Study of the Electronic Structure

5.7.1. Photoluminescence Studies on QD and QR Struc-tures

In this section, we focus on the photoluminescence (PL) properties of the droplet epitaxial non-covered QDs and QRs. The 4 K PL spectra of the QD sample and the temperature dependent PL spectra of the QR sample are shown in Figs 5.16 and 5.17, respectively. At 4 K, three peaks can be seen on the QD spectrum. They can be identied as bound exciton (1.5129 eV) (its intensity is very low), the exciton bound to acceptor line (1.4919 eV) and its longitudinal optical phonon replica (1.4585 eV). At 4 K, the QR spectrum has ve peaks. They can be explained as bound exciton (1.5129 eV), exciton bound to acceptor (1.4892 eV) and its longitudinal optical phonon replica (1.4577 eV). Further on at higher energies two peaks appear (1.5308 and 1.5602 eV). The PL spectra were also recorded as a function of temperature.

To verify the identication of the peaks, the temperature dependence of the band gap energy of GaAs and that of the bound exciton were compared. A good correlation was found, (see Fig 5.18/A).

It can be seen, that for the QD no peak was found at energy higher than the bound exciton, but two peaks appeared for the QR, due the quantum eects. In the following this phenomenon will be explained.

Our nano-structures were prepared without a cap layer. The nano-structures described in the literature are either self supported or conned in another ma-terial. For practical dierentiation, the phenomenon in the rst one is called quantum size eect and in the second one quantum connement, although theoretically the phenomenon is the same. Our nano structures are located somewhere between these two. According to Viswanatha et al.'s calculations a perceptible band gap change in the case of GaAs nano-crystals begins

un-5.16. Fig. The PL spectrum of the QDs, where no levels are observable over the bounded exciton.

#1853 QR 4 K - 300 K

5.17. Fig. The PL spectrum of the QRs, where two levels are observable over the bounded exciton (details see in the text).

der the diameter (dn) size 7 nm [260]. The base diameter of the QD (dQD) investigated was much larger, and its height (h_QD) was also larger, but

com-parable. So, here no quantum eects are expected (compare Fig. 1C and Fig.

5.18/B). Therefore it was impossible to detect a peak shift or peak broad-ening for QD. For QR the laterally wide (d_QR) nano-structure had a height (h_QR) signicantly less than 7 nm, consequently the supposition of quantum connement produces proper result [261]. Fig. 5.18./C shows the calculated energy quantization of GaAs quantum well con-ned among AGaAs barriers.

This corresponds well to the PL peaks of the QR at a higher energy level than that of the bound exciton.

5.7.2. Explanation of the PL Peak Width

Remarks concerning the width of the photoluminescence peaks of QD and of QR: During a PL measurement the laser beam is focused to the mate-rial irradiating a spot with a diameter of about 200 µm, resulting in the simultaneous excitation of several nano-structures. The PL spectra show characteristic peak width, depending on the temperature and the size distri-bution of these structures. At the same temperature a broader size variation results in a broader PL peak. Mano et al. investigated the PL peaks of QRs [275] and found that under similar growth conditions the Full Width at Half Maximum (FWHM) is signicantly narrower (less than one third) than that of the QDs. This comparison was based on the works of Watanabe et al. [259]. They reasoned that the variation of the size distribution of the QRs is smaller than the same parameter of the same parameter of the QDs, producing the great dierence in the FWHM [275].

In our opinion this dierence can be explained by other facts. As it is known, both the QR and the QD is shaped from a gallium droplet. Assume that the volume and its variation of the initial droplets are the same in both cases. The facet of the nanostructures is size dependent and cannot be arbitrarily sized [194]. For the QD let's start from the greater (111) facet (the approx. diameter (2r) is 100 nm [194], see Fig. 5.19). For the QR only the (113) facet can be taken into account because of the smaller volume (the approximate width (w) is 60 nm [194], see Fig. 5.18.) dedicated to a circle segment (see the RHEED patterns and line scans in Ref. [?]). Due to the crystallographic constraints the geometry of the formed QDs and QRs are determined. The height-to-diameter ratio cannot be arbitrary; it can be dened by a single parameter.

If r is the radius of the base circle belonging to the initial droplet the volume of the developing QD, as a function of r, is given by V = 1.58×r³.

GaAs

E =1.5522-5.8x10 T /(T+300) [eV]g -4 2

5.18. Fig. (A) The PL spectrum of the QDs, where no levels are ovservable over the bounded exciton. (B) The Eg variation on the nanocrystal size (dn) using the approximation based on quantum size eect [16]. (C) The scheme of the energy bands, using the approximation based on quantum connement [17].

QD

QR

w

5.19. Fig. Explanation to the dierence of the FWHM of the PL peaks in the case of QDs and QRs (see in the text).

For the QR, from the equality of the volumes, the w parameter can be cal-culated as w = 0.71×r (see Fig 5.19.). (This means that the nano-object with parameter of 2r = 100 nm has (111) facets, and the other one with parameter of w = 0.71×100 ∼ 70 nm or less has (113) facets. It corre-sponds to the above presented measured data.) As was shown above, the height of the nano-structure inuences the quantum behaviour. The heights

of the QD and QR structures can be expressed as a function of their volumes:

m_QD = V^1/3/1.34 and m_QR = V^1/3/6.56, respectively. Assuming the same variations of the volumes, it can be seen that the variation of the height for QR is much smaller than for QD, consequently the corresponding FWHM of the PL peak is smaller [262].