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In0.53Ga0.23Al0.24As quantum wells
Superlattices and Microstructures 46 (2009) 425–434
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Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Electromodulation spectroscopy of In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As quantum wells R. Kudrawiec a,∗ , P. Podemski a , M. Motyka a , J. Misiewicz a , J. Serafińczuk b , A. Somers c , J.P. Reithmaier c,1 , A. Forchel c a
Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
b
Faculty of Microsystem Electronics and Fotonics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland c Technische Physik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
article
info
Article history: Received 20 June 2008 Received in revised form 16 April 2009 Accepted 22 April 2009 Available online 22 May 2009 Keywords: Quantum wells InP Photoreflectance Electroreflectance Band offset
abstract In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As quantum wells (QWs) of various widths have been grown by molecular beam epitaxy on the InP substrate and investigated by electromodulation spectroscopy, i.e. photoreflectance (PR) and contactless electroreflectance (CER). The optical transitions related to the QW barrier and the QW ground and excited states have been clearly observed in PR and CER spectra. The experimental QW transition energies have been compared with theoretical predictions based on an effective mass formalism model. A good agreement between experimental data and theoretical calculations has been observed when the conduction band offset for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface equals ∼60%. In addition, it has been concluded that the conduction band offset for the In0.53 Ga0.23 Al0.24 As/InP interface is close to zero. The obtained results show that InGa(Al)As alloys are very promising materials in the band gap engineering for structures grown on InP substrate. © 2009 Elsevier Ltd. All rights reserved.
∗ Corresponding address: Technische Physik, Institute of Microstructure Technology and Analysis, University of Kassel, Heinrich Plett-Str. 40, D-34132 Kassel, Germany. Tel.: +48 713204280; fax: +48 713204280. E-mail address: [email protected] (R. Kudrawiec). 1 Present address: Technische Physik, Institute of Microstructure Technology and Analysis, University of Kassel, Heinrich Plett-Str. 40, D-34132 Kassel, Germany. 0749-6036/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2009.04.010
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1. Introduction III–V group semiconductors are of potential importance in high speed electronics and optoelectronics applications. Various ternary and quaternary alloys can be band gap engineered to produce structures exhibiting quantum size effect. In the past few years, much of the research and development effort in the semiconductor laser area has been concentrated on quantum well (QW) lasers based on the InGaAs(P) alloy system lattice-matched to InP substrate. The band structure and optical properties of InGaAsP lattice-matched to InP [(InP)1−z (Ga0.47 In0.53 As)z , which is the In1−x Gax Asz P1−z case with x = 0.47z] are well known and have been reviewed in many papers already [1]. InGaAsP is currently employed in commercial optoelectronics (especially in semiconductor lasers emitting at 1.3 and 1.55 µm) and electronics (particularly in high-electronmobility transistors). An alternative material which can be also lattice-matched grown on InP is In1−x−y Gax Aly As where x + y ≈ 0.47 [1–8]. This quaternary alloy covers the same wavelength range but has not received much attention. It is expected that for many applications, the arsenidebased (In1−x Gax As, Al1−x Gax As, and In1−x−y Gax Aly As) materials are an attractive alternative to (Ga, In)(As, P) alloys. The very important advantage of arsenide-based systems is relatively easier growth of InGaAlAs quaternary alloy with the conventional solid source molecular beam epitaxy technique than InGaAsP, since only one group V element (As) is incorporated. In this way the problem of As/P ratio control is avoided. Moreover, it is expected that InGa(Al)As can allow us to grow QWs with a relatively deep confinement potential for electrons [1,4,8]. The deepness can be higher than that in the case of InGaAsP-based QWs. Thus the InGa(Al)As/InGaAlAs QW system is very promising for infrared lasers, including telecommunication wavelengths [8–11] and 1.7–2.3 µm region associated with the pollution spectroscopy [12,13]. However, in order to achieve greater acceptance of such systems, further characterization measurements are necessary. Photoreflectance (PR) and contactless electroreflectance (CER) are known to be nondestructive and powerful techniques for the characterization of semiconductors and their microstructures [14–22]. In these experiments, instead of the optical reflectance of the material, the derivative of the reflected light with respect to the modulating electric field is measured and hence they are known as electromodulation spectroscopies. The derivative nature of electromodulation spectroscopy emphasizes features localized in the photon energy region of interband transitions of semiconductor structures and suppresses uninteresting background effects. Also weak features that may not have been detected in the absolute spectra are often enhanced and a large number of sharp spectral features can be observed even at room temperature. In the