Conditions for formation of germanium quantum dots in amorphous matrices by MeV ions: Comparison with standard thermal annealing

We investigate how MeV ions with different ion-beam parameters (ion type, electronic stopping power, and velocity) influence the formation, arrangement, and ordering quality in three types of ($\mathrm{Ge}+{\mathrm{SiO}}_2)/{\mathrm{SiO}}_2$ multilayer films. The multilayers differ in total thickness, Ge-rich layer thickness, and Ge content. The results show that the most important parameter for structural manipulation with MeV ions is the electronic stopping power $S_e$. Ion velocity is found to be another crucial parameter, while at the same time it can be seen that the multilayer type does not play an important role. The temperature increase within the ion tracks is estimated using the thermal spike model and cluster separation distribution. The structural changes produced by ion beams and estimated temperatures are compared to those obtained by standard thermal annealing. It is concluded that the estimated temperatures within the ion tracks are in excellent agreement with the annealing temperatures and with the structural changes observed in the irradiated multilayers. Furthermore, a characteristic parameter of the temperature profile that presents the model-predicted temperature increase is determined for which the structural changes caused by ion beams are comparable to those achieved by standard annealing.

Figure 1

(a–c) GISAXS maps of ($\mathrm{Ge}+{\mathrm{SiO}}_2)/{\mathrm{SiO}}_2$ multilayer irradiated with $1\times {10}^{15}$ ions/cm${}^2$ oxygen ions with different energies under an angle of ${60}^{\circ }$, with respect to the multilayer surface. (d) GISAXS map of a nonirradiated sample. Dashed lines indicate Bragg sheets, while arrows indicate the irradiation direction. Insets: TEM images corresponding to the GISAXS image shown.

Figure 2

(a–c) GISAXS maps of ($\mathrm{Ge}+{\mathrm{SiO}}_2)/{\mathrm{SiO}}_2$ multilayers irradiated with $1\times {10}^{15}$ ions/cm${}^2$, 15-MeV oxygen ions under different incident angles (indicated in the figure) with respect to the multilayer surface.

Figure 3

(a–c) GISAXS maps of different multilayer types ($S_1$–$S_3$) irradiated with $1\times {10}^{15}$ ions/cm${}^2$, 1-MeV oxygen ions under ${60}^{\circ }$ with respect to the multilayer surface.

Figure 4

GISAXS maps of multilayers irradiated under ${60}^{\circ }$ with (a, b) 6-MeV Si and (c, d) 15-MeV Si ions. The probing x-ray beam was perpendicular ($\perp$) or parallel ($\parallel$) to the irradiation plane as indicated in the upper right corner.

Figure 5

STEM/HAADF ($Z$-contrast) images of films (a) irradiated with 6-MeV Si ions, (b) irradiated with 15-MeV Si ions, and (c) nonirradiated film annealed at 1120 K for a duration of 1 h.

Figure 6

Dependence of the maximal temperature increase ($\Delta T_{\max }$) in the film on time. The maximal temperature in the system ($T_{\max }$) achieved in time $t=t_0$ and the characteristic temperature achieved for width $r=a_0$ and $t=t_0$ are indicated by arrows.

Figure 7

Comparison of the temperature regimes for standard thermal annealing versus ion-beam irradiation concerning effects induced in the material. Shaded areas represent uncertainties for determination of characteristic temperatures.