Role of free electrons in phosphorescence in n-type wide bandgap semiconductors

H. G. Ye ab, Z. C. Su a, F. Tang a, G. D. Chen b, Jian Wang a, Ke Xu c and S. J. Xu *a
aDepartment of Physics, and Shenzhen Institute of Research and Innovation (HKU-SIRI), The University of Hong Kong, Pokfulam Road, Hong Kong, China. E-mail:
bDepartment of Applied Physics, Xi’an Jiaotong University, Xi’an, 710049, China
cSuzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences, Suzhou, 215123, China

Received 24th August 2017 , Accepted 16th October 2017

First published on 16th October 2017

Long persistent phosphorescence is generally known as a phenomenon involving carrier traps induced by defects or impurities in crystals. In this paper, phosphorescence sustained for tens of minutes was found in intentionally undoped ZnO and it was proposed to be a universal phenomenon in wide bandgap semiconductors upon satisfying several conditions. A new model was built to understand this attractive phenomenon within the framework of the traditional trapping–detrapping model but it was modified by considering the free electrons in the conduction band as a significant contributor to the long persistent phosphorescence besides the electrons trapped by shallow donors. This model, explicitly expressed as I(t) ∝ [1 + M(1 − Feγt)−2]eγt, is not only capable of giving a quantitative description of the non-exponential decay of phosphorescence in a wide temperature range but also enables one to determine the depth of shallow donors in semiconductors. The participation of free electrons in phosphorescence was further confirmed by another carefully designed experiment. Thus, this study may represent significant progress in understanding phosphorescence.


Phosphorescence is a striking and fundamental photoluminescence (PL) phenomenon which is caused by the absorption of radiation (e.g., light) and continues for a noticeable time after switching off the optical excitation source. Besides some natural minerals,1–3 phosphorescent materials, such as copper doped ZnS and rare earth ion activated strontium aluminate,4–8 have been successfully synthesized, and widely applied in the fields of decoration, safety displays, life sciences, biomedicine, energy and environmental engineering.9–13 Phosphorescence with a lifetime on the order of milliseconds commonly originates from a “forbidden” transition in the quantum mechanism, such as a triplet-to-singlet transition. Long persistent phosphorescence is the afterglow maintained for minutes or longer after the excitation radiation source is turned off. For the long persistent phosphorescence, a trapping–detrapping (TD) model has been well established to understand it.14–17 In the TD model carriers are assumed to be stored in traps spatially separated from the luminescence center during irradiation, and then are gradually released to the luminescence center after the end of excitation. This model predicts an exponential or power-law decay tendency, namely the first- or second-order dynamics, depending on whether a re-trapping process is taken into account or not.

In technologically important semiconductors such as GaAs and GaN, phosphorescence on the millisecond scale is also often observed,18–20 but long persistent phosphorescence on the minute or even longer scale has seldom been reported. In our recent work green luminescence in an intentionally undoped ZnO bulk crystal was found to exhibit a long persistent afterglow for tens of minutes after switching off a below-band-gap optical excitation source.21 Since attention in the previous work was focused on the fine structures of green luminescence, the mechanism of long persistent phosphorescence has not yet been elucidated. The green phosphorescence (GP) in ZnO exhibits three striking features: (i) it occurs in a high quality crystal which was not intentionally doped; (ii) the GP signal shows a non-exponential decay behavior which follows neither the first- nor the second-order solution of the standard TD model; (iii) the emission intensity and lifetime depend abnormally on the temperature. All these outstanding behaviors challenge our present understanding of phosphorescence, such as the TD model. In this paper, we present an in-depth experimental investigation of the long persistent phosphorescence in ZnO. A plausible new model was developed for understanding the phenomenon and, furthermore, the phenomenon and mechanism were predicted and verified in GaN to be universal in wide bandgap semiconductors. In contrast to the traditional TD model, the new model addresses the significant contribution of free electrons in the conduction band in addition to the trapped electrons by shallow donors. It is capable of giving a quantitative interpretation to the non-exponential temporal behaviors of phosphorescence in a wide temperature range. Therefore, this study represents a significant step towards understanding phosphorescence. In addition, it may provide a technical method for optically examining shallow defects in semiconductors.

