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The Hall mobility and its relationship to the persistent photoconductivity of undoped GaN
PERGAMON
Solid State Communications 111 (1999) 659–663
The Hall mobility and its relationship to the persistent photoconductivity of undoped GaN G. Li*, S.J. Chua, W. Wang Institute of Materials Research and Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 25 February 1999; accepted 16 April 1999 by Z.Z. Gan
Abstract Temperature-variable Hall effect measurements have been used to investigate the electrical properties of undoped GaN, which has electron densities in the order of mid-10 16 cm 23 and the Hall mobility varying from , 50 cm 2/sV to . 500 cm 2/sV. We found that very strong ionized impurity scattering limits the Hall mobility of GaN. Illumination even at 77 K has very little effect on the electron density but can lead to a noticeable persistent increase of the Hall mobility. The induced persistent photoconductivity (PPC) effect is, therefore, related to the Hall mobility through intrinsic electrically active defects. The properties of those defects were further investigated by monitoring the transient change of resistivity after removal of illumination at different temperatures. We have found that the recapturing process of excited electrons into illumination-neutralized defects is the mechanism responsible for the PPC effect of undoped GaN. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; C. Dislocations and disclinations; C. Point defects; D. Photoconductivity and photovoltaics; D. Hall effect
The Hall effect measurements have been widely used to characterize electrical properties of undoped and doped GaN [1,2]. The Hall mobility is indicative of electrical quality of undoped GaN in optimization of growth conditions [3,4]. Although a number of models have been proposed to explain anomalous behavior of the Hall mobility dependency on the electron density [5–7], the mechanism which dominates the Hall mobility of undoped GaN still remains unclear. The yellow-band luminescence (YL) and persistent photoconductivity (PPC) have also been observed and extensively investigated in undoped and doped GaN [8,9]. A recent report claimed that PPC and YL in GaN are related each other through defects associated with a broad deep level [10]. The origins of YL and PPC are still in debate [8–11]. In this * Corresponding author. E-mail address: [email protected] (G. Li)
work, a variety of undoped GaN with electron densities in order of mid-10 16 cm 23 and the Hall mobility varying from , 50 to . 500 cm 2/sV at room temperature were investigated using temperature variable Hall effect measurements. It was aimed to understand better what limits the Hall mobility of undoped GaN as well as its relationship with the PPC effect. Undoped GaN samples were grown on (0001) oriented sapphire by metal organic vapor phase epitaxy (MOVPE). Trimethylgallium (TMGa) and NH3 were used as the precursors. The carrier gas was H2. Growth conditions for undoped 3 mm thick GaN were fixed, while growth parameters used for GaN buffer layers were widely changed to have those different undoped GaN samples. Temperaturevariable Hall effect measurements were carried out using a BIO-RAD Hall effect system over a temperature range of 90–500 K. The samples were in van der Pauw geometry using In dots as ohmic contacts.
