The indentation hardness of silicon measured by instrumented indentation: What does it mean?

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INTRODUCTION

The indentation hardness (IH) of crystalline silicon (c-Si) and other semiconductors has attracted significant interest since its correlation to a pressure-induced (PI) phase transition was first noted.^1,2This phase transition is usually observed upon pressurization in diamond anvil cells, whereby the diamond cubic structure (Si-I) transforms to a soft metallic phase with [beta]-Sn structure (Si-II) at ~11.3 GPa (see, e.g., Refs. 3, 4, and references therein). Upon unloading, Si-II cannot transform back to the original Si-I but instead transforms to more complex crystalline phases (Si-III and Si-XII).^3,4A similar transformation pathway upon indentation loading has been confirmed by scanning electron microscope (SEM) images of extruded material,⁵transmission electron microscopy (TEM) observation of end phases,^6,7and by in situ electrical measurements.^1,8The plastic deformation of c-Si is thus directly correlated to its phase transition behavior and its IH can be quoted as the phase transition pressure since Si-II has a sufficiently low resistance to plastic flow.⁹

In contrast to diamond anvil cell results, however, the end phase in the indentation case is critically dependent on the unloading rate, with slow unloading resulting in the same crystalline phases (Si-III and Si-XII) but fast unloading resulting in a form of amorphous silicon (a-Si), the so-called PI a-Si.^10,11It should be noted that such a recovery of the [beta]-Sn phase to less dense phases represents a form of "reverse plasticity." This means that during unloading, in addition to the usual recovery of the elastically deformed component surrounding the plastic zone, the plastically deformed component of the material can also recover to some extent. Such behavior clearly has to be taken into account when measuring the IH of c-Si by instrumented indentation methods since the slope of the unloading curve is used in the determination of IH. For example, measurement by the Field-Swain method¹²traditionally uses fast partial unloading, yielding PI a-Si beneath the residual impression after final unloading.^6,7In contrast, the Oliver-Pharr method,¹³which traditionally requires reasonably slow unloading rates for a good quality load-displacement curve, results in the formation of the crystalline phases Si-XII/Si-III. Clearly, such very...