- Email: [email protected]
Quantitative prediction of acceptor concentration reduction in boron doped silicon due to electron irradiation
&
Nuclear Instruments
and Methods in Physics Research B 117(I 996) 397-402
__ __
k!lOkAl
B
Beam lntwactlonr with Materials 6 Atoms
I!!3
ELSEVIER
Quantitative prediction of acceptor concentration reduction in boron doped silicon due to electron irradiation J.L. Everaert a9* , F. Verhaegen
a, R.L. Van Meirhaeghe
b, J. Uyttenhove
a, F. Cardon b
a Labomtorium uoor Biomedische Fysica, Krijgsluan 281 S12, 9000 Gent, Belgium b Laborutorium uoor Kristallograjk en Studie van de Vuste Stof: Krijgsluan 281 Sl, 9ooO Gent. Belgium Received 28 March 1996; revised form received 7 June 1996
Abstract The reduction in acceptor concentration due to electron irradiation is determined from C-V characteristics of Ti x Si Y/p-Si Schottky barrier diodes. By using the concept of displacement dose, a method for predicting the reduction in acceptor concentration is succesfully applied for an arbitrary primary electron energy ranging from 4 to 14 MeV.
1. Introduction
2. Experimental
Studies of radiation induced damage in electronic devices are important for basic research and applications. Predicting device performance in radiation fields is a very complex matter. In space, for example, electron radiation can have important effects on device characteristics. The damage introduced by high energy electrons depends on fluence and primary energy of the radiation. It is common to presume that defects are introduced in concentrations proportional to the irradiation fluence. However, the amount of defects is not linear with primary particle energy. For characterizing the damage inflicted to devices as a function of the primary energy of electron radiation, the recently introduced concept of displacement dose [l] can be used. Displacement dose has been succesfully applied on electric characteristics of solar cells for space applications [l] and may become an important tool in future damage studies. As a further test for the general application of this concept, we apply it on the reduction of acceptor concentration in p-Si, as this quantity is directly related to the introduced damage. We use Ti,Si,/p-Si Schottky barrier diodes as an appropriate semiconductor device for which the acceptor concentration can be accurately derived from C-V characteristics. We show that displacement dose unequivocally determines the reduction in acceptor concentration.
2.1. The Schottky barrier diodes The Schottky barrier diodes used in this study were manufactured on p-Si substrates ((11 I> orientation, doped with boron), with a resistivity ranging from 50 to 80 LIcm. Prior to metal evaporation, the substrates were degreased in boiling acetone, trichloroethylene and methanol, dipped in HF for 5 s and rinsed in deionised water. The substrates were placed in a Nanotech vacuum system with oil diffusion pump. Circular Ti contacts, with an area of 0.018 cm* and a thickness of 100 nm, were evaporated onto the Si substrates through a metallic contact mask. The contacts were treated in a rapid thermal processing system (AST Elektronik) at 400°C for one minute under a high-purity Ar atmosphere. In this way, Ti silicide [2] is formed and a possible interfacial oxide, that could have a disturbing influence on the capacitance of the diode, is effectively eliminated. Ohmic contacts were formed on the backsides of the substrates using a In : Ga (24: 76) eutectic mixture. Impedance measurements were performed in the dark. All C-V characteristics were measured automatically at a frequency of 500 kHz at room temperature, using a HP 4192 A impedance analyser. An ac voltage of 10 mV was applied. 2.2. Irradiations and dosimetry
* Corresponding
author. Email: jeanlvc.everaert@?rug.ac.be.
The Si diodes were irradiated at room temperature in air with electrons produced by a 15 MeV linear accelerator. The spectra of the electrons incident on the diodes
0168-583X/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO1 68-583X(96)003461
J.L. Eoeruert et ul./Nucl. Instr. und Meth. m Phys. Res. B 117 (1996) 397-402
398
0.12 6 MrV
4 McV
0
14 MeV
9 MeV
4
a
12
Energy (MeV) Fig. I. Electron fluence spectra, incident on the Si diodes for electrons of 4, 6, 9 and 14 MeV, calculated with EGS4. The spectra are normalized to a total energy of 1 MeV. Table 1 Mean electron energies Primary energy
Average energy
(MeV)
(MeV)
4 6 9 14
0.9 2.8 5.5
10.0
< NIEL > (eV cm* /g) 26 58 78 98
were calculated by Monte Carlo simulation of the irradiation setup with the widely used code EGS4 [3]. This code performs coupled electron-photon transport down to keV energies and allows determination of radiation quantities in any geometry for any material. We simulated the exit window of the accelerator head (2 mm Al/8 mm water/O.5 mm Al) and an air layer of one meter. Fig. 1 shows the calculated spectra for electrons with initial energies of 4, 6, 9 and 14 MeV. Mean electron energies are shown in Table 1. The electron fluxes during irradiations were obtained by measuring the ionizing dose with a Fricke dosimetry system. This was done by deriving the total number of incident electrons from the Fricke measurements and using this number as normalisation factor for the calculated electron spectra.