0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00252-5
660
G. Li et al. / Solid State Communications 111 (1999) 659–663
Table 1 Typical results of undoped GaN obtained using Hall effect measurements at 300 and 90 K. m , n, and R are the Hall mobility, electron density, and resistivity, respectively. The subscript d and i represent measurements carried out in dark, in dark immediately after removal of illumination. Rid was a constant value obtained in dark after removal of illumination Sample 300 K m d (cm 2/sV) nd (10 16 cm 23) 90 K m d (cm 2/sV) nd (10 16 cm 23) Rd (V cm) m i (cm 2/sV) ni (10 16 cm 23) Ri (V cm) Ri 2 Rd =Rd Rid(V cm) Rid 2 Rd =Rd
a
b
25 4 11.4 2.93 18.6 20 3.04 10.1 2 0.46 15.7 2 0.16
c
d
e
f
g
64.7 3.25
124 3.15
175 4.74
377 7.77
401 5.07
517 7.24
57.4 2.28 4.78 67.7 2.44 3.78 2 0.21 4.32 2 0.12
183 1.68 2.03 215 1.7 1.7 2 0.16 1.85 2 0.09
232 2.68 1.05 238 2.78 0.94 2 0.10 1 2 0.05
796 4.56 0.16 838 4.66 0.15 2 0.06 0.15 2 0.06
863 3.13 0.23 915 3.22 0.21 2 0.09 0.22 2 0.04
994 4.89 0.13 1010 5.1 0.12 2 0.08 0.13 2 0.00
The samples were firstly measured at room temperature and then heated up to 500 K in dark. Temperature-variable-Hall effect measurements were carried out from 500 to 90 K in dark. The Hall effect or simple resistivity measurements were conducted under continuous illumination at 90 K. We found no noticeable difference between the use of a torch or UV lights at the wavelength of 325 or 265 nm. After removal of illumination, the Hall effect measurements were performed as temperature rose from 90 to 500 K in dark. Typical results obtained at 300 and 90 K are shown in Table 1. For high quality GaN, the Hall mobility increases with a decrease of temperature and varies roughly as T 21 over a high temperature region due to suppression of polar phonon scattering (see Fig. 1(a) and (b)) [12]. At low temperatures, if the mobility is dominated by ionized impurity scattering, it varies approximately as T 1.5 [11]. The constant mobility at temperatures below 150 K (see Fig. 1(a) and (b)) indicates that the ionized impurity scattering in those high quality samples is not significant regardless of the fact that about 10 7– 10 cm 22 dislocations exist in GaN. Fig. 1(a) and (b) also shows that two traces of the Hall mobility versus the reciprocal temperature, measured when it was cooled down in dark or warmed up in dark after illumination, are quite similar. In fact, the samples with the Hall mobility at room temperature of . 150 cm 2/ sV all showed the similar Hall mobility dependence on temperature. For those samples, illumination at
90 K has little effect on the Hall mobility and electron density (see Table 1, Fig. 1(a) and (b)) By contrast, low-quality GaN, particularly for the samples with a Hall mobility less than ,100 cm 2/sV, shows a distinct Hall mobility dependence on temperature (see Fig. 1(c)). At temperatures below 250 K, the mobility decreases approximately as T 1.5. This clearly indicates that the ionized impurity scattering dominates the Hall mobility of low quality GaN. Furthermore, illumination at 90 K can lead to an increase of the Hall mobility by a factor of ,2 but no noticeable effect on the electron density was observed (see the sample a in Table 1). The illumination-induced increase of the Hall mobility can exist, persistently, after removal of illumination. The PPC effect, as indicated in Table 1 by a persistent decrease of resistivity after illumination at 90 K [ Rid 2 Rd =Rd ] was actually due to a persistent increase of the Hall mobility rather than the electron density. The lower the Hall mobility at room temperature, the stronger the PPC effect at low temperatures. Table 1 shows that when the room temperature Hall mobility decreases from 517 to 25 cm 2/sV, the persistent decrease of resistivity after illumination at 90 K increases from almost 0 to 16% at 90 K. Thus, the PPC effect is related to the Hall mobility in undoped GaN. The presence of the PPC effect also leads to two different traces of the Hall mobility versus the reciprocal temperature obtained in dark before and after illumination (see Fig. 1(c)).
G. Li et al. / Solid State Communications 111 (1999) 659–663
Fig. 1. The Hall mobility as a function of reciprocal temperature. (Solid dots: obtained when the sample was warmed up in dark after removal of illumination and open dots obtained when the sample was cooled down in dark. (a), (b) and (c) were obtained using the samples a, d and g in Table 1, respectively. Solid lines are curves plotted as various functions of temperature.)
