- Email: [email protected]
Furthering the understanding of ion-irradiation-induced electrical isolation in wide band-gap semiconductors
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 243 (2006) 79–82 www.elsevier.com/locate/nimb
Furthering the understanding of ion-irradiation-induced electrical isolation in wide band-gap semiconductors A.I. Titov a, P.A. Karaseov a, S.O. Kucheyev a
b,*
Department of Physical Electronics, St. Petersburg State Polytechnical University, St. Petersburg 195251, Russian Federation b Lawrence Livermore National Laboratory, Materials Science and Technology Division, L-367 Livermore, CA 94550, USA Received 29 July 2005 Available online 23 September 2005
Abstract A model recently developed for ion-irradiation-induced electrical isolation of GaN is extended to describe this process in other wide band-gap semiconductors. In our model, a decrease in the concentration of free carriers responsible for isolation is assumed to be due to the formation of complexes of ion-beam-generated point defects with shallow donor or acceptor dopants. Results show that this model can adequately describe experimental data for electrical isolation not only in n-GaN but also in n-ZnO as well as in n- and p-InGaP. 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Cc; 61.80.Az; 61.80.Jh Keywords: Electrical isolation; Ion-irradiation; Point defects; ZnO; InGaP
1. Introduction Wide band-gap semiconductors are the current materials of choice for a range of (opto)electronic devices. Ion irradiation is an attractive processing tool for electrical isolation of closely spaced devices based on wide bandgap semiconductors. Indeed, previous experimental reports have demonstrated that the electrical resistivity of several wide band-gap semiconductors, such as GaN, ZnO and InGaP, can be increased by several orders of magnitude as a result of lattice defects produced by ion irradiation (see, for example, [1–8]). It has been shown that such a large increase in electrical resistivity is mainly due to the trapping of free carriers at lattice defects produced by the ion beam, whereas the degradation of carrier mobility typically has a relatively small contribution to the overall changes in resistivity [1–8]. Recently, we have proposed a model which can adequately describe experimental data for electrical isolation *
Corresponding author. Tel.: +1 9254225866; fax: +1 9254230785. E-mail address: [email protected] (S.O. Kucheyev).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.08.123
of n-GaN by irradiation with MeV light ions [9]. The details of this model can be found in [9] and will not be reproduced here. In brief, in this model, based on a chemical rate equation approach, a decrease in the concentration of free carriers is assumed to be due to the formation of complexes of ion-beam-generated point defects with shallow donor or acceptor dopants. The model takes into account (i) ionbeam-induced generation of some mobile point defects which are responsible for isolation, (ii) the trapping of these defects at shallow dopants, which is characterized by the reaction constant a and (iii) the capture of ionbeam-produced defects by homogeneously distributed unsaturated sinks, with the reaction time constant s. Based on these assumptions, the following equation has been derived [9]: lnð1 nd =ni Þ ¼ asnd ð1 gU=nd Þ;
ð1Þ
where g is the average number of defects produced by each ion at particular depth, nd is the concentration of complexes of defects with shallow dopants, ni is the concentration of main shallow dopants (which is also the initial concentration of free carriers) and U is ion dose. In
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A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
addition, the carrier concentration nc and sheet resistance Rs can be found from the following equations [9]: nc ¼ ni ð1 nd =ni Þ; 1
Rs ¼ ðelN s Þ
ð2Þ 1
¼ ½elhðnc þ nf Þ ;
ð3Þ
where nf is the final effective free electron concentration for relatively large ion doses when all shallow dopants are compensated by irradiation-produced defects, e is the electron charge and l is effective carrier mobility. In this article, we show that this model can adequately describe ion-irradiation-induced electrical isolation not only in GaN but also in other technologically important wide band-gap semiconductors such as ZnO and InGaP.