tive acceptor concentration, E the permittivity of the silicon and C the parallel capacitance per unit area of the Schottky barrier diode. It is clear that irradiation significantly changes the inclination of the C-V characteristic, indicating a reduction in shallow acceptor levels or compensation by shallow donor levels. The intersection with the voltage axis remains the same. For the barrier height ab calculated from V, [4] a value of 0.63 eV was obtained. This is in agreement with the typical value obtained for these diodes [2]. Qb can not be determined from current-voltage measurements as for these low doped silicon samples thermionic emission is not applicable. From the slope of the C-V characteristic we calculated the acceptor concentration of the unirradiated diodes. We found a value of (3.9 + 0.8) X lOI crnm3 which corresponds well with the resistivity of the silicon substrates. The depth at which N, is measured, necessary for determining the depth where the electron spectra should be calculated, can be obtained from the measured capacitance per unit area by
with W the width of the depletion layer. This formula can only be used if the capacity is not influenced by interfacial charges [S], series resistance [6] or deep levels [7]. As the barrier height calculated from the C-V characteristic matches the generally accepted barrier height [2], influence of possible interfacial charges and series resistance on the C-V characteristic can be neglected. The influence of deep levels on the frequency dependence of the capacitance is avoided by measuring at 500 kHz. This is proved by measurements made at 100 kHz and 500 kHz which gave the same result before as well as after irradiation. This indicates that introduced deep levels do not follow the applied ac voltage and, again, that series resistance can be neglected [6]. From capacitance measurements W can easily be calculated. For the applied reverse voltages (from 1 to 6 V) W ranges from about 2 to 20 pm.
3. Results and discussion 3.1. Radiation efsects on C-V characteristics Fig. 2 shows a typical dark C-V characteristic before and after electron irradiation. The C-V characteristics are described by the Mott-Schottky relation [4]: 1 _=C2
2 eN, E
v,_v_Z e
with V, the flat band potential, V the applied voltage, k the Boltzmann constant, T the temperature, N, the effec-
Fig. 2. C-V characteristics of a Ti,Si, /p-Si Schottky barrier diode: ( +) unirradiated, ( n ) irradiated with 6 MeV electrons upto 120 kGy equivalent dose to water.
J.L. Eueraert et ul./Nucl.
Instr. und Meth. in Phyr. Res. B 117 (1996) 397-402
Diodes (grouped by three) were irradiated with different fluences and energies. Effects on the C-V characteristic as shown in Fig. 2 were observed for each diode. Corresponding to each energy and fluence the mean reduction in effective acceptor concentration was calculated for the three diodes. These data are presented in Fig. 3. Full lines represent weighted regression lines ( y = ax) through the data points. Clearly the acceptor concentration is not only dependent on the applied fluence, but also on the primary energy of the electron beam. Investigations in the past [8] have shown that electron irradiation creates vacancies and self-interstitials. At room temperature these defects are mobile and interact with each other and with the impurities initially contained in the material. In the case of boron doped silicon, self-interstitials interact with substitutional boron atoms and an exchange of position occurs [9]. Bains and Banbury [lo] studied the influence of electron irradiation on boron doped silicon by means of deep level transient spectroscopy (DLTSI and ac hopping conductivity. They used 1.5 MeV electron beams with fluences ranging from 1 to 16 X 10I5 cm- *. At low temperature ( < 18 K) they found that the dominant defects formed by irradiation are boron-interstitials and vacancies. During anneals up to 300 K many previously unreported DLTS peaks were observed indicating the formation of several complexes in which boron may be involved. Neither DLTS nor hopping conductivity measurements presented any evidence for the removal of the boron interstitial. Tipping and Newman [ 1 I] used compensated silicon containing boron and a group V donor at rather high concentrations ( - lOI cm- 3> necessary for IR spectroscopy. Electron irradiations of 2 MeV at 110 K gave rise to boron interstitials. Anneals at 250-300 K lead to complexes that involve more than two interstitial boron atoms.
120
0 0
2
4
6
8
Fluence (IO” cm”) Fig. 3. Change of acceptor concentration AN, after irradiation with electrons of 4, 6, 9 and 14 MeV. Datapoints were obtained by averaging over 3 diodes, error bars represent 1 standard deviation. The full lines are obtained by weighted linear regression analysis.