Experimental details

The ZnO sample studied in the present work was a ∼3 cm long single crystal rod grown using a hydrothermal approach,21 while the GaN samples were a free-standing bulk epilayer (∼300 μm thick) grown using the hydride vapour phase epitaxy (HVPE) method.22 The samples were mounted with silver paint on the cold finger of a Janis closed cycle cryostat, whose temperature was controlled by a Lakeshore temperature controller. Thermoluminescence (TL) signals of the samples were also measured using the cryostat. Both the PL and TL signals were registered with a home-assembled PL system composed of an Acton monochromator with a focal length of 30 cm and a Hamamatsu R928 photomultiplier detector. The excitation light source was an ultraviolet light-emitting diode with a center wavelength of 385 nm and full width at half maximum of 10 nm. Before detecting the decay curve, the continuous-wave optical excitation was kept for 3 min to get a steady-state PL. Measurement of the decay curve was then initiated by opening the shutter of the detector immediately after switching off the optical excitation source.

Results and discussion

As shown in Fig. 1, the characteristic green emission of the ZnO bulk rod sample exhibits long persistent afterglow for hundreds of seconds after the end of the below-band-gap light excitation at temperatures ≤100 K. When the temperature is beyond 100 K, the GP signal becomes unobservable. Meanwhile, a yellow phosphorescence (YP) signal appears at temperatures from 110 to 180 K. All of the data in Fig. 1 were measured under the same conditions except for the temperature variation, so that the signal intensities are meaningful for comparative analysis. Both the GP and YP signals display obviously non-exponential declining tendencies. Furthermore, the declining tendencies show high sensitivity to the temperature change. For example, when the temperature is increased from 10 K to 70 K, the green afterglow becomes brighter and simultaneously continues for a longer time. However, when the temperature is beyond 80 K, the GP signal quenches faster. The strongest GP signal (justified by its integrated intensity) appears at about 70 K. Likewise, the YP signal exhibits an evolution tendency with the increase in temperature from 110 K to 180 K. A difference is that its temperature-induced enhancement process seems very short.
image file: c7cp05796b-f1.tif
Fig. 1 Decay curves (dotted lines) of the phosphorescence signal in ZnO measured at different temperatures. The detection wavelength was 510 nm for upper row figures, while 580 nm for bottom row figures. The solid lines represent the fitting curves with eqn (8). The insets are photographs of the green and yellow afterglow of the ZnO sample.

Fig. 2(a) and (b) show the GP and YP spectra (colorful solid lines) measured at 80 K and 140 K for different decay times, respectively. The steady-state PL spectra (black solid lines) of the ZnO sample at 80 K and 140 K are also illustrated in the figure for comparison. Both GP and YP spectra are broad, and they peak at 510 and 572 nm, respectively. The peak centers are unchanged throughout the whole decay duration. This indicates that the long persistent phosphorescence is not from the recombination of the donor–acceptor pair with different separation distances, which was suggested to be the mechanism of phosphorescence in GaN.23,24 It is interesting to note that the yellow luminescence is observed as phosphorescence only after ceasing the optical excitation regardless of temperature. This is in sharp contrast to the case of GP, i.e., the steady-state PL signal always displays a green color. A possible origin of the YP phosphorescence is schematically shown in the inset in Fig. 2(a), which will be discussed later.

image file: c7cp05796b-f2.tif
Fig. 2 Optical spectra of the phosphorescence measured at 80 K (a) and 140 K (b), respectively, for different delay times. The dashed lines represent two fitting curves with the MBO model for a Huang–Rhys factor of 6.5 and 10, respectively. The black curves are the steady-state luminescence spectra measured at 80 K and 140 K, respectively. The inset in (a) shows a configurational coordinator diagram in which the two downward arrows indicate possible optical transitions for the GP and YP phosphorescence.