In this work, the Hall mobility of GaN was improved by optimizing growth conditions for GaNbuffer layers. A significant difference in the amount of unintentionally introduced dopants like Si and C should not be expected and used to explain a wide variation of the Hall mobility between the samples. Note that all the samples have comparable electron densities. The screening effect of ionized impurities by an increased density of free carriers, which has been used to explain the Hall mobility dependence on the electron density [2,7], is also not applicable in our case. The most likely candidate for the dominant ionized impurity scattering in low quality GaN is intrinsic electrically active defects. The increase of the Hall mobility is the result of those defects reduced
661
Fig. 2. Time dependence of (a) electron density, (b) the Hall mobility, and (c) and resistivity, measured in dark after removal of illumination at different temperatures. Fig. 2(c) was plotted after subtracting the resistivity measured in dark immediately after removal of illumination. The solid lines in Fig. 2(c) are fitting curves based on Eq. (1) in text. P: 300 K; K: 250 K; S: 165 K; W: 150 K; X: 125 K; A: 100 K; and B: 90 K.
by optimizing growth conditions for GaN buffer layers. The density function calculation reveals that common threading screw and edge dislocations in GaN are electrically inactive [13]. It is expected to have no deep defect states in the band gap and without impurity segregation, pure edge dislocation would not act as non-radiative combination center [14]. On the contrary, many reports have shown that the YL emission is related to edge dislocation lines [15], and dislocations are non-radiative recombination centers [16,17]. Recently, it was reported that dislocations are actually charged and play a dominant
662
G. Li et al. / Solid State Communications 111 (1999) 659–663
role in determination of the Hall mobility in n-type GaN [2,7]. Our optimization of growth conditions for GaN buffer layers may have led to a significant reduction of dislocations in GaN but unlikely the amount of point defects which are incorporated during epitaxial growth of GaN. Therefore, we believe that point defects should not play a crucial role by their own. The dislocations become charged when point defects are trapped and filled by electrons [2,7]. Only these charged dislocation-point defect complexes act as strong Coulomb scattering centers in GaN, and consequently limit the Hall mobility. The PPC effect further indicates that those defect complexes possess metastable status. In the DX model, the difference in lattice relaxation between two states gives rise to a barrier that prevents recapture of electrons into stable deep states [18,19]. Since the temperature variation or illumination at low temperatures does not affect the electron density of GaN, applicability of the DX model to the PPC effect in GaN is questionable. The point defects trapped by dislocations are initially neutral before they become negatively charged after capturing electrons [2,7]. So illumination excites electrons from charged defect complexes. This eventually reduces Coulomb scattering effect or leads to an increase of the Hall mobility. After removal of illumination, the Hall mobility may recover to what it was before illumination as the result of recapturing electrons into illumination-neutralized defect complexes. The sample A in Table 1 was chosen to investigate recapturing process. Fig. 2(a) and (b) show that there is no transient change of the electron density, while at low temperatures, the Hall mobility gradually decreases after removal of illumination until it approaches a constant value. This constant Hall mobility is always higher than that obtained before the illumination. As have been discussed above, recovering of the Hall mobility in Fig. 2(b) represents recapturing process of excited electrons into illuminationneutralized defect complexes. The transient change in the Hall mobility implies the presence of a potential barrier preventing recapturing process. Comparing with the Hall effect measurements, resistivity can be very quickly measured within one second. Hence for an almost constant electron density, a transient change of the Hall mobility can be revealed in detail by monitoring a transient change
of resistivity after removal of illumination. The results are shown in Fig. 2(c) and further analyzed according to a stretched exponential model, which has been widely used for relaxation process induced by PPC effect in GaN and others [20]: R t Rid 1 2 exp 2 t=tb 2 Ri ;
1
where Rid is the constant resistivity in dark after removal of illumination, Ri is resistivity measured in dark immediately after removal of illumination, b is deviation from a single exponential decay, and t is the time constant of recapturing process. Using Eq. (1), the best fitting curves are also shown in Fig. 2(c) using solid lines. We found that at different temperatures, b is almost constant at 0.5. The time constant (t ) varies from 120 to 30 s when temperature rises from 90 to 300 K. The potential barrier for recapturing excited electrons, derived using the Arrhenius plot of the time constant versus the reciprocal temperature is 13.3 meV. In conclusion, the Hall mobility is related to the PPC effect through charged dislocation–point defect complexes. The presence of those charged defect complexes limits the Hall mobility and induces the PPC effect in undoped GaN. The PPC effect is further revealed as the result of a persistent increase of the Hall mobility rather than the electron density after illumination at low temperatures. The potential barrier preventing recapture of excited electrons into illumination-neutralized defect complexes is about 13.3 meV. A reduced density of dislocations through optimizing growth conditions of GaN buffer layers can effectively increase the Hall mobility and weaken PPC effect of undoped GaN.
