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The surface photovoltage (SPV) spectra of a series of vertically stacked self-organized InAs/GaAs quantum dot (QD)-based laser structures with different spacer layer (SL) thickness were obtained as a function of temperature (77 K ≤ T ≤ 300 K). A decrease of the compressive stress for thinner SL samples arising from coherent relaxation enables us to designate the effect of material intermixing as the most probable mechanism of the energetic blueshift of the observed structures. The turnaround characteristic of the temperature-dependent spectral intensity shows that the reduced SPV signal at higher temperature is limited by the carrier scattering and at lower temperature it is governed by the magnitude of built-in electric field and the escape efficiency of the photogenerated carriers. The dot states to be blueshifted by material intermixing are expected to have higher escape rate for carriers out of QDs, thus resulting in lower measurable temperature for the detected SPV signal. The relatively higher signal at low temperature for the 10 nm SL sample provides a direct evidence of the tunneling process of carriers in the stacked QD layers.
©2007 Optical Society of America
1. Introduction
Recently, there has been considerable interest in the implementation of semiconductor quantum dots (QDs) because of the relative ease at which they can be grown and offering substantially improved optical and electronic properties associated with three-dimensional quantum confinement of carriers [1–5]. The application of QDs as the active region in a semiconductor laser leads to an ultralow threshold current density and an extremely high thermal stability due to the spatial carrier localization effect within the QDs. Lasers with wavelengths of 1.3 μm, based on self-organized InAs QDs embedded in InGaAs quantum wells, have demonstrated very low threshold current [6]. However, the low surface density of such QDs results in a low maximum optical gain in the QD ground state and excited states lasing at high current and/or high temperature. The operating characteristics of lasers can be readily improved by using an array of vertically coupled QDs (VCQDs) as the active region, i.e., sequences of QD planes separated by narrow spacer layer (SL) [7–9]. This structural arrangement increases the total number of states in the QD ensemble and therefore enhances the optical gain. Also, the use of the thinner VCQD active region can improve the carrier injection efficiency via the tunneling effect.
Optical characterization of vertically coupled self-organized InAs/GaAs QD structures is mainly relied on photoluminescence (PL) [10–12], photoluminescence excitation (PLE) [13,14], as well as photoelectric spectroscopy technique such as photocurrent (PC) [15]. PL detects optical transitions in these structures by recording the radiative recombination processes. However, not all recombination processes in VCQDs are radiative; in such cases PL spectroscopy is unable to provide a complete picture of the system. PLE is an efficient technique, but it necessitates the use of a tunable laser and its implementation is laborious. PC is very sensitive to the absorption of the exciting illumination. However, for PC measurement ohmic contacts with the semiconductor surfaces are required and this may modify the electronic structure of the surface layers.
Surface photovoltage spectroscopy (SPS) has been well established as a powerful technique for studying electronic states of semiconductors. The advantages of using SPS are the simplicity in the measurement setup, contactless, nondestructive, and can be performed on any semiconductor material over a wide temperature range [16]. The formation of a SPS technique requires both charge generation and separation. Therefore, the electrical and optical properties of the nanostructure can be in principle revealed in the surface photovoltage (SPV) spectrum. So far, very little work has been done on multilayer VCQD (N>10) structures using the SPS technique [17,18], and particularly no results are available in the literature concerning SPS experiments carried out at low temperature.
In this work, optical investigation of InAs/GaAs VCQD system with different SL thickness using the SPS technique is performed in the temperature range 77 K ≤ T ≤ 300 K. The optical transitions are well resolved in SPV spectra even at room temperature. The possible origins of the observed blueshift with decreasing SL thickness and the turnaround phenomenon of temperature-dependent spectral intensity will be discussed.
2. Experimental description
InAs QDs were grown via Stranski-Krastanov growth mode on n+ (001) GaAs substrate at 485 °C using solid source molecular beam epitaxy (SSMBE). The growth sequence started with an undoped GaAs buffer followed by a 30 nm AlAs layer, a 60 nm GaAs cladding layer and a 30 InAs QD layers (2.6 monolayer (ML) nominal thickness) separated by GaAs SL with different thickness (10, 15, and 30 nm). Then QDs were capped with a 60 nm GaAs cladding layer, a 30 nm AlAs layer, and a 50 nm GaAs layer to finish the growth. Detailed growth conditions can be found elsewhere [18]. A single QD layer sample was also grown for comparison.
Because the substrate is heavily n-type doped and the rest of the structure is nominally undoped, the energy bands in the structure are bent upwards with respect to the bulk and a space charge region (SCR) with a built-in electric field is present at the interface between the substrate and the structure. As the electric field in the substrate is effectively screened by the carriers (electrons), the SCR develops rather in the structure than in the substrate. Thus the QDs are situated in a region with an electric field.
