Quick Low-k : leaky, traps Interfaces with ESL or cap span between Cu lines Thickness like gate oxide 2 decades ago
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Transcript of "IRPS2007 Gaddi Haase P4 E 2"
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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
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<ul><li>The actual minimum line-to-line spacing is dropping under 60nm for the new technology nodes. </li></ul><ul><li>The traditional methodology for BEOL low- k dielectric lifetime predictions (E-model + Weibull statistics) might seem overly conservative, and might restrict technology scaling. </li></ul><ul><li>Do we have enough data to support more lenient models for extrapolating test data to predict product lifetime? </li></ul><ul><li>Is there any other source of over-conservatism that can be readily removed? </li></ul>Purpose
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<ul><li>Two critically important parts of reliability assessments. </li></ul><ul><li>Physical models for dielectric degradation as a function of E- field. </li></ul><ul><li>Statistical Modeling: </li></ul><ul><ul><li>Is Weibull good for interconnect dielectrics? </li></ul></ul><ul><ul><li>Actual line-to-line spacing distributions </li></ul></ul><ul><ul><li>Lifetime simulations using within-DUT variations </li></ul></ul><ul><ul><li>Lifetime simulations including DUT to DUT variations. </li></ul></ul><ul><ul><li>Are we using the correct Weibull parameters? </li></ul></ul><ul><ul><li>A couple methodologies for extracting the true shape parameter </li></ul></ul><ul><li>Conclusions </li></ul>Outline
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The two parts of reliability assessments <ul><li>What is the functional dependence of the lifetime on the stress? </li></ul><ul><li>Can the lifetime be extrapolated to use conditions? </li></ul><ul><li>2. What statistical function describes dielectric failure? </li></ul><ul><li>Extract lifetime at cumulative failure probability <0.1%, while testing small DUT samples </li></ul><ul><li>Area scaling </li></ul>Characteristic lifetime (usually on a log scale) Stress Example: pdf of the Weibull distribution for different values Time Probability Density
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Extrapolating interconnect dielectric accelerated test data <ul><li>The E -model is generally the most conservative. </li></ul><ul><li>The E-model is backed by a plausible physical model. </li></ul><ul><li>Other models either lack viable physical basis for BEOL-dielectrics, or have no experimental verification. </li></ul><ul><li>Uncertainty in E during test, and limited test time make model exploration & verification difficult. </li></ul><ul><li>Hence, at this point, there is no safe, verified alternative to the E -model. </li></ul>Usage field Lifetime (Log scale) Accelerated test regime
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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… <ul><li>The fit is often poor </li></ul><ul><li>The slope, , appears <1 </li></ul>
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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
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TDDB Simulation: Within DUT variation only <ul><li>All DUTs in the simulated test have the same spacing distribution. </li></ul><ul><li>In this example: All DUTs have the “Center” spacing. </li></ul><ul><li>Divide the test structure into bins i with spacing S i </li></ul><ul><li>Use the E-model to correlate spacing ( S i ) with Field ( E i ) and with characteristic lifetime ( t bd,63%, i ) : </li></ul>Line-to-line spacing (nm) CENTER Noramalized bin probability t bd, 63%,i (s) Acceleration factor =4.0 cm/MV 50V
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<ul><li>All DUTs in the simulated test have the same spacing distribution. </li></ul><ul><li>In this example: All DUTs have the “Center” spacing. </li></ul><ul><li>The probability to find spacing bin i is </li></ul>TDDB Simulation: Within DUT variation only The “ real ” Weibull was taken as 2.0 The “experimentally observed” is <1.7 at 50 V stress <ul><li>Each bin i , with a constant spacing S i , has its own Weibull-ditribution F i (t bd ) with the associated t bd,I,63% , but the same . </li></ul>Lifetime (s) CENTER 50 V Cum failure prob. Ln[-ln(1-F)]
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<ul><li>The wafer is divided to several zones (locations), each having a different spacing-distribution and a lifetime-distribution F zone (t bd ) </li></ul><ul><li>The occurrence of a tested DUT in each zone is: P zone </li></ul><ul><li>The total observed cum. failure probability would be: </li></ul>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)
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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
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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
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<ul><li>Area scaling tests </li></ul><ul><li>Simulations using: </li></ul>Experimental extraction of the correct <ul><li>Center zone sites only </li></ul><ul><li>Used “real” =2.0 </li></ul>Simulated data 50V Center “ Observed” is - 1 / slope ≈ 1.93 <ul><li>Extract from t bd,63 vs. area: </li></ul>= N
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<ul><li>Area scaling tests. </li></ul><ul><li>Simulations using: </li></ul>Experimental extraction of the correct <ul><li>All three zones </li></ul><ul><li>Used “real” =2.0 </li></ul>Simulated data 50V All three zones Simulated data “ Observed” is - 1 / slope ≈ 1.96 <ul><li>Extract from t bd,63 vs. area: </li></ul>= N
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<ul><li>Using V-ramp to breakdown for test structures with various line-length allows more sampling: </li></ul>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
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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.
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Conclusions <ul><li>Simulations of lifetime distributions were performed using: </li></ul><ul><ul><li>Actual line-to-line spacing distributions in a test structure </li></ul></ul><ul><ul><li>Actual across-wafer spacing variations </li></ul></ul><ul><ul><li>Weibull statistics for each spacing bin </li></ul></ul><ul><ul><li>E-model (the most conservative option) </li></ul></ul><ul><li>The resulting “observed” accelerated test lifetime does not appear Weibull distributed. </li></ul><ul><li>A Weibull-plot fit for a typical sample size shows a substantially lower “observed” ( Weibull shape parameter ). </li></ul><ul><li>Simulations at low (usage) voltage show that only the true matters! (which depends only on actual material variations) </li></ul><ul><li>Using the true buys us the extra lifetime margin that we need ( until we have other validated physical degradation models ). </li></ul><ul><li>The true can be approximated from line/area-scaled testing. </li></ul><ul><li>A faster true- extraction can be done using two-ramp rate V-ramp to breakdown on multiple length test structures. </li></ul>
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