(a)
2. Results and discussion 2.1. ZnO For a comparison of results of our model with experimental data on ZnO, we have used data from [7], where 0.6-lm-thick layers of unintentionally doped n-ZnO [with room temperature (RT) values of ni 1017 cm3 and a Hall mobility of 80 V cm2 V1 s1], grown on sapphire substrates, were irradiated at RT with MeV light ions. Ion energies and masses (namely, 0.7 MeV 7Li, 2.0 MeV 16O, and 3.5 MeV 28Si) were chosen to place the damage peak at the ion end-of-range deep into the sapphire substrate, beyond the ZnO epilayer. It should be noted that, although the nature of shallow donors in unintentionally doped ZnO films used in [7] is currently not well understood, our model can still be applied. Indeed, this model is empirical and does not specify which immobile lattice defects or impurities with shallow levels (i.e. dopants) are responsible for the conductivity in as-grown films [9]. According to our model (see Eqs. (1) and (2)), the concentration of defect–impurity complexes nd and, hence, the concentration of free carriers nc = ni(1nd/ni) are determined by gU; i.e. by the total number of ion-beam-produced defects. Therefore, our model predicts that all Rs curves for different ions should coincide when plotted as a function of gU, assuming that electron mobility is independent of ion-irradiation conditions for the same value of gU. To verify this prediction for ZnO, Fig. 1(a) shows Rs(gU) dependencies for data from [7]. In Fig. 1(a), the defect generation efficiency g was assumed to be equal to the efficiency of vacancy generation in the Zn sublattice in ballistic processes gballistic and was calculated with the Zn TRIM code [10,11,15]. It is seen from Fig. 1(a) that Rs(gU) curves for Li and O ions indeed overlap within experimental error. However, in the case of heavier 3.5 MeV 28Si ion bombardment, Fig. 1(a) shows that Rs(gU) is slightly shifted toward higher gU values. Such a shift in the 28Si curve can be due to several reasons, including errors in measurements, simplifications of our model, limitations of the TRIM code, a dependence of electron mobility
(b)
Fig. 1. (a) Sheet resistance of ZnO epilayers irradiated with MeV light ions, as indicated in the legend, as function of the total number of vacancies ballistically generated in the Zn sublattice. (b) Experimental (symbols) and calculated (solid lines) dependencies of the sheet resistance of ZnO epilayers bombarded with MeV light ions, as indicated in the legend. See [7] for additional experimental details.
and the stability of Frenkel pairs on the density of collision cascades, etc. At present, an explanation for such a shift should await additional studies. Fig. 1(b) shows the dependencies of Rs on ion dose, calculated based on Eqs. (1) and (3), in comparison with experimental data points from [7]. Excellent agreement between experiment and theory can be seen from Fig. 1(b). To calculate these curves, we neglected ion-beam-induced changes to electron mobility, and as and g were treated as fitting parameters, based on the procedure discussed in detail in [9]. The values of as and gmodel obtained from such a fitting procedure are given in Table 1 together with the average number of vacancies gballistic ballistically produced by each Table 1 Ion-irradiation conditions; parameters as and gmodel obtained from the fitting of our model to experimental data from [7]; and the average number of vacancies gballistic (per unit of depth) ballistically produced by each ion in Zn and O sublattices in a 0.6-lm-thick ZnO film, calculated with the TRIM code [10,11] Ion
Energy (MeV)
as (1018 cm3)
gmodel (104 cm1)
gballistic Zn (104 cm1)
gballistic O (104 cm1)
7
0.7 2.0 3.5
1.54 3.13 2.88
1.66 4.31 10.8
13.2 73.4 188.7
8.76 51.9 138.2
Li O 28 Si 16
A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
81
ion in the Zn and O sublattices and calculated with the TRIM code [10,11]. It is seen from Table 1 that the values of as are similar for all three irradiation conditions. However, Table 1 also shows that the values of the effective number of ion-beamgenerated defects gmodel obtained from such fitting are about an order of magnitude smaller than the number of ion-beam-generated vacancies gballistic according to ballistic calculations. We attribute this interesting result to efficient recombination of closely spaced Frenkel pair components during the initial stages of the stabilization of collision cascades. Such recombination effectively reduces the number of mobile defects available for interaction with shallow dopants. This interpretation is also consistent with previous experimental observations of extremely efficient defect interaction and annihilation processes in ZnO under ion bombardment; i.e. dynamic annealing processes (see, for example, [16–22]).