399
From these results we expect that the main mechanism to explain the effect on the C-V characteristics is a reduction of the substitutional boron acceptor concentration by involving boron in complex formations. As the effect on the C-V characteristic is clearly explained by defect formation we will use the concept of nonionizing energy loss. 3.2. Nonionizing energy loss of electrons in Si To calculate the absorbed dose from ionizing radiation in a medium, knowledge of the linear energy transfer (LET) 1121, which describes the amount of energy transfered to matter by ionizing energy losses, is required. Similarly, calculation of the displacement damage dose, i.e. the amount of energy expended in a medium by nonionizing interactions, is possible if the energy loss associated with atomic displacements per unit path length of the incident particles is available. This energy loss that depends on the energy of the incident particles has been termed nonionizing energy loss (NIEL) in papers by Summers et al. [13]. NIEL is not linear with the energy and decreases with decreasing energy, contrary to LET, and is dependent on the kind of radiation particle and the material. For the electron radiations used in this work the displacement damage dose can be obtained from @( E)dE,
(3)
ni
where (d E/pd x),~ is the NIEL in eV cm2/g and @p(E) is the differential electron fluence for energy E in cm - *. The conversion factor f is used to obtain the displacement dose in Gy (f = 1.6 X lO-4) or in eV/g (f = 1). From Summers et al. [ 131 we took the NIEL values for electrons in Si with a threshold energy for displacement of 21 eV. In the integral @(E) is the electron spectrum present in the Si. In a first approximation @(El can be calculated analytically by the continuous slowing down approximation. This can however lead to errors due to interfaces, as in our experiment where an air-Si interface exists. To avoid possible errors we calculated @p(E) in Si for the electron radiations in this work by a two-step combined Monte Carlo and analytical calculation. In a first step, the code EGS4 was used to transport the electrons in the Si, taking the complete irradiation setup into account. Transport of the electrons was terminated when their energy becomes less or equal to a cutoff of 200 keV. For electrons with energies less than 200 keV, the geometry can be treated as homogeneous since the residual range for electrons with 200 keV is smaller than the dimensions of the smallest region of interest, i.e. the scoring region which we defined for the calculations as a 20 pm thick Si layer at a depth of 2 pm (as calculated from the capacitance) from the surface facing the electron beam (Fig. 4). The calculation of the
J.L. Everuert et ul. / Nucl. Instr. and Meth. in Phys. Res. B 117 (1996) 397-402
400
InGa eutectic mixture.
Ti,Si,
with the total fluence. Following the suggestion of Xapsos et al. [l], we also calculated the equivalent displacement damage dose Deg. Deq =
f/:““P(E)
@( E)dE.
ml”
electron beam -
ni
Q(E) is a quality factor for the electron energy E, analogous to the quality factor for ionizing radiation effects. For displacement damage the quality factor is defined as:
-1.
----~
2pm
.
353 pm
20pm
Fig. 4. The scoring region depth.
spectrum above the energy cutoff amounts to scoring track lengths of the electrons in energy bins during transport as explained in Verhaegen and Seuntjens [ 141. Each electron that reaches the Monte Carlo cutoff during transport in the scoring region or is created with an energy below this cutoff in it, is stored in a separate spectrum. After completion of the Monte Carlo calculation, this spectrum is then slowed down further below the cutoff down to an energy of 10 keV by the analytical technique of Spencer and Fano [ 151, modified by Spencer and Attix electron
1161. The obtained electron fluences are shown in Fig. 5. These fluences can be characterized by their average NIEL, which is similar to the track average LET [ 121 for ionizing radiation.
(4)
.
E)dE
f”‘@(
The energy of the reference electron radiation E,, was taken as 1 MeV. However, we do not know any physical mechanism that indicates a quadratic dependence of radiation damage to NIEL. 3.3. Correlation of radiation damage and radiation quantities In Fig. 6 the reduction in effective acceptor concentration ANa is plotted versus the average NIEL for the four electron radiations. The datapoints are all normalized to a fluence of lOI cmm2 electrons. On a log-log plot a line with a slope of I .I f 0.3 could be fitted through the datapoints, indicating that the correlation of the damage coefficient and < NIEL > is linear. In Fig. 6 the weighted linear regression line with a slope of 3 X IO” geV-’ cm -5 is also drawn. From the plot of the damage versus the particle fluence in Fig. 3 we obtained 4 separate response curves. These data are replotted in Fig. 7 as a
ml” The calculated
< NIEL > values are given in Table 1. < NIEL >
Ddispcan easily be obtained by multiplying 10 4 McV
-
%
6 McV
9 McV
14 MeV
1
I
2 8 5
0.1
E
0.01 0.001 0
0
20
40
60
80
100
120
-=NIEti (eV.em2/g) 4
8
12
Energy (Mel’) Fig. 5. Electron slowing down spectra at a depth of 2 pm in the silicon, obtained by Monte Carlo calculation with EGS4. The spectra are normalized to an energy deposition of I MeV.
