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Photoreflectance and contactless electroreflectance spectroscopy of GaAs-based structures: The below band gap oscillation features
Applied Surface Science 253 (2006) 266–270 www.elsevier.com/locate/apsusc
Photoreflectance and contactless electroreflectance spectroscopy of GaAs-based structures: The below band gap oscillation features R. Kudrawiec *, M. Motyka, M. Gladysiewicz, P. Sitarek, J. Misiewicz Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland Available online 17 July 2006
Abstract GaAs-based structures characterized below band gap oscillation features (OFs) in photoreflectance (PR) are studied in both PR and contactless electro-reflectance (CER) spectroscopies. It has been shown that the OFs are usually very strong for structures grown on n-type GaAs substrate. The origin of the OFs is the modulation of the refractive index in the sample due to a generation of additional carriers by the modulated pump beam. The presence of OFs in PR spectra complicates the analysis of PR signal related to quantum well transitions. Therefore, PR spectroscopy is often limited to samples grown on semi-insolating (SI) type substrates. However, sometimes the OFs could be observed for structures grown on SI-type GaAs substrates. In this paper we show that the OFs could be successfully eliminated by applying the CER technique instead of PR one because during CER measurements any additional carriers are not generated and hence CER spectra are free of OFs. This advantage of CER spectroscopy is very important in investigations of all structures for which OFs are present in PR spectra. # 2006 Elsevier B.V. All rights reserved. Keywords: Contactless electroreflectance; Photoreflectance; Quantum wells
1. Introduction Photoreflectance (PR) and contactless electro-reflectance (CER) spectroscopies are known to be powerful techniques for the characterization of semiconductors and their microstructures because they are very sensitive at room temperature, a very important aspect of material characterization since devices normally operate around room temperature [1–4]. PR and CER are particularly useful because they are performed in contactless mode that is non-destructive for samples. The parameter which is modulated in the sample during PR and CER measurements is the built-in electric field. Therefore, it could be expected that PR and CER spectra are equivalent because an electro-modulation of internal electric fields takes place for these two techniques. However, the mechanism of the electro-modulation is not the same for the two techniques. Therefore, some difference in PR and CER spectra are expected. In the case of CER, the sample is placed into a capacitor with a semi-transparent top electrode [5]. The second electrode consisting of a metal strip is separated from the top electrode by
* Corresponding author. Tel.: +48 71 320 42 80; fax: +48 71 328 36 96. E-mail address: [email protected] (R. Kudrawiec). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.05.080
an insulating spacer, which is about 0.1 mm larger than the thickness of the sample. Thus there is nothing in direct contact with the front of the sample. An ac modulating voltage usually up to 1 kV peak-to-peak is then applied between the two electrodes. In the case of PR instead of directly applying an ac electric field, the sample is perturbed with a chopped laser pump beam with hv > Eg . When the laser is on, the photo-generated carriers drift in built-in electric field, and are captured by surface/interface trap states, thus reducing this field. When the laser is off, the trap occupation, and hence field, is restored. Note that the photogenerated carriers could also modulate the refractive index, because, as well known, the refractive index depends on the carrier concentration. Thus PR and CER spectra are not fully equivalent, despite the fact that the modulated parameter for both PR and CER is the same, i.e. the built-in electric field. In our previous letter [6] we have show that oscillatory features (OFs) usually observed in photoreflectance (PR) spectra of GaAs-based structures grown on n-type GaAs substrate below the GaAs fundamental gap [7–10] could be eliminated completely by applying CER instead of PR [6]. This finding shows that the origin of OFs is the modulation of the refractive index in the sample due to the generation of additional carriers by modulated pump beam (in the other words the additional carriers mean electron-hole pairs
