- Email: [email protected]
The role of space charge in GaAs-based particle detectors
Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
The role of space charge in GaAs-based particle detectors J.J. Mares\ *, J. Kris\ to"k , P. HubmH k , S. PospmH s\ il Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka& 10, 162 53 Praha 6, Czech Republic Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Br\ ehova& 7, 115 19 Praha 1, Czech Republic
Abstract The direct measurement of the captured charge using the Faraday cup method together with the analysis of current}voltage curves was used for the experimental proof of the existence of the space charge in biased GaAs detector structures. The role of this space charge was discussed using the generalized Ramo}Gunn's theorem which enabled the explanation of the data observed and, moreover, provides a useful criterion for the optimization of GaAs-based particle detectors. 1999 Elsevier Science B.V. All rights reserved. Keywords: Gallium arsenide; Radiation detectors; Space charge; Faraday cup method
The interaction of ionizing particles with a semiconductor is accompanied by the creation of electron}hole pairs, the number of which measures the energy deposited by the particle, practically regardless of its physical nature [1]. This property enables one to construct devices with spectral resolution provided that the e!ective collection of the carriers generated by ionization events in the semiconductor is ensured. Then the crucial problem which one has to face in designing this type of device is the optimization of charge extraction from the sensitive volume of the detector. This is essentially solved [2] for silicon-based detector structures where the transport is controlled by the lifetime of carriers. More complicated, however, is the situation in the structures based on relaxationtime controlled materials, such as not intentionally doped GaAs or InP:Fe. In these semiconductors,
or more exactly semi-insulators (SI), the low-"eld time scale of kinetic processes is given by Maxwell's relaxation time, q "ee /p, where ee is the permit+ tivity and p the conductivity of the material, and no longer by the carrier life times. For this case, the observed current response to any charge redistribution in the volume of the detector is performed rather by the current equalizing charge induced on the electrodes than by the carriers actually reaching these electrodes. Hence we believe that the analysis of the charge collection process in SI-GaAs particle detectors should be based on the application of the generalized Ramo}Gunn's theorem [3], dealing precisely with the induced equalizing currents existing in a system of conductors surrounding the moving charge. According to this theorem, the point charge q moving with the velocity * between two #at parallel electrodes induces, in the external biased circuit, a current i which can be computed from i"!q*(dE/d<)
* Corresponding author. E-mail address: [email protected] (J.J. Mares\ )
(1)
where dE/d< is the derivative of the self-consistent electric "eld in the location of the point charge
0168-9002/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 4 3 2 - 5
II. CHARACTERIZATION/MODELLING
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J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
q with respect to the voltage applied between the electrodes. It should be noted that the usual simpli"ed form of this theorem [4,5], where the derivative dE/d< is reduced to a mere constant, is based on the non-realistic assumption that the distribution of the space charge in the structure is independent of the external bias. This leads inevitably to incorrect predictions about the charge collection e$ciency. In contrast, the general formula (1) re#ects the importance of the movable space charge for the formation of the detector signal. It is apparent at "rst glance that the essential contribution to the induced current pulses originates in the regions where the changes of the electric "eld with the applied bias are considerable, or in other words, where a large amount of mobile space charge immediately screening all bias changes is present. The experimental investigation of the "xed (i.e. that with time constant *q ), and mobile + components of the space charge in GaAs-based detector structures is the subject of the present study. The investigated detector structures were prepared using Czochralski grown, not intentionally doped GaAs polished wafers (conductivity p"6; 10\ S/m, low-"eld mobility k"0.5 m/V s). One side of the wafers was lapped in order to obtain samples of the required thickness, etched in Brmethanol solution and provided with AuGe/Aubased ohmic contacts. The polished side was then brie#y etched in hydro#uoric acid and covered with a thin (&100 nm) evaporated gold layer. The resulting devices, when suitably biased, worked as radiation detectors as published elsewhere [6]. In the reverse bias direction (positive polarity on the ohmic contact, see Fig. 1), their current}voltage curves have shown a sharp transition from the ohmic to the saturated regime at a voltage t which is strongly dependent on the sample thickness ¸. In terms of space charge transport theory [7], such a transition can be interpreted as the point where the space charge injected into the structure and screening of the external "eld just prevails over the equilibrium carriers. According to the Gauss' theorem, a quadratic type of scaling is expected in this case. Indeed, the experimental data, plotting t vs. ¸ (see inset of Fig. 1), con"rm this hypothesis quite
Fig. 1. An example of the reverse bias current}voltage curve of a detector structure (¸"450 lm). Inset: Dependence of the reverse bias transition voltage t on the sample thickness ¸.
well. The observed dependence can be expressed by the formula t"(o/ee )¸#const
(2)
where o is the average density of space charge and the empirical additive constant has a value of &1.13 V. Then the charge density o"9.9; 10\ C/m, determined from the slope of the curve in the inset of Fig. 1, was compared with the charge density obtained by the following experimental technique. For the direct measurement of the charge captured in a biased sample, an improved Faraday cup method [8] was used (see the inset of Fig. 2). Before the measurement, sample S was clamped between two spherical electrodes mounted on #at bronze springs. A current through the sample was established by means of a power supply B (Canberra3002). An electrometer E (General Radio-1230A) connected to the Faraday cup placed below the sample was grounded in order to check the zero reading. Then the electrometer was disconnected from the earth and the sample was released by turning the shorting cam. The sample fell into the Faraday cup and its charge Q was determined from the known capacitance of the arrangement, C , and the voltage < measured by the electrometer, as # Q"C < . The value of C (&31 pF) was obtained # prior to the present measurements by calibration using steel balls of di!erent diameters charged to a de"nite potential. Attention was paid to the
J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
Fig. 2. Histogram of the number of readings of a given captured charge (total of forty readings, ¸"280 lm, A"4;4 mm, reverse bias"30 V). Inset: Schematic of the experimental arrangement used for charge measurements by the Faraday cup method.
elimination of other sources of electri"cation but not due to the capture of charge by the detector structure itself. The spherical electrodes were goldelectroplated in order to suppress their contact potential di!erence with respect to the gold sample electrodes. In order to minimize the residual ohmic voltage drop between the spherical electrodes during the release of the sample, a special treatment was used to keep the contact resistance between the cam and the spring in the milliohm range. Taking into account the geometry and the elastic properties of the switching mechanism, it can be shown that the delay time between shorting and disconnection of the sample is of the same order as the disconnection time itself. This time, being controlled by tunnelling between metallic surfaces, is insensitive to the accelerations involved and may be estimated using quantum mechanical considerations [9] as q "2;10\ s. It is a remarkable fact " that for semi-insulating GaAs, q is of the same " order as q , (for our material q "1.9;10\ s), so + + that the measured captured charge corresponds to just that space charge component which is unable to equalize fast electron}hole pair induced deviations from the potential equilibrium distribution. Fig. 2 presents, in the form of an histogram, a result of charge measurements performed in the regime corresponding to the saturated part of the current}voltage curve. It is quite clear from these data that the charge captured in the structure after its disconnection from the source is far below the
59
total space charge forming the original potential distribution in the biased sample. Taking into account the sample geometry (¸"280 lm, A"4; 4 mm), for the captured charge density we obtain the value o "Q/A¸"2.0;10\ C/m, while the ! total charge density o (obtained from Eq. (2)) should be about "ve times larger. The captured charge is not long-lasting, however, in the sense that its relaxation time constant does not reach the range of seconds. This can be proved experimentally by shorting the sample for a few seconds before its release by the cam. The charge readings in this case were practically zero. The results described above di!er signi"cantly from the data obtained for rather analogous systems based on chromium-doped SI-GaA material (cf. Ref. [10]). For this doped material, the observed values of the charge were very widely scattered and non-reproducible. There were random readings indicating the presence of either quite negligible or huge space charge (&10}10 pC), or even a small charge of opposite sign, the latter probably due to the existence of spontaneous high "eld oscillations sometimes observed in SI materials. The fact that the structures with such a behaviour were also less e$cient as radiation detectors led us to formulate the following empirical rule: the presence of a large amount of mobile space charge is favourable for the operation of bulk SI-GaAs structures as high performance radiation detectors. It is evident that this criterion is practically identical with the conclusions mentioned above, made on the basis of Ramo}Gunn's theorem. Summarizing, direct experimental proof was provided for the existence of space charge in biased SI-GaAs structures and the decisive role of a mobile space charge component for radiation detection by these structures was shown. Although, the technique used is rather cumbersome for the e!ective optimization of real detectors, the results obtained by this method enable a deeper insight into the processes involved.
