(Invited) Large Mobility Modulation Due to Discrete Impurities in Nanowires
Authors: Sano Nobuyuki 
Published: February 2020

Semiconductor nanowires have been receiving great attention over the past decades, owing to their possible applications to chemical/biological sensors as well as future electronic/photonic devices [1,2]. Among other characteristics, the locality of ionized impurities plays a crucial role in optimizing the device performance; carrier transport is critically dependent on where the localized impurities are positioned inside nanoscale channels. In fact, this is the physical origin of the random dopant fluctuation found in threshold voltage, which is now of most serious concerns in integrating nanoscale Si-based devices [3].
Recently, we have theoretically carried out systematic investigations on the effects of the locality of multiple impurities on transport characteristics under quasi-one dimensional (quasi-1D) nanowire structures [4]. We have shown that both phase interference and phase randomization simultaneously play a dominant role in determining the impurity-limited resistance even under the fully coherent circumstances, in which no energy dissipating scattering is involved. In this presentation, we extend our approach further to study the polarity dependence of impurities on transport characteristics. We show that the impurity-limited mobility could be modulated over three orders of magnitude by changing the axial separation among impurities provided that the charge polarity of impurities is opposite to that of carriers.
We employ a cylindrical nanowire with radius of 2 nm and ionized acceptors or donors are distributed at random in the Si channel. Typical potential profiles in the channel region consist of the long-range potential modulation spread over the channel and the localized short-range potential modulation. Here, we would like to point out that some confusion exists in many theoretical analyses, regarding the channel resistance caused by such potential profiles: The long-range potential modulation and the short-range scattering potential are mixed up. The former is caused mainly by the applied gate voltage and the work function difference between the substrate and gate, whereas the latter is attributed to the screened Coulomb potential of impurities and carriers. The channel resistance is dominated by the short-range scattering potential and the long-range potential simply modulates the carrier density in the channel region, rather than the channel resistance. Therefore, in order to calculate the impurity-limited resistance, it is essential to eliminate the long-range potential modulation from the channel potential. In the present calculations, the average impurity density in the channel is fixed at 2 x 1019 cm-3, so that the channel length varies according to the number of impurities doped in the channel, namely, L = 4 nm for a single impurity, 8 nm for two impurities, etc. The conductance is obtained from the Landauer formula in terms of the transmission probability calculated from the Lippmann-Schwinger equation with the short-range scattering potential. The impurity-limited resistance and mobility are then extracted by subtracting the quantum resistance from the inverse of the conductance.
We show that the impurity-limited resistance (mobility) due to two ionized impurities located on the wire axis is greatly modulated as a function of the distance Δ between the impurities: The constructive phase interference is very strong at small Δ even at room temperature, whereas this phase interference diminishes at large Δ. Since no phase randomizing scattering is included in the present calculations, this randomization is attributed to the broadness of the energy spectrum of the incoming electrons from the reservoirs [4]. The most striking feature is that the impurity-limited resistance (mobility) is greatly suppressed (enhanced) at some particular value of Δ (around 1 nm) in the case of donors. We have also carried out more elaborate NEGF simulations with the screened Coulomb potential by placing the donor impurities at random inside the channel region. The above feature is still clearly visible, though the modulation is reduced owing to random impurity distributions. Nevertheless, this large mobility modulation is expected to affect significantly the device performance, especially, in the case of Junctionless-FETs.
This study was supported in part by the MEXT under Grant- in-Aid for Scientific Research (B) (No. 15H03983).
REFERENCES
[1] V. Schmidt, et al., Adv. Mater. 21, 2681 (2009).
[2] R. Rurali, Rev. Mod. Phys. 82, 427 (2010).
[3] A. Asenov, IEEE ED-45, p.2505 (1998); N. Sano, et al., IEDM Tech. Dig. p.275 (2000).
[4] N. Sano, J. Appl. Phys. 118, 244302 (2015); EUROSOI-ULIS 2016, p. 216 (2016).