Physic mechanism

Now we will start to discuss the physic mechanism about strained silicon channel. In this section all we discuss is the conventional (100) silicon wafer.

This is because the different growth orientation wafer has different responses of different kinds of strain due to lattice structure leading to different band structure (e.g. Fig. 27) then if we consider above, it will become more complex.

Hereby in this section we just only simply discuss the conventional (100) silicon wafer.

Fig. 27 The different channel orientations on (a) (100) substrate, (b) (110) substrate, and (c) (111) substrate.

【Mobility-enhancement technologies , Chee Wee Liu, S. Maikap, and C.-Y. Yu , IEEE CIRCUITS & DEVICES MAGAZINE MAY/JUNE 2005】

In Fig. 28 we know when we shrink the device dimension; the applied voltage can’t be shrunk like it. Because of maintaining the sufficient drive current. As a resulting, the vertical field will increases with the dimension scaling down. The increasing vertical field degrades the mobility due to the different scattering mechanism. The reader is referred elsewhere for further discussion of mobility in Si inversion layers.

Fig. 28 Mobility degrades with increasing the vertical field.

【S.Thompson etc. A 90 nm logic technology featuring 50 nm strained silicon channel transistors, 7 layers of Cu interconnects, low k ILD, 2002 IEDM pp61-64】

Therefore, for the higher drive current we must enhance the carrier mobility. Hereby there two approaches are used for enhancing mobility.

1. Strain technology.

2. Size effect.

Below we will discuss them respectively.

There are many methods used for the strained-channel by the naturally different lattice constant, partial process steps or device packaged. In this section we will introduce the substrate-based strain (biaxial train) and process-based strain (uniaxial strain).

z Biaxial strain:

Biaxial strain is also referred as global strain; it is substrate-based strain technology.

The strain exists in the surface parallel to substrate and vertical channel. The schematics Fig. 29 illustrate the structure.

Fig. 29 Biaxial strain illustration.

【Applied Materials】

Under the biaxial strain, there is the same strain in the different position. Biaxial tensile stress could improve both N(electron mobility ) and P(hole mobility) -MOSFETs simultaneously. Although, this is true, it occurs only at low electric field and high stress Because of PMOS degrades at high electric field. (I.e. Fig. 30 ), and we will discuss this phenomena later.

Fig. 30 Biaxial strain illustration

【C.Hu, IEDM-2003】

z Uniaxial strain:

Uniaxial strain is also referred as local strain. There is different strain in different position. And it is relative to device structure, channel length and channel width. The Fig. 30 illustrates the uniaxial strain, and points out what kinds of strain we need.

z Effect of strain on mobility

In Fig. 28 we know the mobility is limited by impurity scattering, phonon scattering and surface roughness scattering. Therefore the performance gain is possibly resulting from light effective mass, reduced inter-valley scattering and having a better heterointerface than that between silicon and silicon dioxide.

Considering the constant energy surface of silicon (100) conduction band in Fig. 31.

Fig. 31 Constant energy surface of conduction band illustration

【S.M.Sze, Semiconductor Device Development in the 1970s and1980s – A perspective,

“Proc. IEEE, 69, 1121(1981).】

The electron transport characteristic is determined by the Six-fold valley and in the equilibrium the Six-fold valley is degenerate, then the occupancy possibility of electrons in the Six-fold valley is equal.

If we consider 2-D transport plane, the 2-fold valley is the optimum electronic system as schematically shown in Fig. 32.This is because the 2-fold valleys have the lower effective mass parallel to the Si/SiO2 interface which increase mobility and the higher effective mass perpendicular to the interface