To verify if carrier trapping occurs in the ZnO sample, TL signals of the sample were obtained by setting a 510 nm detection wavelength for several starting temperatures such as 10, 40, 70 and 100 K. Before heating the sample, we waited for 10 mins or longer time to ensure that the PL afterglow had already disappeared. As shown in Fig. 3, two well-resolved peaks appear at about 100 and 150 K, respectively. Corresponding to the two TL peaks, respectively, the sample displays green and yellow colors, well matched with the GP and YP phosphorescence below and above 100 K. It can be thus concluded that carrier trapping indeed occurs in the sample, and there are two individual trapping levels with different energy depths. Since the intentionally undoped ZnO always exhibits n-type conductivity, the trapped carriers involved within phosphorescence have to be electrons. The first TL peak reaches its strongest intensity for the starting temperature of 70 K. This is because the GP signal attenuates slowly at this temperature, as evidenced in Fig. 1. A weak afterglow remained even though we had waited for 40 (pink curve) and 50 (blue curve) mins before heating up. The second TL peak in Fig. 3 is almost independent of the starting temperature. This implies that the second electron trapping level associated with the YP is much deeper.

image file: c7cp05796b-f3.tif
Fig. 3 TL glow curves registered at different starting temperatures for different waiting times before heating up the sample. The rate of temperature increase was ∼27 K min−1.

Because of the involvement of the trapped electrons, we shall understand the long persistent phosphorescence within the framework of the traditional TD model. Nevertheless, two significant modifications will have to be adopted for giving a self-consistent explanation to the observed time and temperature signatures of the GP and YP phosphorescence. Firstly, the trapping centers are assumed to be the thermally activated shallow donors, being capable of capturing electrons from the conduction band under optical excitation and reversely releasing electrons to the conduction band after ceasing the optical excitation. Under such reasonable assumptions, the concentration of the effective trapping centers increases with the increase intemperature. This is different from the case of rare-earth ion doped aluminate for which the concentration of the trapping centers is a constant. On the other hand, the electron releasing rate of the trapping centers becomes larger at higher temperatures. The former mechanism can lead to an enhancement of the integrated phosphorescence intensity at higher temperatures, while the latter can produce a faster attenuation of the phosphorescence signal with time at higher temperatures. In fact, such mechanisms can be evidently seen in Fig. 1, especially for the GP whose intensity shows a significant increase first, and then exhibits a fast quenching with increasing temperature. Secondly, we assume that a thermal equilibrium between the conduction band and the shallow donors can be easily achieved so that the electron distribution crossing both states follows the Fermi–Dirac distribution function. This assumption implies that the free electron concentration in the conduction band always changes correspondingly with trapping and detrapping of electrons in the shallow donors. In other words, the free electrons in the conduction band can make a significant contribution to the phosphorescence. This is a natural extension to the traditional TD model and is responsible for the non-exponential decay patterns shown in Fig. 1.

For simplifying but not losing generality, one kind of shallow donor with a concentration of ND is taken into account for constructing a theoretical model. The density of effective states at the conduction band minimum is assumed to be NC. The conduction band together with the shallow donor state is treated as a coupling two-level subsystem. Under the thermal equilibrium conditions the number of electrons in the conduction band is equal to the number of activated shallow donors, formulated as

ND(1 − fD) = NCfC,(1)
where fC and fD are the population probabilities described by the Fermi–Dirac distribution function. So we have the following relationship:
image file: c7cp05796b-t1.tif(2)
Here ΔE is the energy separation between the conduction band minimum and the shallow donor level. For conciseness in later expressions the exponential term is denoted by K, i.e. K = exp(−ΔE/kBT), and eqn (2) can be rewritten as
fC = KfD/[1 − (1 − K)fD].(3)

By substituting it into eqn (1), the concentrations of the activated and inactivated shallow donors at different temperatures can be obtained.