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generated by laser beam which is the modulated beam). In the case of CER spectroscopy, any additional carriers are not generated during the modulation hence CER spectra are free of OFs [6]. In this paper we focus on the above mentioned difference between CER and PR spectroscopies. In order to illustrate the advantage of CER spectroscopy we measured PR and CER spectra for different quantum well structures grown on GaAs substrate (n-type and semi-isolating (SI) type). In addition, a sample with strong OFs has been investigated by PR at various modulation conditions, i.e. various modulation power and various modulation wavelengths. 2. Experimental A conventional experimental set-up with a tungsten halogen lamp (150 W) as a probe light source, a 0.55 m monochromator and InGaAs pin photodiode was applied for obtaining the PR and CER spectra. For PR, a frequency doubled YAG laser with 532 nm emission and 20 mW power was used as the pump beam. For PR measurements with the various modulation power and various modulation wavelength, a Chameleon laser of Coherent was used as the pump beam. In the CER experiment, the top electrode consisted of a transparent conducting ATO layer on quartz, which was kept at a distance of 0.1 mm from the sample surface while the sample itself was fixed on the bottom cuprum electrode. A maximum peak-topeak alternating voltage of 0.9 kV was applied. Phase sensitive detection of the PR and CER signals was made using a lock-in amplifier. Other relevant details of the experimental set-up have been described in Refs. [1,4]. The samples used in this study were grown by solid-source molecular beam epitaxy on GaAs substrate (n-type and SItype). Three samples have been selected to present in this paper. The first sample (sample A) is a 20 nm thick GaN0.029As0.873Sb0.098/GaAs QW grown on n-type GaAs substrate. The next two samples (samples B and C) were grown on SI-type GaAs substrate. The sample B is a GaAsSb– GaInAs/GaAs bilayer QW (BQW) structure discussed in details in Ref. [9]. The sample consists of a 350 nm thick GaAs buffer layer and 9-nm-thick BQW composed of 3 nm thick GaAs0.71Sb0.29 and 6 nm thick Ga0.8In0.2As layers and capped by 50 nm of GaAs. The sample C is a 8 nm thick In0.28Ga0.72As/ GaAs QW with following layers InGaP(25 nm)/ GaAs(110 nm)/InGaAs(8 nm)/GaAs(110 nm)/InGaP(25 nm)/ GaAs(SI type substrate).
Fig. 1. Comparison of PR and CER spectra for sample A, i.e. GaN0.029As0.873Sb0.098/GaAs QW.
samples the OF is usually observed in PR spectra and its intensity is comparable with the intensity of PR signal related to the fundamental transition in GaAs or sometimes is much stronger than the GaAs signal. Such a situation complicates the analysis of PR signal associated with QW transitions. Very often a change in the phase detection helps to eliminate OFs without significant weakness of PR signal related to the optical
3. Results and discussion Figs. 1–3 show a comparison of PR and CER spectra measured at room temperature for samples A, B, and C, respectively. For the three samples, OFs are observed below the band gap of GaAs substrate. No OFs are observed in CER spectra. This means that the origin of the OFs is the modulation of refractive index in the sample due to additional carriers generated by the modulated beam [6]. The sample A represents the family of samples grown on n-type GaAs substrate. For such
Fig. 2. Comparison of PR and CER spectra for sample B, i.e. GaAs0.71Sb0.29– Ga0.8In0.2As/GaAs BQW.
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Fig. 3. Comparison of PR and CER spectra for sample C, i.e. In0.28Ga0.72As/ GaAs QW.
transitions. However, for some samples elimination OFs via the selection of appropriate phase leads to loss of PR signal related to the optical transitions (e.g. QW transitions). Such a situation takes place for sample A, see in Fig. 4. Therefore, better approach is to apply CER instead PR. As it is seen in Fig. 1, no PR features related to QW transitions is resolved in PR spectrum while a lot of PR resonances have been resolved in CER spectrum which is free of the OFs. The identification of PR resonances was possible on the basis of the calculations within electron effective mass approximation [11] in the framework of an approach described in Refs. [12,13]. The notation nmH(L) denotes the transition between n-th heavyhole (light-hole) valence sub-band and m-th conduction subband. The resonance at the lowest energy we connect with the 11H transition which is a fundamental one for this SQW. In addition to the 11H transition, PR spectra show a lot of resonances related to transitions between excited QW states. The arrows in Fig. 1 shows energies of QW transitions obtained from the calculations which are summarised in details elsewhere [13]. The example of this sample illustrates that CER spectroscopy have huge advantage in comparison to PR spectroscopy, because CER spectra are free of the OFs. We have observed that the intensity of OFs for GaAs-based structures grown on n-type GaAs substrate is weak if the total thickness of the epilayers is higher that one micrometer. However, no general conclusion about the critical thickness cannot be obtained because the intensity of OFs also depends on other factors such as the content and thickness of the individual epilayers and probably the grown conditions. Such a result confirms that the OFs are related to an interference effect inside the epitaxial layers. The interference effect could be very
Fig. 4. PR spectra measured at different phase detection on lock-in (upper panel) and PR spectrum for one selected phase shown on a separate panel (bottom panel). It is seen on bottom panel that PR signal related to GaAs is very weak and PR features related to QW transitions are not visible if we reduce OF signal to zero via changing the phase detection.
