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GaAs heterostructures
Materials Science and Engineering B 147 (2008) 166–170
Deep traps and optical properties of partially strain-relaxed InGaAs/GaAs heterostructures Ł. Gelczuk a,∗ , M. Motyka b , J. Misiewicz b , M. D˛abrowska-Szata a a
Faculty of Microsystem Electronics and Photonics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland b Institute Of Physics, Wrocław University of Technology, Wybrze˙ze Wyspia´ nskiego 27, 50-370 Wrocław, Poland Received 18 June 2007; received in revised form 27 August 2007; accepted 31 August 2007
Abstract The electrical and optical properties of the lattice-mismatched InGaAs/GaAs heterostructures, with partial strain relaxation, were studied by deep level transient spectroscopy (DLTS) and photoreflectance (PR) spectroscopy, respectively. In the samples one of deep electron traps, revealed by DLTS, was ascribed to misfit dislocations at the interface, for which capture kinetics, concentration depth profiles and the type of electronic states have been specified. Room temperature PR spectroscopy was used for analysing the effect of residual strain on the optical response from the samples, i.e. interband transitions and the valence band splitting. © 2007 Elsevier B.V. All rights reserved. Keywords: Strain relaxation; Dislocations; Electronic states; Optical properties; DLTS; PR spectroscopy
1. Introduction In recent years lattice-mismatched III–V semiconductor heterostructures have found promising technological applications due to a high flexibility in tailoring their physical properties, especially the electrical and optical ones. The pseudomorphic epitaxial growth of such heterostructures is accompanied by elastic strain, arising at the interface, which affects the electronic structure and optical properties of the layers, i.e. changes the band gap energy, reduces or removes the interband or intraband degeneracies or induces coupling between neighbouring bands [1]. In the structures consisting of epitaxial layers with thicknesses exceeding the specific critical value, strain is relieved by the generation of misfit dislocations at the interface between the layer and the substrate. The misfit dislocations are usually accompanied by threading dislocations, which propagate through the whole thickness of the epitaxial layer up to the surface. Extended defects, like dislocations are associated with a large number of deep-lying, closely spaced electronic states in the band gap, forming one-dimensional (1D) energy bands, which
∗
Corresponding author. Tel.: +48 71 3203926; fax: +48 71 3283504. E-mail address: [email protected] (Ł. Gelczuk).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.08.028
usually act as recombination centres or traps for free carriers. Thereby they affect the density of the free charge carriers, their mobility and lifetime [2] and can drastically degrade the semiconductor devices performance and reliability. In this paper, we studied the electrical and optical properties of a set of Inx Ga1−x As/GaAs heterostructures with single, partially relaxed epitaxial layers, having different indium compositions (x = 0.055, 0.077, 0.086) and thicknesses (d = 200, 160, 280 nm). These samples were studied by a combination of DLTS and PR techniques. The DLTS technique [3] was used to study electronic properties of deep traps associated with misfit dislocations. As it was already shown [4], DLTS can be successfully exploited for measuring, beside the fundamental defect characteristics, also such features like non-exponential capacitance transients of electron emission from the dislocation traps or logarithmic capture kinetics of free carriers by the traps. This technique enables us to specify the electronic states at dislocations, as well [5,6]. Next, the PR spectroscopy, due to its high sensitivity and derivative nature in the spectral line shapes [7], was employed to study the effects of residual strain on the optical response from the samples, i.e. interband electronic transitions and the valence band splitting energies. The PR analyse allows us to estimate the extent of strain relaxation and the values of residual strain in the samples, as well.