case of QW structures it is typical that many optical transitions related to the excited QW states are observed in common with the ground state transitions and the QW barrier ones. The analysis of the optical transitions observed in the electromodulation spectra together with theoretical calculations makes it possible to determine material parameters such as the band gap discontinuity or other properties. This kind of procedures has been already applied in PR and CER studies for different semiconductor structures [18–22]. In this paper the same approach has been used to study the band gap discontinuity of the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs. 2. Experiment The samples were grown by molecular beam epitaxy on (001) sulfur doped InP substrates. Before the growth of QW samples, thick InGaAs and InGaAlAs layers were grown in order to calibrate the growth conditions. The In0.53 Ga0.47 As well was grown on a 200 nm thick In0.53 Ga0.23 Al0.24 As layer and then covered again by 100 nm of In0.53 Ga0.47 As layer and 10 nm InP cap layer. Both the well and barrier layers are lattice-matched to the InP substrate. Three samples with the nominal QW thickness of 6, 7 and 8 nm were grown for these studies. The QW thickness was controlled by the growth parameters which were calibrated for thick InGaAs layers. Fig. 1 shows high resolution X -ray (HRXRD) spectra for the three QW structures together with the simulation curves. From the comparison of the HRXRD data with the simulations it has been concluded that the QW structures have parameters (contents and thicknesses) very close to the intended values. In order to measure PR and CER spectra a so-called bright configuration of the setup has been used [23]. Light from a halogen lamp was reflected from the sample and analyzed with use of a lock-in
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 1. HRXRD spectra of InGaAs/InGaAlAs QWs (black lines) together with simulating curves (grey lines).
technique utilizing a single-grating 0.55 m focal length monochromator with an InGaAs PIN detector. The pump beam for PR was provided by the 532 nm line of a CW YAG laser. The laser light was chopped by a mechanical modulator at the frequency of 275 Hz. In the case of CER measurements the sample was mounted in an open air capacitor with the top electrode made of a copper mesh and the bottom electrode made of a copper solid block. The semitransparent top electrode was kept at a distance of approx. 0.1 mm from the sample surface while the sample itself was glued to the bottom copper block. A maximum peak-to-peak alternating voltage of 1.8 kV was used for the modulation at a frequency of 280 Hz. 3. Results and discussion Figs. 2–4 show room temperature PR (bottom) and CER (top) spectra for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs, respectively. In general, the same optical transitions are visible in both PR and CER spectra. In the case of PR spectra, a broad background-like signal is visible through the whole spectra whereas such a signal is not present in the CER spectra. The backgroundlike signal can be associated with below band gap oscillations which are often observed in the region of the sample transparency [24–27]. Such oscillations are usually very strong for GaAs-based structures grown on n-type substrates and they are weak or even invisible for GaAs-based structures grown on semi-insulating GaAs substrates. Since the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW system was grown on n-type InP substrate, a similar below band gap oscillation can be expected in PR spectra. CER spectra are free of the below band gap oscillations due to the different electromodulation mechanisms [26]. It is an advantage of the CER spectroscopy, since it makes it easier to interpret and analyze the spectral features which are associated with the QW transitions. Note that in this case the intensity of the oscillation-like signal in PR spectra is not strong and does not disturb the analysis of the QW transitions. The strongest PR and CER signals at ∼1.06 eV are associated with the photon absorption in In0.53 Ga0.23 Al0.24 As bulk-like QW barriers. The characteristic Franz–Keldysh oscillations (FKO) [28] apparent at higher energy values are due to the built-in electric field in In0.53 Ga0.23 Al0.24 As layers. Because of no doping in In0.53 Ga0.23 Al0.24 As barriers and In0.53 Ga0.47 As QW the electric field in this region is expected to be more or less homogeneous and results from the Fermi-level pinning at
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Fig. 2. Room temperature PR (bottom) and CER (top) spectra of the 6 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
Fig. 3. Room temperature PR (bottom) and CER (top) spectra of the 7 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
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Fig. 4. Room temperature PR (bottom) and CER (top) spectra of the 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
In0.53 Ga0.23 Al0.24 As surface and In0.53 Ga0.23 Al0.24 As/(InP substrate) interface. From the period of FKO, it has been estimated [28] that this field is in the range of 8–17 kV/cm. The PR and CER resonances below the InGaAlAs-related transition are associated with the optical transitions in the In0.53 Ga0.47 As QW. These resonances have been fitted with the low-field electromodulation Lorentzian line-shape functional form [14,29] Eq. (1), with m = 2 which corresponds to an exciton transition.