(a)
(b)
2.2. InGaP We have also applied our model to describe results of ion-irradiation-induced electrical isolation of InGaP recently reported in [8], where n- and p-type In0.49Ga0.51P epilayers grown on semi-insulating GaAs substrates were bombarded at RT with 270 keV 4He ions. The sheet resistance Rs of InGaP epilayers was studied as a function of ion dose U and the initial concentration of free carriers ni. The epilayer thickness was 0.8 lm for n-InGaP and 0.4 lm for p-InGaP [8]. Fig. 2 [23] compares experimental data from [8] with results of our calculations (solid lines) for n-InGaP (Fig. 2(a)) and p-InGaP (Fig. 2(b)). As for the case of ZnO discussed above, calculations were done with Eqs. (1) and (3) with as and g treated as fitting parameters. Table 2 gives the values of as and gmodel obtained from such a fitting procedure as well as the average number of vacancies gballistic in all the three sublattices of InGaP, calculated with the TRIM code [10,11]. It is seen from Table 2 that gmodel is close to gballistic , P particularly for the case of n-InGaP. In addition, Table 2 shows that the values of parameter as decrease with increasing ni for both cases of n- and p-type InGaP. Such a decrease in as with increasing ni can be attributed to the likely increase in the concentration of unsaturated sinks
Fig. 2. Experimental (symbols) and calculated (solid lines) dependencies of the sheet resistance of (a) n-InGaP and (b) p-InGaP bombarded at room temperature with 270 keV 4He ions. The initial carrier concentrations (in cm3) are given in the legend. See [8] for additional experimental details.
(such as extended lattice defects) in InGaP epilayers with increasing the doping level. Indeed, an increase in the concentration of unsaturated sinks decreases s without affecting a. Therefore, product as decreases with increasing ni. Good agreement between theory (solid lines) and experiment (symbols) is seen from Fig. 2, particularly for the cases of small ni values. However, for larger ni, a slight discrepancy between theoretical curves and experimental points can be seen in Fig. 2 for both n- and p-type films. The reason for such a discrepancy requires additional studies. 3. Conclusions In conclusion, we have shown that a model of ion-irradiation-induced electrical isolation recently developed for GaN can adequately describe experimental data for electri-
Table 2 Parameters as and gmodel obtained from the fitting of our model to experimental data from [8], where 0.8-lm-thick n-InGaP and 0.4-lm-thick p-InGaP films were bombarded at room temperature with 270 keV 4He ions; and the average number of vacancies gballistic (per unit of depth) ballistically produced by each ion in In, Ga and P sublattices in InGaP films, calculated with the TRIM code [10,11] Target
ni (cm3)
as (1018 cm3)
gmodel (105 cm1)
gballistic (105 cm1) In
gballistic (105 cm1) Ga
gballistic (105 cm1) P
n-InGaP
4.8 · 1016 6.1 · 1017 2.8 · 1018 1.2 · 1019
42.4 9.71 3.45 0.573
8.47 8.91 7.54 8.55
4.60
3.92
6.73
p-InGaP
3.1 · 1017 5.4 · 1018 1.8 · 1019
13.6 1.69 0.149
5.99 4.61 8.21
3.17
2.68
4.57
82
A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
cal isolation not only in n-GaN but also in n-ZnO as well as in n- and p-InGaP. Better agreement between experiment and theory can be achieved by taking into account (i) the degradation of carrier mobility as a result of ion irradiation, (ii) the nonuniformities of the profile of ion-beam-generated defects and (iii) additional defect interaction processes. Acknowledgements Work at StPSPU was partly supported by the Russian Ministry of Education, Science and Technologies. Work at LLNL was performed under the auspices of the US DOE by the University of California, LLNL under Contract No. W-7405-Eng-48. References [1] S.C. Binari, H.B. Dietrich, G. Kelner, L.B. Rowland, K. Doverspike, D.K. Wickenden, J. Appl. Phys. 78 (1995) 3008. [2] S.J. Pearton, C.B. Vartuli, J.C. Zolper, C. Yuan, R.A. Stall, Appl. Phys. Lett. 67 (1995) 1435. [3] S.J. Pearton, R.G. Wilson, J.M. Zavada, J. Han, R.J. Shul, Appl. Phys. Lett. 73 (1998) 1877. [4] H. Boudinov, S.O. Kucheyev, J.S. Williams, C. Jagadish, G. Li, Appl. Phys. Lett. 78 (2001) 943. [5] S.O. Kucheyev, H. Boudinov, J.S. Williams, C. Jagadish, G. Li, J. Appl. Phys. 91 (2002) 4117. [6] X.A. Cao, S.J. Pearton, G.T. Dang, A.P. Zhang, F. Ren, R.G. Wilson, J.M. Van Hove, J. Appl. Phys. 87 (2000) 1091. [7] S.O. Kucheyev, P.N.K. Deenapanray, C. Jagadish, J.S. Williams, M. Yano, K. Koike, S. Sasa, M. Inoue, K. Ogata, Appl. Phys. Lett. 81 (2002) 3350.
