Retraction of “Thermodynamic Self-Limiting Growth of Heteroepitaxial

Retraction pubs.acs.org/NanoLett

Retraction of “Thermodynamic Self-Limiting Growth of Heteroepitaxial Islands Induced by Nonlinear Elastic Effect” Hao Hu, Xiaobin Niu, and Feng Liu* Nano Lett. 2016, 16 (6), 3919−3924, DOI: 10.1021/acs.nanolett.6b01525 Nano Lett. 2017, 17, DOI: 10.1021/acs.nanolett.6b04086

W

e thank Dr. Daruka for his interest as well as his critical and constructive comments1 on this Letter. In this Letter, we made the argument and derivation that assuming a general nonlinear height-dependent strain field in the strained island: εH(z) = ε0(1 − τ0 z)

(1)

The island strain relaxation energy would have a V term that, in turn, leads to a self-limiting growth. However, using the geometric similarity (scaling) argument shown by Dr. Daruka1 within the framework of linear elastic theory, the correct form of eq 1 should be 4/3

⎡ ⎛ z ⎞⎤ εD(z) = ε0⎢1 − τ0⎜ ⎟⎥ ⎢⎣ ⎝ z 0 ⎠⎥⎦

(2)

where z0 is the original nominal island height. Then the island strain relaxation energy would always scale linearly with island volume V, leading to no self-limiting growth. After reviewing Dr. Daruka’s derivation, all authors agree that the assumption of our original eq 1 is generally incorrect, and the geometric scaling argument might be applicable to higher order strain energy terms as well. The possible cases when the geometric scaling arguments do not apply are additional effects due to strain relaxation in the wetting layer or island edges, which we did not discuss in this article. Given our mistake, all authors have agreed to retract the letter.

■

REFERENCES

(1) Daruka, I. Nano. Lett. 2017, 17, n/a DOI: 10.1021/ acs.nanolett.6b04086.

© XXXX American Chemical Society

A

DOI: 10.1021/acs.nanolett.7b00388 Nano Lett. XXXX, XXX, XXX−XXX