1R R
(E ) = Re
" l X
# Cj · e
E − Ej + i · Γj
i·ϑj
−mj
+ g (E ).
(1)
j =1
In Eq. (1) l is the number of optical transitions (the number of independent spectral functions used in the fitting procedure), Cj and ϑj are the amplitude and phase, Ej and Γj are the energy and the broadening parameter of the j-transition, respectively. The function g (E ) is a function which simulates the background, which can be associated with the below band gap oscillations [24,25]. In the narrow spectral range (a range of one PR resonance) this background can be simulated by a linear or a parabolic function. In broader spectral range it can be a sinus-like function, see the shape of the below band gap oscillation in Refs. [24,25]. In order to simulate the background with the minimal number of fitting parameters, we divided our PR spectra for a few spectral ranges and we assumed that g (E ) is a linear function in each spectral range. The fitting curves are shown by thick lines in Figs. 2–4 together with the moduli of the individual resonances (dashed lines) obtained according to Eq. (2)
Cj
1ρj (E ) =
h
E − Ej
2
+ Γj
2
i m2j .
(2)
The notation nmH(L) in Figs. 2–4 denotes the transition between the nth heavy-hole (light-hole) valence subband and the mth conduction subband. The resonance at the lowest energy originates from the 11H transition, which is the fundamental transition for all QW samples. In addition to the
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 5. Comparison of the experimental data (horizontal dashed lines) with the theoretical predictions obtained for the various QC values (solid curves).
11H transition, the spectra show the 11L transition (i.e. the lowest energy transition for light-holes) and transitions between excited QW states. The identification of the resonances was possible on the basis of the calculations performed in the framework of the effective mass approximation. Relevant details of the calculations can be found in our previous papers [20–22]. All the material parameters for the In1−x−y Gax Aly As alloy have been obtained by a linear interpolation between the parameters of a relevant binary semiconductor alloy [1] according to Eq. (3). Q (x, y) = x · QGaAs + (1 − x − y) · QInAs + y · QAlAs ,
(3)
where Qi is an electron effective mass or a stiffness constant of a binary compound (GaAs, InAs or AlAs). The conduction band offset (QC ) is defined by Eq. (4) as
1EC × 100% (4) (1EC + 1EV ) where 1EC and 1EV are the conduction and valence band discontinuities at the heterojunction QC =
for unstrained materials (individual bulk alloys). In the case of QWs investigated in this paper the ‘‘unstrained’’ QC is the same as the ‘‘strained’’ QC since both the QW and barrier layers are latticematched to the InP substrate. The band gap energy of QW barriers has been acquired from fitting of PR and CER data whereas the band gap energy of In0.53 Ga0.47 As has been calculated after the well-known quadratic formula for In1−x Gax As with the bowing parameter C = 0.477 eV [1]. All calculations have been performed for the nominal contents and thicknesses of the QWs. However, it has been found that the ground state transition in PR and CER spectra is observed at a higher energy. Thus finally the content of the In0.53 Ga0.47 As layer has been corrected by <2% and in this way the theoretical ground state transition has been adjusted to the experimental data. It is also worth noting that the differences between energy levels are weakly sensitive to the changes in the In0.53 Ga0.47 As band gap energy [20]. Therefore, the analysis of the energy difference between 22H and 11H transitions (or 31H and 11H ones) is a good way to determine the band gap discontinuity for QWs. This procedure has also been applied in this paper. Fig. 5(a), (b) and (c) show the theoretical calculations as a function of QC performed for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW, respectively, together with the experimental data
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 6. Method used to analyze the QC in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs with (a) 6 nm, (b) 7 nm and (c) 8 nm thicknesses. The horizontal dashed lines correspond to the energy difference between the 31H and 11H transitions taken from the experimental data. Solid curves correspond to the energy difference between the 31H and 11H transitions obtained from the theoretical calculations in a function of QC .