Acknowledgements This work was partly supported by the Grant Agencies of the Czech Republic, Contract No.
II. CHARACTERIZATION/MODELLING
60
J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
202/96/0021, and of the Academy of Sciences, Contract No. A1010806. The authors greatly appreciate the technical assistance of Ms. J. S[ idaH kovaH .
References [1] U. Fano, Phys. Rev. 70 (1946) 44. [2] D.S. McGregor, J.E. Kammeraad, in: T.E. Schlesinger, R.B. James (Eds.), Semiconductors and Semi-metals, vol. 43, Academic Press, New York, 1996, p. 384.
[3] J.B. Gunn, Solid State Electron. 7 (1964) 739. [4] D.G. Vass, Nucl. Instr. and Meth. 86 (1970) 5. [5] G. Cavalleri, E. Gatti, G. Fabri, D. Svelto, Nucl. Instr. and Meth. 92 (1971) 137. [6] J.J. Mares\ , J. Kris\ to"k, P. HubmH k, K. Jurek, S. PospmH s\ il, J. Kubas\ ta, J. Appl. Phys. 82 (1997) 3358. [7] M.A. Lampert, P. Mark, Current Injection in Solids, Academic Press, New York, 1970, p. 55. [8] R.W. Smith, A. Rose, Phys. Rev. 97 (1955) 1531. [9] W.R. Harper, Contact and Frictional Electri"cation, Clarendon Press, Oxford, 1967, p. 235. [10] J.J. Mares\ , J. Kris\ to"k, V. S[ mmH d, F. Deml, Solid State Electron. 31 (1988) 1309.
The role of space charge in GaAs-based particle detectors J.J. Mares\ *, J. Kris\ to"k , P. HubmH k , S. PospmH s\ il Institute of Physics, Academy of Sciences of the Czech Republic, Cukrovarnicka& 10, 162 53 Praha 6, Czech Republic Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Br\ ehova& 7, 115 19 Praha 1, Czech Republic
Abstract The direct measurement of the captured charge using the Faraday cup method together with the analysis of current}voltage curves was used for the experimental proof of the existence of the space charge in biased GaAs detector structures. The role of this space charge was discussed using the generalized Ramo}Gunn's theorem which enabled the explanation of the data observed and, moreover, provides a useful criterion for the optimization of GaAs-based particle detectors. 1999 Elsevier Science B.V. All rights reserved. Keywords: Gallium arsenide; Radiation detectors; Space charge; Faraday cup method
The interaction of ionizing particles with a semiconductor is accompanied by the creation of electron}hole pairs, the number of which measures the energy deposited by the particle, practically regardless of its physical nature [1]. This property enables one to construct devices with spectral resolution provided that the e!ective collection of the carriers generated by ionization events in the semiconductor is ensured. Then the crucial problem which one has to face in designing this type of device is the optimization of charge extraction from the sensitive volume of the detector. This is essentially solved [2] for silicon-based detector structures where the transport is controlled by the lifetime of carriers. More complicated, however, is the situation in the structures based on relaxationtime controlled materials, such as not intentionally doped GaAs or InP:Fe. In these semiconductors,
or more exactly semi-insulators (SI), the low-"eld time scale of kinetic processes is given by Maxwell's relaxation time, q "ee /p, where ee is the permit+ tivity and p the conductivity of the material, and no longer by the carrier life times. For this case, the observed current response to any charge redistribution in the volume of the detector is performed rather by the current equalizing charge induced on the electrodes than by the carriers actually reaching these electrodes. Hence we believe that the analysis of the charge collection process in SI-GaAs particle detectors should be based on the application of the generalized Ramo}Gunn's theorem [3], dealing precisely with the induced equalizing currents existing in a system of conductors surrounding the moving charge. According to this theorem, the point charge q moving with the velocity * between two #at parallel electrodes induces, in the external biased circuit, a current i which can be computed from i"!q*(dE/d<)
* Corresponding author. E-mail address: [email protected] (J.J. Mares\ )
(1)
where dE/d< is the derivative of the self-consistent electric "eld in the location of the point charge
