Strained Silicon ...

A simple example shows how powerful the use of ab initio software could be: By calculations electronic properties of strained silicon can be predicted without the usage of expensive experiments


Fig. 1 MOSFET with a SiGe-substrat and a Si-Layer in the channel. The SiGe-substrate introduces a strain to the Si-Layer. This way a improvement of the conductivity is achieved.

In practice, a thin layer of silicon is deposited on silicon doped with germanium, which leads to a distortion. Because of its small dimensions, an experimental determination of physical properties is very difficult. At this point, the major advantages of ab initio calculations come to their use. Without much effort, physical properties may be determined (structural, thermal, electronic, etc.), for which in other cases various experimental measurement arrangements were necessary. In addition to the calculations, the exact structures of the electronic properties were also determined. Conclusions about the relationship between crystal lattice and other physical quantities could be made. In chapter 1 the structure of SiGe is determined. Using the structure obtained from chapter 1, in chapter 2 the electronic properties of strained silicon are calculated. To demonstrate an allocation of 25% germanium, Si3Ge is used.

Bracing to improve the conductivity

MOSFET's are the main important components of the semiconductor industry. Due to the decreasing feature size of these devices, the development encounters its limits. Unwanted side effects are inevitable. Another way to increase the performance of MOSFETs without down scaling them, is the tension of the silicon. Because of the tension it comes through a change in the band structure to an increase in conductivity. This allows the electrons to pass through the channel of the transistor and switch faster. However, applications of a mechanical stress on very small length scales are very difficult to achieve [1].

As a solution it could be used the doping with elements from the 5th Main group of the periodic table. Based on the same lattice structure and the different lattice constants of these elements, the introduction of germanium or carbon are leading to increase the crystal volume. Leaving now on such a SiGe structure, a thin layer of silicon to grow up, so this attempt to take on the larger lattice constant. This causes stretching in the appropriate level. On the 8th of June 2001 external link to IBMIBM announced the first use of strained silicon to increase and reached a speed by 35% of their chips.

Determination of the Si3Ge-structure

Fig. 2 crystal structure of silicon (left), germanium (right) und SiGe(bottom). Si has a slightly smaller lattice constant as Ge. The lattice constant of SiGe fits in between.

To compare the results, the FCC lattice of Si and Ge were calculated for comparison. The volume of the 16-atom cells be VSi = 2.1304 * 103 Bohr3, VGE = 2856 * 103 Bohr3 and VSi3Ge = 2163 * 103 Bohr3. In fact of to the lower volume of the silicon cell, the cell gets larger at the doping with germanium (see Figure 2).

Calculation of the electronic properties of strained-Silicon

Fig. 3 stretch of the silicon lattice

The expansion of the SiGe cell is now determining the stretch of the silicon lattice. Trying to keep its volume constant the silicon cell opposed to a stretching in the x-y- plane, a compression in the z-direction (see Figure 3).

Bandstruktur von ungestreckten (oben) und gestreckten Silizium (unten). Die Streckung führt zu einer Veränderung der Bandstrucktur und Leitfähigkeit.
Fig. 4: Band structure of unstrained (top) and strained Silicon (bottem). The strain introduces changes in both band structure and conductivity.

This stretch has a direct impact to the band structure. The change in the valence and in the conduction bands are in particular of interest. The mobility of electrons and holes is directly proportional to the curvature of the corresponding bands. Figure 4 shows the stretched and unstretched bandstructur of silicon. Taking a close look, you can see that it came to a splitting of the bands because of the stretching and thus, altering the curvature of the band edge. The calculation of the effective mass of the band structure results in an increase in the effective mass of holes and a reduction in the electrons. Because mobility is proportional to the reciprocal effective mass, an extension makes only sense for n-doping.

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Further reading ...

  • Decai Yu, Yu Zhang, and Feng Liu, Phys. Rev. B 78, 245204 (2008)