Ł. Gelczuk et al. / Materials Science and Engineering B 147 (2008) 166–170
2. Experimental details The metalorganic vapour phase epitaxy (MOVPE) technique was used to grow the single Inx Ga1−x As epitaxial layers on the (0 0 1)-oriented n+ -GaAs substrates. The atmospheric pressure MOVPE system was equipped with AIX-200 R&D horizontal reactor manufactured by AIXTRON. The standard organometallic group III precursors, i.e. TMGa (trimethylgallium) and TMIn (trimethylindium), were used. They were transported by passing H2 through bubblers and controlled by the pressure level in bubblers. Next, AsH3 was used as the arsenic source reactant. The growth temperature was equal to 670 ◦ C. The samples had different indium compositions 0.055 (sample A), 0.077 (sample B), 0.086 (sample C) and thicknesses equal to 200, 160, 280 nm, respectively. The Inx Ga1−x As layers were unintentionally doped with donors at about 2 × 1016 cm−3 . Between the Inx Ga1−x As epitaxial layer and the GaAs substrate 500 nm thick GaAs buffer layer, doped with Si at about 2 × 1017 cm−3 , was used. The compositions of all the epitaxial layers were determined by high resolution X-ray diffraction (HRXRD) rocking curve measurements, by means of high resolution Philips HR-XRD diffractometer. The structural analysis of the 2D reciprocal lattice maps (RLMs) indicated that the samples were partially relaxed. The calculated indium contents correspond to the difference in the lattice parameter between GaAs and the ternary compound of about 0.39% (sample A), 0.55% (sample B) and 0.62% (sample C), respectively. It results in the generation of 2D network of 60◦ misfit dislocations lying along two orthogonal 1 1 0 crystallographic directions at the (0 0 1) interface [8]. The electrical characteristics were measured for the Schottky diodes, produced by evaporation of 0.44 mm2 circular Au layer, by standard lift-off on the front side of the sample. Prior to the Schottky contacts formation, the ohmic contact was obtained on the whole backside of the n+ -GaAs substrate by Au/Ge alloy evaporation and annealing was carried out in 600 ◦ C for several seconds. The quality of the Schottky barrier was checked up by the I–V–T and C–V–T measurements, showing good rectifying characteristics. The DLTS spectra were taken using the deep level transient spectroscopy (DLTS) technique within the 200–400 K temperature range with the help of the DLS-82E
167
spectrometer manufactured by Semitrap (Hungary), equipped with 1 MHz capacitance bridge and the lock-in type integrator [9]. In order to ensure that the observed DLTS-signal comes from the narrow part of the depletion region including the interface between the epitaxial layer and the substrate, the double correlation DLTS method (DDLTS) was used [10]. The optical characteristics were obtained by analyzing the PR spectra measured at room temperature, using a conventional experimental set-up with a tungsten halogen lamp (150 W) as a probe light source and a 632.8 nm laser, used as a modulation source. A phase sensitive detection of the PR signal was made using a lock-in amplifier and a Si photodiode. The other relevant details of the PR set-up are described in Ref. [11]. 3. Results and discussion 3.1. DLTS analysis The DLTS analysis involved a precise selection of the measurement conditions, i.e. a reverse voltage as well as filling-pulse voltages, in order to probe the region included interface between the Inx Ga1−x As epitaxial layer and the GaAs substrate. The use of the Schottky barriers allows us to investigate only the majority carriers in the upper half of the band gap. Finally, we established the bias conditions as follows: quiescent reverse voltage UR = −1 V and two filling pulses, U1 = 0 V and U2 = −0.5 V. The measurements were performed for the two samples B and C, with 0.077 and 0.086 indium content, respectively. In the sample B only one deep electron trap labelled E1 was clearly observed in the DLTS spectrum (Fig. 1a). The latter trap labelled E2, on the high-temperature side of the spectrum was poorly visible, so its analysis was difficult. Next, in the sample C, the two deep electron traps were clearly visible in the spectrum (Fig. 1b). The DLTS-line of the trap E1 is asymmetrically broadened with a longer tail on the low-temperature side of the peak (Fig. 1a and b) compared to the line of the latter trap E2 (Fig. 1b). Such a line broadening is frequently observed in DLTS measurements for the case of lattice-mismatched compound semiconductors and it is associated with non-exponential capacitance transients
Fig. 1. Representative DLTS temperature spectra of the Inx Ga1−x As/GaAs heterostructures, measured at the lock-in frequency equals to 25 Hz in DDLTS mode, (a) sample B with x = 0.077; (b) sample C with x = 0.086. Reverse bias UR = −1 V, filling-pulse height U1 = 0 V, U2 = −0.5 V, width of the pulses tp = 20 s.
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mainly attributed to the presence of a dislocations network itself or dislocation-related defects [12]. Its origin is related to the formation of deep-lying closely spaced energy levels in the form of 1D energy bands as opposed to isolated energy levels, typical for the point defects (exponential transients). The ratio of the full width at a half maximum to the peak temperature (FWHM/Tp ) was found to be 0.23 (sample B) and 0.32 (sample C) for E1 trap and 0.13 for E2 trap (only sample C), respectively. This suggests that E1 trap can be connected with the presence of dislocations contrary to the trap E2, because according to the overall conviction, this ratio is expected to be approximately 0.1 for the deep levels associated with simple point defects [13]. The DLTS-spectra, taken for several lock-in frequencies and the same width of the filling pulse equal to 20 s, made possible to construct the Arrhenius plots, i.e. the relation of en /T2 vs. 1000/T, where en stands for the electron emission rate at a temperature T. Using a standard least square fitting procedure of the experimental data shown in Fig. 2, the activation energies, i.e. energy level positions (EC − ET ) and the capture cross-sections (σ n ) of the traps, were obtained. The trap E2 with a deep level at 0.72 eV and a capture crosssection equal to 4.22 × 10−14 cm2 , as calculated from the slope of the Arrhenius plot, was ascribed to the EL2 electron trap, well known as a dominant native point defect in GaAs and GaAsbased semiconductors, related to the arsenic antisite defect AsGa . On the other hand, the deep energy level position of the trap E1 was equal to 0.57 eV in sample B and 0.43 eV in sample C, respectively. The reason, why the energy level positions of the trap E1 differ in both the samples, can be explained by a different composition of the Inx Ga1−x As films, which affect the change of the band gap energy and thus the activation energy of this trap [14]. The precise evaluation of its activation energy can be also slightly disturbed by the close location of the relatively large EL2 peak in the DLTS spectrum (Fig. 1b) due to partial overlapping of both peaks [12]. The capture cross-section for the trap E1 was not calculated, because it was changing with time for dislocation traps. As the charge of the dislocation builds up during the capture process, the
Fig. 2. Arrhenius plots for the traps E1 and E2 revealed in the Inx Ga1−x As/GaAs heterostructures with x = 0.077 (sample B) and x = 0.086 (sample C). The dotted lines represent the best least squares fitting to the experimental data.
