Advantageous Strains and Wafer Orientations

The general expression of conductivity for n- or p-MOSFETs operating in inversion condition can be described by

⎥⎦

where q, n, τ , and mc are the elementary charge, carrier density, scattering relaxation time, and conductivity effective mass along channel direction, respectively. The subscript denotes the first and second subband in the inversion layer of MOSFETs.

For high performance and low power requirements, advantageous strains need to meet following criteria [2], [24]-[26]: (1) small conductivity effective mass of the lowest subband, m_c1, for enhancing the mobility since most of carriers occupy the lowest subband; (2) large quantization effective mass along the out-of-plane direction of the lowest subband, which enhances the carrier population by lowering the quantization energy in the inversion layer; (3) large 2D DOS effective mass, or large transverse effective mass, of the lowest subband which also increases the carrier population of the lowest subband; (4) large energy splitting of the two lowest subbands for lowering the intervalley (optical phonon) scattering; and (5) the strain-induced subband shift and confinement effect in inversion layer are additive,

that is, the band shifted down by strain must also have a larger quantization effective mass, whereas the band shifted up by strain must have a smaller quantization effective mass. The requirement not only enhances mobility due to increased carrier population in lowest subband which have small conductivity effective mass, but also reduces the power dissipation due to decreased gate direct tunneling current (details will be discussed in Chapter 4).

Let us first examine the potential stress types and wafer orientations with these criteria for nMOSFETs, then, for pMOSFETs. The quantization, conductivity, and DOS effective masses of the lowest subbands for nMOSFETs operating in inversion conditions are given by [27]-[29] and listed in Table. 2.5. For conservative reason, we assume the stress is not large enough to perturb significantly the original system described in [27]-[29]. Under this assumption, the effective masses keep constant under strain, that is, strain has no influences on the criteria 1-3. In addition, the total carrier density in inversion layer does not change significantly when the carriers repopulate from one subband to another subband due to the strain-induce subband energy shift.

For criterion 5, uniaxial longitudinal, uniaxial transverse, and biaxial tension are advantageous strains for (001) wafer since these strains lift the Δ4 valleys, which have smaller quantization effective mass, and shift down the Δ2 valleys, which have larger quantization effective mass [see Equation (2.13) and Table 2.4]. On the other hand, the uniaxial longitudinal compression are advantageous strains for (110) wafer since these strains lift the 2 valleys, which have smaller quantization effective mass, and shift down the 4 valleys, which have larger quantization effective mass. Note that the 4 valleys are the conduction band minima along [100], [

Δ Δ

Δ 100], [010], and

[010] directions while Δ2 valleys are the minima along [001] and [001] directions on both (001) and (110) wafer [27]. For the (111) wafer, the six valleys are degenerate

in inversion layer and have the same conductivity effective mass, that is, the strain-induced subband energy shift does not provide additional benefits for the conductivity.

For comparing the (001) and (110) wafer, let us consider the same carriers concentration in inversion layer on (001) and (110) wafer. The quantization effective mass of the lower valleys on (001) wafer is much larger than that of (110) wafer while for higher valleys, it remains the same. That is, the occupation ratio of the lower valleys is larger on (001) wafer than that on (110) wafer due to the much lower subband energy of lower valleys compared to higher valleys on (001) wafer. In addition, the conductivity effective mass of the lower valleys is smaller on (001) wafer than that on (110) wafer while for the higher valleys it is equivalent on both wafers. Moreover, the magnitudes of strain-induced subband energy shift are equivalent since the directions of uniaxial longitudinal stress on (001) and (110) wafers have the same crystal symmetry. Therefore, the conductivity on (001) wafer is better than that on (110) wafer. However, experiments and accurate numerical simulations must be conducted to corroborate this argument.

Next, let us examine these stress types and wafer orientations for pMOSFETs using the criteria, the simulation results, Fig. 2.6-2.30, and the effective masses summarized in Table 2.6. For criterion 5, the disadvantageous strains producing smaller quantization effective mass for top band and larger quantization effective mass for second band are marked with a strikethrough on the quantization effective mass. Then, for criteria 1-3, the advantageous strains producing smallest conductivity effective mass, largest transverse effective mass, and best quantization effective mass among these stress types and wafer orientations are emphasized with bold effective mass.

In Table 2.6, it can be seen that the uniaxial longitudinal compression on both

(001) and (110) wafers is better among all advantageous strains. For uniaxial longitudinal compression on (001) wafer, it can provide smallest conductivity effective mass and largest transverse effective mass of the top band, but the quantization effective masses are not as desirable as that on (110) wafer. On the other hand, uniaxial longitudinal compression on (110) wafer can provide the smallest conductivity effective mass as that on (100) wafer, the largest quantization effective mass of the top band, and the smallest quantization effective mass of the second band, which not only increases the carrier population in top band, but also reduces the gate direct tunneling current. However, the transverse effective masses are small comparing with that on (001) wafer. Moreover, the magnitudes of strain-induced band edge shift on both wafers are equivalent as shown in Fig. 2.10(a) and Fig. 2.13(a).

Indeed, there are reported simulation results [26] indicating that the mobility on (110) wafer is larger than that on (001) wafer below about 1.3GPa, but the situation is reverse above 1.3GPa. Nevertheless, the conductivity and total drive current, which relate to the carrier density and occupation ratio of each subband, were not reported in the work. Therefore, there are advantages and disadvantages on each wafer orientation, but for low power application, (110) wafer may be better than (001) wafer.