Problem Variations

1
Problem Variations!

• Global
• Material properties of wafer, resists, etc.
• Lens aberration, flow turbulence, oven
  temperature, etc.
• Implant dose, diffusion time, focus, exposure
  energy, etc.
• Bhavnagarwala, 2004.
• Lg, W, oxide thickness, layer thickness, doping,
  etc.
• Local
• Line Edge Roughness (LER).
• Random dopant fluctuations.
• Statistical fluctuations in number and position
  of dopant atoms in the channel spatially
  uncorrelated.
• Discrete oxide thickness.

2
Read Stability
Corner B
Corner A
Bhavnagarwala et al, 2001
3
Hold Stability

• Similar to Read Stability analysis without access
  transistor.

4
Write Stability
Mukhopadhyay et al, 2004
5
Read Access
Mukhopadhyay et al, 2004
6
Memory Design as Robust Optimization

• Robust optimization under yield constraints.
• Metrics and yield constraints in memory design
  can be expressed as polynomial equations.
• Problem minimization of a scalar function under
  certain yield constraints.
• Scalar function can represent area/power/leakage
  (or a mix) and can be expressed as a function of
  VDD, (W/L) ratios, WL/BL voltages, cell per
  column/row, etc.
• Yield constraints can be represented as

7
Double-gate MOSFET

• Back-gate biasing of a thin-body MOSFET remains
  effective for dynamic control of Vt with
  transistor scaling, and can provide improved
  control of short-channel effects as well.

• Back-gated (BG) MOSFET
• Independent front and back gates
• One switching gate and Vth control gate

Double-gated (DG) MOSFET
8
SRAM Cell Architecture
9
Layouts