4.3 Silicon-Germanium

This section gives a brief summary of application examples as well as material properties of silicon-germanium alloys. SiGe thermogenerators have been successfully used in a couple of applications. Probably the most fascinating of them are thermoelements powered by radioisotopes (RTGs), which proved to be a reliable power source on several space missions as well as in remote weather stations [11]. The material has been chosen due to its high reliability as well as high operating temperatures in order to match the conditions provided by the nuclear fuel.

Furthermore, the SiGe material system serves as an ideal basis for simulation studies for thermoelectric device optimization due to its well known material parameters from main stream microelectronics. Especially the introduction of strain techniques to commercially available devices [130,131,132] caused major research efforts on the properties as well as processability of Si/SiGe devices. Due to the widely available data and models, only the most important material data are briefly summarized in the sequel. Detailed analysis and material characterization of SiGe alloys with its emphasis on physical modeling for device simulation can be found in [133]. Besides this, a review on the validity of several models at high temperatures with a focus on mobility modeling has been carried out in [134].

Compared to the corresponding pure materials, SiGe alloys are interesting candidates for thermoelectric applications due to the different influence of the material composition on thermal conductivity and mobility. Theoretical calculations on the maximum figure of merit have been carried out in [135,19]. While in [135], a two-band model has been used, the second conduction band has been considered in [19] resulting in a wider temperature range covered by the model.

The lattice thermal conductivity for SiGe decreases significantly with increasing germanium content of up to $50\,\%$ . Above $50\,\%$ , the trend reverses to finally approach the value of pure germanium. This characteristics is caused by the important role of alloy disorder scattering of phonons due to the large mass difference of silicon and germanium as well as the random distribution of the constituents in the alloy [136]. Fig. 4.3 illustrates the material composition dependence of SiGe thermal conductivity for $300\,\ensuremath{\mathrm{K}}$ , $500\,\ensuremath{\mathrm{K}}$ , and $700\,\ensuremath{\mathrm{K}}$ . Several measurement data found in literature are in good agreement to the model [95,106,137,138,139,140,141]. Accordingly, lower values in sintered samples are reported in [142] due to additional phonon scattering at grain boundaries.

Figure 4.3: Thermal conductivity of silicon-germanium alloys with respect to material composition for different temperatures.

Constantly low sensitivity of the thermal conductivity on the material composition over a wide range of germanium contents results in a good figure of merit for sintered composites, as often used in thermoelectric applications. This is beneficial especially in inhomogeneous samples, where clusters normally cause relatively large local deviations of the material parameters.

Material composition dependent mobilities for n-type silicon-germanium samples are illustrated in Fig. 4.4. The symbols depict data obtained by Monte Carlo simulations, while the lines show data obtained by the according models [143]. In contrast to the thermal conductivity, the mobility decreases more slowly with increasing Ge content resulting in a range with good figures of merit.

Several measurements of the Seebeck coefficient for both pure silicon and germanium as well as several alloys can be found in literature [106,97,98,144,145]. At the lower temperature range, the coefficients are elevated by the phonon-drag effect [146,147,148,149] in pure silicon, which is not the case in SiGe alloys due to the short phonon mean free paths [19]. Interestingly, the electronic contribution does not change noticeably for different material compositions, thus modeling of the Seebeck coefficients for SiGe samples can be reduced to the electronic contribution.

Figure 4.4: Electron mobility vs. material composition for silicon-germanium alloys for different at room temperature.

In spite of their outstanding reliability, some attention has to be paid on degradation of SiGe thermoelectric generators [150] causing a reduction of the figure of merit over the device lifetime. At high temperature conditions, sublimation can cause both thermal and electrical shortcuts due to deposition in the surrounding. Under extreme conditions, erosion occurs and may cause device failures by open circuits or mechanical damage. A coating of silicon nitride reduces temperature dependent loss rates by sublimation by a factor of approximately 10 [150]. Furthermore, accordingly high doping concentrations, which are favored in order to achieve high figures of merit, tend to build up local accumulations. Such accumulations cause a reduction of the free carrier concentration and thus increase the electric resistivity resulting in worse figures of merit. Boron-doped p-type samples are less sensitive to this effect than n-type samples doped with phosphorus due to the comparably lower diffusion rates of the dopants.

M. Wagner: Simulation of Thermoelectric Devices