Under the continuous below-band-gap excitation, a new quasi-thermal equilibrium state may be built. Since it is a below-band-gap excitation, the valence band is undisturbed. Additional electrons are pumped from the localized state (deep level) into the subsystem composed of the conduction band and shallow donors. The distribution of electrons is considered to still follow the Fermi–Dirac distribution. That is

ND(1 − fD′) + Ne = NCfC′,(4)
where Ne represents the excess concentration of electrons excited by optical excitation, fC′ and fD′ are the new Fermi–Dirac probabilities which are still correlated by eqn (3). By solving eqn (4), the excess electrons in the conduction band and those trapped by the shallow donors are derived as ΔnC = NC(fC′ − fC) and ΔnD = ND(fD′ − fD), respectively, and ΔnC + ΔnD = Ne.

When the excitation is switched off suddenly, the system will return from the new quasi-thermal equilibrium state to the original thermal equilibrium state. For the slow phosphorescence, it is very reasonable for one to assume that the subsystem can be always described by the Fermi–Dirac distribution function. The speed of the decay process is controlled by the thermal activation of shallow donors, which can be assumed as

nD(t) = n0D + ΔnD[thin space (1/6-em)]exp(−γt)(5)
where n0D stands for the initial shallow donors holding electrons, and γ is the thermal activation rate of the shallow donors. The instantaneous concentration of electrons in the conduction band nC(t) can be derived viaeqn (3). It is
image file: c7cp05796b-t2.tif(6)

Ignoring the time consumption for charge transfer in the conduction band and recombination in the luminescence center, the intensity of light emission is proportional to the reduction rate of the electrons from both the conduction band and shallow donors.

image file: c7cp05796b-t3.tif(7)

Substituting eqn (5) and (6) into (7) yields

image file: c7cp05796b-t4.tif(8)

Here F = ΔnD/[ND/(1 − K) − n0D] may be termed as the filling factor with a value of 0 < F < 1, approximately representing the ratio of re-occupancy of the thermally activated shallow donors under the continuous optical excitation. M = NCNDK/[ND − (1 − K)n0D]2 is a comprehensive parameter depending on the concentration and depth of the shallow donors, as well as the temperature. It is easy for one to draw a conclusion that eqn (8) will reduce to a single exponential decay function for M = 0, just the so-called “first-order” solution of the traditional TD model. Actually, this approximation can be well justified for the conditions with a large ΔE, since K = exp(−ΔE/kBT) approaches zero for a large enough ΔE. In fact, this is a satisfactory condition in insulating materials with large bandgaps. Nevertheless, when the shallow donors are treated as the trapping centers, this term cannot be ignored.

Obviously, eqn (8) contains two terms: the first represents a standard single exponential process as predicted by the TD model, while the second conveys a fast decay process. As shown by the solid lines in Fig. 1, the temporal behaviors of both the GP and YP signals can be well interpreted with eqn (8) in the whole temperature range from 10 K to 180 K. A slight deviation in the temperature range from 90 K to 120 K is due to the overlap of the GP and YP signals in this temperature range. From the fitting results of eqn (8), the temperature dependence of γ, one can further obtain the trapping depth ΔE according to the relation γ(T) ∝ exp(−ΔE/kBT), where kB is the Boltzmann constant. ln(γ) shall be linearly dependent on 1/T for an actual ΔE. The results are depicted in Fig. 4. Two electron trapping depths of 85 meV and 290 meV, respectively, are determined for the GP and YP by fitting the linear part of the curves in Fig. 4. The deviation from linearity of the curves in Fig. 4 originates from the distribution of the shallow donors over energy, as schematically shown in the inset of Fig. 4, which is generally valid in real semiconductors. The electron trapping depth determined with such a method is an average depth of the activated shallow donors, which may vary with the temperature in a relatively low temperature range. In a number of theoretical and experimental studies, shallow donors with an activation energy of ∼85 meV are suggested to be responsible for the n-type electrical conductivity in ZnO.25–30 Regarding the deep donors located at ∼290 meV, they were also identified in ZnO by Von Wenckstern et al.31

image file: c7cp05796b-f4.tif
Fig. 4 Obtained γ values (solid circles) of GP (a) and YP (b) by fitting the measured decay curves with eqn (8). The solid lines are drawn just to guide the eye, while the dashed lines represent the linear fitting curves of the obtained γ values in certain temperature ranges. The insets illustrate schematic diagrams of the locations of shallow donors derived from the fitting.