In SPS measurements, the photovoltage was measured between the sample and a reference metal grid electrode in a capacitive manner as a function of the photon energy of the probe beam. A soft contact mode was used to enhance the photovoltage signals. The method consisted of placing a thin indium wire around the edge of the sample surface with the metal grid pressing lightly on top. The illumination system consisted of a 150 W quartz-halogen lamp chopped at 200 Hz and a grating monochromator. A beam splitter was placed in the path of the incident light. The intensity of the incident beam was monitored by a pyroelectric detector and was maintained at a constant level of ∼10-5 W/cm2 by a stepping motor connected to a variable neutral density filter, which was also placed in the path of the incident beam. The photovoltage spectrum on the metal grid was measured with a copper plate as the ground electrode, using a buffer circuit and a lock-in amplifier. For temperature-dependent SPS measurements, a closed-cycle cryogenic refrigerator equipped with a digital thermometer controller was used. The measurements were recorded over a temperature range of 77-300 K with a temperature stability of 0.5 K or better.
3. Results and discussion
Figure 1 displays the SPV spectra of 30 layers vertically stacked InAs/GaAs QD structures with different SL width 10, 15, and 30 nm at 150 and 300 K, respectively. The SPV spectrum of the reference sample with only one QD layer taken at 300 K is also shown for the purpose of comparison. Each peak position in the figure has been evaluated by Gaussian fitting and is marked by an arrow [19]. For the spectra obtained at 150 K, the discrete excitonic lines from QDs are better resolved for the excited energy states due to a reduction of the thermal broadening. The spectral feature at 150 K shows the blueshift as the temperature decreases, realized by the increment of energy band gap as the sample temperature decreases. At room temperature several common features (labeled QD1-QD3) in the range of 0.90–1.20 eV are clearly visible in all the samples. An increase of the photon energy, corresponding to the ground state transition (QD1), is first observed in the 0.994–1.092 eV energy range (depending on SL). A second step in the energy range between 1.078 and 1.144 eV corresponds to the first excited state transition (QD2), followed by a third rise 1.116–1.188 eV denoting as the second excited state transition (QD3). One may doubt whether higher lying states QD2-QD4 are ground state transitions from other QD population with different size distributions or not. Indeed, the size of the QDs might vary in successive layers depending on growth condition, but the main PL peak for the 30 nm SL samples at 300 K can be fitted by a single Gaussian, as shown in Fig. 2 of Ref. 18 where a 38 meV full width at half-maximum (FWHM) is observed, indicating that the dot formation has only one dominant size distribution. In Fig. 1, the deconvolution of SPV spectra for both the reference and the 30 nm SL samples into three Gaussian lines is illustrated. The sharp QD related features are clearly observable in the reference sample, reflecting the higher homogeneity of the single dot layer. In the SPV spectra of all VCQD structures we can observe that the spectral lineshape of the optical transitions is broadened comparing to that of the reference sample. Energy level variations in the ensemble of QDs are mainly caused by size fluctuations in the stacked layers. The transition energies of QD states of the 30 nm SL sample are essentially the same as those of the reference sample. This observation concurs well with the theoretical prediction that the well-confined states would have little electrical and structural couplings for SL of this width. The SPV spectra for VCQD structures with SL width of 15 and 10 nm show an additional feature labeled QD4 at energy above second excited quantum dot state. The strong structural coupling for thinner SL, as typically shown in the transmission electron microscopy (TEM) image of Fig. 2 (SL=15 nm), complicates the strain field distribution in and around buried QDs, which can significantly modify the band structure and is possibly responsible for the presence of this feature [17].
Fig. 1. The SPV spectra of 30 layers vertically stacked InAs/GaAs QDs with different spacer layer thickness at the temperature of 150 and 300 K. For the purpose of comparison, the SPV spectrum of the single QD layer (reference sample) at 300 K is also displayed. The arrows indicate QD related transition energies obtained from the fitting. The dotted lines in the reference and the 30 nm SL samples show the deconvolution of SPV spectra into three Gaussian features.
Fig. 2. The cross-sectional TEM image of the InAs/GaAs VCQDs with 15 nm GaAs SL. Several dot columns with vertical alignment are present.