Fig. 6. The linear relation between AN, and < NIEL > for the electron radiations. The datapoints and the error bars are the averages and standard deviations over all diodes irradiated with a specific electron energy, after normalisation to a fluence of lOI electrons cm-*. The fall line through the datapoints is obtained by weighted linear regression analysis.
J.L. Everoerr et al./Nucl.
Instr. and Meth. in Phys. Res. B I I7 (1996) 397-402
function of the displacement damage dose Ddisp. We see that now all datapoints are more or less grouped around one central line with a slope of 2.8 X 10e3 geV_’ cmM3. This means that both < NIEL > and Ddisp are appropriate quantities for predicting the reduction in acceptor concentration in p-Si for electron radiation in a wide energy range. A similar conclusion can not be drawn from the plot of the damage data versus the equivalent dose Deq presented in Fig. 8. The data for the 4 MeV electrons deviate strongly from the regression line. This indicates that Des is not an adequate radiation quantity to predict the reduction in acceptor concentration.
0
2
4
401
6 D, (lOI
3.4. Physical interpretation The quantity Ddispallows estimation for the concentration of the introduced self-interstitials [Sii] or vacancies in the scoring region: [Si,]
=
.$!S, th
with p the density and Eth the threshold energy for displacement. Complex formation is neglected so only directly introduced damage is calculated. The regression line in Fig. 7 can be written as: IA&l = ~Ddis,,.
(8)
From formulae (7) and (8) we find: P (YE g
IAN,1
IO
12
Fig. 8. The data from Fig. 3 plotted versus the equivalent damage dose Deq for the electron radiations. Data for 4 MeV electrons clearly deviate from the full line which represents the weighted linear regression line through all datapoints.
temperature. As interactions and complex formations are strongly temperature dependent [IO,1 I], we expect the same for the coefficient (Y. Using formula (7) an estimate of directly displaced boron can be roughly calculated by reducing p with a factor of about 10-s regarding the doping concentration. For Ddisp= lOI eV/g a concentration of -- IO’ cmm3 is calculated which is not detectable with C-V characteristics and can be neglected compared to the ANa values. This indicates that complex formations as described in Section 3.1 are necessary to explain the observed effect on C-V characteristics.
(9)
[Si,] ’
which shows that (Y is a measure for the fraction of self interstitials that interact with boron. The value found in Section 3.3 for (Y indicates that the fraction ]AN#[Si,] is about 3%. This value is only valid at room temperature because measurements and radiations are done at room
f
8 eV/g)
4. Conclusion Electron irradiation creates a reduction in acceptor concentration in boron doped Si. The main mechanism can be ascribed to a complex formation in which boron is involved. The reduction in acceptor concentration can be determined for an arbitrary primary energy by calculating the displacement dose using the nonionizing energy loss. A linear relationship between the reduction in acceptor concentration and the displacement dose is found.
80v
”
2
60 -
f g_
40-
Acknowledgements The authors wish to thank Prof. Dr. Ir. W. Mondelaers from the Department of Radiation Physics and Subatomic Physics at the University of Gent for irradiating the diodes.
0
1
2
3
4
Ddilp(10” eV/g) Fig. 7. ‘The data from Fig. 3 plotted versus the displacement damage dose Ddisp for the electron radiations. Dam are grouped around the full line, obtained by weighted linear regression analysis.
References [I] M.A. Xapsos, G.P. Summers, C.C. Blatchley, C.W. Colerico, E.A. Burke, S.R. Messenger Nucl. Sci. 41 (1994) 1945.
and P. Shapiro,
IEEE Trans.
402
J.L. Eoeraerr et ul./Nucl.