As above-argued, a critical idea in the proposed model is to recognize the significant contribution of free electrons to the phosphorescence. To further test this idea, we conducted the following experiment for phosphorescence in ZnO. The temperature was quickly increased from 60 to 80 K or decreased from 60 to 4 K during the GP decay process. Relative to the normal decay curve at 60 K, as shown in Fig. 5, considerable enhancement of the GP signal is observed for both increase and decrease of the temperature. The former enhancement is easy to understand because the de-trapping rate of electrons from the shallow donors increases with increasing temperature. The latter enhancement induced by the temperature reduction is very attractive but seems somewhat difficult to understand. Actually, this unusual phenomenon can be exclusively understood with the model, taking into consideration the contribution of free electrons in the conduction band. With the rapid reduction of temperature, the equilibrium following the Fermi–Dirac distribution was broken and the conduction band became overfilled. Additional free electrons will have to drop from the conduction band to the luminescence center and result in the substantial enhancement of the GP signal. It is noteworthy that there is a short and slight weakening process before the rise of the GP signal when the temperature is suddenly increased from 60 K. That is because the equilibrium was also broken by a sudden increase in temperature; the electrons in the conduction band became insufficient and consequently less electrons took part in light emission. Therefore, this supplemental experiment provides firm demonstrating evidence for the important contribution of free electrons to the phosphorescence.

image file: c7cp05796b-f5.tif
Fig. 5 Normal decay curve (black solid lines) of the GP signal in ZnO measured at a constant temperature of 60 K, and disturbed decay traces (red solid lines) by quick temperature variations during the normal decay. The blue solid lines represent temperature variation curves recorded by the temperature controller.

Now we are in a position to give a short discussion on the luminescence spectra of the GP and YP signals. As shown in Fig. 2(a), the GP signal has the same luminescence spectrum as the steady-state green luminescence. It has been confirmed to be from a Cu ion luminescence center, experimentally and theoretically.32,33 Its broad spectrum with periodic fine structures can be well interpreted as phonon-assisted luminescence.21,34 The GP spectrum, as shown in Fig. 2(a), can be well reproduced by means of the multimode Brownian oscillator (MBO) model with a Huang–Rhys factor of 6.5. As for the YP phosphorescence and its spectrum, let us address a fact again. The YP phosphorescence was only observed after ceasing the excitation. Additionally, the YP spectrum seems to share the same zero-phonon line with the GP, and it can be reproduced approximately by using the MBO model by only changing the Huang–Rhys factor from 6.5 to 10. Therefore, we think that the YP stems from the same luminescence center as the GP but with a stronger electron–phonon coupling. The electron–phonon coupling strength might be largely altered by the ionization of the deeper trapping state at ∼290 meV, since such ionization can induce a considerable lattice relaxation around it. The relevant luminescence center is thus affected by the lattice relaxation. It is likely impossible for the YP to be from another type of luminescence center. Otherwise, it has to be simultaneously observed with the GP because the electrons released into the conduction band can be captured by both of them.