Fig. 3. DLTS-peak amplitudes of E1 and E2 traps vs. filling-pulse duration.
defect becomes more repulsive and less attractive for free charge carriers. It is a consequence of existing the time-dependent electrostatic potential built up at the dislocation, which limits the successive capture of carriers [4]. This specific feature, called a logarithmic capture law can be measured by DLTS as the variation of the DLTS-peak amplitudes vs. logarithm of the filling-pulse duration (tp ). The results of such an analysis was presented in Fig. 3. As one can see, the DLTS-peak amplitudes of the trap E1 in both the samples show a linear dependence on the logarithm of the time tp , while the amplitude corresponding to the defect E2 indicates a distinct saturation for long filling-pulse times. These findings indicate the assignment of the trap E1 to dislocations, while the latter trap E2 to isolated point defects, what is in a good agreement with the previous attribution of this trap to the EL2 point defect. The DLTS technique makes also possible to determine the nature of dislocation traps, namely to classify the electronic states at dislocations as “bandlike” or “localized”, as it was proposed by Schr¨oter at al. [5,6]. We have recently shown that a complex analysis of the DLTS-line shape and DLTS-line behaviour as well as capture kinetics measurements, makes possible to distinguish between the point defects and dislocations and clearly specify the type of dislocation-related electronic states [15]. In our recent papers [16,17], the nature of the trap E1, evidently connected with dislocations, was investigated. On the basis of the framework proposed, for analysing the variation of the DLTS-line maximum and shape with the filling-pulse time, we did not observe any distinct shift of the broadened E1-peak maximum, while its high-temperature sides match to each other and the low-temperature sides split after normalizing (see Ref. [16]). It enables us to attribute the E1 electron trap to “localized” states at dislocations. Furthermore, the depth concentration profiles for this trap revealed a distinct maximum near the epilayer-substrate interface of the samples that indicated the attribution of the trap E1 to electron states at 60◦ misfit dislocations, lying at the interface (see Ref. [17]). Finally, we have shown in Ref. [16] that the activation energy of the E1 trap scales linearly with the change of the band gap energy, owing to the different composition of the ternary compound. A similar dependence appears in the case of the well known electron trap,
Ł. Gelczuk et al. / Materials Science and Engineering B 147 (2008) 166–170
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Table 1 The values of the interband transition energies (EHH , ELH ) and the valence band splitting obtained both from experimental studies (Eexp ) and theoretical calculations (Etheor ) Sample
A B C
Fig. 4. PR spectra of Inx Ga1−x As/GaAs heterostructures (thin solid squares), (a) sample A (x = 0.055); (b) sample B (x = 0.077); (c) sample C (x = 0.086). The bars mark the excitonic transition energies obtained from the best fits (thick solid lines). Dashed lines represent the modulus of resonances of the individual lines.
called ED1, and associated with misfit or threading dislocations in many lattice-mismatched AIII BV heterostructures [12,14,18]. Both the traps revealed the same constant position of their energy levels with respect to the top of the valence band. On the basis of these findings we identified the trap E1 as the ED1 one. 3.2. PR analysis The room temperature PR spectra of all the investigated Inx Ga1−x As/GaAs heterostructures with x = 0.055 (sample A), 0.077 (sample B) and 0.086 (sample C), respectively, were shown in Fig. 4. There are three transitions observed for every structure. The transition near the energy 1.42 eV is related to the photon absorption in the GaAs buffer layer. The other two features in the low energy part of the spectrum correspond to the photon absorption in the Inx Ga1−x As epilayer. These features are composed of two resonances related to the absorption between the heavy hole (HH) and light hole (LH) valence band and the conduction band. The energy difference between these two resonances is related to the valence band splitting between LH and HH bands, that is directly related to strain in epitaxial layers. The transitions are interpreted as H11 and L11 (marked by the bars in Fig. 4); the notation H(L)mn means the transition between the mth valence subband and the nth conduction subband. Pseudomorphic InGaAs epitaxial layers grown on (0 0 1)oriented GaAs substrate are submitted to the in-plane biaxial strain, which causes a tetragonal compression of the layer [1].