References [1] W. Go¨tz, L.T. Romano, J. Walker, N.M. Johnson, R.J. Molnar, Appl. Phys. Lett. 71 (1997) 1214. [2] H.M. Ng, D. Doppalapudi, T.D. Moustakas, N.G. Weimann, L.F. Eastman, Appl. Phys. Lett. 73 (1998) 821. [3] S. Nakamura, Y. Harada, M. Seno, Appl. Phys. Lett. 58 (1991) 2021. [4] T. Kachi, K. Tomita, K. Itoh, H. Tadano, Appl. Phys. Lett. 72 (1998) 704. [5] E. Oh, H. Park, Y. Part, Appl. Phys. Lett. 72 (1998) 1848. [6] J.W. Orton, C.T. Foxon, Semicond. Sci. Technol. 13 (1998) 31.
G. Li et al. / Solid State Communications 111 (1999) 659–663 [7] N.G. Weimann, L.F. Eastman, D. Doppalapudi, H.M. Ng, T.D. Moustakes, J. Appl. Phys. 83 (1998) 3656. [8] E.F. Schubert, I.D. Goepfert, J.M. Redwing, Appl. Phys. Lett. 71 (1997) 3224. [9] H.M. Chen, Y.F. Chen, M.C. Lee, M.S. Feng, J. Appl. Phys. 82 (1997) 899. [10] C.V. Reddy, K. Balakrishnan, H. Okumura, S. Yoshida, Appl. Phys. Lett. 73 (1998) 244. [11] G. Li, S.J. Chua, S.J. Xu, W. Wang, P. Li, B. Beaumont, P. Gibart, in press. [12] D.A. Anderson, N. Apsley, Semicon. Sci. Technol. 1 (1986) 187. [13] J. Elsner, R. Jones, P.K. Sitch, V.D. Porezag, M. Elstner, Th. ¨ berg, P.R. Briddon, Phys. Rev. Frauenheim, M.I. Heggie, S. O Lett. 79 (1997) 3672.
663
[14] Y. Xin, S.J. Pennycook, N.D. Browning, P.D. Nellist, S. Sivananthan, F. Omne`s, B. Beaumont, J.P. Faurie, P. Gibart, Appl. Phys. Lett. 72 (1997) 2680. [15] F.A. Ponce, D.P. Bour, W. Go¨tz, P.J. Wright, Appl. Phys. Lett. 68 (1996) 57. [16] S.J. Rosner, E.C. Carr, M.J. Ludowise, G. Girolami, H.I. Erikson, Appl. Phys. Lett. 70 (1997) 420. [17] T. Sugapara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L.T. Romano, S. Sakai, Jpn J. Appl. Phys. 37 (1998) L398. [18] D.V. Lang, R.A. Logan, Phys. Rev. Lett. 39 (1977) 635. [19] D.J. Chadi, K.J. Chang, Phys. Rev. Lett. 61 (1988) 873. [20] G. Beadie, W.S. Rabinovich, A.E. Wickenden, D.D. Koleske, S.C. Binari, J.A. Freitas Jr, Appl. Phys. Let. 71 (1997) 1092.