complex if the sample has lot of epilayers with different refractive indexes. However, we suppose that the main contribution to OFs originates from the epilayer/substrate interface, because in order to obtain a signal in PR the refractive index has to change differently in the two neighbours layers. It is possible if the two layers have different carrier concentrations. Usually the refractive index of epitaxial layers is different sensitive to the additional carriers that the refractive index of an n-type GaAs substrate. Therefore, an efficient modulation of the difference of refractive indexes could appear during PR measurements where the modulated beam generates additional carriers. The photogenerated carriers are able to change the refractive index. In the case of CER such mechanism of the refractive index modulation is absent because in this technique we do not use the laser beam which is the origin of additional carriers. The effective modulation of the refractive index is difficult to obtain if the refractive index in the two neighbours layers is almost the same and/or are similarly sensitive to additional carriers. Such a situation often takes place for GaAs-based structures grown on SI-type GaAs substrate. In this case possible OFs are very weak or are not observed in PR spectra. In our experience, the OFs are very rarely observed for semiconductor structures grown on SI-type GaAs substrate. In most samples we have measured, the intensity of OFs was below the detection limit of our PR setup (DR/R < 10 7). For this paper we selected samples with the strongest OFs which we have observed so far for structures grown on SI-type GaAs
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substrate. Note, that PR resonances related to QW transitions are resolved in these spectra despite the presence of OFs. If the OFs are visible and their intensity is weaker than the intensity of PR signal related to QW transitions than the energies of QW transitions can be quite precisely extracted from such spectra [9,10]. However, better is to measure CER instead of PR because CER spectra are without the OF, as seen in the bottom panel of Figs. 2 and 3. As was mentioned in the introduction, the reason is that in CER spectroscopy any addition carriers are not generated hence CER spectra are free of OFs [6]. This finding shows that OFs are related to the modulation of the refractive index due to a change in the carrier concentration by the modulated beam. In order to investigate the behaviour of the below band gap OFs, we have preformed PR measurements at various modulation wavelengths. Fig. 5 shows PR spectra obtained for the sample A at the modulation wavelength below the GaAs band gap wavelength at 740 nm (upper panel) and above GaAs band gap wavelength at 980 nm (bottom panel). In addition, these measurements were preformed at various power densities of the modulated beam in order to control possible changes in the shape of PR spectra due to the various modulation intensity. It has been found, that the shape of PR spectra do not change with the increase in the density of the modulation beam, only the intensity of PR signal rises with the increase in the density of the modulation beam, see in Fig. 6. Note, that the shape of OFs is also the same for the two different modulation wavelengths, only a small difference between the relative
Fig. 5. PR spectra of GaN0.029As0.873Sb0.098/GaAs QW measured at various modulation intensities for two different modulation wavelengths: 740 nm (upper panel) and 980 nm (bottom panel).
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Fig. 6. The intensity of PR signal at 1.13 eV measured for various power densities of the modulated beam: (&) modulation wavelength of 740 nm; (*) modulation wavelength of 980 nm.
intensities of OF and GaAs signals has been found, i.e. it has been observed that for the below GaAs band gap modulation, the GaAs related signal is about 20% stronger in comparison to the OF signal. The main difference found between PR spectra measured at the modulation wavelength above (740 nm) and below (980 nm) GaAs absorption edge is a decrease of the OF intensity for the below band gap modulation. This phenomenon is illustrated in Fig. 6. Such a behaviour of the OF signal intensity is expected because this signal should be proportional to photo-generated carriers. The quantity of the carriers decreases rapidly if the modulation wavelength is longer than GaAs absorption edge (870 nm). However, the photo-generated carriers do not decrease to zero because absorption of the modulated beam takes place within the GaNAsSb/GaAs QW. Thus, we concluded that for this sample we cannot eliminate the OFs completely by a change in the modulation wavelength or the modulation intensity. If we reduce the photo-generated carriers using (i) below GaAs band gap modulation (lmod > 870 nm) and (ii) a reduction of on the modulation intensity we are able to achieve a decrease of the intensity of the OF signal, as presented in Fig. 7. However, the weakness of OF signals does not help to resolve PR features associated with QW
Fig. 7. The intensity of PR signal at 1.13 eV measured for various modulation wavelengths. The modulation intensity was 160 W/cm2.
