Spin resonance of electron states in a $\mathrm{Ge}∕\mathrm{Si}$ heterosystem with Ge quantum dots has been investigated. Electron localization in the strain-induced potential wells in Si in the vicinity of the Ge dots is confirmed by an analysis of the obtained $g$-tensor values. A well pronounced anisotropy of the linewidth is explained in terms of an effective magnetic field, lying in the plane of the quantum dot array. This magnetic field arises during the tunneling of electrons between quantum dots and leads to an acceleration of the spin relaxation. The origin of the field is the structure-induced asymmetry of electron potential wells. Two ways of increasing the spin lifetime are suggested: (1) the creation of a higher symmetry confinement potential for electrons and (2) the growth of a well-separated quantum dot array.

We investigate theoretically the spin transport in an array of Ge/Si quantum dots. In the frame of the tight-binding approach we calculate the probability of hole spin-flip for resonant tunneling between localized states in neighboring quantum dots. The tunneling between hole ground states occurs mainly with conservation of the spin. For excited states the probability of the spin-flip is higher. We find that the main source of the spin-flip is the structure-inversion asymmetry (SIA) of the Ge quantum dot. Every tunneling event is accompanied by the small rotation of the angular momentum and this provokes the spin-flip. Simple estimations of the time of spin relaxation caused by the SIA-mechanism give ${\tau }_{\mathrm{SIA}}\sim {10}^{-5}\mathrm{s}$.

Electron paramagnetic resonance and spin-echo methods are used to probe the spin dynamics in Ge/Si heterostructures with quantum dots. A spin coherence time of up to $20\mu \text{s}$ is obtained for electrons confined in strain-induced Si potential wells near the apices of Ge quantum dots. The measurements of spin echo confirm the model of spin relaxation through the spin precession in the effective magnetic field lying in the plane of a quantum dot array. Existence of two electron groups with different spin-relaxation times is suggested to explain a nonexponential spin-echo behavior observed in the structures under study.

Electron states in an inhomogeneous Ge/Si quantum dot array with groups of closely spaced quantum dots were studied by the conventional continuous-wave electron spin resonance and spin-echo techniques. We have found that the existence of quantum dot groups allows increasing the spin relaxation time in the system. The created structures permit us to change the effective localization radius of electrons by an external magnetic field. With the localization radius being close to the size of a quantum dot group, we obtain a fourfold increase in the spin relaxation time ${T}_{1}$ as compared to conventional homogeneous quantum dot arrays. This effect is attributed to an averaging of the local magnetic fields produced by ${}^{29}$Si nuclear spins and a stabilization of the ${S}_{z}$ polarization during the electron back-and-forth motion within a quantum dot group.

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.