Indium content
Experiment
Theory
EH11 (eV)
EL11 (eV)
Eexp (eV)
Etheor (eV)
0.055 0.077 0.086
1.344 1.290 1.268
1.366 1.317 1.295
0.022 0.027 0.027
0.029 0.039 0.044
For the E0 critical point the strain can be decomposed into a hydrostatic component, which shifts the energy gap between the valence bands and the lowest lying conduction band, and an uniaxial component, which splits the heavy hole and light hole valence bands [7,19]. The analysis of the PR spectra shown in Fig. 4 on the basis of the so-called deformation potential theory [1,7] makes possible to express the resulting energy gap and splitting in terms of the in-plane residual strain in the partially relaxed Inx Ga1−x As epitaxial layers. The PR spectra were analyzed by using the typical line shape functional form, characterizing the electromodulated signals in bulk semiconductors, and interpreted according to the well known Aspnes’ relation [20]. The energies of H11 and L11 transitions determined from the best fit of experimental data and energy splitting, were shown in Table 1. By using the energy splitting Eexp obtained from PR experiment we were able to calculate the residual strain values in our partially relaxed Inx Ga1−x As epitaxial layers. Furthermore, a comparison of the experimentally obtained valence band splitting Eexp of the partially relaxed samples with the splitting Etheor calculated theoretically for the case of fully strained pseudomorphic layers (shown in Table 1), allowed us to estimate the extent of strain relaxation in the Inx Ga1−x As epitaxial layers. The calculated percentage difference of H11–L11 splitting between the fully strained and partially relaxed layers is 24, 31 and 39% for the sample A, B and C, respectively. It may be treated as the percentage estimation of the extent of strain relaxation. The results were shown in Fig. 5. As one can see,
Fig. 5. Residual strain values and the extent of strain relaxation vs. In content in the partially relaxed Inx Ga1−x As/GaAs heterostructures, determined from PR analysis.
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when the extent of partial strain relaxation increases, the residual strain decreases inducing the lower valence band splitting. It is a consequence of the fact that when the strain in the epitaxial layer is starting to relax due to the generation of misfit dislocations, the valence band splitting is decreasing. 4. Conclusions In conclusion, the electrical and optical properties of the partially strain-relaxed Inx Ga1−x As/GaAs heterostructures with different compositions and thicknesses, grown by MOVPE, were investigated. The DLTS technique revealed two deep electron traps. The analysis of the DLTS-data connected with the electron trap labelled E1, with the activation energy 0.43 and 0.57 eV (depending on composition), enabled us to attribute this trap to “localized” states at 60◦ misfit dislocations, lying at the interface between the epitaxial layer and the substrate, and to identify the E1 trap as ED1 one. The latter electron trap, called E2, with the activation energy 0.72 eV, was identified as the well known EL2 native point defect. The PR spectroscopy was employed to study the effects of residual strain on the optical response from the samples. The analysis of PR spectra yielded the values of residual strain and the extent of strain relaxation in the epitaxial layers. It was found that the investigated Inx Ga1−x As epilayers with x = 0.055, 0.077 and 0.086 are relaxed in 24, 31 and 39%, respectively. Acknowledgement The authors are grateful to D. Radziewicz (Wrocław University of Technology) for growing the InGaAs/GaAs heterostructures.
