-2s-1
-1800
N=1015cm-2s-1, flatband
-2000 0.00 cathode
-800 -1000 -1200 -1400 -1600
N=1014cm-2s-1, flatband
-1600
-600
0.04
0.06
X (cm)
Flux=1014cm-2s-1, flatband Flux=1015cm-2s-1 Flux=1015cm-2s-1, flatband
-1800 -2000 0.00 cathode
0.02
Flux=1014cm-2s-1
0.08
0.10 anode
Fig. 2. Comparison of electric field profiles for the small band bending and for flatband conditions at both contact interfaces.
described in Ref. [5], where this extreme was named the ‘‘pinch point’’. Holes traveling from the generation point to the cathode are trapped left to the pinch point, while electrons are trapped in the region between the pinch point and the anode. Fig. 2 shows the comparison of electric field profiles for the small band bending and for flatband conditions at both contact interfaces. It is apparent, that even a small band bending influences the formation of pinch point and its position within the detector. 4:3 FCdTe 4 FAu In the next section, we will discuss the case of slightly p-type semi-insulated CdTe (FCdTe ¼5.5 eV4 FAu ¼5.35 eV). The bands at both interfaces are bent downwards; negative space charge is formed at the electrodes. Fig. 3 shows the evolution of the pinch point similar to Fig. 1. The profiles of the field at fluxes 1014 and 1015 cm 2 s 1 are compared to the ideal situation of flatband conditions at both interfaces in Fig. 4. A significant difference in the position and electric field of the pinch point minimum at flux 1015 cm 2 s 1 is
0.02
0.04
0.06
X (cm)
0.08
0.10 anode
Fig. 4. The profiles of the field at fluxes 1014 and 1015 cm 2 s 1 compared with the ideal situation of flatband conditions at both interfaces.
apparent. While under flatband conditions, the pinch point is clearly seen and is located deep in the sample, band bending effectively stops its formation. The negative space charge formed at the electrodes prevails over the positive charge from trapped photo holes at this flux.
3. Conclusions We conclude, that the electric field in a non-irradiated sample is strongly distorted by space charge even at very small bend bending at the interfaces ( o150 meV). The space charge originating from trapped photo-carriers starts to dominate at fluxes 1015–1016 cm 2 s 1, when the influence of contacts starts to be negligible. Formation and position of electric field minimum (pinch point) is also influenced by contacts. The minimum can completely disappear with an increasing band bending.
Acknowledgments This work is a part of the research plan MSM 0021620834 that is financed by the Ministry of Education of the Czech Republic. It
S102
J. Franc et al. / Nuclear Instruments and Methods in Physics Research A 633 (2011) S100–S102
was also supported by the Grant Agency of Charles University (No. 7692/2007). References ¨ szan, IEEE Trans. Nucl. Sci NS-49 (2002) 1960. [1] M.A. Hossain, E.J. Morton, M.E. O [2] H.W. Yao, R.B. James, E.C. Erikson, Proc. SPIE 3115 (1997) 62.
[3] A.E. Bolotnikov, G.S. Camarda, Y. Cui, A. Hossain, G. Yang, H.W. Yao, R.B. James, IEEE Trans. Nucl. Sci. NS-56 (2009) 791. [4] A. Cola, I. Farella, A.M. Mancini, A. Donati, IEEE Trans. Nucl. Sci. NS-54 (2007) 868. [5] D Bale, C Szeles, Phys. Rev. B. 77 (2008) 033205. [6] R.Lide David (Ed.), CRC Handbook on Chemistry and Physics, CRC Press, New York, 1999. [7] A.W. Brinkman, Properties of Narrow Gap Cadmium based Compounds, EMIS Datareviews Series no. 10, INSPEC, 1994, p. 575.