(horizontal dashed lines). In addition to the allowed 11H, 11L, 22H and 22L transitions, calculations for the partially allowed 31H transition is plotted in these figures. A reasonable agreement for all the samples is found for the QC = 60%. The same conclusion has been obtained by analyzing the energy difference between 31H and 11H transitions (see Fig. 6). In the case of the QW samples, the resonance related to the 31H transition does not interfere with the other QW resonances and hence the analysis of the energy difference between 31H and 11H transitions is a good criterion for the determination of the QC for this system. In the case of the resonance related to the 22H transition a contribution of the 12H transition is significant and hence a disagreement between the calculations and the experimental data is observed for this transition for the 8 nm wide QW (see Fig. 5(c)). In order to support this conclusion, the low temperature PR measurements have been performed for the three QW structures. The temperature decrease narrows PR resonances and so helps to separate individual QW transitions. Fig. 7(a), (b) and (c) show low temperature PR spectra in the region of QW transitions for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs, respectively. It is clearly visible that the spectral feature attributed to the 22H transition at room temperature is composed of the two resonances with very similar intensities. These resonances are associated with the 12H and 22H transitions. The relatively strong intensity of the 12H transition, in comparison with the 22H one, is due to the significant imperfections in the square-like profile of the QW potential. In our case, these imperfections can be associated with the surface electric field [30] since the QW is close to the sample surface and the existence of the built-in electric field in the QW region is confirmed by the InGaAlAs-related FKO. It is worth noting that the built-in electric field is neglected in our calculations because of small Stark shift of QW transitions in this regime of electric fields (see in Fig. 8 that the shift is smaller than 5 meV for 7 nm width In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW when the electric field is smaller than 20 kV/cm). On the other hand it known that even small electric field (e.g. F >5 kV/cm) influences the integral intensity very strongly if the electron (or hole) level is weakly confined in the QW potential, i.e. the QW level is located close to the barrier energy. Such a situation takes place for the second electron and the third heavy-hole levels in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs. It explains why 13H and 21H transitions are relatively strong in PR and CER spectra and they are observed even
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 7. Low temperature PR spectra of (a) 6 nm, (b) 7 nm and (c) 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs.
Fig. 8. Stark shift of optical transitions for 7 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW. The square corresponds to the range of the built-in electric field in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW samples.
at low temperatures. For this system it is also possible that an atom interdiffusion at QW interfaces leads to some imperfections in the square-like QW profile. But this effect is small for unannealed QWs and therefore it is expected that in our case this effect can influence only the electron–hole overlap integrals for the 13H and 21H transitions. Fig. 9 shows the band gap discontinuities for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As/InP system. After Ref. [1] it has been assumed that the QC for In0.53 Ga0.47 As/InP interface is 40%. This value is well known for this system and is generally accepted. In this work it has been found that the QC for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface is ∼60%. In this case the direct comparison of the obtained value of the QC and the literature data is limited since there are no reports on this subject precisely. However, some data for the In0.53 Ga0.23 Al0.24 As/InP interface are available and hence a conclusion concerning the QC for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface can be obtained.
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1.6
energy (eV)
1.2
0.8
0.4
0.0 III-V compound Fig. 9. Band gap discontinuities and QC values for the whole InP/In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As/InP system.
On the other hand the QC for the In0.53 Ga0.23 Al0.24 As/InP interface can be determined knowing the QC for the In0.53 Ga0.47 As/InP and In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interfaces. Assuming that the QC for the In0.53 Ga0.47 As/InP interface is 40% [1] it has been found that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is smaller than 13% (and if the QC for the In0.53 Ga0.47 As/InP is equal to 35% it has been found that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is less than 2%). The obtained values of the QC for the In0.53 Ga0.23 Al0.24 As/InP interface are consistent with the literature data since it has been reported that the conduction band lineup for this system changes from type I to type II at the Al content of ∼22%–26% [6,31]. 4. Summary PR and CER have been applied to study the optical transitions in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs with various thicknesses. The ground 11H and 11L transitions and the excited state transitions such as 31H and 22H have been clearly observed in both PR and CER spectra. The experimental QW transition energies have been compared with the theoretical predictions based on an effective mass formalism model. Satisfactory agreement between the experimental data and the theoretical calculations has been found for QC = 60%. It has been additionally concluded that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is less than 13%. The obtained results show that QWs with the sufficiently deep confinement potential for both electrons and holes can be grown on InP substrate with the use of InGa(Al)As alloys. Acknowledgment R.K. acknowledges the financial support from the Foundation for Polish Science. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
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Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Electromodulation spectroscopy of In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As quantum wells R. Kudrawiec a,∗ , P. Podemski a , M. Motyka a , J. Misiewicz a , J. Serafińczuk b , A. Somers c , J.P. Reithmaier c,1 , A. Forchel c a
Institute of Physics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
b
Faculty of Microsystem Electronics and Fotonics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland c Technische Physik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
article
info
Article history: Received 20 June 2008 Received in revised form 16 April 2009 Accepted 22 April 2009 Available online 22 May 2009 Keywords: Quantum wells InP Photoreflectance Electroreflectance Band offset
abstract In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As quantum wells (QWs) of various widths have been grown by molecular beam epitaxy on the InP substrate and investigated by electromodulation spectroscopy, i.e. photoreflectance (PR) and contactless electroreflectance (CER). The optical transitions related to the QW barrier and the QW ground and excited states have been clearly observed in PR and CER spectra. The experimental QW transition energies have been compared with theoretical predictions based on an effective mass formalism model. A good agreement between experimental data and theoretical calculations has been observed when the conduction band offset for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface equals ∼60%. In addition, it has been concluded that the conduction band offset for the In0.53 Ga0.23 Al0.24 As/InP interface is close to zero. The obtained results show that InGa(Al)As alloys are very promising materials in the band gap engineering for structures grown on InP substrate. © 2009 Elsevier Ltd. All rights reserved.