References [1] G.L. Bir, G. Pikus, Symmetry and Strain-Induced Effects in Semiconductors, Wiley, New York, 1974. [2] E.R. Weber, Physica B 340–342 (2003) 1–14. [3] D.V. Lang, J. Appl. Phys. 45 (1974) 3023–3032. [4] T. Figielski, Phys. Stat. Sol. 121 (1990) 187–193. [5] W. Schr¨oter, J. Kronewitz, U. Gnauert, F. Riedel, M. Seibt, Phys. Rev. B 52 (1995) 13726–13729. [6] W. Schr¨oter, H. Hedemann, V. Kveder, F. Riedel, J. Phys.: Condens. Matter 14 (2002) 13047–13059. [7] 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. [8] J. te Nijenhuis, P.J. van der Wel, E.R.H. van Eck, L.J. Giling, J. Phys. D: Appl. Phys. 29 (1996) 2961–2970. [9] G. Ferenczi, J. Kiss, Acta Phys. Acad. Sci. Hung. 50 (1981) 285–290. [10] H. Lefevre, M. Schulz, Appl. Phys. 12 (1977) 45–53. [11] J. Misiewicz, P. Sitarek, G. S˛ek, R. Kudrawiec, Mater. Sci. Poland 21 (2003) 263–318. [12] O. Yastrubchak, T. Wosi´nski, A. M˛akosa, T. Figielski, A.L. T´oth, Physica B 308–310 (2001) 757–760. [13] L.C. Kimerling, J.R. Patel, Appl. Phys. Lett. 34 (1979) 73–75. [14] T. Wosi´nski, O. Yastrubchak, A. M˛akosa, T. Figielski, J. Phys.: Condens. Matter 12 (2000) 10153–10159. [15] Ł. Gelczuk, M. D˛abrowska-Szata, G. J´oz´ wiak, Mater. Sci. Poland 23 (2005) 625–641. [16] Ł. Gelczuk, M. D˛abrowska-Szata, G. J´oz´ wiak, D. Radziewicz, Physica B 388 (2007) 195–199. [17] Ł. Gelczuk, M. D˛abrowska-Szata, G. J´oz´ wiak, D. Radziewicz, J. Serafi´nczuk, P. Dłu˙zewski, Phys. Stat. Sol. C 4 (2007) 3037– 3042. [18] T. Wosi´nski, J. Appl. Phys. 65 (1989) 1566–1570. [19] M. Geddo, G. Guizzetti, M. Patrini, T. Ciabattoni, L. Seravalli, P. Frigeri, S. Franchi, Appl. Phys. Lett. 87 (2005) 263120. [20] D.E. Aspnes, Surf. Sci. 37 (1973) 418–442.
Deep traps and optical properties of partially strain-relaxed InGaAs/GaAs heterostructures Ł. Gelczuk a,∗ , M. Motyka b , J. Misiewicz b , M. D˛abrowska-Szata a a
Faculty of Microsystem Electronics and Photonics, Wrocław University of Technology, Janiszewskiego 11/17, 50-372 Wrocław, Poland b Institute Of Physics, Wrocław University of Technology, Wybrze˙ze Wyspia´ nskiego 27, 50-370 Wrocław, Poland Received 18 June 2007; received in revised form 27 August 2007; accepted 31 August 2007
Abstract The electrical and optical properties of the lattice-mismatched InGaAs/GaAs heterostructures, with partial strain relaxation, were studied by deep level transient spectroscopy (DLTS) and photoreflectance (PR) spectroscopy, respectively. In the samples one of deep electron traps, revealed by DLTS, was ascribed to misfit dislocations at the interface, for which capture kinetics, concentration depth profiles and the type of electronic states have been specified. Room temperature PR spectroscopy was used for analysing the effect of residual strain on the optical response from the samples, i.e. interband transitions and the valence band splitting. © 2007 Elsevier B.V. All rights reserved. Keywords: Strain relaxation; Dislocations; Electronic states; Optical properties; DLTS; PR spectroscopy
1. Introduction In recent years lattice-mismatched III–V semiconductor heterostructures have found promising technological applications due to a high flexibility in tailoring their physical properties, especially the electrical and optical ones. The pseudomorphic epitaxial growth of such heterostructures is accompanied by elastic strain, arising at the interface, which affects the electronic structure and optical properties of the layers, i.e. changes the band gap energy, reduces or removes the interband or intraband degeneracies or induces coupling between neighbouring bands [1]. In the structures consisting of epitaxial layers with thicknesses exceeding the specific critical value, strain is relieved by the generation of misfit dislocations at the interface between the layer and the substrate. The misfit dislocations are usually accompanied by threading dislocations, which propagate through the whole thickness of the epitaxial layer up to the surface. Extended defects, like dislocations are associated with a large number of deep-lying, closely spaced electronic states in the band gap, forming one-dimensional (1D) energy bands, which
∗
Corresponding author. Tel.: +48 71 3203926; fax: +48 71 3283504. E-mail address: [email protected] (Ł. Gelczuk).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.08.028
usually act as recombination centres or traps for free carriers. Thereby they affect the density of the free charge carriers, their mobility and lifetime [2] and can drastically degrade the semiconductor devices performance and reliability. In this paper, we studied the electrical and optical properties of a set of Inx Ga1−x As/GaAs heterostructures with single, partially relaxed epitaxial layers, having different indium compositions (x = 0.055, 0.077, 0.086) and thicknesses (d = 200, 160, 280 nm). These samples were studied by a combination of DLTS and PR techniques. The DLTS technique [3] was used to study electronic properties of deep traps associated with misfit dislocations. As it was already shown [4], DLTS can be successfully exploited for measuring, beside the fundamental defect characteristics, also such features like non-exponential capacitance transients of electron emission from the dislocation traps or logarithmic capture kinetics of free carriers by the traps. This technique enables us to specify the electronic states at dislocations, as well [5,6]. Next, the PR spectroscopy, due to its high sensitivity and derivative nature in the spectral line shapes [7], was employed to study the effects of residual strain on the optical response from the samples, i.e. interband electronic transitions and the valence band splitting energies. The PR analyse allows us to estimate the extent of strain relaxation and the values of residual strain in the samples, as well.
