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MODELING OF INTERCONNECT DIELECTRIC LIFETIME UNDER STRESS CONDITIONS AND NEW EXTRAPOLATION METHODOLOGIES FOR TIME-DEPENDENT DIELECTRIC BREAKDOWN Gaddi S. Haase ,  Joe W. McPherson Texas Instruments, Dallas, TX, USA 4E.2
[object Object],[object Object],[object Object],[object Object],Purpose
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Outline
The two parts of reliability assessments ,[object Object],[object Object],[object Object],[object Object],[object Object],Characteristic lifetime  (usually on a log scale) Stress Example: pdf of the Weibull distribution for different    values Time Probability Density
Extrapolating interconnect dielectric accelerated test data ,[object Object],[object Object],[object Object],[object Object],[object Object],Usage field Lifetime (Log scale) Accelerated test regime
Area scaling requires that: Weibull distribution Is Weibull statistics viable for BEOL dielectric BD?   F (t)   =  cum. failure probability at   ≤  t   N =  area factor.   Correct  ONLY  if the cap dielectric properties & thickness are homogeneous A two param. solution Linearized Weibull Plot  = ~0.9 But trying to fit TDDB data to a Weibull distribution… ,[object Object],[object Object]
The actual line-to-line spacing distribution  in a 65nm technology comb-comb test structure The observed spacing distributions, from many cross-sectional electron micrographs for each test structure, were fitted with asymmetric normal distributions (solid curves) for ease of use in the simulation. M1 M2 M1
TDDB Simulation: Within DUT variation only ,[object Object],[object Object],[object Object],[object Object],Line-to-line spacing (nm) CENTER Noramalized bin probability t bd, 63%,i  (s) Acceleration factor   =4.0 cm/MV 50V
[object Object],[object Object],[object Object],TDDB Simulation: Within DUT variation only The “ real ” Weibull     was taken as 2.0 The “experimentally observed”    is <1.7  at 50 V stress ,[object Object],Lifetime  (s) CENTER 50 V Cum failure prob. Ln[-ln(1-F)]
[object Object],[object Object],[object Object],Adding the DUT-to-DUT (across wafer) variations: Note: The lifetime of DUTs from different zones are  independent. Simulated,  using only the “center” and “edge” zones with equal contribution  ( P zone =0.5)
Simulated apparent TDDB   Using DUTs from  three  spacing-distribution zones.  However, the “true”    used in this simulation was 2.0 The “apparent”    is only ~1 Simulated data Note: The true    is dictated by the actual  material  variation
At low voltage,    appears again as 2.0 Extending the simulation to operating voltage :   Simulated data At operating voltages, the spacing variations do not affect the lifetime uncertainty as much as at test voltages ! The “true”    value can be used for product reliability assessment
[object Object],[object Object],Experimental extraction of the correct   ,[object Object],[object Object],Simulated data 50V Center “ Observed”      is  - 1 / slope   ≈ 1.93 ,[object Object],= N
[object Object],[object Object],Experimental extraction of the correct   ,[object Object],[object Object],Simulated data 50V All three zones Simulated data “ Observed”      is  - 1 / slope   ≈ 1.96 ,[object Object],= N
[object Object],TDDB tests are slow. A faster way to evaluate   Every spacing bin  S i  has its own  V bd   distribution with a characteristic  V bd,63%,i   A. Berman, 1981 0.001 0.002 0.003 0.004 0.005 0.006
Evaluating the true   with V-ramp tests Simulated data Simulated data Using V-ramp to  breakdown  at  two ramp rates ,  s i /   can be extracted at  F =63%, and used to derive    from V bd,63%  vs. area curves.
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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IRPS2007 Gaddi Haase P4 E 2

  • 1. MODELING OF INTERCONNECT DIELECTRIC LIFETIME UNDER STRESS CONDITIONS AND NEW EXTRAPOLATION METHODOLOGIES FOR TIME-DEPENDENT DIELECTRIC BREAKDOWN Gaddi S. Haase , Joe W. McPherson Texas Instruments, Dallas, TX, USA 4E.2
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7. The actual line-to-line spacing distribution in a 65nm technology comb-comb test structure The observed spacing distributions, from many cross-sectional electron micrographs for each test structure, were fitted with asymmetric normal distributions (solid curves) for ease of use in the simulation. M1 M2 M1
  • 8.
  • 9.
  • 10.
  • 11. Simulated apparent TDDB Using DUTs from three spacing-distribution zones. However, the “true”  used in this simulation was 2.0 The “apparent”  is only ~1 Simulated data Note: The true  is dictated by the actual material variation
  • 12. At low voltage,  appears again as 2.0 Extending the simulation to operating voltage : Simulated data At operating voltages, the spacing variations do not affect the lifetime uncertainty as much as at test voltages ! The “true”  value can be used for product reliability assessment
  • 13.
  • 14.
  • 15.
  • 16. Evaluating the true  with V-ramp tests Simulated data Simulated data Using V-ramp to breakdown at two ramp rates , s i /  can be extracted at F =63%, and used to derive  from V bd,63% vs. area curves.
  • 17.

Notas del editor

  1. Quick Low-k : leaky, traps Interfaces with ESL or cap span between Cu lines Thickness like gate oxide 2 decades ago
  2. 3 Fast!