0168-9002/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 4 3 2 - 5
II. CHARACTERIZATION/MODELLING
58
J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
q with respect to the voltage applied between the electrodes. It should be noted that the usual simpli"ed form of this theorem [4,5], where the derivative dE/d< is reduced to a mere constant, is based on the non-realistic assumption that the distribution of the space charge in the structure is independent of the external bias. This leads inevitably to incorrect predictions about the charge collection e$ciency. In contrast, the general formula (1) re#ects the importance of the movable space charge for the formation of the detector signal. It is apparent at "rst glance that the essential contribution to the induced current pulses originates in the regions where the changes of the electric "eld with the applied bias are considerable, or in other words, where a large amount of mobile space charge immediately screening all bias changes is present. The experimental investigation of the "xed (i.e. that with time constant *q ), and mobile + components of the space charge in GaAs-based detector structures is the subject of the present study. The investigated detector structures were prepared using Czochralski grown, not intentionally doped GaAs polished wafers (conductivity p"6; 10\ S/m, low-"eld mobility k"0.5 m/V s). One side of the wafers was lapped in order to obtain samples of the required thickness, etched in Brmethanol solution and provided with AuGe/Aubased ohmic contacts. The polished side was then brie#y etched in hydro#uoric acid and covered with a thin (&100 nm) evaporated gold layer. The resulting devices, when suitably biased, worked as radiation detectors as published elsewhere [6]. In the reverse bias direction (positive polarity on the ohmic contact, see Fig. 1), their current}voltage curves have shown a sharp transition from the ohmic to the saturated regime at a voltage t which is strongly dependent on the sample thickness ¸. In terms of space charge transport theory [7], such a transition can be interpreted as the point where the space charge injected into the structure and screening of the external "eld just prevails over the equilibrium carriers. According to the Gauss' theorem, a quadratic type of scaling is expected in this case. Indeed, the experimental data, plotting t vs. ¸ (see inset of Fig. 1), con"rm this hypothesis quite
Fig. 1. An example of the reverse bias current}voltage curve of a detector structure (¸"450 lm). Inset: Dependence of the reverse bias transition voltage t on the sample thickness ¸.
well. The observed dependence can be expressed by the formula t"(o/ee )¸#const
(2)
where o is the average density of space charge and the empirical additive constant has a value of &1.13 V. Then the charge density o"9.9; 10\ C/m, determined from the slope of the curve in the inset of Fig. 1, was compared with the charge density obtained by the following experimental technique. For the direct measurement of the charge captured in a biased sample, an improved Faraday cup method [8] was used (see the inset of Fig. 2). Before the measurement, sample S was clamped between two spherical electrodes mounted on #at bronze springs. A current through the sample was established by means of a power supply B (Canberra3002). An electrometer E (General Radio-1230A) connected to the Faraday cup placed below the sample was grounded in order to check the zero reading. Then the electrometer was disconnected from the earth and the sample was released by turning the shorting cam. The sample fell into the Faraday cup and its charge Q was determined from the known capacitance of the arrangement, C , and the voltage < measured by the electrometer, as # Q"C < . The value of C (&31 pF) was obtained # prior to the present measurements by calibration using steel balls of di!erent diameters charged to a de"nite potential. Attention was paid to the
J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
Fig. 2. Histogram of the number of readings of a given captured charge (total of forty readings, ¸"280 lm, A"4;4 mm, reverse bias"30 V). Inset: Schematic of the experimental arrangement used for charge measurements by the Faraday cup method.