Instr. uml Merh. in Phys. Res. B 117 (1996) 397-402
[2] W. De Bosscher, R.L. Van Meirhaeghe, P.L. Hanselaer, L. Caenepeel, W.H. Laflere and F. Cardon. Semicond. Sci. Technol. 1 (1986) 376. [3] W. Nelson and D. Rogers, in: Monte Carlo Transport of Electrons and Photons, eds. M. Jenkins, W. Nelson and A. Rindi (Plenum Press, New York and London, 1988) p. 287. [4] E.H. Rhodetick, Metal-Semiconductor Contacts (Clarendon Press, Oxford, 1980). [5] R.L. Van Meirhaeghe, W.H. Laflere, Yu-Min Li and F. Cardon, J. Phys. D 14 (1981) 1505. [6] D.A. Vandenbroucke, R.L. Van Meirhaeghe, W.H. Laflere and F. Cardon, J. Phys. D 18 (1985) 73 I. [7) L.C. Kimerling, J. Appl. Phys. 45 (1974) 1839. [8] J.C. Bourgoin, in: Instabilities in Silicon Devices, Vol. 2,
[9] [IO] [I I] [12] [13]
[ 141 [15] [I61
eds. Ci. Barbottin and A. Vapaille (Elsevier, Amsterdam, 1989) Chap. 17. G.D. Watkins, Phys.Rev. B 12 (1975) 5824. S.K. Bains and P.C. Banbury, Semicond. Sci. Technol. 2 (1987) 20. A.K. Tipping and R.C. Newman, Semicond. Sci. Technol. 2 (1987) 389. ICRU Rep. 16 (Intern. Commission on Radiation Units and Measurements, Bethesda, MD, 1970). G.P. Summers, E.A. Burke, P. Shapiro, S.R. Messenger and R.J. Walters, IEEE Trans. Nucl. Sci. 40 (1993) 1372. F. Verhaegen and J. Seuntjens, Radiat. Res. 143 (1995) 334. L. Spencer and U. Fano, Phys. Rev. 93 (1954) I 172. L. Spencer and F. Attix, Radiat. Res. 3 (1955) 239.
Nuclear Instruments
and Methods in Physics Research B 117(I 996) 397-402
__ __
k!lOkAl
B
Beam lntwactlonr with Materials 6 Atoms
I!!3
ELSEVIER
Quantitative prediction of acceptor concentration reduction in boron doped silicon due to electron irradiation J.L. Everaert a9* , F. Verhaegen
a, R.L. Van Meirhaeghe
b, J. Uyttenhove
a, F. Cardon b
a Labomtorium uoor Biomedische Fysica, Krijgsluan 281 S12, 9000 Gent, Belgium b Laborutorium uoor Kristallograjk en Studie van de Vuste Stof: Krijgsluan 281 Sl, 9ooO Gent. Belgium Received 28 March 1996; revised form received 7 June 1996
Abstract The reduction in acceptor concentration due to electron irradiation is determined from C-V characteristics of Ti x Si Y/p-Si Schottky barrier diodes. By using the concept of displacement dose, a method for predicting the reduction in acceptor concentration is succesfully applied for an arbitrary primary electron energy ranging from 4 to 14 MeV.
1. Introduction
2. Experimental
Studies of radiation induced damage in electronic devices are important for basic research and applications. Predicting device performance in radiation fields is a very complex matter. In space, for example, electron radiation can have important effects on device characteristics. The damage introduced by high energy electrons depends on fluence and primary energy of the radiation. It is common to presume that defects are introduced in concentrations proportional to the irradiation fluence. However, the amount of defects is not linear with primary particle energy. For characterizing the damage inflicted to devices as a function of the primary energy of electron radiation, the recently introduced concept of displacement dose [l] can be used. Displacement dose has been succesfully applied on electric characteristics of solar cells for space applications [l] and may become an important tool in future damage studies. As a further test for the general application of this concept, we apply it on the reduction of acceptor concentration in p-Si, as this quantity is directly related to the introduced damage. We use Ti,Si,/p-Si Schottky barrier diodes as an appropriate semiconductor device for which the acceptor concentration can be accurately derived from C-V characteristics. We show that displacement dose unequivocally determines the reduction in acceptor concentration.
2.1. The Schottky barrier diodes The Schottky barrier diodes used in this study were manufactured on p-Si substrates ((11 I> orientation, doped with boron), with a resistivity ranging from 50 to 80 LIcm. Prior to metal evaporation, the substrates were degreased in boiling acetone, trichloroethylene and methanol, dipped in HF for 5 s and rinsed in deionised water. The substrates were placed in a Nanotech vacuum system with oil diffusion pump. Circular Ti contacts, with an area of 0.018 cm* and a thickness of 100 nm, were evaporated onto the Si substrates through a metallic contact mask. The contacts were treated in a rapid thermal processing system (AST Elektronik) at 400°C for one minute under a high-purity Ar atmosphere. In this way, Ti silicide [2] is formed and a possible interfacial oxide, that could have a disturbing influence on the capacitance of the diode, is effectively eliminated. Ohmic contacts were formed on the backsides of the substrates using a In : Ga (24: 76) eutectic mixture. Impedance measurements were performed in the dark. All C-V characteristics were measured automatically at a frequency of 500 kHz at room temperature, using a HP 4192 A impedance analyser. An ac voltage of 10 mV was applied. 2.2. Irradiations and dosimetry
* Corresponding
author. Email: jeanlvc.everaert@?rug.ac.be.
