Multi-Gate FETs

SiGe/Si material for PMOS application



The scaling of CMOS devices has led an exploration of new materials to replace silicon (Si). SiGe has shown promise as a new channel material for PMOS type of devices. Ge offers highest hole mobility (1900 cm2/V-s) among all group IV or III-V class of materials. However Ge has issues in fabricating a good insulator, hence SiGe alloy offers an attractive alternate option. Ge has a larger lattice constant than Si (~4.2% mismatch) leading to SiGe being compressively strained when grown pseudomorphically on Si.

Table 1 Bulk mobility in different materials*

*Germanium-based technologies: from materials to devices By Cor L. Claeys, Eddy Simoen


We have developed a sp3s*d5 tight-binding based virtual crystal approximation TB-VCA model [2] for bandstructure calculations of Silicon Germanium (SiGe) alloy. In VCA each atom is a pseudo atom with averaged properties of Si1-xGex alloy material.

Silicon has X valley as its conduction band minima while Ge has L valley as its CB minima. As the composition is varied in bulk relaxed Si1-xGex alloy there is a transition from X to L as the CB minima at x~84%.
Compressive strain leads to splitting of 6 fold X valley into 4 fold inplane and 2 fold out of plane degenerate energy levels with the 4 fold energy level being the conduction band minima. More drastic effect happens in the valence band with compressive band breaking the Heavy Hole-Light Hole (HH-LH) degeneracy at the Г point. HH-LH splitting leads top most band having a light in-plane mass and heavier out-of-plane mass. This property is exploited to achieve larger current in PMOS type devices.

SiGe/Si Core/Shell – Nanowire MOSFET using VCA

SiGe/Si core/shell structure provides a good combination for both the NMOS and PMOS device designs. SiGe forms a natural channel for holes and Si forms a natural channel for electrons because of their respective band structures. Using the semi classical top-of-the-barrier 2D transport model charge and current were calculated self consistently. The figure below shows the calculated ON state current with their spatial variation inside the SiGe/Si core/shell nanowire gate all around (GAA) MOSFET.

Mobility - Alloy Scattering

SiGe is an alloyed material and VCA approach misses out on the inherent randomness. This randomness leads to a form of scattering called – Alloy scattering. Alloy scattering in a binary alloy is commonly modeled as scattering due to random potential wells due to different atoms. The potential difference between the constituent atoms – ΔU (eV) is known as the Alloy scattering potential. Very simply an empirical expression for mobility can be calculated using ΔU as the scattering operator. This approach has been used by researchers for a long time however ΔU has eluded any theoretical justification. Due to this reason ΔU has become essentially a fitting parameter.
It can be shown that using a tight –binding based atomistic representation of SiGe, alloy scattering can be treated accurately (Fig 3). This approach captures the fitted scattering potentials and bulk SiGe mobility closely, for both electrons and holes.

Associated Publications:

  • Saumitra Mehrotra, Abhijeet Paul, Gerhard Klimeck, “Atomistic Approach to Alloy Scattering in Si1-xGex” Applied Physics Lett., Vol. 98 Issue 18, May 2011
  • Abhijeet Paul, Saumitra Mehrotra, Mathieu Luisier, Gerhard Klimeck, 
    "Performance Prediction of Ultra-scaled SiGe/Si Core/Shell Electron and Hole Nanowire MOSFETs" IEEE Electron Device Lett., Vol. 31 pg. 278-280 (2010);doi:10.1109/LED.2010.2040577
  • Abhijeet Paul, Saumitra Mehrotra, Mathieu Luisier, and Gerhard Klimeck, 
    "Study of Ultra-scaled SiGe/Si Core/Shell Nanowire FETs for CMOS Applications", ISDRS 2009, December 9-11, 2009, College Park, MD, USA.
  • Saumitra R Mehrotra, Abhijeet Paul, Mathieu Luisier, and Gerhard Klimeck,  "Atomistic simulations for SiGe pMOS devices Bandstructure to Transport"
    ISDRS 2009, December 9-11, 2009, College Park, MD, USA.
  • Abhijeet Paul, Saumitra Mehrotra, Mathieu Luisier, Gerhard Klimeck, 
    "Atomistic approach to study charge and current distribution in ultra-scaled SiGe/Si core/shell nanowire FETs"
    American Physical Society, March Meeting, March 15–19, 2010; Portland, Oregon (2010)
  • Saumitra Mehrotra, Abhijeet Paul, Mathieu Luisier, Gerhard Klimeck, 
    "A Tight-Binding approach for SiGe Bandstructure Calculations"
    TECHCON, Austin, Texas ,Sept. 13-14,2010
  • Saumitra Mehrotra, Abhijeet Paul, Gerhard Klimeck, 
    "Tight-binding based alloy scattering calculations in Si1-xGex"
    APS March Meeting, Dallas, Texas, March 23, 2011.

Group member involved: