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A model for prediction the photostriction effect in silicon microcantilevers is built up based on the fundamentals of mechanics and semiconductor physics. By considering the spatial distribution and surface recombination of photoinduced carriers in silicon, the model interprets the cause of the photoinduced bending. The results from our model much more closely approximate the experimental values than the former model built up by Datskos, Rajic and Datskou [

The so called photostriction effect in semiconductors was found in germanium by Figielski in 1961 [

Under illumination with light with an energy above the band gap of silicon, the lattice in the microcantilever will be strained as the presence of excess electron-hole-pairs. Different from Datskos's assumption of homogeneous excess carriers, we suppose that the light intensity will be reduced along the depth of the cantilever (x direction in

Assuming that the light intensity at the top surface of the microcantilever is a constant, _{0}

Following Datskos's deduction, the density of photoinduced excess carriers is given by [

The photoinduced strain is given by

Derived from equations (

For a cantilever with a rectangular cross section, the deformation curvature of the structure can be given by [_{y}

The maximum displacement _{max} due to photoinduced carriers can then be written as [

In order to compare with Datskos's expression in reference [^{−αH}, which is the photo absorptivity of silicon [

By comparing our

Two obvious differences between the two equations can be seen. One is that in our equation, there is

Furthermore, the recombination of the photoinduced excess carriers at the top and bottom surfaces must be considered in the prediction of the deformation, because the thickness of the microcantilever is as thin as some hundreds nanometers (e.g. 500 nm in [

Suppose that excess carrier density at the etched surface equals to 0, while the carrier recombination at the polished surface can be omitted. Under this assumption, the bending moment _{max}

To verify our model, the calculated results from our model are compared with the theoretical and experimental data in [^{3} to 3×10^{3}cm^{-1}. In our calculation, we set

The x ordinate of the plot is power density P instead of absorbed power Φ used in [_{0}

From the figure, higher accuracy of our model is obvious. For

In summary, we have introduced a model to calculate the photoinduced bending of a Si microcantilever, based on the theory of the gradient of photoinduced excess carrier and the carrier recombination at the two surfaces of the microcantilever. The result from our model is 0.85 times that of the measurement, which is much more accurate than the results from the former model. It has been revealed that the photoinduced bending is induced by the gradient of photoinduced excess carrier and the different recombination velocity between top and bottom surface on the cantilever.

This research work is supported by the Natural Science Foundation of China under Grant No.

Schematic of a Si microcantilever under incident light and the coordinate system

Theoretical results from our model with

The experimental conditions in [

100 μm | 20 μm | 500nm | 780nm | 0.95 |