TY - JOUR
T1 - Suppression of Midinfrared Plasma Resonance Due to Quantum Confinement in δ -Doped Silicon
AU - Young, Steve M.
AU - Katzenmeyer, Aaron M.
AU - Anderson, Evan M.
AU - Luk, Ting S.
AU - Ivie, Jeffrey A.
AU - Schmucker, Scott W.
AU - Gao, Xujiao
AU - Misra, Shashank
PY - 2023/8/1
Y1 - 2023/8/1
N2 - The classical Drude model provides an accurate description of the plasma resonance of three-dimensional materials, but only partially explains two-dimensional systems where quantum mechanical effects dominate such as P:δ layers - atomically thin sheets of phosphorus dopants in silicon that induce electronic properties beyond traditional doping. Previously it was shown that P:δ layers produce a distinct Drude tail feature in ellipsometry measurements. However, the ellipsometric spectra could not be properly fit by modeling the δ layer as a discrete layer of classical Drude metal. In particular, even for large broadening corresponding to extremely short relaxation times, a plasma resonance feature was anticipated but not evident in the experimental data. In this work, we develop a physically accurate description of this system, which reveals a general approach to designing thin films with intentionally suppressed plasma resonances. Our model takes into account the strong charge-density confinement and resulting quantum mechanical description of a P:δ layer. We show that the absence of a plasma resonance feature results from a combination of two factors: (i) the sharply varying charge-density profile due to strong confinement in the direction of growth; and (ii) the effective mass and relaxation time anisotropy due to valley degeneracy. The plasma resonance reappears when the atoms composing the δ layer are allowed to diffuse out from the plane of the layer, destroying its well-confined two-dimensional character that is critical to its distinctive electronic properties.
AB - The classical Drude model provides an accurate description of the plasma resonance of three-dimensional materials, but only partially explains two-dimensional systems where quantum mechanical effects dominate such as P:δ layers - atomically thin sheets of phosphorus dopants in silicon that induce electronic properties beyond traditional doping. Previously it was shown that P:δ layers produce a distinct Drude tail feature in ellipsometry measurements. However, the ellipsometric spectra could not be properly fit by modeling the δ layer as a discrete layer of classical Drude metal. In particular, even for large broadening corresponding to extremely short relaxation times, a plasma resonance feature was anticipated but not evident in the experimental data. In this work, we develop a physically accurate description of this system, which reveals a general approach to designing thin films with intentionally suppressed plasma resonances. Our model takes into account the strong charge-density confinement and resulting quantum mechanical description of a P:δ layer. We show that the absence of a plasma resonance feature results from a combination of two factors: (i) the sharply varying charge-density profile due to strong confinement in the direction of growth; and (ii) the effective mass and relaxation time anisotropy due to valley degeneracy. The plasma resonance reappears when the atoms composing the δ layer are allowed to diffuse out from the plane of the layer, destroying its well-confined two-dimensional character that is critical to its distinctive electronic properties.
UR - http://www.scopus.com/inward/record.url?scp=85168718108&partnerID=8YFLogxK
U2 - 10.1103/PhysRevApplied.20.024043
DO - 10.1103/PhysRevApplied.20.024043
M3 - Article
SN - 2331-7019
VL - 20
JO - Physical Review Applied
JF - Physical Review Applied
IS - 2
ER -