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transitions because the intensity of these features also decreases. According to the study of other authors [8,14,15] the ratio of OFs and a PR signal related to optical transitions (e.g. QW transitions) depends on many factors: temperature, wavelength and frequency of modulated beam, the phase of the lock-in detection, and an additional illumination of the sample. In general, our investigations confirm that the ratio varies with mentioned parameters. However, we have found a lot of samples for which we are not able to obtain such an optimal ratio for these two signals (e.g. sample A). For these samples an analysis of PR features related to QW transitions is difficult. CER spectroscopy has this advantage that it gives possibility to investigate QW transitions in such samples.
Acknowledgements
4. Conclusions
[1] F.H. Pollak, in: T.S. Moss (Ed.), Modulation Spectroscopy of Semiconductors and Semiconductor Microstructures Handbook on Semiconductors, vol. 2, Elsevier Science, Amsterdam, 1994, pp. 527–635. [2] O.J. Glembocki, Proc. SPIE 1286 (1990) 2. [3] F.H. Pollak, Mater. Sci. Eng. B 80 (2001) 178. [4] J. Misiewicz, P. Sitarek, G. Sek, R. Kudrawiec, Mater. Sci. 21 (2003) 263. [5] X. Yin, F.H. Pollak, Appl. Phys. Lett. 59 (1991) 2305. [6] R. Kudrawiec, P. Sitarek, J. Misiewicz, S.R. Bank, H.B. Yuen, M.A. Wistey, J.S. Harris Jr., Appl. Phys. Lett. 86 (2005) 091115. [7] D. Huang, D. Mui, H. Morkoc, J. Appl. Phys. 66 (1989) 358. [8] N. Kallergi, B. Roughani, J. Aubel, S. Sundaram, J. Appl. Phys. 68 (1990) 4656. [9] R. Kudrawiec, K. Ryczko, G. Sek, J. Misiewicz, J.C. Harmand, Appl. Phys. Lett. 84 (2004) 3453. [10] R. Kudrawiec, E.-M. Pavelescu, J. Andrzejewski, J. Misiewicz, A. Gheorghiu, T. Jouhti, M. Pessa, J. Appl. Phys. 96 (2004) 2909. [11] G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, Les Editions de Physique, Paris, 1992. [12] R. Kudrawiec, K. Ryczko, J. Misiewicz, H.B. Yuen, S.R. Bank, M.A. Wistey, H.P. Bae, J.S. Harris Jr., Appl. Phys. Lett. 86 (2005) 141908. [13] R. Kudrawiec, M. Gladysiewicz, J. Misiewicz, H.B. Yuen, S.R. Bank, M.A. Wistey, H.P. Bae, J.S. Harris Jr., Solid State Commun. 137 (2006) 138. [14] H.K. Lipsanen, V.M. Airaksinen, Appl. Phys. Lett. 63 (1993) 2863. [15] G. Blume, T.J.C. Hosea, S.J. Sweeney, S.R. Johnson, Y.-H. Zhang, International Workshop on Modulation Spectroscopy of Semiconductor Structures, Wroclaw, Poland, July 1–3, 2004 (will be published in Phys. Stat. Solidi A).
PR and CER measurements were preformed for semiconductor structures grown on both n-type and SI-type GaAs substrates. It has been observed that OFs are typical of samples grown on n-type GaAs substrate. In most samples grown on SItype GaAs substrate, the OFs were not observed or their intensity was below the detection limit of our PR setup (10 7). For some samples quite strong OFs have been observed. The OFs could be successfully eliminated by applying the CER technique instead of PR because during CER measurements any additional carriers are not generated and hence CER spectra are free of OFs. In addition, the behaviour of OFs has been investigated at various modulation intensities and modulation wavelengths. It has been found that the shape of OFs do not change with the increase in the modulation intensity and modulation wavelength only changes signal intensities. For the below band gap modulation the intensity of OFs significantly decreases due to weaker photo-generation of the additional carriers, i.e. weaker modulation of the refractive index. However, this decrease in the OF intensity does not help to resolve PR signal related to QW transitions because PR features related to QW transitions are weak in the case of the below band gap modulation.
The authors would like to thank Prof. James S. Harris Jr., from Stanford University in USA for the GaNAsSb/GaAs samples, Dr. J.C. Harmand from Laboratoire de Photonique et de Nanostructures in France for the GaAsSb–GaInAs/GaAs samples, and Dr. J. Wojcik from McMaster Universitity in Canada for the InGaAs/GaAs samples. Also we acknowledge the support from the Foundation for Polish Science through a Subsidy 8/2005. R. Kudrawiec acknowledges the financial support from the Foundation for Polish Science.