Solid State Communications 111 (1999) 659–663
The Hall mobility and its relationship to the persistent photoconductivity of undoped GaN G. Li*, S.J. Chua, W. Wang Institute of Materials Research and Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 25 February 1999; accepted 16 April 1999 by Z.Z. Gan
Abstract Temperature-variable Hall effect measurements have been used to investigate the electrical properties of undoped GaN, which has electron densities in the order of mid-10 16 cm 23 and the Hall mobility varying from , 50 cm 2/sV to . 500 cm 2/sV. We found that very strong ionized impurity scattering limits the Hall mobility of GaN. Illumination even at 77 K has very little effect on the electron density but can lead to a noticeable persistent increase of the Hall mobility. The induced persistent photoconductivity (PPC) effect is, therefore, related to the Hall mobility through intrinsic electrically active defects. The properties of those defects were further investigated by monitoring the transient change of resistivity after removal of illumination at different temperatures. We have found that the recapturing process of excited electrons into illumination-neutralized defects is the mechanism responsible for the PPC effect of undoped GaN. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; C. Dislocations and disclinations; C. Point defects; D. Photoconductivity and photovoltaics; D. Hall effect
The Hall effect measurements have been widely used to characterize electrical properties of undoped and doped GaN [1,2]. The Hall mobility is indicative of electrical quality of undoped GaN in optimization of growth conditions [3,4]. Although a number of models have been proposed to explain anomalous behavior of the Hall mobility dependency on the electron density [5–7], the mechanism which dominates the Hall mobility of undoped GaN still remains unclear. The yellow-band luminescence (YL) and persistent photoconductivity (PPC) have also been observed and extensively investigated in undoped and doped GaN [8,9]. A recent report claimed that PPC and YL in GaN are related each other through defects associated with a broad deep level [10]. The origins of YL and PPC are still in debate [8–11]. In this * Corresponding author. E-mail address: [email protected] (G. Li)
work, a variety of undoped GaN with electron densities in order of mid-10 16 cm 23 and the Hall mobility varying from , 50 to . 500 cm 2/sV at room temperature were investigated using temperature variable Hall effect measurements. It was aimed to understand better what limits the Hall mobility of undoped GaN as well as its relationship with the PPC effect. Undoped GaN samples were grown on (0001) oriented sapphire by metal organic vapor phase epitaxy (MOVPE). Trimethylgallium (TMGa) and NH3 were used as the precursors. The carrier gas was H2. Growth conditions for undoped 3 mm thick GaN were fixed, while growth parameters used for GaN buffer layers were widely changed to have those different undoped GaN samples. Temperaturevariable Hall effect measurements were carried out using a BIO-RAD Hall effect system over a temperature range of 90–500 K. The samples were in van der Pauw geometry using In dots as ohmic contacts.