elimination of other sources of electri"cation but not due to the capture of charge by the detector structure itself. The spherical electrodes were goldelectroplated in order to suppress their contact potential di!erence with respect to the gold sample electrodes. In order to minimize the residual ohmic voltage drop between the spherical electrodes during the release of the sample, a special treatment was used to keep the contact resistance between the cam and the spring in the milliohm range. Taking into account the geometry and the elastic properties of the switching mechanism, it can be shown that the delay time between shorting and disconnection of the sample is of the same order as the disconnection time itself. This time, being controlled by tunnelling between metallic surfaces, is insensitive to the accelerations involved and may be estimated using quantum mechanical considerations [9] as q "2;10\ s. It is a remarkable fact " that for semi-insulating GaAs, q is of the same " order as q , (for our material q "1.9;10\ s), so + + that the measured captured charge corresponds to just that space charge component which is unable to equalize fast electron}hole pair induced deviations from the potential equilibrium distribution. Fig. 2 presents, in the form of an histogram, a result of charge measurements performed in the regime corresponding to the saturated part of the current}voltage curve. It is quite clear from these data that the charge captured in the structure after its disconnection from the source is far below the
59
total space charge forming the original potential distribution in the biased sample. Taking into account the sample geometry (¸"280 lm, A"4; 4 mm), for the captured charge density we obtain the value o "Q/A¸"2.0;10\ C/m, while the ! total charge density o (obtained from Eq. (2)) should be about "ve times larger. The captured charge is not long-lasting, however, in the sense that its relaxation time constant does not reach the range of seconds. This can be proved experimentally by shorting the sample for a few seconds before its release by the cam. The charge readings in this case were practically zero. The results described above di!er signi"cantly from the data obtained for rather analogous systems based on chromium-doped SI-GaA material (cf. Ref. [10]). For this doped material, the observed values of the charge were very widely scattered and non-reproducible. There were random readings indicating the presence of either quite negligible or huge space charge (&10}10 pC), or even a small charge of opposite sign, the latter probably due to the existence of spontaneous high "eld oscillations sometimes observed in SI materials. The fact that the structures with such a behaviour were also less e$cient as radiation detectors led us to formulate the following empirical rule: the presence of a large amount of mobile space charge is favourable for the operation of bulk SI-GaAs structures as high performance radiation detectors. It is evident that this criterion is practically identical with the conclusions mentioned above, made on the basis of Ramo}Gunn's theorem. Summarizing, direct experimental proof was provided for the existence of space charge in biased SI-GaAs structures and the decisive role of a mobile space charge component for radiation detection by these structures was shown. Although, the technique used is rather cumbersome for the e!ective optimization of real detectors, the results obtained by this method enable a deeper insight into the processes involved.
Acknowledgements This work was partly supported by the Grant Agencies of the Czech Republic, Contract No.
II. CHARACTERIZATION/MODELLING
60
J.J. Mares\ et al. / Nuclear Instruments and Methods in Physics Research A 434 (1999) 57}60
202/96/0021, and of the Academy of Sciences, Contract No. A1010806. The authors greatly appreciate the technical assistance of Ms. J. S[ idaH kovaH .
References [1] U. Fano, Phys. Rev. 70 (1946) 44. [2] D.S. McGregor, J.E. Kammeraad, in: T.E. Schlesinger, R.B. James (Eds.), Semiconductors and Semi-metals, vol. 43, Academic Press, New York, 1996, p. 384.
[3] J.B. Gunn, Solid State Electron. 7 (1964) 739. [4] D.G. Vass, Nucl. Instr. and Meth. 86 (1970) 5. [5] G. Cavalleri, E. Gatti, G. Fabri, D. Svelto, Nucl. Instr. and Meth. 92 (1971) 137. [6] J.J. Mares\ , J. Kris\ to"k, P. HubmH k, K. Jurek, S. PospmH s\ il, J. Kubas\ ta, J. Appl. Phys. 82 (1997) 3358. [7] M.A. Lampert, P. Mark, Current Injection in Solids, Academic Press, New York, 1970, p. 55. [8] R.W. Smith, A. Rose, Phys. Rev. 97 (1955) 1531. [9] W.R. Harper, Contact and Frictional Electri"cation, Clarendon Press, Oxford, 1967, p. 235. [10] J.J. Mares\ , J. Kris\ to"k, V. S[ mmH d, F. Deml, Solid State Electron. 31 (1988) 1309.