References
Photoreflectance and contactless electroreflectance spectroscopy of GaAs-based structures: The below band gap oscillation features R. Kudrawiec *, M. Motyka, M. Gladysiewicz, P. Sitarek, J. Misiewicz Institute of Physics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland Available online 17 July 2006
Abstract GaAs-based structures characterized below band gap oscillation features (OFs) in photoreflectance (PR) are studied in both PR and contactless electro-reflectance (CER) spectroscopies. It has been shown that the OFs are usually very strong for structures grown on n-type GaAs substrate. The origin of the OFs is the modulation of the refractive index in the sample due to a generation of additional carriers by the modulated pump beam. The presence of OFs in PR spectra complicates the analysis of PR signal related to quantum well transitions. Therefore, PR spectroscopy is often limited to samples grown on semi-insolating (SI) type substrates. However, sometimes the OFs could be observed for structures grown on SI-type GaAs substrates. In this paper we show that the OFs could be successfully eliminated by applying the CER technique instead of PR one because during CER measurements any additional carriers are not generated and hence CER spectra are free of OFs. This advantage of CER spectroscopy is very important in investigations of all structures for which OFs are present in PR spectra. # 2006 Elsevier B.V. All rights reserved. Keywords: Contactless electroreflectance; Photoreflectance; Quantum wells
1. Introduction Photoreflectance (PR) and contactless electro-reflectance (CER) spectroscopies are known to be powerful techniques for the characterization of semiconductors and their microstructures because they are very sensitive at room temperature, a very important aspect of material characterization since devices normally operate around room temperature [1–4]. PR and CER are particularly useful because they are performed in contactless mode that is non-destructive for samples. The parameter which is modulated in the sample during PR and CER measurements is the built-in electric field. Therefore, it could be expected that PR and CER spectra are equivalent because an electro-modulation of internal electric fields takes place for these two techniques. However, the mechanism of the electro-modulation is not the same for the two techniques. Therefore, some difference in PR and CER spectra are expected. In the case of CER, the sample is placed into a capacitor with a semi-transparent top electrode [5]. The second electrode consisting of a metal strip is separated from the top electrode by
* Corresponding author. Tel.: +48 71 320 42 80; fax: +48 71 328 36 96. E-mail address: [email protected] (R. Kudrawiec). 0169-4332/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2006.05.080
an insulating spacer, which is about 0.1 mm larger than the thickness of the sample. Thus there is nothing in direct contact with the front of the sample. An ac modulating voltage usually up to 1 kV peak-to-peak is then applied between the two electrodes. In the case of PR instead of directly applying an ac electric field, the sample is perturbed with a chopped laser pump beam with hv > Eg . When the laser is on, the photo-generated carriers drift in built-in electric field, and are captured by surface/interface trap states, thus reducing this field. When the laser is off, the trap occupation, and hence field, is restored. Note that the photogenerated carriers could also modulate the refractive index, because, as well known, the refractive index depends on the carrier concentration. Thus PR and CER spectra are not fully equivalent, despite the fact that the modulated parameter for both PR and CER is the same, i.e. the built-in electric field. In our previous letter [6] we have show that oscillatory features (OFs) usually observed in photoreflectance (PR) spectra of GaAs-based structures grown on n-type GaAs substrate below the GaAs fundamental gap [7–10] could be eliminated completely by applying CER instead of PR [6]. This finding shows that the origin of OFs is the modulation of the refractive index in the sample due to the generation of additional carriers by modulated pump beam (in the other words the additional carriers mean electron-hole pairs
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generated by laser beam which is the modulated beam). In the case of CER spectroscopy, any additional carriers are not generated during the modulation hence CER spectra are free of OFs [6]. In this paper we focus on the above mentioned difference between CER and PR spectroscopies. In order to illustrate the advantage of CER spectroscopy we measured PR and CER spectra for different quantum well structures grown on GaAs substrate (n-type and semi-isolating (SI) type). In addition, a sample with strong OFs has been investigated by PR at various modulation conditions, i.e. various modulation power and various modulation wavelengths. 