0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00252-5
660
G. Li et al. / Solid State Communications 111 (1999) 659–663
Table 1 Typical results of undoped GaN obtained using Hall effect measurements at 300 and 90 K. m , n, and R are the Hall mobility, electron density, and resistivity, respectively. The subscript d and i represent measurements carried out in dark, in dark immediately after removal of illumination. Rid was a constant value obtained in dark after removal of illumination Sample 300 K m d (cm 2/sV) nd (10 16 cm 23) 90 K m d (cm 2/sV) nd (10 16 cm 23) Rd (V cm) m i (cm 2/sV) ni (10 16 cm 23) Ri (V cm) Ri 2 Rd =Rd Rid(V cm) Rid 2 Rd =Rd
a
b
25 4 11.4 2.93 18.6 20 3.04 10.1 2 0.46 15.7 2 0.16
c
d
e
f
g
64.7 3.25
124 3.15
175 4.74
377 7.77
401 5.07
517 7.24
57.4 2.28 4.78 67.7 2.44 3.78 2 0.21 4.32 2 0.12
183 1.68 2.03 215 1.7 1.7 2 0.16 1.85 2 0.09
232 2.68 1.05 238 2.78 0.94 2 0.10 1 2 0.05
796 4.56 0.16 838 4.66 0.15 2 0.06 0.15 2 0.06
863 3.13 0.23 915 3.22 0.21 2 0.09 0.22 2 0.04
994 4.89 0.13 1010 5.1 0.12 2 0.08 0.13 2 0.00
The samples were firstly measured at room temperature and then heated up to 500 K in dark. Temperature-variable-Hall effect measurements were carried out from 500 to 90 K in dark. The Hall effect or simple resistivity measurements were conducted under continuous illumination at 90 K. We found no noticeable difference between the use of a torch or UV lights at the wavelength of 325 or 265 nm. After removal of illumination, the Hall effect measurements were performed as temperature rose from 90 to 500 K in dark. Typical results obtained at 300 and 90 K are shown in Table 1. For high quality GaN, the Hall mobility increases with a decrease of temperature and varies roughly as T 21 over a high temperature region due to suppression of polar phonon scattering (see Fig. 1(a) and (b)) [12]. At low temperatures, if the mobility is dominated by ionized impurity scattering, it varies approximately as T 1.5 [11]. The constant mobility at temperatures below 150 K (see Fig. 1(a) and (b)) indicates that the ionized impurity scattering in those high quality samples is not significant regardless of the fact that about 10 7– 10 cm 22 dislocations exist in GaN. Fig. 1(a) and (b) also shows that two traces of the Hall mobility versus the reciprocal temperature, measured when it was cooled down in dark or warmed up in dark after illumination, are quite similar. In fact, the samples with the Hall mobility at room temperature of . 150 cm 2/ sV all showed the similar Hall mobility dependence on temperature. For those samples, illumination at
90 K has little effect on the Hall mobility and electron density (see Table 1, Fig. 1(a) and (b)) By contrast, low-quality GaN, particularly for the samples with a Hall mobility less than ,100 cm 2/sV, shows a distinct Hall mobility dependence on temperature (see Fig. 1(c)). At temperatures below 250 K, the mobility decreases approximately as T 1.5. This clearly indicates that the ionized impurity scattering dominates the Hall mobility of low quality GaN. Furthermore, illumination at 90 K can lead to an increase of the Hall mobility by a factor of ,2 but no noticeable effect on the electron density was observed (see the sample a in Table 1). The illumination-induced increase of the Hall mobility can exist, persistently, after removal of illumination. The PPC effect, as indicated in Table 1 by a persistent decrease of resistivity after illumination at 90 K [ Rid 2 Rd =Rd ] was actually due to a persistent increase of the Hall mobility rather than the electron density. The lower the Hall mobility at room temperature, the stronger the PPC effect at low temperatures. Table 1 shows that when the room temperature Hall mobility decreases from 517 to 25 cm 2/sV, the persistent decrease of resistivity after illumination at 90 K increases from almost 0 to 16% at 90 K. Thus, the PPC effect is related to the Hall mobility in undoped GaN. The presence of the PPC effect also leads to two different traces of the Hall mobility versus the reciprocal temperature obtained in dark before and after illumination (see Fig. 1(c)).
G. Li et al. / Solid State Communications 111 (1999) 659–663
Fig. 1. The Hall mobility as a function of reciprocal temperature. (Solid dots: obtained when the sample was warmed up in dark after removal of illumination and open dots obtained when the sample was cooled down in dark. (a), (b) and (c) were obtained using the samples a, d and g in Table 1, respectively. Solid lines are curves plotted as various functions of temperature.)