∗ Corresponding address: Technische Physik, Institute of Microstructure Technology and Analysis, University of Kassel, Heinrich Plett-Str. 40, D-34132 Kassel, Germany. Tel.: +48 713204280; fax: +48 713204280. E-mail address: [email protected] (R. Kudrawiec). 1 Present address: Technische Physik, Institute of Microstructure Technology and Analysis, University of Kassel, Heinrich Plett-Str. 40, D-34132 Kassel, Germany. 0749-6036/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2009.04.010
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1. Introduction III–V group semiconductors are of potential importance in high speed electronics and optoelectronics applications. Various ternary and quaternary alloys can be band gap engineered to produce structures exhibiting quantum size effect. In the past few years, much of the research and development effort in the semiconductor laser area has been concentrated on quantum well (QW) lasers based on the InGaAs(P) alloy system lattice-matched to InP substrate. The band structure and optical properties of InGaAsP lattice-matched to InP [(InP)1−z (Ga0.47 In0.53 As)z , which is the In1−x Gax Asz P1−z case with x = 0.47z] are well known and have been reviewed in many papers already [1]. InGaAsP is currently employed in commercial optoelectronics (especially in semiconductor lasers emitting at 1.3 and 1.55 µm) and electronics (particularly in high-electronmobility transistors). An alternative material which can be also lattice-matched grown on InP is In1−x−y Gax Aly As where x + y ≈ 0.47 [1–8]. This quaternary alloy covers the same wavelength range but has not received much attention. It is expected that for many applications, the arsenidebased (In1−x Gax As, Al1−x Gax As, and In1−x−y Gax Aly As) materials are an attractive alternative to (Ga, In)(As, P) alloys. The very important advantage of arsenide-based systems is relatively easier growth of InGaAlAs quaternary alloy with the conventional solid source molecular beam epitaxy technique than InGaAsP, since only one group V element (As) is incorporated. In this way the problem of As/P ratio control is avoided. Moreover, it is expected that InGa(Al)As can allow us to grow QWs with a relatively deep confinement potential for electrons [1,4,8]. The deepness can be higher than that in the case of InGaAsP-based QWs. Thus the InGa(Al)As/InGaAlAs QW system is very promising for infrared lasers, including telecommunication wavelengths [8–11] and 1.7–2.3 µm region associated with the pollution spectroscopy [12,13]. However, in order to achieve greater acceptance of such systems, further characterization measurements are necessary. Photoreflectance (PR) and contactless electroreflectance (CER) are known to be nondestructive and powerful techniques for the characterization of semiconductors and their microstructures [14–22]. In these experiments, instead of the optical reflectance of the material, the derivative of the reflected light with respect to the modulating electric field is measured and hence they are known as electromodulation spectroscopies. The derivative nature of electromodulation spectroscopy emphasizes features localized in the photon energy region of interband transitions of semiconductor structures and suppresses uninteresting background effects. Also weak features that may not have been detected in the absolute spectra are often enhanced and a large number of sharp spectral features can be observed even at room temperature. In the case of QW structures it is typical that many optical transitions related to the excited QW states are observed in common with the ground state transitions and the QW barrier ones. The analysis of the optical transitions observed in the electromodulation spectra together with theoretical calculations makes it possible to determine material parameters such as the band gap discontinuity or other properties. This kind of procedures has been already applied in PR and CER studies for different semiconductor structures [18–22]. In this paper the same approach has been used to study the band gap discontinuity of the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs. 2. Experiment The samples were grown by molecular beam epitaxy on (001) sulfur doped InP substrates. Before the growth of QW samples, thick InGaAs and InGaAlAs layers were grown in order to calibrate the growth conditions. The In0.53 Ga0.47 As well was grown on a 200 nm thick In0.53 Ga0.23 Al0.24 As layer and then covered again by 100 nm of In0.53 Ga0.47 As layer and 10 nm InP cap layer. Both