Strain relaxation in silicon-germanium microstructures observed by resonant tunneling spectroscopy

Abstract

We have measured the resonant tunneling current-voltage I(V) characteristics of strained p-Si/Si 1Ϫx Ge x double-barrier microstructures ranging from 1.0 to 0.1 m in lateral extent. The bias spacing between resonant current peaks in the I(V) reflects the energy separation of the Si 1Ϫx Ge x quantum well subbands, which is partially determined by the strain. As the lateral size of the structures decreases, we observe consistent shifts in the I(V) peak spacing corresponding to strain energy relaxation of ϳ30% in smaller structures. An additional I(V) fine structure is observed in the 0.1 m device, consistent with lateral quantization due to nonuniform strain.

Eigenproblems in nanomechanics

“…Figure 1 demonstrates the comparison of the values of the frequencies described by Eqs. (12) and the value corresponding to the Euler beam model which is given by the relation:…”

“…In the present analysis the electron effective mass m i is assumed to be constant on the quantum dot and the matrix for every fixed energy level λ E and is taken as [12]:…”

Magnetotunneling spectroscopic probe of quantization due to inhomogeneous strain in a Si/SiGe vertical quantum dot

“…When a quantum dot is etched out of the strained heterostructure, the biaxial strain can relax as demonstrated by Raman spectroscopy 7 and resonant tunneling measurements. 8,9 Recently, experiments have confirmed that the strain relaxation in the quantum dot is inhomogeneous, which induces additional lateral confinement of holes in the quantum well. [8][9][10] We have utilized RT measurement to probe the inhomogeneous strain in an individual Si/Si 0.8 Ge 0.2 double-barrier quantum dot.…”

“…8,9 Recently, experiments have confirmed that the strain relaxation in the quantum dot is inhomogeneous, which induces additional lateral confinement of holes in the quantum well. [8][9][10] We have utilized RT measurement to probe the inhomogeneous strain in an individual Si/Si 0.8 Ge 0.2 double-barrier quantum dot. The fine structure in the HH I(V) characteristics reveals the discrete hole states confined by the in-plane ringlike potential associated with an axially symmetric strain distribution in the quantum well.…”

“…The applied bias between the top contact and the substrate aligns the hole states in the emitter electrode with the quantized hole states in the Si/SiGe quantum well, leading to resonant I(V) peaks. 2,8 The heavy-hole and light-hole branches of the hole dispersion give rise to separate two-dimensional ͑2D͒ subbands and hence I(V) peaks. In this paper we will focus on the HH I(V) peak, because the HH states have a lighter in-plane mass 11 and hence are more sensitive to inhomogeneous-strain-induced lateral potentials we are interested in.…”