Electron spatial localization tuned by strain in Ge/Si quantum dot heterostructures

A new type of quantum dot (QD) structure that enables us to control a spatial localization of electrons by changing the strain distribution in the vicinity of QDs is proposed. The structures represent a combination of large ($\sim 200\mathrm{nm}$) GeSi disklike quantum dots (nanodisks) and groups of smaller ($\sim 30\mathrm{nm}$) laterally ordered QDs grown over a nanodisk template. Electron localization has been studied by the electron spin resonance (ESR) method. Analysis of experimental results has been supported by calculations of electron binding energies and carrier distribution probabilities taking into account strain effects and real geometry of nano-objects. Results show that the strain field produced by the nanodisk can be used for tuning the energy levels of electrons in different $\mathrm{\Delta }$ valleys and makes possible successful realization of simultaneous localization of two electrons with different $g$ factors in the vicinity of the same QD.

Figure 1

AFM image ($1\times 1\mu {\mathrm{m}}^2$) of the compact QD groups grown by deposition of 5 monolayers (ML) of Ge at $600{}^{\circ }\mathrm{C}$ (left panel) and 5.5 Ge ML at $580{}^{\circ }\mathrm{C}$ (right panel) on the substrate with GeSi nanodisks, incorporated under the surface at the depth of 35 nm and serving as templates for nucleation of these ordered QD groups. Image sides are oriented along $\langle 110\rangle$ directions.

Figure 2

A schematic structure of the sample with optimal configuration of QDs for observation of simultaneous localization of electrons in different $\mathrm{\Delta }$ valleys. The first and second QD layers as well as the third and fourth QD layers are separated by 3 nm Si spacers, while the distance between the second and third QD layers is 5 nm.

Figure 3

Strain distribution (top panel), conduction band edge landscape in ${\mathrm{\Delta }}_z$ valley (center panel), and conduction band edge landscape in ${\mathrm{\Delta }}_x$ valley (bottom panel) in the structure with optimal configuration of QDs for observation of simultaneous localization of electrons in different $\mathrm{\Delta }$ valleys. Sections of $XZ$ plane passing through the center of the compact QD group are shown, $Z$ is the growth direction of the structures [001].

Figure 4

$Z$ profiles (top panel) and $X$ profiles (bottom panel) of conduction band edge, crossing through sites 1, 2, 3, 4, 5 (profile directions are shown by dashed lines in Fig. 3). Profiles through sites 1, 2, 4 are related to ${\mathrm{\Delta }}_z$ valley, profiles through sites 3 and 5 correspond to ${\mathrm{\Delta }}_x$ valley.

Figure 5

Wave functions of the electron ground state in ${\mathrm{\Delta }}_x$ valley (located at the QD edges) and electron ground state in ${\mathrm{\Delta }}_z$ valleys (located at the QD apexes) in different QD structures: with constant spacer thickness $d=3\mathrm{nm}$ (top panel) and with varied spacer thickness $d=3,5,3\mathrm{nm}$ (center panel). Sections of $XZ$ plane passing through the center of the compact QD group are shown (top and center panels). Section of $XY$ plane passing through the base of third QD layer ($z_0=48\mathrm{nm}$). The conditions of experimental observation are indicated (dark or light). QD geometry is shown by dashed lines. The scales in $x, y, z$ directions are different.

Figure 6

ESR signals observed in the dark (top panel) and under continuous illumination (bottom panel) for the heterostructure with four layers of ordered QD groups, separated by 3 nm bottom and top Si spacer layers and 5 nm central Si spacer, grown on the template with one GeSi nanodisk (No. 937). Microwave power $P=0.063\mathrm{mW}$ and frequency $\nu =9.68484$ GHz, modulation amplitude $H_m=0.3$ Oe, $T=5$ K. The magnetic field is directed along the growth direction of the nanostructure.

Figure 7

ESR spectra of electrons localized in the structure with modulated spacer thickness (No. 937) for different sample orientations in the magnetic field, microwave power $P=0.063\mathrm{mW}$ and frequency $\nu =9.68694$ GHz, modulation amplitude $H_m=0.3$ Oe, $T=5$ K. The magnetic field direction is changed from the growth direction of the structure ($\theta =0^{\circ }$) to the in-plane direction [110].

Figure 8

ESR signals observed in the dark and under continuous illumination for the heterostructure with four layers of ordered QD groups, separated by 3 nm Si spacer layers, grown on the template with one GeSi nanodisk (No. 907). Microwave power $P=0.063$ mW and frequency $\nu =9.69673$ GHz, modulation amplitude $H_m=0.3$ Oe, $T=5$ K. The magnetic field is directed along the growth direction of the structure.