The Si diodes were irradiated at room temperature in air with electrons produced by a 15 MeV linear accelerator. The spectra of the electrons incident on the diodes
0168-583X/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO1 68-583X(96)003461
J.L. Eoeruert et ul./Nucl. Instr. und Meth. m Phys. Res. B 117 (1996) 397-402
398
0.12 6 MrV
4 McV
0
14 MeV
9 MeV
4
a
12
Energy (MeV) Fig. I. Electron fluence spectra, incident on the Si diodes for electrons of 4, 6, 9 and 14 MeV, calculated with EGS4. The spectra are normalized to a total energy of 1 MeV. Table 1 Mean electron energies Primary energy
Average energy
(MeV)
(MeV)
4 6 9 14
0.9 2.8 5.5
10.0
< NIEL > (eV cm* /g) 26 58 78 98
were calculated by Monte Carlo simulation of the irradiation setup with the widely used code EGS4 [3]. This code performs coupled electron-photon transport down to keV energies and allows determination of radiation quantities in any geometry for any material. We simulated the exit window of the accelerator head (2 mm Al/8 mm water/O.5 mm Al) and an air layer of one meter. Fig. 1 shows the calculated spectra for electrons with initial energies of 4, 6, 9 and 14 MeV. Mean electron energies are shown in Table 1. The electron fluxes during irradiations were obtained by measuring the ionizing dose with a Fricke dosimetry system. This was done by deriving the total number of incident electrons from the Fricke measurements and using this number as normalisation factor for the calculated electron spectra.
tive acceptor concentration, E the permittivity of the silicon and C the parallel capacitance per unit area of the Schottky barrier diode. It is clear that irradiation significantly changes the inclination of the C-V characteristic, indicating a reduction in shallow acceptor levels or compensation by shallow donor levels. The intersection with the voltage axis remains the same. For the barrier height ab calculated from V, [4] a value of 0.63 eV was obtained. This is in agreement with the typical value obtained for these diodes [2]. Qb can not be determined from current-voltage measurements as for these low doped silicon samples thermionic emission is not applicable. From the slope of the C-V characteristic we calculated the acceptor concentration of the unirradiated diodes. We found a value of (3.9 + 0.8) X lOI crnm3 which corresponds well with the resistivity of the silicon substrates. The depth at which N, is measured, necessary for determining the depth where the electron spectra should be calculated, can be obtained from the measured capacitance per unit area by
with W the width of the depletion layer. This formula can only be used if the capacity is not influenced by interfacial charges [S], series resistance [6] or deep levels [7]. As the barrier height calculated from the C-V characteristic matches the generally accepted barrier height [2], influence of possible interfacial charges and series resistance on the C-V characteristic can be neglected. The influence of deep levels on the frequency dependence of the capacitance is avoided by measuring at 500 kHz. This is proved by measurements made at 100 kHz and 500 kHz which gave the same result before as well as after irradiation. This indicates that introduced deep levels do not follow the applied ac voltage and, again, that series resistance can be neglected [6]. From capacitance measurements W can easily be calculated. For the applied reverse voltages (from 1 to 6 V) W ranges from about 2 to 20 pm.
3. Results and discussion 3.1. Radiation efsects on C-V characteristics Fig. 2 shows a typical dark C-V characteristic before and after electron irradiation. The C-V characteristics are described by the Mott-Schottky relation [4]: 1 _=C2
2 eN, E
v,_v_Z e
with V, the flat band potential, V the applied voltage, k the Boltzmann constant, T the temperature, N, the effec-
Fig. 2. C-V characteristics of a Ti,Si, /p-Si Schottky barrier diode: ( +) unirradiated, ( n ) irradiated with 6 MeV electrons upto 120 kGy equivalent dose to water.
J.L. Eueraert et ul./Nucl.
Instr. und Meth. in Phyr. Res. B 117 (1996) 397-402
Diodes (grouped by three) were irradiated with different fluences and energies. Effects on the C-V characteristic as shown in Fig. 2 were observed for each diode. Corresponding to each energy and fluence the mean reduction in effective acceptor concentration was calculated for the three diodes. These data are presented in Fig. 3. Full lines represent weighted regression lines ( y = ax) through the data points. Clearly the acceptor concentration is not only dependent on the applied fluence, but also on the primary energy of the electron beam. Investigations in the past [8] have shown that electron irradiation creates vacancies and self-interstitials. At room temperature these defects are mobile and interact with each other and with the impurities initially contained in the material. In the case of boron doped silicon, self-interstitials interact with substitutional boron atoms and an exchange of position occurs [9]. Bains and Banbury [lo] studied the influence of electron irradiation on boron doped silicon by means of deep level transient spectroscopy (DLTSI and ac hopping conductivity. They used 1.5 MeV electron beams with fluences ranging from 1 to 16 X 10I5 cm- *. At low temperature ( < 18 K) they found that the dominant defects formed by irradiation are boron-interstitials and vacancies. During anneals up to 300 K many previously unreported DLTS peaks were observed indicating the formation of several complexes in which boron may be involved. Neither DLTS nor hopping conductivity measurements presented any evidence for the removal of the boron interstitial. Tipping and Newman [ 1 I] used compensated silicon containing boron and a group V donor at rather high concentrations ( - lOI cm- 3> necessary for IR spectroscopy. Electron irradiations of 2 MeV at 110 K gave rise to boron interstitials. Anneals at 250-300 K lead to complexes that involve more than two interstitial boron atoms.