In this work, the Hall mobility of GaN was improved by optimizing growth conditions for GaNbuffer layers. A significant difference in the amount of unintentionally introduced dopants like Si and C should not be expected and used to explain a wide variation of the Hall mobility between the samples. Note that all the samples have comparable electron densities. The screening effect of ionized impurities by an increased density of free carriers, which has been used to explain the Hall mobility dependence on the electron density [2,7], is also not applicable in our case. The most likely candidate for the dominant ionized impurity scattering in low quality GaN is intrinsic electrically active defects. The increase of the Hall mobility is the result of those defects reduced
661
Fig. 2. Time dependence of (a) electron density, (b) the Hall mobility, and (c) and resistivity, measured in dark after removal of illumination at different temperatures. Fig. 2(c) was plotted after subtracting the resistivity measured in dark immediately after removal of illumination. The solid lines in Fig. 2(c) are fitting curves based on Eq. (1) in text. P: 300 K; K: 250 K; S: 165 K; W: 150 K; X: 125 K; A: 100 K; and B: 90 K.
by optimizing growth conditions for GaN buffer layers. The density function calculation reveals that common threading screw and edge dislocations in GaN are electrically inactive [13]. It is expected to have no deep defect states in the band gap and without impurity segregation, pure edge dislocation would not act as non-radiative combination center [14]. On the contrary, many reports have shown that the YL emission is related to edge dislocation lines [15], and dislocations are non-radiative recombination centers [16,17]. Recently, it was reported that dislocations are actually charged and play a dominant
662
G. Li et al. / Solid State Communications 111 (1999) 659–663
role in determination of the Hall mobility in n-type GaN [2,7]. Our optimization of growth conditions for GaN buffer layers may have led to a significant reduction of dislocations in GaN but unlikely the amount of point defects which are incorporated during epitaxial growth of GaN. Therefore, we believe that point defects should not play a crucial role by their own. The dislocations become charged when point defects are trapped and filled by electrons [2,7]. Only these charged dislocation-point defect complexes act as strong Coulomb scattering centers in GaN, and consequently limit the Hall mobility. The PPC effect further indicates that those defect complexes possess metastable status. In the DX model, the difference in lattice relaxation between two states gives rise to a barrier that prevents recapture of electrons into stable deep states [18,19]. Since the temperature variation or illumination at low temperatures does not affect the electron density of GaN, applicability of the DX model to the PPC effect in GaN is questionable. The point defects trapped by dislocations are initially neutral before they become negatively charged after capturing electrons [2,7]. So illumination excites electrons from charged defect complexes. This eventually reduces Coulomb scattering effect or leads to an increase of the Hall mobility. After removal of illumination, the Hall mobility may recover to what it was before illumination as the result of recapturing electrons into illumination-neutralized defect complexes. The sample A in Table 1 was chosen to investigate recapturing process. Fig. 2(a) and (b) show that there is no transient change of the electron density, while at low temperatures, the Hall mobility gradually decreases after removal of illumination until it approaches a constant value. This constant Hall mobility is always higher than that obtained before the illumination. As have been discussed above, recovering of the Hall mobility in Fig. 2(b) represents recapturing process of excited electrons into illuminationneutralized defect complexes. The transient change in the Hall mobility implies the presence of a potential barrier preventing recapturing process. Comparing with the Hall effect measurements, resistivity can be very quickly measured within one second. Hence for an almost constant electron density, a transient change of the Hall mobility can be revealed in detail by monitoring a transient change
of resistivity after removal of illumination. The results are shown in Fig. 2(c) and further analyzed according to a stretched exponential model, which has been widely used for relaxation process induced by PPC effect in GaN and others [20]: R t Rid 1 2 exp 2 t=tb 2 Ri ;
1
where Rid is the constant resistivity in dark after removal of illumination, Ri is resistivity measured in dark immediately after removal of illumination, b is deviation from a single exponential decay, and t is the time constant of recapturing process. Using Eq. (1), the best fitting curves are also shown in Fig. 2(c) using solid lines. We found that at different temperatures, b is almost constant at 0.5. The time constant (t ) varies from 120 to 30 s when temperature rises from 90 to 300 K. The potential barrier for recapturing excited electrons, derived using the Arrhenius plot of the time constant versus the reciprocal temperature is 13.3 meV. In conclusion, the Hall mobility is related to the PPC effect through charged dislocation–point defect complexes. The presence of those charged defect complexes limits the Hall mobility and induces the PPC effect in undoped GaN. The PPC effect is further revealed as the result of a persistent increase of the Hall mobility rather than the electron density after illumination at low temperatures. The potential barrier preventing recapture of excited electrons into illumination-neutralized defect complexes is about 13.3 meV. A reduced density of dislocations through optimizing growth conditions of GaN buffer layers can effectively increase the Hall mobility and weaken PPC effect of undoped GaN.