2. Experimental A conventional experimental set-up with a tungsten halogen lamp (150 W) as a probe light source, a 0.55 m monochromator and InGaAs pin photodiode was applied for obtaining the PR and CER spectra. For PR, a frequency doubled YAG laser with 532 nm emission and 20 mW power was used as the pump beam. For PR measurements with the various modulation power and various modulation wavelength, a Chameleon laser of Coherent was used as the pump beam. In the CER experiment, the top electrode consisted of a transparent conducting ATO layer on quartz, which was kept at a distance of 0.1 mm from the sample surface while the sample itself was fixed on the bottom cuprum electrode. A maximum peak-topeak alternating voltage of 0.9 kV was applied. Phase sensitive detection of the PR and CER signals was made using a lock-in amplifier. Other relevant details of the experimental set-up have been described in Refs. [1,4]. The samples used in this study were grown by solid-source molecular beam epitaxy on GaAs substrate (n-type and SItype). Three samples have been selected to present in this paper. The first sample (sample A) is a 20 nm thick GaN0.029As0.873Sb0.098/GaAs QW grown on n-type GaAs substrate. The next two samples (samples B and C) were grown on SI-type GaAs substrate. The sample B is a GaAsSb– GaInAs/GaAs bilayer QW (BQW) structure discussed in details in Ref. [9]. The sample consists of a 350 nm thick GaAs buffer layer and 9-nm-thick BQW composed of 3 nm thick GaAs0.71Sb0.29 and 6 nm thick Ga0.8In0.2As layers and capped by 50 nm of GaAs. The sample C is a 8 nm thick In0.28Ga0.72As/ GaAs QW with following layers InGaP(25 nm)/ GaAs(110 nm)/InGaAs(8 nm)/GaAs(110 nm)/InGaP(25 nm)/ GaAs(SI type substrate).
Fig. 1. Comparison of PR and CER spectra for sample A, i.e. GaN0.029As0.873Sb0.098/GaAs QW.
samples the OF is usually observed in PR spectra and its intensity is comparable with the intensity of PR signal related to the fundamental transition in GaAs or sometimes is much stronger than the GaAs signal. Such a situation complicates the analysis of PR signal associated with QW transitions. Very often a change in the phase detection helps to eliminate OFs without significant weakness of PR signal related to the optical
3. Results and discussion Figs. 1–3 show a comparison of PR and CER spectra measured at room temperature for samples A, B, and C, respectively. For the three samples, OFs are observed below the band gap of GaAs substrate. No OFs are observed in CER spectra. This means that the origin of the OFs is the modulation of refractive index in the sample due to additional carriers generated by the modulated beam [6]. The sample A represents the family of samples grown on n-type GaAs substrate. For such
Fig. 2. Comparison of PR and CER spectra for sample B, i.e. GaAs0.71Sb0.29– Ga0.8In0.2As/GaAs BQW.
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Fig. 3. Comparison of PR and CER spectra for sample C, i.e. In0.28Ga0.72As/ GaAs QW.
transitions. However, for some samples elimination OFs via the selection of appropriate phase leads to loss of PR signal related to the optical transitions (e.g. QW transitions). Such a situation takes place for sample A, see in Fig. 4. Therefore, better approach is to apply CER instead PR. As it is seen in Fig. 1, no PR features related to QW transitions is resolved in PR spectrum while a lot of PR resonances have been resolved in CER spectrum which is free of the OFs. The identification of PR resonances was possible on the basis of the calculations within electron effective mass approximation [11] in the framework of an approach described in Refs. [12,13]. The notation nmH(L) denotes the transition between n-th heavyhole (light-hole) valence sub-band and m-th conduction subband. The resonance at the lowest energy we connect with the 11H transition which is a fundamental one for this SQW. In addition to the 11H transition, PR spectra show a lot of resonances related to transitions between excited QW states. The arrows in Fig. 1 shows energies of QW transitions obtained from the calculations which are summarised in details elsewhere [13]. The example of this sample illustrates that CER spectroscopy have huge advantage in comparison to PR spectroscopy, because CER spectra are free of the OFs. We have observed that the intensity of OFs for GaAs-based structures grown on n-type GaAs substrate is weak if the total thickness of the epilayers is higher that one micrometer. However, no general conclusion about the critical thickness cannot be obtained because the intensity of OFs also depends on other factors such as the content and thickness of the individual epilayers and probably the grown conditions. Such a result confirms that the OFs are related to an interference effect inside the epitaxial layers. The interference effect could be very
Fig. 4. PR spectra measured at different phase detection on lock-in (upper panel) and PR spectrum for one selected phase shown on a separate panel (bottom panel). It is seen on bottom panel that PR signal related to GaAs is very weak and PR features related to QW transitions are not visible if we reduce OF signal to zero via changing the phase detection.