[8] I. Danilov, J.P. de Souza, H. Boudinov, J. Bettini, M.M.G. de Carvalho, J. Appl. Phys. 92 (2002) 4261. [9] A.I. Titov, S.O. Kucheyev, J. Appl. Phys. 92 (2002) 5740. [10] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. [11] Ballistic calculations presented in this article were performed with the TRIM code (version SRIM-2003.17) [10] with threshold displacement energies (Eth) of 57 eV for Zn and O sublattices; and 7, 7 and 9 eV for In, Ga and P sublattices, respectively. Such values of Eth were chosen based on experimental data by Locker and Meese [12,13] for ZnO and Bauerlein [14] for InGaP. [12] J.M. Meese, D.R. Locker, Solid State Commun. 11 (1972) 1547. [13] D.R. Locker, J.M. Meese, IEEE Trans. Nucl. Sci. 19 (1972) 237. [14] R. Ba¨uerlein, Z. Phys. 176 (1963) 498. [15] It should be mentioned that Rs(gU) dependencies shown in Fig. 1(a) are qualitatively similar for gballistic calculated for either Zn or O sublattice. [16] H.M. Naguib, R. Kelly, Radiat. Eff. 25 (1975) 1. [17] C.W. White, L.A. Boatner, P.S. Sklad, C.J. McHargue, S.J. Pennycook, M.J. Aziz, G.C. Farlow, J. Rankin, Mat. Res. Soc. Symp. Proc. 74 (1987) 357. [18] E. Sonder, R.A. Zuhr, R.E. Valiga, J. Appl. Phys. 64 (1988) 1140. [19] D.C. Look, D.C. Reynolds, J.W. Hemsky, R.L. Jones, J.R. Sizelove, Appl. Phys. Lett. 75 (1999) 811. [20] F.D. Auret, S.A. Goodman, M. Hayes, M.J. Legodi, H.A. van Laarhoven, D.C. Look, Appl. Phys. Lett. 79 (2001) 3074. [21] S.O. Kucheyev, J.S. Williams, C. Jagadish, J. Zou, C. Evans, A.J. Nelson, A.V. Hamza, Phys. Rev. B 67 (2003) 094115. [22] S.O. Kucheyev, J.S. Williams, C. Jagadish, Vacuum 73 (2004) 93. [23] Fig. 2 shows that, for large doses, Rs exhibits a decrease with further irradiation. Such a decrease in Rs can be attributed to the onset of pronounced hopping conduction with increasing the concentration of ion-beam-produced defects. This effect is not considered in our model.