References [1] W. Go¨tz, L.T. Romano, J. Walker, N.M. Johnson, R.J. Molnar, Appl. Phys. Lett. 71 (1997) 1214. [2] H.M. Ng, D. Doppalapudi, T.D. Moustakas, N.G. Weimann, L.F. Eastman, Appl. Phys. Lett. 73 (1998) 821. [3] S. Nakamura, Y. Harada, M. Seno, Appl. Phys. Lett. 58 (1991) 2021. [4] T. Kachi, K. Tomita, K. Itoh, H. Tadano, Appl. Phys. Lett. 72 (1998) 704. [5] E. Oh, H. Park, Y. Part, Appl. Phys. Lett. 72 (1998) 1848. [6] J.W. Orton, C.T. Foxon, Semicond. Sci. Technol. 13 (1998) 31.
G. Li et al. / Solid State Communications 111 (1999) 659–663 [7] N.G. Weimann, L.F. Eastman, D. Doppalapudi, H.M. Ng, T.D. Moustakes, J. Appl. Phys. 83 (1998) 3656. [8] E.F. Schubert, I.D. Goepfert, J.M. Redwing, Appl. Phys. Lett. 71 (1997) 3224. [9] H.M. Chen, Y.F. Chen, M.C. Lee, M.S. Feng, J. Appl. Phys. 82 (1997) 899. [10] C.V. Reddy, K. Balakrishnan, H. Okumura, S. Yoshida, Appl. Phys. Lett. 73 (1998) 244. [11] G. Li, S.J. Chua, S.J. Xu, W. Wang, P. Li, B. Beaumont, P. Gibart, in press. [12] D.A. Anderson, N. Apsley, Semicon. Sci. Technol. 1 (1986) 187. [13] J. Elsner, R. Jones, P.K. Sitch, V.D. Porezag, M. Elstner, Th. ¨ berg, P.R. Briddon, Phys. Rev. Frauenheim, M.I. Heggie, S. O Lett. 79 (1997) 3672.
663
[14] Y. Xin, S.J. Pennycook, N.D. Browning, P.D. Nellist, S. Sivananthan, F. Omne`s, B. Beaumont, J.P. Faurie, P. Gibart, Appl. Phys. Lett. 72 (1997) 2680. [15] F.A. Ponce, D.P. Bour, W. Go¨tz, P.J. Wright, Appl. Phys. Lett. 68 (1996) 57. [16] S.J. Rosner, E.C. Carr, M.J. Ludowise, G. Girolami, H.I. Erikson, Appl. Phys. Lett. 70 (1997) 420. [17] T. Sugapara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L.T. Romano, S. Sakai, Jpn J. Appl. Phys. 37 (1998) L398. [18] D.V. Lang, R.A. Logan, Phys. Rev. Lett. 39 (1977) 635. [19] D.J. Chadi, K.J. Chang, Phys. Rev. Lett. 61 (1988) 873. [20] G. Beadie, W.S. Rabinovich, A.E. Wickenden, D.D. Koleske, S.C. Binari, J.A. Freitas Jr, Appl. Phys. Let. 71 (1997) 1092.