The vertical bars in Figure indicate the calculated relative strengths (overlap integrals) of the optical transitions in the InGaAs QW under zero electric field (flat band) conditions.
Carrier confinement in InGaAs QRs
We initially studied the effect of the As (As2and As4) source used during MBE growth on the optical properties of QRs. A comparison of room temperature PPR spectra at two perpendicular polarization angles for As4- and As2-grown QR35 samples (Figure ) illustrates some notable characteristics. In particular, the low-energy QR-related features in the experimental spectra are red shifted for the As4-grown structure compared to the As2-grown samples. In contrast, there is a blue shift in the QW-related features. Moreover, the intensity of the PL (not shown) and PR signal is significantly enhanced when an As4source is used.
Figure 2 Room temperature PPR spectra at two perpendicular polarization angles (symbols). (a) As4-grown and (b) As2-grown QR35 samples. GS and ES denote optical transition energies in InGaAs QRs, involving ground and excited states, respectively. The modulus of (more ...)
The relative red shift of QR-like and blue shift of QW-like optical transitions for the As4
-grown QR sample were analyzed in terms of the carrier confinement, defined as the energy spacing ΔE
between the lowest QW-related transition and the QR ground-state transition. By following the corresponding peak energies of the PPR modulus (dashed and dotted curves in Figure ), one can ascertain that the use of an As4
flux results in better carrier confinement compared to the use of As2
; the energy spacings ΔE
are 195 and 160 meV, respectively. Such an increase in carrier confinement for As4
-grown QRs is also evident from the significantly larger energy spacing between QR ground- (GS) and excited- (ES) states for the As4
-grown sample (61 meV) compared to the As2
-grown one (49 meV). The increased energy level spacing in the As4
-grown QR structures may be attributed to the electron wavefunctions being more tightly confined, as discussed in [14
]. This could be important for improving the recombination efficiency and PL intensity in QR devices, such as SOAs. These results suggest that there is better carrier confinement in As4
-grown QRs because of an increased indium composition contrast between the InGaAs QRs and the surrounding InGaAs QW layer [7
Polarization properties of InGaAs QRs and QWs
Optical anisotropy in the (001) plane of InGaAs nanorods was explored by PPR and PPL using two linear light polarizations, along the
and  crystal axes. Room temperature PPR spectra at these two perpendicular polarization angles (Figure ) revealed significantly different PPR signal intensities for QR-related optical features both for As4
- and As2
-grown samples. This optical anisotropy was confirmed by PPL measurements (Figure ). However, for the QW-related transitions, a negligible polarization dependance was observed.
To gain a deeper insight into the effect of the QR aspect ratio (height/diameter) on the optical anisotropy of InGaAs QRs, we systematically analyzed the PPR and PPL responses as a function of SL period number N. The polarized PR and PL spectra (Figures and ) were evaluated by a quantitative measure, the degree of polarization (DOP):
denote signal intensities for
light polarizations (two perpendicular polarizer positions), or alternatively for two transverse electric modes,
Figure shows room temperature PPR and PPL spectra at two perpendicular polarization angles in the (001) plane for the As2-grown QR samples: (a) QR10, (b) QR20, and (c) QR35. From the PPL data, it was found that the in-plane degree of polarization, DOP(001), increases almost linearly with the SL period number N. In particular, for small aspect ratio (2.0:1) QRs (QR10), the degree of polarization is small, DOP(001)≈25%, and comparable to the DOP values for conventional self-assembled QDs. Increasing the SL period to N=20 (aspect ratio: 3.2:1) results in an increase of DOP value to ≈41%. Finally, for high aspect ratio QRs of 4.1:1 (QR35), the in-(001)-plane DOP reaches the value of ≈55%, close to the value (DOP(001)≈60%) estimated for the As4-grown QR35 structure.
Room temperature PPR and PPL spectra in the (001) plane for the As2-grown QR samples. (a) QR10, (b) QR20, and (c) QR35. PPL optical anisotropy of the GS interband transitions in the QRs is indicated by the DOP values.
The polarization anisotropy, estimated from the analysis of PPR modulus spectra, shows similar increase with SL period number N, however to a smaller extent. In particular, for the samples QR10, QR20, and QR35, we estimated DOP values of 37%, 43%, and 46%, respectively.
