Naoya Morioka

Quantum-confinement effect on holes in silicon nanowires: Relationship between wave function and band structure

The authors theoretically studied the valence band structure and hole effective mass of rectangular cross-sectional Si nanowires (NWs) with the crystal orientation of [110], [111], and [001]. The E–k dispersion and the wave function were calculated using an sp3d5s∗ tight-binding method and analyzed with the focus on the nature of p orbitals constituting the subbands. In [110] and [111] nanowires, longitudinal/transverse p orbitals are well separated and longitudinal component makes light (top) subbands and transverse component makes heavy subbands. The heavy subbands are located far below the top light band when NW has square cross-section, but they gain their energy with the increase in the NW width and come near the band edge. This energy shift of heavy bands in [110] NWs shows strong anisotropy to the direction of quantum confinement whereas that in [111] NWs does not have such anisotropy. This anisotropic behavior and the difference among orientations are understandable by the character of the wave fu...

Mobility oscillation by one-dimensional quantum confinement in Si-nanowire metal-oxide-semiconductor field effect transistors

Si-nanowire p-channel metal-oxide-semiconductor field effect transistors (MOSFETs), in which the typical cross section of the nanowire is a rectangular shape with 3 nm height and 18 nm width, have been fabricated and the current-voltage characteristics have been measured from 101 to 396 K. The transconductance has shown oscillation up to 309 K. The carrier transport has been theoretically analyzed, assuming that the acoustic phonon scattering is dominant. The electronic states have been determined from the effective mass approximation and the mobility from the relaxation time approximation as a function of the Fermi level. Relation between the gate voltage and the Fermi level has been estimated from the MOSFET structure. The calculated mobility has shown the oscillation with change in the Fermi level (the gate voltage), resulting in the transconductance oscillation. The oscillation originates from one-dimensional density of states (∝E−0.5).

Orientation and Shape Effects on Ballistic Transport Properties in Gate-All-Around Rectangular Germanium Nanowire nFETs

The electron transport properties of square and rectangular cross-sectional germanium nanowire (GeNW) field-effect transistors (FETs) with [001], [110], [111], and [112] crystal orientations are investigated. The electronic states of GeNWs are calculated by using an sp3d5s* tight-binding model coupled to a Poisson equation self-consistently. A semiclassical ballistic FET model is used to evaluate the electron transport characteristics. For the square cross section, electron injection velocity dominates the drive current in GeNW FETs because the inversion electron density in the GeNW channels is mainly determined by the capacitance of the gate insulator, and a [110] GeNW FET achieves the highest drive current of all the orientations. In the case of rectangular cross section, the electron density in GeNWs is dependent on their orientations and cross-sectional geometries due to the small quantum capacitance, and the difference of the density of states of GeNWs significantly affects the drive current. A [112] GeNW FET on a (11̅0) face exhibits the highest injection velocity of all the calculated FETs but low drive current because of its insufficient density of states. As a result, a [110] GeNW FET on a (001) face, which has both large density of states and high injection velocity, achieves the highest drive current.

Bandgap shift by quantum confinement effect in 〈100〉 Si-nanowires derived from threshold-voltage shift of fabricated metal-oxide-semiconductor field effect transistors and theoretical calculations

Si-nanowire (Si-NW) MOSFETs, the cross-sectional size (square root of the cross-sectional area of NWs) of which was changed from 18 to 4 nm, were fabricated and characterized. Both n- and p-channel MOSFETs have shown a nearly ideal subthreshold swing of 63 mV/decade. The threshold voltage of n-/p-channel MOSFETs has gradually increased/decreased with decreasing the cross-sectional size. The bandgap shift from bulk Si has been derived from the threshold-voltage shift. The bandgap of Si-NWs was calculated by a density functional theory, tight binding method, and effective mass approximation. The calculated bandgap shows good agreement with that derived from threshold voltage. The theoretical calculation indicates that the bandgap is dominated by the cross-sectional size (area) and is not very sensitive to the shape within the aspect-ratio range of 1.0-2.5.