Nuclear Instruments and Methods in Physics Research B 243 (2006) 79–82 www.elsevier.com/locate/nimb
Furthering the understanding of ion-irradiation-induced electrical isolation in wide band-gap semiconductors A.I. Titov a, P.A. Karaseov a, S.O. Kucheyev a
b,*
Department of Physical Electronics, St. Petersburg State Polytechnical University, St. Petersburg 195251, Russian Federation b Lawrence Livermore National Laboratory, Materials Science and Technology Division, L-367 Livermore, CA 94550, USA Received 29 July 2005 Available online 23 September 2005
Abstract A model recently developed for ion-irradiation-induced electrical isolation of GaN is extended to describe this process in other wide band-gap semiconductors. In our model, a decrease in the concentration of free carriers responsible for isolation is assumed to be due to the formation of complexes of ion-beam-generated point defects with shallow donor or acceptor dopants. Results show that this model can adequately describe experimental data for electrical isolation not only in n-GaN but also in n-ZnO as well as in n- and p-InGaP. 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Cc; 61.80.Az; 61.80.Jh Keywords: Electrical isolation; Ion-irradiation; Point defects; ZnO; InGaP
1. Introduction Wide band-gap semiconductors are the current materials of choice for a range of (opto)electronic devices. Ion irradiation is an attractive processing tool for electrical isolation of closely spaced devices based on wide bandgap semiconductors. Indeed, previous experimental reports have demonstrated that the electrical resistivity of several wide band-gap semiconductors, such as GaN, ZnO and InGaP, can be increased by several orders of magnitude as a result of lattice defects produced by ion irradiation (see, for example, [1–8]). It has been shown that such a large increase in electrical resistivity is mainly due to the trapping of free carriers at lattice defects produced by the ion beam, whereas the degradation of carrier mobility typically has a relatively small contribution to the overall changes in resistivity [1–8]. Recently, we have proposed a model which can adequately describe experimental data for electrical isolation *
Corresponding author. Tel.: +1 9254225866; fax: +1 9254230785. E-mail address: [email protected] (S.O. Kucheyev).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.08.123
of n-GaN by irradiation with MeV light ions [9]. The details of this model can be found in [9] and will not be reproduced here. In brief, in this model, based on a chemical rate equation approach, a decrease in the concentration of free carriers is assumed to be due to the formation of complexes of ion-beam-generated point defects with shallow donor or acceptor dopants. The model takes into account (i) ionbeam-induced generation of some mobile point defects which are responsible for isolation, (ii) the trapping of these defects at shallow dopants, which is characterized by the reaction constant a and (iii) the capture of ionbeam-produced defects by homogeneously distributed unsaturated sinks, with the reaction time constant s. Based on these assumptions, the following equation has been derived [9]: lnð1 nd =ni Þ ¼ asnd ð1 gU=nd Þ;
ð1Þ
where g is the average number of defects produced by each ion at particular depth, nd is the concentration of complexes of defects with shallow dopants, ni is the concentration of main shallow dopants (which is also the initial concentration of free carriers) and U is ion dose. In
80
A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
addition, the carrier concentration nc and sheet resistance Rs can be found from the following equations [9]: nc ¼ ni ð1 nd =ni Þ; 1
Rs ¼ ðelN s Þ
ð2Þ 1
¼ ½elhðnc þ nf Þ ;
ð3Þ
where nf is the final effective free electron concentration for relatively large ion doses when all shallow dopants are compensated by irradiation-produced defects, e is the electron charge and l is effective carrier mobility. In this article, we show that this model can adequately describe ion-irradiation-induced electrical isolation not only in GaN but also in other technologically important wide band-gap semiconductors such as ZnO and InGaP.
(a)
2. Results and discussion 2.1. ZnO For a comparison of results of our model with experimental data on ZnO, we have used data from [7], where 0.6-lm-thick layers of unintentionally doped n-ZnO [with room temperature (RT) values of ni 1017 cm3 and a Hall mobility of 80 V cm2 V1 s1], grown on sapphire substrates, were irradiated at RT with MeV light ions. Ion energies and masses (namely, 0.7 MeV 7Li, 2.0 MeV 16O, and 3.5 MeV 28Si) were chosen to place the damage peak at the ion end-of-range deep into the sapphire substrate, beyond the ZnO epilayer. It should be noted that, although the nature of shallow donors in unintentionally doped ZnO films used in [7] is currently not well understood, our model can still be applied. Indeed, this model is empirical and does not specify which immobile lattice defects or impurities with shallow levels (i.e. dopants) are responsible for the conductivity in as-grown films [9]. According to our model (see Eqs. (1) and (2)), the concentration of defect–impurity complexes nd and, hence, the concentration of free carriers nc = ni(1nd/ni) are determined by gU; i.e. by the total number of ion-beam-produced defects. Therefore, our model predicts that all Rs curves for different ions should coincide when plotted as a function of gU, assuming that electron mobility is independent of ion-irradiation conditions for the same value of gU. To verify this prediction for ZnO, Fig. 1(a) shows Rs(gU) dependencies for data from [7]. In Fig. 1(a), the defect generation efficiency g was assumed to be equal to the efficiency of vacancy generation in the Zn sublattice in ballistic processes gballistic and was calculated with the Zn TRIM code [10,11,15]. It is seen from Fig. 1(a) that Rs(gU) curves for Li and O ions indeed overlap within experimental error. However, in the case of heavier 3.5 MeV 28Si ion bombardment, Fig. 1(a) shows that Rs(gU) is slightly shifted toward higher gU values. Such a shift in the 28Si curve can be due to several reasons, including errors in measurements, simplifications of our model, limitations of the TRIM code, a dependence of electron mobility
(b)
Fig. 1. (a) Sheet resistance of ZnO epilayers irradiated with MeV light ions, as indicated in the legend, as function of the total number of vacancies ballistically generated in the Zn sublattice. (b) Experimental (symbols) and calculated (solid lines) dependencies of the sheet resistance of ZnO epilayers bombarded with MeV light ions, as indicated in the legend. See [7] for additional experimental details.
