Body Bias Voltage Computations for Process and Temperature Compensation

1
Body Bias Voltage Computations for Process and
Temperature Compensation

• M.S. (Electrical Engineering) Defense
• September 2006

Sanjay Kumar
Department of Electrical and Computer
Engineering University of Minnesota
2
Outline

• Adaptive Body Bias (ABB)
• ABB Control Systems
• Problem Statement
• Solution
• Algorithms for ABB Voltage Selection
• Simulation Results
• Conclusion

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Motivation
S.Borkar Intel
caused due to process and temperature variations
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Body Bias
PMOS Device Configuration
S
VS
VG
VD
G
B
D
VB
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Adaptive Body Bias
Measure the delay and leakage of a circuit block.
D D
D D
Apply Reverse Body Bias
Apply Forward Body Bias
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ABB Control Systems
Critical path replica based control systems
Intel Circuit Research Labs
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ABB Control Systems
Look-up table based control systems

• Look up table stores bias values.
• Temperature sensor references LUT.
• Values pre-determined before run-time.
• Can simulate/measure delay and leakage of the
  entire circuit to pre-compute.

TSFC
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Problem Statement

• Determine the right amount of body bias to
  compensate for
• process variations
• temperature variations
• Minimize the amount of tester time
• determine voltages based on minimum amount of
  tester measurements

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System Level Block Diagram
Circuit Block with Biasable NWELL and PWELL
To NWELL
To PWELL
Temperature Sensor
ROM (Look up Table)
vbp
vbn
From Body Bias Generator
To Body Bias Generator
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Algorithms for ABB Voltage Selection

• Bounded Enumeration based ABB
• Mathematically Assisted ABB
• PTABB
• PABB - TABB

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Enumeration
Delay increases Leakage decreases
Final Solution
Leakage under budget?
Set of points which do not meet delay
Set of points which meet delay
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Enumeration
Drawbacks
Strengths

• Guaranteed optimal solution
• Very few searches required if solution close to
  (vbnmax, vbpmax)

• Complexity O(n2)
• For solutions which require RBB, very large
  run-time
• Tester cost may be too high if n is large.

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Mathematically Assisted ABB
Find the exact solution that lies along the blue
line.

• Formulate an NLPP
• Minimize L(vbn,vbp) s.t.
• D(vbn,vbp) D
• vbnmin vbn vbnmax
• vbpmin vbp vbpmax.
• Need models for L(vbn,vbp) and D(vbn,vbp).
• Use 4th order polynomial best fit expressions.
• Measure leakage and delay of the CUT at sample
  points on the tester.

Set of points which do not meet delay
Set of points which meet delay
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PTABB Algorithm
vbn
Measure delay leakage
vbp
Circuit Block
Build models for delay and leakage
Snap to nearest vstep
Formulate NLPP Min L(vbn,vbp) s.t. D(vbn,vbp)
D vbnmin vbn vbnmax vbpmin vbp vbpmax
Determine (vbn,vbp)
Performed at each compensatory temperature
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PABB - TABB
Process Adaptive Body Bias (PABB)
Temperature Adaptive Body Bias (TABB)
Ambient Temperature Conditions
Ideal Process Conditions
Determine voltages (vbnP,vbpP)
Determine voltages (vbnT,vbpT)
Process ABB Temperature ABB
Compute voltages (vbnPT,vbpPT)
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Independence of Variations
Temperature Variations
Process Variations
Channel length (L) Oxide thickness (tox) Dopant
concentration (NA)
Mobility of electrons and holes (µ) Silicon work
function (Fs)
Affect transistor threshold voltage (Vth)
Can we orthogonalize their effects?
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Monte Carlo Simulation Results for a Ring
Oscillator
Varying parameters L, Vthn, Vthp, T
Delay through SPICE simulations
Delay at some P, T D(P,T0)
Delay at some T, P D(P0,T)
Sum of ?Delays ?D(P0,T) ?D(P,T0)
Error ?
Actual ?Delay D(P,T) D(P0,T0)
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PABB-TABB Algorithm
(vbnPT,vbpPT) (vbnP,vbpP) (vbnT,vbpT)

(vbnP,vbpP)
TABB values for each block determined through
simulations.
PABB values for each block determined by solving
NLPP
PTABB values for each block at each compensating
temperature
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Summary
n No. of body bias voltages (n gt m) m No. of
vbn/vbp values used for polynomial interpolation
(m 3) k No. of temperature compensatory points
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Testing the Algorithms

• Determine the vbn, vbp values to populate the
  LUT.
• Estimate no of (D,L) measurements required (run
  time).
• Compare accuracy of PTABB and PABB-TABB with
  enumeration.
• Tested using 10 ISCAS85 benchmarks.

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Variations and Performance Spread
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C6288 65nm Technology
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C6288 45nm Technology
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Run time () Accuracy Comparison
Error in back-annotated delay values from PTABB
and PABB-TABB
No of tester measurements required before
finding the optimal solution.
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Conclusion

• Bidirectional ABB can be used to improve the
  yield of dies for reasonable ranges of
  operating temperatures and process variations
• One-time compensation for process variations and
  run-time compensation for temperature variations
  performed.
• Minimal tester measurement based schemes
  developed.
• Accuracy-run time trade-offs explored.

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Backup
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Grid Snapping

• Snap to NE corner vbn and vbp to higher vstep.
• Snap to SE corner vbp to lower vstep and vbn to
  higher vstep.
• Snap to NW corner vbp to higher vstep and vbn
  to lower vstep.
• Compare the delay and leakage of the 3 points and
  snap.

vbp
vbn
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Temperature Dependence

• Negative Temp Dep
• D increases with T.
• Higher body bias needed to meet D.
• More leakage.
• Positive Temp Dep
• D decreases with T.
• Can RBB to save leakage.
• Delay still monotonically decreases with
  (vbn,vbp)
• No change to algorithm.