Understanding Line-Edge Roughness Problems with Metrology. Chris Mack

Transcription

1 Understanding ine-edge Roughness Problems with Metrology Chris Mak

2 Outline Measuring line-edge roughness (ER) Any attempt to understand ER begins with data Soures of bias in ER measurement SEM noise SEM low and high frequeny ut-offs Eliminating bias from ER measurements () 008

3 ER Measurement Capture image with single san Proess image off-line to detet edges Measure edge deviation (or width) at eah pixel or set distane δ along the line Result: hundreds of edge measurements give adequate preision But what about the auray of the measurement? () 008 3

4 Measuring ER ER measurements are biased (have systemati errors) for two reasons First reason: SEM images are full of SEM noise, resulting in a biased measurement measured ER = + SEM noise Unbiased measurement of ER requires first a separate measurement of the SEM noise () 008 4

5 Noise in SEM Measurements SEM noise an be redued by inreasing the eletron dose in the SEM (and thus inreasing the seondary eletron signal and reduing its shot noise) 193 nm resists are affeted by eletron dose (resist shrinking/line slimming) ose dose/high noise SEM images are a fat of life at 193 nm litho Fous and stigmati errors will inrease noise as well Sine typial SEM measurement algorithms involve smoothing, measured ER may be higher or lower than the atual ER ER measurement requires different setting than CD measurement! () 008 5

6 Bias-Free ER Measurement Turn off image smoothing (binning) Pik the eletron dose you want, ut it in half, and take two SEM images (m1 and m) Use the (RMS) differene between the two images as a measure of the SEM noise ER = m 1 + m SEM noise Alternately, haraterize SEM noise ahead of time (on exat same substrate/material), then subtrat J. S. Villarrubia and B. D. Bunday, Unbiased Estimation of inewidth Roughness, SPIE Vol. 575 (005) pp A. Yamaguhi, et al., Single-shot method for bias-free ER/WR evaluation with little damage, Miroeletroni Engineering, v. 84 (007) pp () 008 6

7 Measuring ER ER is more than just a magnitude, it has frequeny ontent and information as well Use the Power Spetral Density (PSD) to examine frequeny ontent of roughness it is the edge variane per unit spatial frequeny: iπ f PSD( f ) = Δ( y) e dy where Δ is the deviation of the line edge as a funtion of position y along the line. y () 008 7

8 Power Spetral Density P. Naulleaua and J. Cain, Experimental and model-based study of the robustness of line-edge roughness metri extration in the presene of noise, J. Va. Si. Tehnol. B5 No. 5 (Sep/Ot 007) pp () 008 8

9 Power Spetral Density PSD (nm /μm -1 ) PSD(0) 1/ Slope = 1 + α / n Spatial Frequeny πf (μm) -1 α = roughness (Hurst) exponent = fratal dimension = orrelation length n = noise (SEM resolution) limit () 008 9

10 What Causes this PSD? Unorrelated random noise is white the same power for all spetral regions This aounts for the low-frequeny region Below a orrelation length, roughness is orrelated, giving a fratal response of 1/f (1+α) The ommon ase of α = 0.5 is alled 1/f noise The SEM resolution limit, n, is related to the larger of pixel size or spot size (resolution) of the SEM. Interative demo (white noise smoothed): ()

11 Correlation Funtion The orrelation funtion is R( τ ) = lim 1 / Empirially (and by analogy to other systems), the orrelation funtion probably looks like / Δ( y) Δ( y + τ ) dy R( τ ) = e ( ) τ / α ()

12 Correlation Funtion and PSD The PSD is the Fourier Transform of the orrelation funtion (for wide-sense stationary proesses, meaning that the mean and variane of the line edge are not hanging) For α = 0.5, an analytial solution exists: PSD( f ) = 1+ (π f ) () 008 1

13 Adding Noise to the PSD Adding a (white) noise/resolution floor to the PSD measurements, PSD( f ) = 1+ (π f ) + 1+ ( / n ) Fitting the measured PSD to this model allows and n to be measured (use an average of many PSDs!) ()

14 Analytial PSD PSD (nm 3 ) ER = 1.5 nm = 5 nm n = 1.5 nm Spatial Frequeny f (μm -1 ) ()

15 What does the PSD tell us? Every PSD an be haraterized by four parameters: ER,, α, and n n must be low enough to not affet the measurement of the other parameters ( n «) Over a reasonable range, α does not seem to affet the CD of small-width gates (but it s impat on I off is still to be investigated) Both ER and have an impat on the average CD of a small-width gate Y. Ma, et al., ine Edge Roughness Impat on Critial Dimension Variation, SPIE Vol (007) pp ()

16 Measuring ER the Other Bias One annot measure the PSD over all frequenies f max = 1 πδ f min = π 1 box where δ = distane between edge measurements along the line, and box is the length of the line being measured ()

17 Measuring ER the Other Bias Parseval s Theorem: = ) df But what we measure is: f PSD ( measured = f f = max min 0 PSD( PSD( f f ) df ) df ()

18 () Measuring ER the Other Bias Using our PSD expression, et s assume that f min is speially hosen to orrespond to n (we ll see why in a moment) df f f f n measured = max min ) / ( 1 ) ( 1 π

19 () Measuring ER the Other Bias + + = tan tan n box n box n meas π π For» n, n n tan 1 π n n box n + 1 These two anel

20 Measuring ER the Other Bias Thus, for» n and by piking δ = n, the highfrequeny bias is approximately eliminated For box», meas meas 1 tan π 1 1 π box box () 008 0

21 ( box ) ow Frequeny Bias meas / ER To remove low frequeny bias, either make box very big, or measure and orret the measured roughness box / () 008 1

22 ER Measurement Bias Conlusions Three soures of ER measurement bias: SEM noise makes measured ER systematially bigger High-frequeny measurement limit an make measured ER systematially bigger or smaller, depending on how the measurement distane δ ompares to the resolution limit n ow-frequeny measurement limit (the size of the measurement box) makes measured ER systematially smaller Eah bias omponent an be removed, but most ER values from the literature do not do so! Reported values may be systematially too high or too low there is usually no way of knowing Sine the low-frequeny bias depends on, it is resist dependent () 008