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Low-temperature mobility of holes in Si /SiGe p-channel heterostructures

Mathematics and Statistics

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Low-temperature mobility of holes in Si /SiGe p-channel heterostructures

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Recently, there has been considerable interest in the incorporation of a strained SiGe layer into p-channel metal-oxide-semiconductor structures, to give increases in hole mobility and high-field drift velocity.1-3 However, low-temperaturemeasurements reveal the following striking phenomena. First, the hole mobilities are significantly less than the electron ones. For the two-dimensional electron gas (2DEG) in a Si n-channel, peak low-temperature mobilities were reported to be ,43105 cm2 /V s,3 while for the two-dimensional hole gas (2DHG) in a strained SiGe p-channel, the best mobilities reported not exceeding ,23104 cm2 /V s.4-6 Second, the hole mobility is degraded when increasing the Gecontent despite a reduction in effective hole mass.3,7-9

It has been shown9-13 that all so-far known scattering mechanisms such as impurity doping, alloy disorder, and surface roughness are unable to account for the earlier experimental data. Therefore, several authors had to invoke the concept of interface charges as a key scattering source at low temperatures. This enables a somewhat satisfactory description of the 2DHG mobility in different strained Si /SiGe heterostructures with a suitable choice of the interface charge density as a fitting parameter.

Nevertheless, there are several drawbacks in the previous theories. First, it was indicated3,9,10 that the nature of inter-face charges has been, to date, quite unclear. It was supposed that they can originate from impurity contamination of epitaxial layers during and after growth. The areal impurity density for such an unintentional doping has to be claimed high,9-13 up to ,1011 cm−2. The mechanisms for trapping and charging impurities at the heterointerface Si /SiGe are also not clarified.

Second, the decrease observed3,8 in the low-temperature 2DHG mobility of strained SiGe layers when increasing the Ge content is also still unclear, since alloy disorder was demonstrated1,7,9-13 likely not to be a dominant scattering source at a low carrier density, e.g., of ,1011 cm−2. Plews and co-workers14 have obtained strong experimental evidence that for Si /SiGe /Si systems screening of any scattering potential, whatever its nature, is important, especially, at low values of temperature, carrier density, and Ge content. As a result, with screening included, one cannot fit the ob-served data simply on the basis of alloy disorder scattering alone, even by taking an unjustifiably large value of the alloy potential.1,9,13

Third, it was proved15-19 that interface roughness gives rise to random variations in all components of the strain field in actual lattice-mismatched heterostructures. As a result, Feenstra and Lutz16 found that for an n-channel Si /SiGe sys-tem these fluctuations cause a random nonuniform shift of the conduction band edge. This implies a random deforma-tion potential acting on electrons as a source of scattering, which yields much better agreement with experimental data about the 2DEG mobility20 than surface roughness scattering does. The existing calculations9,11,12 of the 2DHG mobility in a p-channel Si /SiGe system have been carried out with an extension of the idea of Feenstra and Lutz to the valence band edge, based on the assumption that the deformation potential for holes is almost identical to that for electrons. As seen later, this is in fact invalid.

Finally, in the last years some experimental evidences for piezoelectricity of strained SiGe layers in Si /SiGe systems have been found.21-24 Further, interface roughness was shown17-19 to induce a fluctuating density of piezoelectric charges. Scattering by them is to be included in a full treat-ment of the hole mobility.

Thus, the goal of this paper is to present a theory of the low-temperature 2DHG mobility in strained SiGe layers of Si /SiGe p-channel heterostructures. Our theory is to be developed for explaining the experimental data recently reported in Refs. 3, 8, 11, and 12. Moreover, the theory must not be based on the unclear concept of interface impurity charges, but adequately include the possible sources of scat-tering: alloy disorder, surface roughness, deformation poten-tial, and piezoelectric charges. In particular, the deformation potential for holes must be rigorously derived.

The paper is organized as follows. In Sec. II, we formulate our model and basic equations used to calculate the disorder-limited 2DHG mobility, taking explicitly into ac-count the finiteness of the potential barrier height. In Sec. III, the autocorrelation functions for diverse scattering mecha-nisms are derived. Section IV is devoted to numerical results and comparison with experiment. Finally, a summary in Sec. V concludes the paper.

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