Ł. Gelczuk et al. / Materials Science and Engineering B 147 (2008) 166–170
2. Experimental details The metalorganic vapour phase epitaxy (MOVPE) technique was used to grow the single Inx Ga1−x As epitaxial layers on the (0 0 1)-oriented n+ -GaAs substrates. The atmospheric pressure MOVPE system was equipped with AIX-200 R&D horizontal reactor manufactured by AIXTRON. The standard organometallic group III precursors, i.e. TMGa (trimethylgallium) and TMIn (trimethylindium), were used. They were transported by passing H2 through bubblers and controlled by the pressure level in bubblers. Next, AsH3 was used as the arsenic source reactant. The growth temperature was equal to 670 ◦ C. The samples had different indium compositions 0.055 (sample A), 0.077 (sample B), 0.086 (sample C) and thicknesses equal to 200, 160, 280 nm, respectively. The Inx Ga1−x As layers were unintentionally doped with donors at about 2 × 1016 cm−3 . Between the Inx Ga1−x As epitaxial layer and the GaAs substrate 500 nm thick GaAs buffer layer, doped with Si at about 2 × 1017 cm−3 , was used. The compositions of all the epitaxial layers were determined by high resolution X-ray diffraction (HRXRD) rocking curve measurements, by means of high resolution Philips HR-XRD diffractometer. The structural analysis of the 2D reciprocal lattice maps (RLMs) indicated that the samples were partially relaxed. The calculated indium contents correspond to the difference in the lattice parameter between GaAs and the ternary compound of about 0.39% (sample A), 0.55% (sample B) and 0.62% (sample C), respectively. It results in the generation of 2D network of 60◦ misfit dislocations lying along two orthogonal 1 1 0 crystallographic directions at the (0 0 1) interface [8]. The electrical characteristics were measured for the Schottky diodes, produced by evaporation of 0.44 mm2 circular Au layer, by standard lift-off on the front side of the sample. Prior to the Schottky contacts formation, the ohmic contact was obtained on the whole backside of the n+ -GaAs substrate by Au/Ge alloy evaporation and annealing was carried out in 600 ◦ C for several seconds. The quality of the Schottky barrier was checked up by the I–V–T and C–V–T measurements, showing good rectifying characteristics. The DLTS spectra were taken using the deep level transient spectroscopy (DLTS) technique within the 200–400 K temperature range with the help of the DLS-82E
167
spectrometer manufactured by Semitrap (Hungary), equipped with 1 MHz capacitance bridge and the lock-in type integrator [9]. In order to ensure that the observed DLTS-signal comes from the narrow part of the depletion region including the interface between the epitaxial layer and the substrate, the double correlation DLTS method (DDLTS) was used [10]. The optical characteristics were obtained by analyzing the PR spectra measured at room temperature, using a conventional experimental set-up with a tungsten halogen lamp (150 W) as a probe light source and a 632.8 nm laser, used as a modulation source. A phase sensitive detection of the PR signal was made using a lock-in amplifier and a Si photodiode. The other relevant details of the PR set-up are described in Ref. [11]. 3. Results and discussion 3.1. DLTS analysis The DLTS analysis involved a precise selection of the measurement conditions, i.e. a reverse voltage as well as filling-pulse voltages, in order to probe the region included interface between the Inx Ga1−x As epitaxial layer and the GaAs substrate. The use of the Schottky barriers allows us to investigate only the majority carriers in the upper half of the band gap. Finally, we established the bias conditions as follows: quiescent reverse voltage UR = −1 V and two filling pulses, U1 = 0 V and U2 = −0.5 V. The measurements were performed for the two samples B and C, with 0.077 and 0.086 indium content, respectively. In the sample B only one deep electron trap labelled E1 was clearly observed in the DLTS spectrum (Fig. 1a). The latter trap labelled E2, on the high-temperature side of the spectrum was poorly visible, so its analysis was difficult. Next, in the sample C, the two deep electron traps were clearly visible in the spectrum (Fig. 1b). The DLTS-line of the trap E1 is asymmetrically broadened with a longer tail on the low-temperature side of the peak (Fig. 1a and b) compared to the line of the latter trap E2 (Fig. 1b). Such a line broadening is frequently observed in DLTS measurements for the case of lattice-mismatched compound semiconductors and it is associated with non-exponential capacitance transients
Fig. 1. Representative DLTS temperature spectra of the Inx Ga1−x As/GaAs heterostructures, measured at the lock-in frequency equals to 25 Hz in DDLTS mode, (a) sample B with x = 0.077; (b) sample C with x = 0.086. Reverse bias UR = −1 V, filling-pulse height U1 = 0 V, U2 = −0.5 V, width of the pulses tp = 20 s.