which increases inversion layer capacitance. Both of causations the occupancy of 2-fold valleys contribute to higher current drive of MOSFETs., Therefore if we increase the 2-fold valley occupancy , the electrons will transport by lighter effective mass then increase the electron mobility .The occupancy of 2-fold valleys is determined by the subband energy difference between the 2-fold valleys and 4-fold valleys. Hereby when we increase the splitting energy, the mobility will be enhanced due to increased 2-fold valleys occupancy, as schematically shown in Fig. 33. In Fig. 33 we know size effect and strain can increase the splitting energy. Fig. 34 shows when the thickness of Si channel on Insulator is between 3nm and 5nm, the mobility is increased due to the all electrons populate in 2-fold valleys-Except strain and size effect, the vertical electric field can also increase the splitting energy. And this is why the electron mobility enhancement is still maintained at high electric field! It is not only because reduced effective mass but also reduce intervalley scattering due to energy splitting. For a given strain, quantifying the effective mass reduction and comparing it to the enhanced Mobility reveals that mass reduction alone explains only part of the mobility enhancement Hence, electron scattering must also be reduced due to the conduction valleys splitting into two sets of energy levels, which lowers the rate of Inter-valley phonon scattering between the 2-fold valley and 4-fold valleys. Quantifying the improvement due to scattering has been difficult using acceptable scattering parameters, but reduced scattering is still believed to account for the rest of the mobility enhancement.

Now we will discuss why the Gate voltage-induced quantum confinement (vertical field) also affects the splitting of 2-fold and 4-fold valleys. As schematically shown in Fig. 36, the vertical field affects the position of ground stares of 2-fold and 4-fold valleys is determined by the out-of-plane effective mass of 2-fold and 4-fold valley. As a resulting, the total splitting energy is equal to the strain-induced energy splitting plus the vertical field-induced energy splitting. According to this result, when the splitting energy is increased some scattering path will be suppressed. It is also contributed to the mobility enhancement.

Fig. 32 Schematic subband structure of 2-D electron on (100) and the characteristics of two kinds of subbands ; the 2-fold and 4-fold valley.

【Subband structure engineering for performance enhancement of Si MOSFETs IEDM-97 pp219-222】

錯誤!

Fig. 33 Two device structure to enhance the electron occupancy of the 2-fold valleys by increasing the energy different.

【Mobility-enhancement technologies , Chee Wee Liu, S. Maikap, and C.-Y. Yu , IEEE CIRCUITS & DEVICES MAGAZINE MAY/JUNE 2005】

Fig. 34 Schematic diagrams of the band structure of SOI MOSFETs with different Si channel thickness

【Mobility-enhancement technologies , Chee Wee Liu, S. Maikap, and C.-Y. Yu , IEEE CIRCUITS & DEVICES MAGAZINE MAY/JUNE 2005】

Fig. 35 Strain-induced band splitting

【Mobility-enhancement technologies , Chee Wee Liu, S. Maikap, and C.-Y. Yu , IEEE CIRCUITS & DEVICES MAGAZINE MAY/JUNE 2005】

Fig. 36 Strained MOSFET inversion layer

【Mobility-enhancement technologies , Chee Wee Liu, S. Maikap, and C.-Y. Yu , IEEE CIRCUITS & DEVICES MAGAZINE MAY/JUNE 2005】

Up to now we only discuss the electron mobility enhancement under the biaxial tensile strain, the hole mobility enhancement is similar to electron, but there are something different. The electron mobility enhancement is resulting from the repopulation of electrons and reduced intervalley scattering. The hole mobility enhancement mainly is resulting from the reduced effective mass due to strain-induced valence band warping, As schematically shown in Fig. 37, hole constant-energy band surfaces for the top band obtained from six-band k • p calculations for common types of 1-GPa stresses: (a) unstressed (b) biaxial tension, (c) longitudinal compression on (001) wafer, and (d) longitudinal compression on (110) wafer (note significant differences in stress induced band warping altering the effective mass). By comparing the figure 11(a) and (b) we can understand why the holes mobility degrades at high field under biaxial tensile. This is because of the different out-of-plane effective mass between top band and second band (here the top band and second band differ from the light-hole band and heavy-hole band, because the light-hole band and heavy-hole band lose their meaning). This situation is opposite to the electron , because the splitting energy between top and second bands is decreased by vertical field increasing interband scattering , as schematically shown in Fig 38.

Fig. 37 Lattice classify

【S.M.Sze, Semiconductor Device Development in the 1970s and1980s – A perspective,

“Proc. IEEE, 69, 1121(1981).】

Fig. 38 Vertical field

【S.Thompson etc Uniaxial-process-induced strained-Si extending the CMOS roadmap ,E.D, vol.53,pp1010】