the well and barrier layers are lattice-matched to the InP substrate. Three samples with the nominal QW thickness of 6, 7 and 8 nm were grown for these studies. The QW thickness was controlled by the growth parameters which were calibrated for thick InGaAs layers. Fig. 1 shows high resolution X -ray (HRXRD) spectra for the three QW structures together with the simulation curves. From the comparison of the HRXRD data with the simulations it has been concluded that the QW structures have parameters (contents and thicknesses) very close to the intended values. In order to measure PR and CER spectra a so-called bright configuration of the setup has been used [23]. Light from a halogen lamp was reflected from the sample and analyzed with use of a lock-in
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 1. HRXRD spectra of InGaAs/InGaAlAs QWs (black lines) together with simulating curves (grey lines).
technique utilizing a single-grating 0.55 m focal length monochromator with an InGaAs PIN detector. The pump beam for PR was provided by the 532 nm line of a CW YAG laser. The laser light was chopped by a mechanical modulator at the frequency of 275 Hz. In the case of CER measurements the sample was mounted in an open air capacitor with the top electrode made of a copper mesh and the bottom electrode made of a copper solid block. The semitransparent top electrode was kept at a distance of approx. 0.1 mm from the sample surface while the sample itself was glued to the bottom copper block. A maximum peak-to-peak alternating voltage of 1.8 kV was used for the modulation at a frequency of 280 Hz. 3. Results and discussion Figs. 2–4 show room temperature PR (bottom) and CER (top) spectra for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs, respectively. In general, the same optical transitions are visible in both PR and CER spectra. In the case of PR spectra, a broad background-like signal is visible through the whole spectra whereas such a signal is not present in the CER spectra. The backgroundlike signal can be associated with below band gap oscillations which are often observed in the region of the sample transparency [24–27]. Such oscillations are usually very strong for GaAs-based structures grown on n-type substrates and they are weak or even invisible for GaAs-based structures grown on semi-insulating GaAs substrates. Since the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW system was grown on n-type InP substrate, a similar below band gap oscillation can be expected in PR spectra. CER spectra are free of the below band gap oscillations due to the different electromodulation mechanisms [26]. It is an advantage of the CER spectroscopy, since it makes it easier to interpret and analyze the spectral features which are associated with the QW transitions. Note that in this case the intensity of the oscillation-like signal in PR spectra is not strong and does not disturb the analysis of the QW transitions. The strongest PR and CER signals at ∼1.06 eV are associated with the photon absorption in In0.53 Ga0.23 Al0.24 As bulk-like QW barriers. The characteristic Franz–Keldysh oscillations (FKO) [28] apparent at higher energy values are due to the built-in electric field in In0.53 Ga0.23 Al0.24 As layers. Because of no doping in In0.53 Ga0.23 Al0.24 As barriers and In0.53 Ga0.47 As QW the electric field in this region is expected to be more or less homogeneous and results from the Fermi-level pinning at
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Fig. 2. Room temperature PR (bottom) and CER (top) spectra of the 6 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
Fig. 3. Room temperature PR (bottom) and CER (top) spectra of the 7 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
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Fig. 4. Room temperature PR (bottom) and CER (top) spectra of the 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW together with the fitting curves (thick solid lines) and the moduli of the individual resonances (dashed lines).
In0.53 Ga0.23 Al0.24 As surface and In0.53 Ga0.23 Al0.24 As/(InP substrate) interface. From the period of FKO, it has been estimated [28] that this field is in the range of 8–17 kV/cm. The PR and CER resonances below the InGaAlAs-related transition are associated with the optical transitions in the In0.53 Ga0.47 As QW. These resonances have been fitted with the low-field electromodulation Lorentzian line-shape functional form [14,29] Eq. (1), with m = 2 which corresponds to an exciton transition.