120
0 0
2
4
6
8
Fluence (IO” cm”) Fig. 3. Change of acceptor concentration AN, after irradiation with electrons of 4, 6, 9 and 14 MeV. Datapoints were obtained by averaging over 3 diodes, error bars represent 1 standard deviation. The full lines are obtained by weighted linear regression analysis.
399
From these results we expect that the main mechanism to explain the effect on the C-V characteristics is a reduction of the substitutional boron acceptor concentration by involving boron in complex formations. As the effect on the C-V characteristic is clearly explained by defect formation we will use the concept of nonionizing energy loss. 3.2. Nonionizing energy loss of electrons in Si To calculate the absorbed dose from ionizing radiation in a medium, knowledge of the linear energy transfer (LET) 1121, which describes the amount of energy transfered to matter by ionizing energy losses, is required. Similarly, calculation of the displacement damage dose, i.e. the amount of energy expended in a medium by nonionizing interactions, is possible if the energy loss associated with atomic displacements per unit path length of the incident particles is available. This energy loss that depends on the energy of the incident particles has been termed nonionizing energy loss (NIEL) in papers by Summers et al. [13]. NIEL is not linear with the energy and decreases with decreasing energy, contrary to LET, and is dependent on the kind of radiation particle and the material. For the electron radiations used in this work the displacement damage dose can be obtained from @( E)dE,
(3)
ni
where (d E/pd x),~ is the NIEL in eV cm2/g and @p(E) is the differential electron fluence for energy E in cm - *. The conversion factor f is used to obtain the displacement dose in Gy (f = 1.6 X lO-4) or in eV/g (f = 1). From Summers et al. [ 131 we took the NIEL values for electrons in Si with a threshold energy for displacement of 21 eV. In the integral @(E) is the electron spectrum present in the Si. In a first approximation @(El can be calculated analytically by the continuous slowing down approximation. This can however lead to errors due to interfaces, as in our experiment where an air-Si interface exists. To avoid possible errors we calculated @p(E) in Si for the electron radiations in this work by a two-step combined Monte Carlo and analytical calculation. In a first step, the code EGS4 was used to transport the electrons in the Si, taking the complete irradiation setup into account. Transport of the electrons was terminated when their energy becomes less or equal to a cutoff of 200 keV. For electrons with energies less than 200 keV, the geometry can be treated as homogeneous since the residual range for electrons with 200 keV is smaller than the dimensions of the smallest region of interest, i.e. the scoring region which we defined for the calculations as a 20 pm thick Si layer at a depth of 2 pm (as calculated from the capacitance) from the surface facing the electron beam (Fig. 4). The calculation of the
J.L. Everuert et ul. / Nucl. Instr. and Meth. in Phys. Res. B 117 (1996) 397-402
400
InGa eutectic mixture.
Ti,Si,
with the total fluence. Following the suggestion of Xapsos et al. [l], we also calculated the equivalent displacement damage dose Deg. Deq =
f/:““P(E)
@( E)dE.
ml”
electron beam -
ni
Q(E) is a quality factor for the electron energy E, analogous to the quality factor for ionizing radiation effects. For displacement damage the quality factor is defined as:
-1.
----~
2pm
.
353 pm
20pm
Fig. 4. The scoring region depth.
spectrum above the energy cutoff amounts to scoring track lengths of the electrons in energy bins during transport as explained in Verhaegen and Seuntjens [ 141. Each electron that reaches the Monte Carlo cutoff during transport in the scoring region or is created with an energy below this cutoff in it, is stored in a separate spectrum. After completion of the Monte Carlo calculation, this spectrum is then slowed down further below the cutoff down to an energy of 10 keV by the analytical technique of Spencer and Fano [ 151, modified by Spencer and Attix electron
1161. The obtained electron fluences are shown in Fig. 5. These fluences can be characterized by their average NIEL, which is similar to the track average LET [ 121 for ionizing radiation.
(4)
.