complex if the sample has lot of epilayers with different refractive indexes. However, we suppose that the main contribution to OFs originates from the epilayer/substrate interface, because in order to obtain a signal in PR the refractive index has to change differently in the two neighbours layers. It is possible if the two layers have different carrier concentrations. Usually the refractive index of epitaxial layers is different sensitive to the additional carriers that the refractive index of an n-type GaAs substrate. Therefore, an efficient modulation of the difference of refractive indexes could appear during PR measurements where the modulated beam generates additional carriers. The photogenerated carriers are able to change the refractive index. In the case of CER such mechanism of the refractive index modulation is absent because in this technique we do not use the laser beam which is the origin of additional carriers. The effective modulation of the refractive index is difficult to obtain if the refractive index in the two neighbours layers is almost the same and/or are similarly sensitive to additional carriers. Such a situation often takes place for GaAs-based structures grown on SI-type GaAs substrate. In this case possible OFs are very weak or are not observed in PR spectra. In our experience, the OFs are very rarely observed for semiconductor structures grown on SI-type GaAs substrate. In most samples we have measured, the intensity of OFs was below the detection limit of our PR setup (DR/R < 10 7). For this paper we selected samples with the strongest OFs which we have observed so far for structures grown on SI-type GaAs
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substrate. Note, that PR resonances related to QW transitions are resolved in these spectra despite the presence of OFs. If the OFs are visible and their intensity is weaker than the intensity of PR signal related to QW transitions than the energies of QW transitions can be quite precisely extracted from such spectra [9,10]. However, better is to measure CER instead of PR because CER spectra are without the OF, as seen in the bottom panel of Figs. 2 and 3. As was mentioned in the introduction, the reason is that in CER spectroscopy any addition carriers are not generated hence CER spectra are free of OFs [6]. This finding shows that OFs are related to the modulation of the refractive index due to a change in the carrier concentration by the modulated beam. In order to investigate the behaviour of the below band gap OFs, we have preformed PR measurements at various modulation wavelengths. Fig. 5 shows PR spectra obtained for the sample A at the modulation wavelength below the GaAs band gap wavelength at 740 nm (upper panel) and above GaAs band gap wavelength at 980 nm (bottom panel). In addition, these measurements were preformed at various power densities of the modulated beam in order to control possible changes in the shape of PR spectra due to the various modulation intensity. It has been found, that the shape of PR spectra do not change with the increase in the density of the modulation beam, only the intensity of PR signal rises with the increase in the density of the modulation beam, see in Fig. 6. Note, that the shape of OFs is also the same for the two different modulation wavelengths, only a small difference between the relative
Fig. 5. PR spectra of GaN0.029As0.873Sb0.098/GaAs QW measured at various modulation intensities for two different modulation wavelengths: 740 nm (upper panel) and 980 nm (bottom panel).
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Fig. 6. The intensity of PR signal at 1.13 eV measured for various power densities of the modulated beam: (&) modulation wavelength of 740 nm; (*) modulation wavelength of 980 nm.
intensities of OF and GaAs signals has been found, i.e. it has been observed that for the below GaAs band gap modulation, the GaAs related signal is about 20% stronger in comparison to the OF signal. The main difference found between PR spectra measured at the modulation wavelength above (740 nm) and below (980 nm) GaAs absorption edge is a decrease of the OF intensity for the below band gap modulation. This phenomenon is illustrated in Fig. 6. Such a behaviour of the OF signal intensity is expected because this signal should be proportional to photo-generated carriers. The quantity of the carriers decreases rapidly if the modulation wavelength is longer than GaAs absorption edge (870 nm). However, the photo-generated carriers do not decrease to zero because absorption of the modulated beam takes place within the GaNAsSb/GaAs QW. Thus, we concluded that for this sample we cannot eliminate the OFs completely by a change in the modulation wavelength or the modulation intensity. If we reduce the photo-generated carriers using (i) below GaAs band gap modulation (lmod > 870 nm) and (ii) a reduction of on the modulation intensity we are able to achieve a decrease of the intensity of the OF signal, as presented in Fig. 7. However, the weakness of OF signals does not help to resolve PR features associated with QW
Fig. 7. The intensity of PR signal at 1.13 eV measured for various modulation wavelengths. The modulation intensity was 160 W/cm2.
