Mobility enhanced by local strained-si

In order to improve the degradation mobility caused by High-k gate stacks, strained-Si are required to improve drive current. When deciding on a strained-Si process flow, it is first necessary to comprehend the potential magnitude for electron versus hole mobility enhancement and whether the mobility enhancement results from

relationship for semiconductors depends on nearest neighbor atomic spacing, certain stress (in particular shear stress) warps the valence bands (although less so for conduction band but some warping for shear stress) [38]. The warping of the valence band provides dramatic changes to the constant-energy surfaces in k space and can lead to large hole mobility enhancement via reduced conductivity mass in the channel direction. Mobility enhancement via reduced mass (as opposed to reduced scattering) is key in nanoscale MOSFETs and often not appreciated. Only mobility enhancement from reduced mass (unlike reduced scattering) is maintained at the very short 15–20-nm channel lengths (35-nm gate length) devices currently in production. A strained-Si flow, which is scalable for multiple technology nodes, thus, needs to focus on reducing the hole conductivity mass with the goal of improving the n/p ratio from

~2 to ~1. Therefore, we first focus on strain-enhanced hole mobility from reduced conductivity mass. As a starting point, it is helpful to visualize the effect of strain on the valence-band constant-energy surfaces in k space for bulk Si. Fig. 2-3 [37] shows the surfaces obtained using six band k • p and band parameters in [39]. The strain-altered surfaces for the top two bands are shown at 1 GPa for the common stresses of interest: longitudinal compression on (001) and (110) hybrid wafer orientation and biaxial tensile stress. Note from the constant-energy surfaces in Fig.

2-3, the heavy and light hole bands lose their meaning and we label the bands (first,

second, etc.) in this paper. Some important differences in the band structure under the various stresses at 500 MPa are summarized in Fig. 2-4 [37] for the in-plane and out-of-plane conductivity effective masses and density of states at the band edge.

Before covering strain-altered hole mobility calculations, we will briefly cover a qualitative model for strained-enhanced electron mobility since the concepts are

similar for electrons and holes. The electron mobility in bulk strained- Si along <110>

direction is determined by occupation and scattering in the Δ2 and Δ4 valleys and can

be expressed as:

where q, n, τ , and m are the electron charge, concentration, relaxation time, and

conductivity mass in the MOSFET channel direction, respectively. Strain improves the mobility by increasing the electron concentration in the Δ₂ valley. The

repopulation improves the average in-plane conductivity mass (unstressed: m_t = 0.19m₀ versus m_l = 0.98m₀) and some further improvement is possible for stresses that warp the conduction valleys and lower m_t [38]. Reduced intervalley scattering by the strain-induced splitting between Δ₂ and Δ₄ plays some role (enhances long channel mobility) when the splitting becomes comparable or larger than the optical phonon energy. In addition to a low in-plane mass, a high out-of-plane mass for the Δ₂ valley

(taken as the z-direction in this paper) is quantized. This quantization in addition to strain alters the position of the energy levels. The quantization leads to bands becoming subbands since only discrete wave vectors kz are allowed. Including quantization, the total inversion-layer electron energy is given by discrete values of energy (En) added to the electron energy in the x- and y-directions (in the plane of the MOSFET) [40]

Each step in energy is called a subband with En the energy of the bottom of the subband. As an example, self-consistent solution of Schrödinger and Poisson equation for 500 MPa of uniaxial tensile stress and an inversion-layer vertical field of 1 MV/cm gives the energy levels, as shown in Fig. 2-5 [37]. Since the subband separation is greater than kT, nearly all the electrons in most cases occupy the bottom

two subbands [ground state n = 0 typically called Eo (from Δ2) and Eo’ (from Δ4)]. The ground state energy is significantly lower for the Δ₂ valleys because of the higher quantization mass (Δ₂: m_z = 0.98m₀ versus Δ₄: m_z = 0.19m₀) which leads to increased

splitting between the bottom two subbands and confinement and strain splitting being additive (for the common biaxial and uniaxial tensile stress). The strong confinement in an MOSFET shifts the energy levels more than the moderate 500-MPa stress

mass in the bottom subband (top subband for holes) is an important requirement for the strainaltered band structure. Lastly, in addition to a low in-plane and high out-of-plane effective mass, a high in-plane mass perpendicular to the channel direction is also important. The density of states per unit area for the quantized system is , which results in the density-of-states mass approximated by . Though strain does not significantly alter the electron subband density of states, as discussed next, a high will be shown to be important for maintaining a hole concentration in the top subband. Similar to strained-enhanced electron mobility, hole mobility in an inversion layer can qualitatively be described as resulting from occupation and scattering in the top two bands

However, hole transport is more complicated since strain significantly warps the valence band (as seen in Fig. 2-3) altering both the in- and out-of-plane mass and

. Further, the mass changes with stress and is not constant in k space. After the previous discussion on strain-enhanced electron transport, an advantageous strain for holes needs to warp the valence band to create both a low in-plane and high out-of-plane mass and, if possible, a large mass in the plane of the MOSFET

perpendicular to the channel direction (creates a large ).

2.3 Local strained-si induced Serious hot carrier injection