Emission line widths statistics

It is found that the observed median emission line widths ˜εare proportional to the QDs’ internal dipole moments µas illustrated in Fig. 5.2. The link between µ and

˜

ε can be understood within the framework of the linear quantum-confined Stark effect (QCSE) [85,86] introduced in Sec.3.7, page37and spectral diffusion [38,129].

The strong built-in electric field in the order of MV/cm [34] in wurtzite GaN/AlN QDs causes a spatial separation of the electron and hole centers of masses on the order of nanometers, resulting in dipole moments scaling between e.g. 1.55 e·nm and 0.47 e·nm for an AR of 0.2 (QD height of 2.4 - 1.2 nm), cf. Fig.5.2b. Generally, any external electric field F~ causes exciton emission energy shifts ∆E due to the linear QCSE [24]:

∆E(t) =~µ·F~(t) (5.1)

If the electric field is time-dependent and fluctuates statistically around a mean value, then the exciton emission energy will follow this fluctuation. For fluctua-tions faster than the detector integration time one observes inhomogeneously broad-ened, Gaussian-like emission lines instead of Lorentzian shaped and only homoge-neously broadened QD emissions [38]. The standard deviation of the exciton energy

5.1 Phenomenon of spectral diffusion 67 σ_∆E now trivially relates to the FWHM ε of a Gaussian-shaped emission line by ε= 2√

2 ln2·σ∆E. If it is assumed that the overall strength of the field fluctuations is the same for all investigated QDs then ˜εis indeed directly proportional toµ, pre-cisely matching the observation depicted in Fig. 5.2. This argumentation is further strengthened by the observation of a decreasing absolute slope of the calculated ex-citonic dipole moment trend towards larger emission energies that is in agreement with the measured evolution of the slope related to the median emission line widths.

The conjunction of σ_∆E and the theoretically derivedµ now facilitates a consistent estimation of the average electric field strengths resulting in e.g. ≈2 MV/m for the entire data set under the assumption of a QD AR of 0.2. Such AR of 0.2 is experi-mentally most frequently observed in contrast to more rarely occurring, rather flat QDs with an AR of 0.1. Hence, in a first approximation, any singly charged defect situated directly above or below the GaN QD center at a distance of ≈8 nm could cause the determined electric field strength. As a direct consequence, an energetic shift of the excitonic emission line would be induced, which exhibits the same order of magnitude as the emission line width. It is particularly likely that charges might be trapped in the interface region above or below the QDs. A 5 - 10 nm thick AlN capping layer was deposited after the growth of the QDs at a comparably low growth temperature of 975℃in order to preserve the QD formation (see Chap. 2, page16).

Hence, such an AlN layer will be defect-rich with a high density of charge trapping sites. However, the interface region between the QD bottoms and the underlying AlN matrix material is also a veritable candidate for charge trapping sites as the presence of strain and e.g. material intermixing may contribute to an additional defect formation. Interestingly, a sophisticated analysis by means of scanning trans-mission electron microscopy (STEM) presented in Sec. 6.4, page 86 even suggests the sidewall facets of the QDs as a viable region for such charge fluctuations.

A detailed stochastical analysis ofhow a distribution of fluctuating charges induces a distribution of line widths resides beyond the scope of this thesis and will be published elsewhere. Finally, it is the giant built-in dipole moment µ that causes the observed huge emission line widths and results in the general high sensitivity of nitride QDs to a fluctuating charge environment. Even extreme QD geometry variations like a change in the AR of 0.1 to 0.2 as shown in Fig.5.2b cannot explain the observed broad emission line widths distribution. This observation is especially true for smaller wurtzite GaN QDs (≈4 eV), whose excitonic dipole moment is less affected by QD geometry changes, clearly revealing spectral diffusion as most dominating origin for the occurring FWHM.

The presented line widths broadening phenomenon in nitride QDs stands in contrast to less polar e.g. zincblende arsenide QDs. Here, generally smaller excitonic dipole moments occur [131,132] and the observed emission line widths are typically on

the order of µeV, three orders of magnitude smaller than in nitrides [89,133]. This observation provides a strong motivation for the growth of GaN QDs on less-polar substrates or even the analysis of cubic GaN QDs [55], naturally yielding lower single QD emission line widths due to the presence of smaller excitonic dipole moments.

Another option for such a beneficial reduction of the excitonic dipole moment is the growth of even smaller wurtzite GaN QDs [134] with emission energies beyond 4 eV as shown in the following Chap. 5.3. However, the apparent line width differences between e.g. mature arsenide- and rather novel nitride-based QD systems are not exclusively caused by varying excitonic dipole moments, but also by still deviating point and extended structural defect concentrations in the matrix material.

Based on theµ-PL analysis one can further determine that the characteristic timescale of spectral diffusion is not larger than a few, detector-limited, tens of milliseconds at a temperature of 8 K for most of the analyzed GaN QDs. The identification of the physical origin related to the charged defects causing the electric field fluctuations remains a task for future work. However, the most relevant defects prove to be of an energetically shallow nature as already a rise of the temperature towards 20 K causes an increase of spectral diffusion and spectral jittering effects in the µ-PL spectra, the latter taking place on a time scale of a few hundreds of ms. For comparison, the characteristic spectral diffusion timescaleτ_SD was first exemplarily measured for selenide QDs and yielded τ_SD≈4 ns [129]. In contrast, recent g⁽²⁾-correlation func-tion measurements [39] have shown that the low-ns regime can mostly be excluded as the timescale for spectral diffusion in similar selected, high quality, wurtzite GaN QDs embedded in AlN. Only particular GaN QDs exhibit τ_SD values in the mid-ns regime (25 ns) as recently described in Ref. [40]. Additionally, cathodoluminescence experiments on InGan QDs pointed towards larger τ_SD values on the order of ms to s in nitrides [24]. Though, the fundamentally different excitation mechanisms in photo- and cathodoluminescence hinder a truly direct comparison between the determined τ_SD values.

Furthermore, this chapter demonstrated that the experimental trend for the emission line widths from Fig. 5.2a is still predominantly evoked by spectral diffusion [38]

and not by an exciton acoustic phonon interaction via e.g. a deformation potential and piezoelectric coupling [135]. Generally, the elastic and inelastic interaction of acoustic phonons with the charge carriers inherent to the QD influence the overall emission line shape and line width [136]. Even though the entire exciton acoustic phonon coupling strength scales with the excitonic dipole moment in GaN QDs, similar to the trend for the line widths from Fig.5.2a, the absolute line widths values in the meV range cannot be explained. It was shown that the previously measured, rather broad zero phonon emission line widths of wurtzite GaN QDs cannot be modeled without the inclusion of spectral diffusion, as solely considering the exciton