E)dE
f”‘@(
The energy of the reference electron radiation E,, was taken as 1 MeV. However, we do not know any physical mechanism that indicates a quadratic dependence of radiation damage to NIEL. 3.3. Correlation of radiation damage and radiation quantities In Fig. 6 the reduction in effective acceptor concentration ANa is plotted versus the average NIEL for the four electron radiations. The datapoints are all normalized to a fluence of lOI cmm2 electrons. On a log-log plot a line with a slope of I .I f 0.3 could be fitted through the datapoints, indicating that the correlation of the damage coefficient and < NIEL > is linear. In Fig. 6 the weighted linear regression line with a slope of 3 X IO” geV-’ cm -5 is also drawn. From the plot of the damage versus the particle fluence in Fig. 3 we obtained 4 separate response curves. These data are replotted in Fig. 7 as a
ml” The calculated
< NIEL > values are given in Table 1. < NIEL >
Ddispcan easily be obtained by multiplying 10 4 McV
-
%
6 McV
9 McV
14 MeV
1
I
2 8 5
0.1
E
0.01 0.001 0
0
20
40
60
80
100
120
-=NIEti (eV.em2/g) 4
8
12
Energy (Mel’) Fig. 5. Electron slowing down spectra at a depth of 2 pm in the silicon, obtained by Monte Carlo calculation with EGS4. The spectra are normalized to an energy deposition of I MeV.
Fig. 6. The linear relation between AN, and < NIEL > for the electron radiations. The datapoints and the error bars are the averages and standard deviations over all diodes irradiated with a specific electron energy, after normalisation to a fluence of lOI electrons cm-*. The fall line through the datapoints is obtained by weighted linear regression analysis.
J.L. Everoerr et al./Nucl.
Instr. and Meth. in Phys. Res. B I I7 (1996) 397-402
function of the displacement damage dose Ddisp. We see that now all datapoints are more or less grouped around one central line with a slope of 2.8 X 10e3 geV_’ cmM3. This means that both < NIEL > and Ddisp are appropriate quantities for predicting the reduction in acceptor concentration in p-Si for electron radiation in a wide energy range. A similar conclusion can not be drawn from the plot of the damage data versus the equivalent dose Deq presented in Fig. 8. The data for the 4 MeV electrons deviate strongly from the regression line. This indicates that Des is not an adequate radiation quantity to predict the reduction in acceptor concentration.
0
2
4
401
6 D, (lOI
3.4. Physical interpretation The quantity Ddispallows estimation for the concentration of the introduced self-interstitials [Sii] or vacancies in the scoring region: [Si,]
=
.$!S, th
with p the density and Eth the threshold energy for displacement. Complex formation is neglected so only directly introduced damage is calculated. The regression line in Fig. 7 can be written as: IA&l = ~Ddis,,.
(8)
From formulae (7) and (8) we find: P (YE g
IAN,1
IO
12
Fig. 8. The data from Fig. 3 plotted versus the equivalent damage dose Deq for the electron radiations. Data for 4 MeV electrons clearly deviate from the full line which represents the weighted linear regression line through all datapoints.
temperature. As interactions and complex formations are strongly temperature dependent [IO,1 I], we expect the same for the coefficient (Y. Using formula (7) an estimate of directly displaced boron can be roughly calculated by reducing p with a factor of about 10-s regarding the doping concentration. For Ddisp= lOI eV/g a concentration of -- IO’ cmm3 is calculated which is not detectable with C-V characteristics and can be neglected compared to the ANa values. This indicates that complex formations as described in Section 3.1 are necessary to explain the observed effect on C-V characteristics.
(9)
[Si,] ’
which shows that (Y is a measure for the fraction of self interstitials that interact with boron. The value found in Section 3.3 for (Y indicates that the fraction ]AN#[Si,] is about 3%. This value is only valid at room temperature because measurements and radiations are done at room
f
8 eV/g)
4. Conclusion Electron irradiation creates a reduction in acceptor concentration in boron doped Si. The main mechanism can be ascribed to a complex formation in which boron is involved. The reduction in acceptor concentration can be determined for an arbitrary primary energy by calculating the displacement dose using the nonionizing energy loss. A linear relationship between the reduction in acceptor concentration and the displacement dose is found.
80v
”
2
60 -
f g_
40-
Acknowledgements The authors wish to thank Prof. Dr. Ir. W. Mondelaers from the Department of Radiation Physics and Subatomic Physics at the University of Gent for irradiating the diodes.
0
1
2
3
4
Ddilp(10” eV/g) Fig. 7. ‘The data from Fig. 3 plotted versus the displacement damage dose Ddisp for the electron radiations. Dam are grouped around the full line, obtained by weighted linear regression analysis.
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J.L. Eoeraerr et ul./Nucl.
Instr. uml Merh. in Phys. Res. B 117 (1996) 397-402
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