Note that QD related transitions in stacked QDs exhibit a pronounced blueshift with decreasing SL thickness, while experimental work mainly demonstrated a redshift [20–22]. Early stacked QD experiments show that the blueshift can be achieved for dots grown with a low growth rate, and is explained by strain induced intermixing [23]. In this work, a relative low InAs growth rate of 0.029 ML/s was used in the dot formation, possibly giving rise to the energetic blueshift of QD transitions. In addition to the growth rate related to the energetic shift of QD transitions, the probable mechanism of SL thickness dependence on the QD related transitions for VCQDs will be discussed as follows.
As the thickness of GaAs region between dots is small enough, the InAs dots in different layers have a strong tendency to align vertically due to long-ranged strain field, which leads to an enhanced electronic coupling between charge carriers. The electronic coupling increases the localization energy of carriers and correspondingly shifts the optical transition energy to lower values [9]. However, our work seems contrary to the aforementioned reasoning. Two models in pervious research have been proposed for interpreting the mechanisms of the blueshift behaviors. One is attributed to the distribution of the complex strain fields existing in and around the closely VCQDs [24], and the other to the material intermixing during the growth process [21]. In order to clarify which is the dominant factor, the distribution of strain field has to be evaluated. The strain field of a single dot shape is calculated using a Green's function method, which can be superposed to form the field within the stacked QD column [25].
Shown in Fig. 3(a) is a schematic drawing of the layered VCQD structure used in our calculation. The geometry of the QD as observed from the TEM images can be approximately modeled as a truncated pyramid with a square base size of about 22 nm x 22 nm and a height of 9 nm. It is stressed that the exact geometry and size of the dots can not be precisely determined from the image due to the impact of strain fields on the image contrast. The line scans are in the growth direction through the center of the array, where the origin of the coordinate system is at the center of the bottom QD. By exploiting the symmetry of the pyramid, the shear strain components vanish and the value of εxx is equal to that of εyy along this direction. Figures 3(b)–(e) show the diagonal strain elements of εxx and εzz for a single QD layer and those for VCQDs with SL width of 30, 15, and 10 nm, respectively. There are two common properties visible in all the structures. One is that the strength of the strain components is largest near the QD/matrix interface and then relaxes rapidly in the matrix material. The other is that the compressive stress exists within QDs and the strength of εxx is less than the initial lattice misfit strain (εxx ∼ -6.68 %), revealing the occurrence of strain relaxation. It is worth noting that the magnitude of εxx in the QD at the center of the stacked column is less than that in the reference sample. For example, at the bottom side inside the middle dot layer, the values of εxx(εzz) for SL thicknesses of 10, 15, and 30 nm are -4.257 % (-0.636 %), -4.573 % (-0.002 %), and -4.879 % (0.609 %), respectively, while for the reference sample the values are -4.890 % (0.633 %). Apart from a minor difference of εxx (εzz) between the 30 nm SL sample and the reference one, it is also found that the strain distribution for the 30 nm SL VCQDs represents a series of isolated QDs, implying that the larger separation prevents any structural and electronic couplings of neighboring layers. Also noted is that the value of εxx increases with the decrease of SL thickness, while that of εzz shows the opposite. This indicates the compressive stress inside QDs is further relaxed with decreasing SL thickness. The resultant strain field within the QD column obtained by the superposition of individual field from the constituent dot is enhanced for thinner SL, and consequently leads to an increase of the strain energy in QDs. In order to reduce the energy, the strain surrounding QDs can relax coherently during overgrowth and therefore shifts the energy level of QDs toward longer wavelength [26]. Furthermore, an increase of QD size is usually accompanied with elastic strain relaxation, as verified by the TEM images of Fig. 2. Both of them should result rather in an energetic redshift. This shows that the significant blueshift can not be solely ascribed to the contribution from the complicated strain field. Hence, the most probable mechanism associated with the blueshift is assigned to the material interdiffusion between InAs QDs and GaAs SL, where large strain field for thinner SL may serve as a driving force for substantial intermixing between InAs/GaAs in the dots. For the intermixing, the In atoms of the InAs QD and its covering layer may be replaced by Ga atoms, and the reduction of In content in QDs leads to a blueshift due to the increment of band gap energy.
It is worth noting in Fig. 1 that QD1 and QD2 are blueshifted from the 30 nm structure to the 15 nm one, whereas QD3 shows a redshift. As for the 10 nm SL, all spectral peaks are blueshifted with respect to the 30 nm SL sample. The higher QD level (QD3) is expected to have a stronger electronic coupling effect than lower ones (QD1 and QD2) because of the extent of the wave functions of the higher level is increased due to finite potential, and therefore the higher level couples more readily. Electronic coupling of charge carriers will shift the spectral position to the lower energy side. However in the 15 nm SL sample, the effect of material intermixing is not strong enough to counteract the electronic coupling effect, thus resulting in the energetic redshift of QD3 with respect to the 30 nm SL sample. For the 10 nm SL sample, the enhanced material intermixing prevails over the electronic coupling effect. Therefore all spectral peaks are shifted to higher energy with respect to the 30 nm SL sample.