1R R
(E ) = Re
" l X
# Cj · e
E − Ej + i · Γj
i·ϑj
−mj
+ g (E ).
(1)
j =1
In Eq. (1) l is the number of optical transitions (the number of independent spectral functions used in the fitting procedure), Cj and ϑj are the amplitude and phase, Ej and Γj are the energy and the broadening parameter of the j-transition, respectively. The function g (E ) is a function which simulates the background, which can be associated with the below band gap oscillations [24,25]. In the narrow spectral range (a range of one PR resonance) this background can be simulated by a linear or a parabolic function. In broader spectral range it can be a sinus-like function, see the shape of the below band gap oscillation in Refs. [24,25]. In order to simulate the background with the minimal number of fitting parameters, we divided our PR spectra for a few spectral ranges and we assumed that g (E ) is a linear function in each spectral range. The fitting curves are shown by thick lines in Figs. 2–4 together with the moduli of the individual resonances (dashed lines) obtained according to Eq. (2)
Cj
1ρj (E ) =
h
E − Ej
2
+ Γj
2
i m2j .
(2)
The notation nmH(L) in Figs. 2–4 denotes the transition between the nth heavy-hole (light-hole) valence subband and the mth conduction subband. The resonance at the lowest energy originates from the 11H transition, which is the fundamental transition for all QW samples. In addition to the
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 5. Comparison of the experimental data (horizontal dashed lines) with the theoretical predictions obtained for the various QC values (solid curves).
11H transition, the spectra show the 11L transition (i.e. the lowest energy transition for light-holes) and transitions between excited QW states. The identification of the resonances was possible on the basis of the calculations performed in the framework of the effective mass approximation. Relevant details of the calculations can be found in our previous papers [20–22]. All the material parameters for the In1−x−y Gax Aly As alloy have been obtained by a linear interpolation between the parameters of a relevant binary semiconductor alloy [1] according to Eq. (3). Q (x, y) = x · QGaAs + (1 − x − y) · QInAs + y · QAlAs ,
(3)
where Qi is an electron effective mass or a stiffness constant of a binary compound (GaAs, InAs or AlAs). The conduction band offset (QC ) is defined by Eq. (4) as
1EC × 100% (4) (1EC + 1EV ) where 1EC and 1EV are the conduction and valence band discontinuities at the heterojunction QC =
for unstrained materials (individual bulk alloys). In the case of QWs investigated in this paper the ‘‘unstrained’’ QC is the same as the ‘‘strained’’ QC since both the QW and barrier layers are latticematched to the InP substrate. The band gap energy of QW barriers has been acquired from fitting of PR and CER data whereas the band gap energy of In0.53 Ga0.47 As has been calculated after the well-known quadratic formula for In1−x Gax As with the bowing parameter C = 0.477 eV [1]. All calculations have been performed for the nominal contents and thicknesses of the QWs. However, it has been found that the ground state transition in PR and CER spectra is observed at a higher energy. Thus finally the content of the In0.53 Ga0.47 As layer has been corrected by <2% and in this way the theoretical ground state transition has been adjusted to the experimental data. It is also worth noting that the differences between energy levels are weakly sensitive to the changes in the In0.53 Ga0.47 As band gap energy [20]. Therefore, the analysis of the energy difference between 22H and 11H transitions (or 31H and 11H ones) is a good way to determine the band gap discontinuity for QWs. This procedure has also been applied in this paper. Fig. 5(a), (b) and (c) show the theoretical calculations as a function of QC performed for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW, respectively, together with the experimental data
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 6. Method used to analyze the QC in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs with (a) 6 nm, (b) 7 nm and (c) 8 nm thicknesses. The horizontal dashed lines correspond to the energy difference between the 31H and 11H transitions taken from the experimental data. Solid curves correspond to the energy difference between the 31H and 11H transitions obtained from the theoretical calculations in a function of QC .