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transitions because the intensity of these features also decreases. According to the study of other authors [8,14,15] the ratio of OFs and a PR signal related to optical transitions (e.g. QW transitions) depends on many factors: temperature, wavelength and frequency of modulated beam, the phase of the lock-in detection, and an additional illumination of the sample. In general, our investigations confirm that the ratio varies with mentioned parameters. However, we have found a lot of samples for which we are not able to obtain such an optimal ratio for these two signals (e.g. sample A). For these samples an analysis of PR features related to QW transitions is difficult. CER spectroscopy has this advantage that it gives possibility to investigate QW transitions in such samples.
Acknowledgements
4. Conclusions
[1] F.H. Pollak, in: T.S. Moss (Ed.), Modulation Spectroscopy of Semiconductors and Semiconductor Microstructures Handbook on Semiconductors, vol. 2, Elsevier Science, Amsterdam, 1994, pp. 527–635. [2] O.J. Glembocki, Proc. SPIE 1286 (1990) 2. [3] F.H. Pollak, Mater. Sci. Eng. B 80 (2001) 178. [4] J. Misiewicz, P. Sitarek, G. Sek, R. Kudrawiec, Mater. Sci. 21 (2003) 263. [5] X. Yin, F.H. Pollak, Appl. Phys. Lett. 59 (1991) 2305. [6] R. Kudrawiec, P. Sitarek, J. Misiewicz, S.R. Bank, H.B. Yuen, M.A. Wistey, J.S. Harris Jr., Appl. Phys. Lett. 86 (2005) 091115. [7] D. Huang, D. Mui, H. Morkoc, J. Appl. Phys. 66 (1989) 358. [8] N. Kallergi, B. Roughani, J. Aubel, S. Sundaram, J. Appl. Phys. 68 (1990) 4656. [9] R. Kudrawiec, K. Ryczko, G. Sek, J. Misiewicz, J.C. Harmand, Appl. Phys. Lett. 84 (2004) 3453. [10] R. Kudrawiec, E.-M. Pavelescu, J. Andrzejewski, J. Misiewicz, A. Gheorghiu, T. Jouhti, M. Pessa, J. Appl. Phys. 96 (2004) 2909. [11] G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, Les Editions de Physique, Paris, 1992. [12] R. Kudrawiec, K. Ryczko, J. Misiewicz, H.B. Yuen, S.R. Bank, M.A. Wistey, H.P. Bae, J.S. Harris Jr., Appl. Phys. Lett. 86 (2005) 141908. [13] R. Kudrawiec, M. Gladysiewicz, J. Misiewicz, H.B. Yuen, S.R. Bank, M.A. Wistey, H.P. Bae, J.S. Harris Jr., Solid State Commun. 137 (2006) 138. [14] H.K. Lipsanen, V.M. Airaksinen, Appl. Phys. Lett. 63 (1993) 2863. [15] G. Blume, T.J.C. Hosea, S.J. Sweeney, S.R. Johnson, Y.-H. Zhang, International Workshop on Modulation Spectroscopy of Semiconductor Structures, Wroclaw, Poland, July 1–3, 2004 (will be published in Phys. Stat. Solidi A).
PR and CER measurements were preformed for semiconductor structures grown on both n-type and SI-type GaAs substrates. It has been observed that OFs are typical of samples grown on n-type GaAs substrate. In most samples grown on SItype GaAs substrate, the OFs were not observed or their intensity was below the detection limit of our PR setup (10 7). For some samples quite strong OFs have been observed. The OFs could be successfully eliminated by applying the CER technique instead of PR because during CER measurements any additional carriers are not generated and hence CER spectra are free of OFs. In addition, the behaviour of OFs has been investigated at various modulation intensities and modulation wavelengths. It has been found that the shape of OFs do not change with the increase in the modulation intensity and modulation wavelength only changes signal intensities. For the below band gap modulation the intensity of OFs significantly decreases due to weaker photo-generation of the additional carriers, i.e. weaker modulation of the refractive index. However, this decrease in the OF intensity does not help to resolve PR signal related to QW transitions because PR features related to QW transitions are weak in the case of the below band gap modulation.
The authors would like to thank Prof. James S. Harris Jr., from Stanford University in USA for the GaNAsSb/GaAs samples, Dr. J.C. Harmand from Laboratoire de Photonique et de Nanostructures in France for the GaAsSb–GaInAs/GaAs samples, and Dr. J. Wojcik from McMaster Universitity in Canada for the InGaAs/GaAs samples. Also we acknowledge the support from the Foundation for Polish Science through a Subsidy 8/2005. R. Kudrawiec acknowledges the financial support from the Foundation for Polish Science.
References