It is well known that the shallow-donor-induced n-type electrical conductivity and deep-center-induced visible emissions generally coexist in wide bandgap semiconductors such as ZnO and GaN. According to the model we proposed in the present study, phosphorescence shall be observed in all high-quality n-type semiconductors when excited by below-band-gap light. The requirement of high quality crystals stems from the fact that the non-radiative channels in a low quality sample might obliterate the trapped electrons. To verify the universality of this model, we employed an n-type and a high-resistance GaN sample. Indeed, a similar phosphorescence phenomenon was only observed in the n-type sample but not in the high-resistance sample. As shown in Fig. 6, the temperature dependence of the decay traces of the phosphorescence signal in GaN is completely consistent with that of ZnO. In the GaN case, the GP signal is observed at temperatures below 40 K. This implies that the donors in GaN are located at relatively shallower depths. Unlike the ZnO case, no succeeding yellow phosphorescence was observed in the GaN case at higher temperatures, and correspondingly only one TL peak was observed, suggesting the existence of only one kind of electron trapping center in the studied GaN sample.

image file: c7cp05796b-f6.tif
Fig. 6 (a and b) Decay curves of the visible emission band in an n-type GaN sample measured at temperatures from 10 and 40 K. (c) Steady-state PL spectrum of the GaN sample at 4 K. The visible region was enlarged by 20 fold. (d) TL signal of the GaN sample.


The phenomenon and mechanism of long persistent phosphorescence in ZnO and GaN semiconductors were investigated in this paper. A new analytical model was developed by addressing the significant contributions of free electrons in the conduction band of semiconductors besides the trapped electrons in shallow donors, which is able to quantitatively interpret the non-exponential decay patterns of the phosphorescence signal and abnormal temperature behaviors. This is an important step towards understanding long persistent phosphorescence. It may produce a long-term significant impact on phosphorescence science and technology due to the generalization of the model for quantitative interpretation of phosphorescence in high-quality n-type wide bandgap semiconductors, as well as technical application in the examination of shallow donors in semiconductors.

Conflicts of interest

There are no conflicts to declare.


This work was supported by a Hong Kong RGC-GRF Grant (Grant No. HKU 705812P), the National Natural Science Foundation of China (Grant No. 11374247, 11204231, 21373156), and HKU SRT on New Materials, as well as in part by HK-UGC AoE Grants (Grant No. AoE/P-03/08).