Fig. 3. (a) The layered structure of 30 layers coupled-dot system is illustrated. The origin of the coordinate system is at the QD center in the base dot layer; (b) The strain components εxx and εzz, plotted along the growth direction (Z axis) are presented for a single QD embedded in a GaAs matrix. (c)-(e) display the calculated values of strain components εxx and εzz for the VCQD structures with SL thickness of 30, 15, and 10 nm, respectively.
Another interesting phenomenon that we have observed is the influence of the temperature on the details of the SPV spectra. In Figs. 4(a)–(c), we display the evolution of the data with temperature for the samples with SL width of 30, 15, and 10 nm, respectively. We show only the lowest temperature for which the prominent QD1 feature is observed. Regarding the 10 nm SL sample, the QD1 has a minimum detection temperature of 77 K. For the 15 nm SL sample, QD1 is visible above 90 K while for the sample with 30 nm SL, it is only detectable at about 130 K.
Fig. 4. Temperature dependent SPV spectra of 30 layers vertically stacked InAs/GaAs QDs with GaAs space layer of (a) 30 nm, (b) 15 nm, and (c) 10 nm. The inset in each diagram shows the variation in spectral peak intensity of QD1 with temperature.
In the inset of Fig. 4(a) for the 30 nm SL sample, the temperature dependence of QD1 intensity exhibits a turnaround behavior, i.e., the intensity initially increases as temperature decreases from 300 to 190 K and then decreases as temperature is reduced further. It is apparent that the mechanisms acted on the two temperature intervals behave differently. The SPV spectrum of a QD structure in the energy region below the band gap of the substrate is a product of two functions: (1) the absorption in the QD as a function of energy, and (2) a function describing the escape of carriers from the quantum dot and their separation in the electric field [27]. The second function is strongly temperature-dependent. The SPV signal S can be written as
Where αQD(hν) is the absorption coefficient in the QD as a function of energy, fe(hν,T) [fh(hν,T)] is the escape efficiency of the generated electrons (holes) from the QD followed by a further separation in the electric field over the distance d1 (d2) where d1 is the distance between QD and substrate, and d2 is the distance between QD and surface.
As mentioned above, the SPV spectrum reflects partially the optical absorption in QDs, but carriers that are photogenerated in QDs have to escape and be separated by the built-in electric field in order to contribute to the SPV signal. As a result, carrier transport plays a major role in determining the SPV spectrum and is governed by the temperature and the magnitude of the built-in electric field. At temperature above 190 K, the increased phonon concentration causes lattice scattering, thus preventing carriers from reaching the surface [28]. At temperature lower than 190 K, the SPV signal is affected by the reduction of electric field being a direct consequence of carrier freeze-out and decrease of the escape efficiency of the photogenerated carriers [29]. The temperature-dependant spectra of the 15 nm SL sample is similar to that of the 30 nm one, except for a lower detection temperature. As compared to the SPV spectra in 15 and 30 nm SL samples, a relatively higher SPV signal at lower temperature in the 10 nm SL sample is observed. This enhancement of tunneling for a thinner SL supports higher intensity of the SPV signal. Moreover, the lifted dot states caused by the material intermixing for 10 and 15 nm SL samples are supposed to have a higher escape rate out of QDs and a lower detection temperature can therefore be achieved.
4. Conclusion
In this article, we present a SPV study of a set of thirty layers of vertically coupled InAs/GaAs QD-based laser structures with different spacer layer thicknesses (SL = 10-30 nm), measured in the temperature range of 77 K ≤ T ≤ 300 K. More QD features are clearly resolved in the room-temperature SPV spectra. A reduced compressive stress in VCQDs with thinner SL allows us to identify the effect of material intermixing to be responsible for the blueshift. The turnaround behavior showing in temperature-dependent spectral intensity indicates that at higher temperature, the SPV signal is subjected to the phonon scattering and at lower temperature is affected by the strength of electric field and the escape efficiency of the photogenerated carriers. As verified from the temperature-dependent SPV experiments, the dot states to be raised by material intermixing for thinner SL are expected to have larger escape probability away from QDs so that lower measurement temperature can be achieved. The relatively higher signal at low temperature for the 10 nm SL sample provides a concrete evidence of the tunneling process of carriers in the stacked QD layers.
Acknowledgments
This work is supported by the National Science Council of Taiwan under Grant Nos. NSC93-2215-E-011-001 and NSC95-2221-E-011-171.
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