Double ellipsoid model for conductivity effective mass along [110] orientation in (100) Si-based strained p-channel metal-oxide-semiconductor

The performance of a Si metal-oxide-semiconductor field-effect transistor can be enhanced effectively by the strain technology and the orientation engineering. For example, the [110] direction is usually used as the channel direction in the Si p-channel metal-oxide-semiconductor (PMOS) on 100 oriented substrate. While SunEdison company rotates the channel direction 45 degrees to the [100] direction, its hole mobility is 1.15 times larger than the hole mobility of the former.The orientation engineering is based on the anisotropy of the hole effective mass along different directions. The enhancement of carrier mobility naturally occurs when we choose the direction with the smaller carrier effective mass as the channel direction.However, according to the reported results in the literature, the hole effective mass values along the [110] and [100] orientation are about 0.6m0 and 0.29m0, respectively. The former is twice larger than the latter, which cannot explain that the experimental result increases 1.15 times.We find that the effective mass values along both the long axis and the short axis should be taken into consideration, and the value of 0.6m0 can only represent the long axis term by observing the equivalent energy diagram of the first sub-band in Si PMOS.In view of this, the double ellipsoid model is given for the conductivity effective mass along the [110] direction in (100) Si PMOS, which explains the reason why the hole mobility along the [100] direction is 1.15 times larger than that along the [110] direction in Si PMOS. And then, based on the E-k relation of the inversion layer in Si-based strained PMOS, we study the conductivity effective mass along the [110] direction in (100) Si-based strained PMOS by the above method.The results show that 1) the [110] oriented hole conductivity effective mass of biaxially strained Si PMOS can be calculated directly by its spherical equivalent energy diagram; 2) in the case of biaxially strained Si1-xGex PMOS, its conductivity effective mass needs to be calculated by the double ellipsoid method; 3) the [110] oriented hole conductivity effective mass of uniaxially strained Si PMOS should be solved approximately by two different sizes of ellipsoid.Our valid models can provide the valuable references for studying and designing the Si-based strained PMOS device.