  1. E. N. Harvey, A History of Luminescence: From the Earliest Times until 1900, American Philosophical Society, Philadelphia, 1957 Search PubMed.
  2. B. Valeur and M. N. Berberan-Santos, J. Chem. Educ., 2011, 88, 731 CrossRef CAS.
  3. M. Lastusaari, T. Laamanen, M. Malkamäki, K. O. Eskola, A. Kotlov, S. Carlson, E. Welter, H. F. Brito, M. Bettinelli and H. Jungner, Eur. J. Mineral., 2012, 24, 885 CrossRef CAS.
  4. T. Matsuzawa, Y. Aoki, N. Takeuchi and Y. Murayama, J. Electrochem. Soc., 1996, 143, 2670 CrossRef CAS.
  5. W. Jia, H. Yuan, L. Lu, H. Liu and W. M. Yen, J. Lumin., 1998, 76, 424 CrossRef.
  6. H. Yamamoto and T. Matsuzawa, J. Lumin., 1997, 72, 287 CrossRef.
  7. T. Aitasalo, J. Hölsä, H. Jungner, M. Lastusaari and J. Niittykoski, J. Phys. Chem. B, 2006, 110, 4589 CrossRef CAS PubMed.
  8. T. Aitasalo, J. Hölsä, H. Jungner, M. Lastusaari and J. Niittykoski, J. Lumin., 2001, 94, 59 CrossRef.
  9. T. Maldiney, A. Lecointre, B. Viana, A. Bessiere, M. Bessodes, D. Gourier, C. Richard and D. Scherman, J. Am. Chem. Soc., 2011, 133, 11810 CrossRef CAS PubMed.
  10. H. Terraschke and C. Wickleder, Chem. Rev., 2015, 115, 11352 CrossRef CAS PubMed.
  11. L. Zhang, R. Zhang, P. Cui, W. Cao and F. Gao, Chem. Commun., 2013, 49, 8102 RSC.
  12. Y. Seino, H. Sasabe, Y.-J. Pu and J. Kido, Adv. Mater., 2014, 26, 1612 CrossRef CAS PubMed.
  13. R. Pang, Y. Jia, R. Zhao, H. Li, J. Fu, W. Sun, L. Jiang, S. Zhang, C. Li and Q. Su, Dalton Trans., 2014, 43, 9661 RSC.
  14. Y. Li, M. Gecevicius and J. Qiu, Chem. Soc. Rev., 2016, 45, 2090 RSC.
  15. W. M. Yen, S. Shionoya and H. Yamamoto, Practical Applications of Phosphors, CRC Press, 2006 Search PubMed.
  16. C. Furetta, Handbook of Thermoluminescence, World Scientific, 2010 Search PubMed.
  17. S. W. S. McKeever, Thermoluminescence of Solids, Cambridge University Press, 1988 Search PubMed.
  18. A. M. Gilinsky and K. S. Zhuravlev, Appl. Phys. Lett., 2001, 79, 3455 CrossRef CAS.
  19. M. A. Reshchikov, M. Zafar Iqbal, S. S. Park, K. Y. Lee, D. Tsvetkov, V. Dmitriev and H. Morkoç, Phys. B, 2003, 340–342, 444 CrossRef CAS.
  20. M. A. Reshchikov, J. Appl. Phys., 2014, 115, 103503 CrossRef.
  21. H. G. Ye, Z. C. Su, F. Tang, M. Z. Wang, G. D. Chen, J. Wang and S. J. Xu, Sci. Rep., 2017, 7, 41460 CrossRef CAS PubMed.
  22. M. Z. Wang and S. J. Xu, Semicond. Sci. Technol., 2016, 31, 095004 CrossRef.
  23. D. G. Thomas, J. J. Hopfield and W. M. Augustyniak, Phys. Rev., 1965, 140, A202 CrossRef.
  24. I. Pelant and J. Valenta, Luminescence Spectroscopy of Semiconductors, Oxford University Press, Oxford, 2012 Search PubMed.
  25. D. C. Look, J. W. Hemsky and J. R. Sizelove, Phys. Rev. Lett., 1999, 82, 2552 CrossRef CAS.
  26. C. G. Van de Walle, Phys. Rev. Lett., 2000, 85, 1012 CrossRef CAS PubMed.
  27. D. M. Hofmann, A. Hofstaetter, F. Leiter, H. Zhou, F. Henecker, B. K. Meyer, S. B. Orlinskii, J. Schmidt and P. G. Baranov, Phys. Rev. Lett., 2002, 88, 045504 CrossRef PubMed.
  28. C. H. Park, S. B. Zhang and S.-H. Wei, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 073202 CrossRef.
  29. B. K. Meyer, J. Sann, D. M. Hofmann, C. Neumann and A. Zeuner, Semicond. Sci. Technol., 2005, 20, S62 CrossRef CAS.
  30. G. A. Shi, M. Stavola, S. J. Pearton, M. Thieme, E. V. Lavrov and J. Weber, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 195211 CrossRef.
  31. H. von Wenckstern, S. Weinhold, G. Biehne, R. Pickenhain, H. Schmidt, H. Hochmuth and M. Grundmann, in Book Advances in Solid State Physics, ed. B. Kramer, Springer, Berlin, Heidelberg, 2006, vol. 45, pp. 263–274 Search PubMed.
  32. Y. N. Chen, C. C. Zheng, J. Q. Ning, R. X. Wang, C. C. Ling and S. J. Xu, Superlattices Microstruct., 2016, 99, 208 CrossRef CAS.
  33. J. L. Lyons, A. Alkauskas, A. Janotti and C. G. Van de Walle, Appl. Phys. Lett., 2017, 111, 042101 CrossRef.
  34. S. L. Shi, G. Q. Li, S. J. Xu, Y. Zhao and G. H. Chen, J. Phys. Chem. B, 2006, 110, 10475 CrossRef CAS PubMed.

This journal is © the Owner Societies 2017