The significantly different DOP values obtained from PPR and PPL spectra (Figure ) may be related to the fact that PR is an absorption-based spectroscopic method, which probes the maximum in the density of states, whilst PL probes the states of lowest energy. Alternatively, the different DOP values may be due to interference effects in the PR signal [15
In general, for low-dimensional structures, the PR signal intensity is associated with the quantum-confined Stark effect (QCSE), the squared overlap integral of the electron and heavy-hole wavefunctions, |Mcv
, modulation efficiency, and the built-in electric field [16
]. In QRs, the lowest state electron wavefunction spans the whole length of the QR, whereas the hole wavefunctions of the two lowest states are well-localized at the top and the bottom of the QR. This confinement of holes is mainly driven by the large heavy-hole effective mass and strain-related modification of confinement potential in the growth direction [17
]. The recorded PR signal of ground-state transition in a QR is thus a superposition of two signals involving two well-confined hole states. Due to the difference in optical paths (the probed areas are spatially separated over the QR height), the contributed signals may arrive with a different phase and thus interfere constructively or destructively.
It is tentatively suggested that under influence of an electric field (the QCSE), with localization of the lowest heavy-hole states at the top and the bottom of the QR, the recorded PR intensity is modified due to the interference of the two spatially separated signals. This can be further explored using different modulation sources for the PR experiments.
The PPR spectra in Figure also show a decrease of QR-related transition intensities relative to the lowest energy peak in the QW as the number of periods, N, in the SL increases. This behavior is attributed to a decrease in the overlap integral of the electron and heavy-hole wavefunctions with increase of QR height.
It should be noted that the strong anisotropy in the (001) plane cannot be explained purely in terms of the in-plane elongated shape of the QR along the
direction which is normally up to about 30%. Other possible effects leading to the polarization asymmetry are material composition gradients (fluctuations), asymmetric strain distributions, piezoelectricity, and in-plane modulation of the InGaAs content — all need to be considered equally. For example, material composition fluctuations involving valence band mixing cause up to 40% polarization anisotropy, even in highly symmetrical QDs [18
]. However, the situation in QRs is even more complicated. Recent TEM observations by Mukai et al. [19
] suggested that polarization features may be governed by problems in the growth process such as the bending of the stacking direction during the formation of columnar QDs with a high aspect ratio. However, a very recent optical anisotropy investigation of stacked InAs/GaAs QD structures [4
] revealed that a large optical anisotropy could be ascribed to the hole wavefunction orientation along
axis, which suppresses the TE
Our experimental findings suggest that the PL polarization properties (intensity of TE versus TM mode) from cleaved facet surfaces should be different for the (110) and
facets. When considering the optical anisotropy from cleaved facet surfaces [
and (110) planes] of QR samples, the degree of polarization can be defined by
where z is the QR growth direction, and TE (TM) is the intensity of the transverse electric (magnetic) mode. In this case, the DOPis characterized by the Miller indices of the crystallographic facet plane.
Room temperature, linearly polarized PL spectra at two perpendicular polarization angles (Figure ) show that for high aspect ratio (4.1:1) QRs (QR35), a flip of DOP sign occurs for both As4
- and As2
-grown InGaAs QR structures. As a result, the TM mode is dominant from the
), whilst from the (110) surface, the TE mode prevails (
). The DOP values for As4
-grown QRs (Figure a,c) of DOP(110)
= + 50%
exceed the corresponding DOP values of DOP(110)
= + 33%
-grown QRs (Figure b,d).
Figure 4 Room temperature linearly polarized photoluminescence spectra split into TE and TM modes for QR35 samples. The samples were grown using As4(a, c) and As2(b, d) sources. PL spectra are normalized to the most intense peak of the GS transitions in the InGaAs (more ...)
It should be noted that in lens-like QDs, optical transitions involving light-hole states are suppressed (by highly negative biaxial strain); therefore, the intensity of the TM mode becomes insignificant. As the QR height increases, biaxial strain reduces, simultaneously decreasing heavy- and light-hole sub-band splitting. Therefore, for high aspect ratio QRs, the light- and heavy-hole bands are almost degenerate and, thus, manifest themselves by TE and TM modes of comparable intensity. It is thus suggested that light- and heavy-hole sub-band mixing favors an increase of the TM
mode. This is supported by calculated hydrostatic and biaxial strain profiles for InAs/GaAs QD stacks of different heights, as reported in ref. [4
]. Finally, the evidence of sign reversal in the degree of polarization estimated from the PPL spectra fulfills the promise of QD shape engineering and shows a huge potential for QRs for potential applications, such as polarization insensitive SOAs.