and the stability of Frenkel pairs on the density of collision cascades, etc. At present, an explanation for such a shift should await additional studies. Fig. 1(b) shows the dependencies of Rs on ion dose, calculated based on Eqs. (1) and (3), in comparison with experimental data points from [7]. Excellent agreement between experiment and theory can be seen from Fig. 1(b). To calculate these curves, we neglected ion-beam-induced changes to electron mobility, and as and g were treated as fitting parameters, based on the procedure discussed in detail in [9]. The values of as and gmodel obtained from such a fitting procedure are given in Table 1 together with the average number of vacancies gballistic ballistically produced by each Table 1 Ion-irradiation conditions; parameters as and gmodel obtained from the fitting of our model to experimental data from [7]; and the average number of vacancies gballistic (per unit of depth) ballistically produced by each ion in Zn and O sublattices in a 0.6-lm-thick ZnO film, calculated with the TRIM code [10,11] Ion
Energy (MeV)
as (1018 cm3)
gmodel (104 cm1)
gballistic Zn (104 cm1)
gballistic O (104 cm1)
7
0.7 2.0 3.5
1.54 3.13 2.88
1.66 4.31 10.8
13.2 73.4 188.7
8.76 51.9 138.2
Li O 28 Si 16
A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
81
ion in the Zn and O sublattices and calculated with the TRIM code [10,11]. It is seen from Table 1 that the values of as are similar for all three irradiation conditions. However, Table 1 also shows that the values of the effective number of ion-beamgenerated defects gmodel obtained from such fitting are about an order of magnitude smaller than the number of ion-beam-generated vacancies gballistic according to ballistic calculations. We attribute this interesting result to efficient recombination of closely spaced Frenkel pair components during the initial stages of the stabilization of collision cascades. Such recombination effectively reduces the number of mobile defects available for interaction with shallow dopants. This interpretation is also consistent with previous experimental observations of extremely efficient defect interaction and annihilation processes in ZnO under ion bombardment; i.e. dynamic annealing processes (see, for example, [16–22]).
(a)
(b)
2.2. InGaP We have also applied our model to describe results of ion-irradiation-induced electrical isolation of InGaP recently reported in [8], where n- and p-type In0.49Ga0.51P epilayers grown on semi-insulating GaAs substrates were bombarded at RT with 270 keV 4He ions. The sheet resistance Rs of InGaP epilayers was studied as a function of ion dose U and the initial concentration of free carriers ni. The epilayer thickness was 0.8 lm for n-InGaP and 0.4 lm for p-InGaP [8]. Fig. 2 [23] compares experimental data from [8] with results of our calculations (solid lines) for n-InGaP (Fig. 2(a)) and p-InGaP (Fig. 2(b)). As for the case of ZnO discussed above, calculations were done with Eqs. (1) and (3) with as and g treated as fitting parameters. Table 2 gives the values of as and gmodel obtained from such a fitting procedure as well as the average number of vacancies gballistic in all the three sublattices of InGaP, calculated with the TRIM code [10,11]. It is seen from Table 2 that gmodel is close to gballistic , P particularly for the case of n-InGaP. In addition, Table 2 shows that the values of parameter as decrease with increasing ni for both cases of n- and p-type InGaP. Such a decrease in as with increasing ni can be attributed to the likely increase in the concentration of unsaturated sinks
Fig. 2. Experimental (symbols) and calculated (solid lines) dependencies of the sheet resistance of (a) n-InGaP and (b) p-InGaP bombarded at room temperature with 270 keV 4He ions. The initial carrier concentrations (in cm3) are given in the legend. See [8] for additional experimental details.
