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In-surface Buckling of Silicon Nanowires on Elastomeric Substrates

Jianliang Xiao's picture

Buckling of thin layers or aligned arrays of stiff materials on elastomeric substrates has many important applications, such as stretchable electronics, precision metrology and flexible optoelectronics.  These systems show one common phenomenon, the stiff thin layers buckle normal to the substrate surface (out-of-surface buckling).  By contrast, we recently reported for the first time that silicon nanowires (SiNWs) on elastomeric substrates buckle only within the substrate surface, i.e. in-surface buckling.  Experimental process to obtain buckled SiNWs is described.  Buckling wavelength and amplitude are obtained analytically by mechanics.  Comparison between mechanics and experimental results gives the Young's modulus of SiNWs to be ~140 GPa, which agrees well with previously reported values.  It is shown that the energy associated with in-surface buckling is lower than the out-of-surface buckling, which explains why only in-surface buckling of SiNWs is observed in experiment. 

This result is recently published on Nano Letters, and here is the link: Lateral Buckling Mechanics in Silicon Nanowires on Elastomeric Substrates


LG's picture

Dear Jianliang,

Congratulations to your new job!  I realize you have delivered series of good jobs related to 'buckling of the coating attach to the substrate'.  I am now doing few job refer to nonlinear problems.  Please allow me to express few inquires about your good jobs.

To our understanding, the definition of the linear means "for any P and Q, and constants a and b, the function satisfy F(aP+bQ)=aF(P)+bF(Q)". Otherwisw, we should call the function F as nonlinear.

1. The nonlinear buckling in your job means the geometry or constitution?  Do you mean the large deformation of the coating was taken into account ? How about the substrate? Do you summed the strain energy of the two parts (coating and substrate) by superposition?   (As far i understand, the mimimal potential energy theorem is valid for linear elastic body,  the principle of virtual work should be applied to solve dynamics and inelastics. Furthermore, superposition is only valid to linear problems.)

2. For one nonlinear system (coating or substrate),  Did you use the perturbation method to reduce the nonlinear problem to summantion of few linear terms?

Best Wishes, Liu Gang


Jianliang Xiao's picture

Dear Gang,

Thanks for your interest!

Here are my comments to your questions. 

1.  In our model, only geometrical nonlinearity of the beam (nanowire) is taken into account. Specifically, the deformation of the beam is considered as small strain but finite rotation (source of nonlinearity), which is a normal treatment for the buckling problem of a beam. Both the beam and the substrate are linear elastic, so the total potential energy is obtained by summation of the energies in two parts.

 2. For the beam, the energy is composed of two parts, the bending energy and membrane energy. If you need to include nonlinearity for the substrate, perturbation method is a good way to solve the problem.

If you need more details, I will be happy to provide my unpublished manuscript with detailed mechanics analysis.


LG's picture

Dear Jianliang, Well done!  Also thanks a lot for your explanation. Please keep in touch, and wish you good luck.

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