Phonon-Limited Electron Mobility in Rectangular Cross-Sectional Ge Nanowires

The phonon-limited electron mobility in rectangular cross-sectional germanium (Ge) nanowires (NWs) with various orientations was theoretically investigated. The electronic states were calculated by a tight-binding model and the phononic states were calculated by a valence force field model. Then, transition probability was calculated by Fermis golden rule, and Boltzmanns transport equation was solved for calculating low-field mobility. The electron mobility of Ge NWs strongly depends on the wire orientations and cross-sectional shapes, and this dependence can be explained by the conduction band structure of Ge NWs. Among several geometries investigated in this paper, [110]-oriented NWs with wider width along [001] showed the highest electron mobility at low carrier concentration, and [112] NWs with wider width along [11̅0] showed the highest electron mobility at high carrier concentration. This result indicates that these kinds of Ge NWs are suitable as n-channel material.

Geometrical and band-structure effects on phonon-limited hole mobility in rectangular cross-sectional germanium nanowires

We calculated the phonon-limited hole mobility in rectangular cross-sectional [001], [110], [111], and [112]-oriented germanium nanowires, and the hole transport characteristics were investigated. A tight-binding approximation was used for holes, and phonons were described by a valence force field model. Then, scattering probability of holes by phonons was calculated taking account of hole-phonon interaction atomistically, and the linearized Boltzmanns transport equation was solved to calculate the hole mobility at low longitudinal field. The dependence of the hole mobility on nanowire geometry was analyzed in terms of the valence band structure of germanium nanowires, and it was found that the dependence was qualitatively reproduced by considering an average effective mass and the density of states of holes. The calculation revealed that [110] germanium nanowires with large height along the [001] direction show high hole mobility. Germanium nanowires with this geometry are also expected to exhibit high electron mobility in our previous work, and thus they are promising for complementary metal-oxide-semiconductor (CMOS) applications.

Quantum-confinement effects on conduction band structure of rectangular cross-sectional GaAs nanowires

The conduction band structure and electron effective mass of GaAs nanowires with various cross-sectional shapes and orientations were calculated by two methods, a tight-binding method and an effective mass equation taking the bulk full-band structure into account. The effective mass of nanowires increases as the cross-sectional size decreases, and this increase in effective mass depends on the orientations and substrate faces of nanowires. Among [001], [110], and [111]-oriented rectangular cross-sectional GaAs nanowires, [110]-oriented nanowires with wider width along the [001] direction showed the lightest effective mass. This dependence originates from the anisotropy of the Γ valley of bulk GaAs. The relationship between effective mass and bulk band structure is discussed.

Etching-limiting process and origin of loading effects in silicon etching with hydrogen chloride gas

The etching-limiting step in slow Si etching with HCl/H2 at atmospheric pressure was investigated. The etching was performed at a low etching rate below 10 nm/min in the temperature range of 1000?1100 ?C. In the case of bare Si etching, it was confirmed that the etching rate showed little temperature dependence and was proportional to the equilibrium pressure of the etching by-product SiCl2 calculated by thermochemical analysis. In addition, the etching rates of Si(100) and (110) faces were almost the same. These results indicate that SiCl2 diffusion in the gas phase is the rate-limiting step. In the etching of the Si surface with SiO2 mask patterns, a strong loading effect (mask/opening pattern dependence of the etching rate) was observed. The simulation of the diffusion of gas species immediately above the Si surface revealed that the loading effect was attributed to the pattern-dependent diffusion of SiCl2.

Impacts of orientation and cross-sectional shape on hole mobility of Si nanowire MOSFETs

We fabricated 〈100〉, 〈110〉, 〈111〉, and 〈112〉 p-channel gate-all-around Si nanowire (SiNW) MOSFETs, cross sections of which are rectangles with various widths, and investigated the hole mobility of the SiNW MOSFETs using the double L_m method. Measured hole mobilities of SiNW MOSFETs were about 80-140 cm²/Vs at surface carrier density of 1 × 10¹³ cm^-2. The dependences of the hole mobility on orientations and cross-sectional shapes of nanowires were analyzed. The orientation and geometry dependences can be explained by the band structures calculated by tight-binding approximation.

Orientation and size effects on phonon-limited hole mobility in rectangular cross-sectional germanium nanowires

The phonon-limited hole mobility in rectangular cross-sectional [001], [110], [111], and [112]-oriented germanium nanowires was calculated and the hole transport characteristics were compared. The calculation revealed that [110] germanium nanowires with larger height along [001] show high hole mobility and are favorable for p-channel FETs.