Gate-Bias Dependent Phonon Softening Observed in Ge MOSFETs

1. Introduction
Heavy impurity doping is known to soften the lattice system in Ge, experimentally [1]. Theoretically, the origin of this phenomena is considered to be the free carrier effect explained by the carrier redistribution model [2] and the Fano-type interaction model [3]. However, no clear evidence of the free carrier effect has been reported, because it is quite difficult to experimentally distinguish it from the dopant atom effect. Furthermore, these two models are based on the rigid band model, in spite of the fact that electronic band structure is also modulated by the heavy doping [4]. Then, the objective of this work is to experimentally and directly demonstrate the free carrier effect on the lattice softening, and to propose the new model for understanding both phonon and electron structure modulation, simultaneously and self-consistently.

2. Experiment
The back-gated Ge-on-insulator (GeOI) MOSFET was fabricated with lightly-doped p-type GeOI substrate, as schematically shown in the inset of Fig. 1. The doping concentration of Ge was below 1x10¹⁵ /cm³, and the top surface of Ge was covered with Y₂O₃ to minimize the interface defects [5]. Then, the carrier density in Ge can be controlled by the back-gate bias, while only a few dopant atoms are contained. The zone-center optical phonon frequency was characterized by the microscopic Raman measurement with Ar laser (λ=488 nm, 0.4 mW), with applying the back-gate bias.

3. Results and Discussion
Raman spectroscopy measurement is quite powerful tool for analyzing the zone-center optical phonon energy, which can be the indicator for inspecting the phonon system in Ge. Fig. 1 shows the back gate voltage dependence of the Raman peak position in lightly-doped p-GeOI. The significant red-shift is clearly observed by applying the negative V_g (on state of the FET). It demonstrates that the zone-centered phonon energy decreases with the hole accumulation in lightly-doped Ge. To our knowledge, this is the first and direct evidence of the free carrier effect on the phonon softening.
We propose a model for the intuitive interpretation of experimental results, from the viewpoint of a modification of the covalent bonding by free carrier accumulation. Suppose the simple covalent bonding of two atoms with sp3 hybridized orbital. When an additional carrier is added in this system, there is still an energy gain in the covalent bonding. However, it should be decreased due to a reduction of the number of valence electrons. In addition, the hybridization gain could be also reduced by the screening. Since free carriers are 10^-4~10^-6 of Ge atoms, it may be more appropriate to describe the high carrier density region in Ge as the weakened covalent bonding system. The energy gain modulation is more realistically described by the Lennard-Jones type potential for a molecular formation. The reduction of the energy gain in the covalent bonding may result in the increase of the curvature near the energy minimum, which is described by kx2 [6]. Then, it is expected that the force constant k becomes smaller under free carriers. This is considered to be the origin for the phonon softening observed in Raman measurement. Interestingly, this model can reasonably explain the band structure modulation in heavily doped semiconductors [4], as well.
Furthermore, this effect should be taken into consideration in discussing the phonon scattering of carriers, because the phonon deformation potential is not a constant but dependent on free carrier density. This has been totally ignored in the carrier transport analysis so far. Note that it will be more important in nano-scale devices, because the atomic nature will become more dominant.

4. Conclusion
We have experimentally demonstrated the free carrier effect on phonon softening for the first time. This effect is explainable by the model that the covalency is weakened by free carriers. This view can simultaneously interpret both the phonon and electron structure modulation in heavily-doped Ge. Furthermore, it is pointed out that the present consideration will be more significant in nano-scale devices such as Fin FET or ET-GeOI FET.

ACKNOLEDGEMENTS
This work was partially supported by JSPS Core-to-Core Program.

REFERENCES
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[6] N. Ashcroft et al., "Solid State Physics", (Thomson Learning, 1976).