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mainly attributed to the presence of a dislocations network itself or dislocation-related defects [12]. Its origin is related to the formation of deep-lying closely spaced energy levels in the form of 1D energy bands as opposed to isolated energy levels, typical for the point defects (exponential transients). The ratio of the full width at a half maximum to the peak temperature (FWHM/Tp ) was found to be 0.23 (sample B) and 0.32 (sample C) for E1 trap and 0.13 for E2 trap (only sample C), respectively. This suggests that E1 trap can be connected with the presence of dislocations contrary to the trap E2, because according to the overall conviction, this ratio is expected to be approximately 0.1 for the deep levels associated with simple point defects [13]. The DLTS-spectra, taken for several lock-in frequencies and the same width of the filling pulse equal to 20 s, made possible to construct the Arrhenius plots, i.e. the relation of en /T2 vs. 1000/T, where en stands for the electron emission rate at a temperature T. Using a standard least square fitting procedure of the experimental data shown in Fig. 2, the activation energies, i.e. energy level positions (EC − ET ) and the capture cross-sections (σ n ) of the traps, were obtained. The trap E2 with a deep level at 0.72 eV and a capture crosssection equal to 4.22 × 10−14 cm2 , as calculated from the slope of the Arrhenius plot, was ascribed to the EL2 electron trap, well known as a dominant native point defect in GaAs and GaAsbased semiconductors, related to the arsenic antisite defect AsGa . On the other hand, the deep energy level position of the trap E1 was equal to 0.57 eV in sample B and 0.43 eV in sample C, respectively. The reason, why the energy level positions of the trap E1 differ in both the samples, can be explained by a different composition of the Inx Ga1−x As films, which affect the change of the band gap energy and thus the activation energy of this trap [14]. The precise evaluation of its activation energy can be also slightly disturbed by the close location of the relatively large EL2 peak in the DLTS spectrum (Fig. 1b) due to partial overlapping of both peaks [12]. The capture cross-section for the trap E1 was not calculated, because it was changing with time for dislocation traps. As the charge of the dislocation builds up during the capture process, the
Fig. 2. Arrhenius plots for the traps E1 and E2 revealed in the Inx Ga1−x As/GaAs heterostructures with x = 0.077 (sample B) and x = 0.086 (sample C). The dotted lines represent the best least squares fitting to the experimental data.
Fig. 3. DLTS-peak amplitudes of E1 and E2 traps vs. filling-pulse duration.
defect becomes more repulsive and less attractive for free charge carriers. It is a consequence of existing the time-dependent electrostatic potential built up at the dislocation, which limits the successive capture of carriers [4]. This specific feature, called a logarithmic capture law can be measured by DLTS as the variation of the DLTS-peak amplitudes vs. logarithm of the filling-pulse duration (tp ). The results of such an analysis was presented in Fig. 3. As one can see, the DLTS-peak amplitudes of the trap E1 in both the samples show a linear dependence on the logarithm of the time tp , while the amplitude corresponding to the defect E2 indicates a distinct saturation for long filling-pulse times. These findings indicate the assignment of the trap E1 to dislocations, while the latter trap E2 to isolated point defects, what is in a good agreement with the previous attribution of this trap to the EL2 point defect. The DLTS technique makes also possible to determine the nature of dislocation traps, namely to classify the electronic states at dislocations as “bandlike” or “localized”, as it was proposed by Schr¨oter at al. [5,6]. We have recently shown that a complex analysis of the DLTS-line shape and DLTS-line behaviour as well as capture kinetics measurements, makes possible to distinguish between the point defects and dislocations and clearly specify the type of dislocation-related electronic states [15]. In our recent papers [16,17], the nature of the trap E1, evidently connected with dislocations, was investigated. On the basis of the framework proposed, for analysing the variation of the DLTS-line maximum and shape with the filling-pulse time, we did not observe any distinct shift of the broadened E1-peak maximum, while its high-temperature sides match to each other and the low-temperature sides split after normalizing (see Ref. [16]). It enables us to attribute the E1 electron trap to “localized” states at dislocations. Furthermore, the depth concentration profiles for this trap revealed a distinct maximum near the epilayer-substrate interface of the samples that indicated the attribution of the trap E1 to electron states at 60◦ misfit dislocations, lying at the interface (see Ref. [17]). Finally, we have shown in Ref. [16] that the activation energy of the E1 trap scales linearly with the change of the band gap energy, owing to the different composition of the ternary compound. A similar dependence appears in the case of the well known electron trap,
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Table 1 The values of the interband transition energies (EHH , ELH ) and the valence band splitting obtained both from experimental studies (Eexp ) and theoretical calculations (Etheor ) Sample
A B C
Fig. 4. PR spectra of Inx Ga1−x As/GaAs heterostructures (thin solid squares), (a) sample A (x = 0.055); (b) sample B (x = 0.077); (c) sample C (x = 0.086). The bars mark the excitonic transition energies obtained from the best fits (thick solid lines). Dashed lines represent the modulus of resonances of the individual lines.