(such as extended lattice defects) in InGaP epilayers with increasing the doping level. Indeed, an increase in the concentration of unsaturated sinks decreases s without affecting a. Therefore, product as decreases with increasing ni. Good agreement between theory (solid lines) and experiment (symbols) is seen from Fig. 2, particularly for the cases of small ni values. However, for larger ni, a slight discrepancy between theoretical curves and experimental points can be seen in Fig. 2 for both n- and p-type films. The reason for such a discrepancy requires additional studies. 3. Conclusions In conclusion, we have shown that a model of ion-irradiation-induced electrical isolation recently developed for GaN can adequately describe experimental data for electri-
Table 2 Parameters as and gmodel obtained from the fitting of our model to experimental data from [8], where 0.8-lm-thick n-InGaP and 0.4-lm-thick p-InGaP films were bombarded at room temperature with 270 keV 4He ions; and the average number of vacancies gballistic (per unit of depth) ballistically produced by each ion in In, Ga and P sublattices in InGaP films, calculated with the TRIM code [10,11] Target
ni (cm3)
as (1018 cm3)
gmodel (105 cm1)
gballistic (105 cm1) In
gballistic (105 cm1) Ga
gballistic (105 cm1) P
n-InGaP
4.8 · 1016 6.1 · 1017 2.8 · 1018 1.2 · 1019
42.4 9.71 3.45 0.573
8.47 8.91 7.54 8.55
4.60
3.92
6.73
p-InGaP
3.1 · 1017 5.4 · 1018 1.8 · 1019
13.6 1.69 0.149
5.99 4.61 8.21
3.17
2.68
4.57
82
A.I. Titov et al. / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 79–82
cal isolation not only in n-GaN but also in n-ZnO as well as in n- and p-InGaP. Better agreement between experiment and theory can be achieved by taking into account (i) the degradation of carrier mobility as a result of ion irradiation, (ii) the nonuniformities of the profile of ion-beam-generated defects and (iii) additional defect interaction processes. Acknowledgements Work at StPSPU was partly supported by the Russian Ministry of Education, Science and Technologies. Work at LLNL was performed under the auspices of the US DOE by the University of California, LLNL under Contract No. W-7405-Eng-48. References [1] S.C. Binari, H.B. Dietrich, G. Kelner, L.B. Rowland, K. Doverspike, D.K. Wickenden, J. Appl. Phys. 78 (1995) 3008. [2] S.J. Pearton, C.B. Vartuli, J.C. Zolper, C. Yuan, R.A. Stall, Appl. Phys. Lett. 67 (1995) 1435. [3] S.J. Pearton, R.G. Wilson, J.M. Zavada, J. Han, R.J. Shul, Appl. Phys. Lett. 73 (1998) 1877. [4] H. Boudinov, S.O. Kucheyev, J.S. Williams, C. Jagadish, G. Li, Appl. Phys. Lett. 78 (2001) 943. [5] S.O. Kucheyev, H. Boudinov, J.S. Williams, C. Jagadish, G. Li, J. Appl. Phys. 91 (2002) 4117. [6] X.A. Cao, S.J. Pearton, G.T. Dang, A.P. Zhang, F. Ren, R.G. Wilson, J.M. Van Hove, J. Appl. Phys. 87 (2000) 1091. [7] S.O. Kucheyev, P.N.K. Deenapanray, C. Jagadish, J.S. Williams, M. Yano, K. Koike, S. Sasa, M. Inoue, K. Ogata, Appl. Phys. Lett. 81 (2002) 3350.
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