(horizontal dashed lines). In addition to the allowed 11H, 11L, 22H and 22L transitions, calculations for the partially allowed 31H transition is plotted in these figures. A reasonable agreement for all the samples is found for the QC = 60%. The same conclusion has been obtained by analyzing the energy difference between 31H and 11H transitions (see Fig. 6). In the case of the QW samples, the resonance related to the 31H transition does not interfere with the other QW resonances and hence the analysis of the energy difference between 31H and 11H transitions is a good criterion for the determination of the QC for this system. In the case of the resonance related to the 22H transition a contribution of the 12H transition is significant and hence a disagreement between the calculations and the experimental data is observed for this transition for the 8 nm wide QW (see Fig. 5(c)). In order to support this conclusion, the low temperature PR measurements have been performed for the three QW structures. The temperature decrease narrows PR resonances and so helps to separate individual QW transitions. Fig. 7(a), (b) and (c) show low temperature PR spectra in the region of QW transitions for 6, 7 and 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs, respectively. It is clearly visible that the spectral feature attributed to the 22H transition at room temperature is composed of the two resonances with very similar intensities. These resonances are associated with the 12H and 22H transitions. The relatively strong intensity of the 12H transition, in comparison with the 22H one, is due to the significant imperfections in the square-like profile of the QW potential. In our case, these imperfections can be associated with the surface electric field [30] since the QW is close to the sample surface and the existence of the built-in electric field in the QW region is confirmed by the InGaAlAs-related FKO. It is worth noting that the built-in electric field is neglected in our calculations because of small Stark shift of QW transitions in this regime of electric fields (see in Fig. 8 that the shift is smaller than 5 meV for 7 nm width In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW when the electric field is smaller than 20 kV/cm). On the other hand it known that even small electric field (e.g. F >5 kV/cm) influences the integral intensity very strongly if the electron (or hole) level is weakly confined in the QW potential, i.e. the QW level is located close to the barrier energy. Such a situation takes place for the second electron and the third heavy-hole levels in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs. It explains why 13H and 21H transitions are relatively strong in PR and CER spectra and they are observed even
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(a) 6nm
(b) 7nm
(c) 8nm
Fig. 7. Low temperature PR spectra of (a) 6 nm, (b) 7 nm and (c) 8 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs.
Fig. 8. Stark shift of optical transitions for 7 nm wide In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW. The square corresponds to the range of the built-in electric field in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QW samples.
at low temperatures. For this system it is also possible that an atom interdiffusion at QW interfaces leads to some imperfections in the square-like QW profile. But this effect is small for unannealed QWs and therefore it is expected that in our case this effect can influence only the electron–hole overlap integrals for the 13H and 21H transitions. Fig. 9 shows the band gap discontinuities for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As/InP system. After Ref. [1] it has been assumed that the QC for In0.53 Ga0.47 As/InP interface is 40%. This value is well known for this system and is generally accepted. In this work it has been found that the QC for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface is ∼60%. In this case the direct comparison of the obtained value of the QC and the literature data is limited since there are no reports on this subject precisely. However, some data for the In0.53 Ga0.23 Al0.24 As/InP interface are available and hence a conclusion concerning the QC for the In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interface can be obtained.
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1.6
energy (eV)
1.2
0.8
0.4
0.0 III-V compound Fig. 9. Band gap discontinuities and QC values for the whole InP/In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As/InP system.
On the other hand the QC for the In0.53 Ga0.23 Al0.24 As/InP interface can be determined knowing the QC for the In0.53 Ga0.47 As/InP and In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As interfaces. Assuming that the QC for the In0.53 Ga0.47 As/InP interface is 40% [1] it has been found that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is smaller than 13% (and if the QC for the In0.53 Ga0.47 As/InP is equal to 35% it has been found that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is less than 2%). The obtained values of the QC for the In0.53 Ga0.23 Al0.24 As/InP interface are consistent with the literature data since it has been reported that the conduction band lineup for this system changes from type I to type II at the Al content of ∼22%–26% [6,31]. 4. Summary PR and CER have been applied to study the optical transitions in In0.53 Ga0.47 As/In0.53 Ga0.23 Al0.24 As QWs with various thicknesses. The ground 11H and 11L transitions and the excited state transitions such as 31H and 22H have been clearly observed in both PR and CER spectra. The experimental QW transition energies have been compared with the theoretical predictions based on an effective mass formalism model. Satisfactory agreement between the experimental data and the theoretical calculations has been found for QC = 60%. It has been additionally concluded that the QC for the In0.53 Ga0.23 Al0.24 As/InP interface is less than 13%. The obtained results show that QWs with the sufficiently deep confinement potential for both electrons and holes can be grown on InP substrate with the use of InGa(Al)As alloys. Acknowledgment R.K. acknowledges the financial support from the Foundation for Polish Science. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
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