called ED1, and associated with misfit or threading dislocations in many lattice-mismatched AIII BV heterostructures [12,14,18]. Both the traps revealed the same constant position of their energy levels with respect to the top of the valence band. On the basis of these findings we identified the trap E1 as the ED1 one. 3.2. PR analysis The room temperature PR spectra of all the investigated Inx Ga1−x As/GaAs heterostructures with x = 0.055 (sample A), 0.077 (sample B) and 0.086 (sample C), respectively, were shown in Fig. 4. There are three transitions observed for every structure. The transition near the energy 1.42 eV is related to the photon absorption in the GaAs buffer layer. The other two features in the low energy part of the spectrum correspond to the photon absorption in the Inx Ga1−x As epilayer. These features are composed of two resonances related to the absorption between the heavy hole (HH) and light hole (LH) valence band and the conduction band. The energy difference between these two resonances is related to the valence band splitting between LH and HH bands, that is directly related to strain in epitaxial layers. The transitions are interpreted as H11 and L11 (marked by the bars in Fig. 4); the notation H(L)mn means the transition between the mth valence subband and the nth conduction subband. Pseudomorphic InGaAs epitaxial layers grown on (0 0 1)oriented GaAs substrate are submitted to the in-plane biaxial strain, which causes a tetragonal compression of the layer [1].
Indium content
Experiment
Theory
EH11 (eV)
EL11 (eV)
Eexp (eV)
Etheor (eV)
0.055 0.077 0.086
1.344 1.290 1.268
1.366 1.317 1.295
0.022 0.027 0.027
0.029 0.039 0.044
For the E0 critical point the strain can be decomposed into a hydrostatic component, which shifts the energy gap between the valence bands and the lowest lying conduction band, and an uniaxial component, which splits the heavy hole and light hole valence bands [7,19]. The analysis of the PR spectra shown in Fig. 4 on the basis of the so-called deformation potential theory [1,7] makes possible to express the resulting energy gap and splitting in terms of the in-plane residual strain in the partially relaxed Inx Ga1−x As epitaxial layers. The PR spectra were analyzed by using the typical line shape functional form, characterizing the electromodulated signals in bulk semiconductors, and interpreted according to the well known Aspnes’ relation [20]. The energies of H11 and L11 transitions determined from the best fit of experimental data and energy splitting, were shown in Table 1. By using the energy splitting Eexp obtained from PR experiment we were able to calculate the residual strain values in our partially relaxed Inx Ga1−x As epitaxial layers. Furthermore, a comparison of the experimentally obtained valence band splitting Eexp of the partially relaxed samples with the splitting Etheor calculated theoretically for the case of fully strained pseudomorphic layers (shown in Table 1), allowed us to estimate the extent of strain relaxation in the Inx Ga1−x As epitaxial layers. The calculated percentage difference of H11–L11 splitting between the fully strained and partially relaxed layers is 24, 31 and 39% for the sample A, B and C, respectively. It may be treated as the percentage estimation of the extent of strain relaxation. The results were shown in Fig. 5. As one can see,
Fig. 5. Residual strain values and the extent of strain relaxation vs. In content in the partially relaxed Inx Ga1−x As/GaAs heterostructures, determined from PR analysis.
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when the extent of partial strain relaxation increases, the residual strain decreases inducing the lower valence band splitting. It is a consequence of the fact that when the strain in the epitaxial layer is starting to relax due to the generation of misfit dislocations, the valence band splitting is decreasing. 4. Conclusions In conclusion, the electrical and optical properties of the partially strain-relaxed Inx Ga1−x As/GaAs heterostructures with different compositions and thicknesses, grown by MOVPE, were investigated. The DLTS technique revealed two deep electron traps. The analysis of the DLTS-data connected with the electron trap labelled E1, with the activation energy 0.43 and 0.57 eV (depending on composition), enabled us to attribute this trap to “localized” states at 60◦ misfit dislocations, lying at the interface between the epitaxial layer and the substrate, and to identify the E1 trap as ED1 one. The latter electron trap, called E2, with the activation energy 0.72 eV, was identified as the well known EL2 native point defect. The PR spectroscopy was employed to study the effects of residual strain on the optical response from the samples. The analysis of PR spectra yielded the values of residual strain and the extent of strain relaxation in the epitaxial layers. It was found that the investigated Inx Ga1−x As epilayers with x = 0.055, 0.077 and 0.086 are relaxed in 24, 31 and 39%, respectively. Acknowledgement The authors are grateful to D. Radziewicz (Wrocław University of Technology) for growing the InGaAs/GaAs heterostructures.
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