Full 3D Statistical Simulation of Line Edge Roughness in sub-100nm ...

LER (3∆) [nm]151050ASET (i-line)IBM (i-line)IMEC (i-line)SANDIA (EUV)SONY (e-beam)SIA Roadmap (1999)50 100 150 200Line Width [nm]Fig.1: Actual data from various advanced lithographyprocesses reported by different labs [4-9] show that LERdoes not scale with line width and exceeds Roadmaprequirements below 100 nm.Autocorrelation0.80.60.40.20DetectedΛ G=29.3 nmΛ E=25.3 nmOriginalEdge Detected0 25 50 75 100 125Distance [nm]Fig. 2: Autocorrelation of LER captured from 100 nm EUVlines [6]. Correlation lengths obtained from Gaussian (Λ G ) andexponential (Λ E ) fits to raw data extracted from edges detectionof the original SEM micrograph.S(q) [arb.]10864∆ = 2 nmΛ = 12 nmExponentialGaussian200 0.5 1 1.5 2wavenumber [10 9 m -1 ]H(x) [nm]6420-2-4-60 100 200 300 400 500Distance [nm]Fig. 3: LER model used in this work for 3D devicesimulations. Both power spectra in reciprocal space (top)and corresponding lines obtained from inverse FFT(bottom) are shown for two spectral options.Fig. 4: Potential distribution in a 50×200 nm MOSFET withsource and drain LER parameters corresponding to ∆=3nm andΛ=10nm. No correlation between the two edges is assumed.6040Λ = 2.5 nmDrainDrain20frequency604020Λ = 10 nm50nm50nm60Λ = 20 nm40202.5×10 -4 3.0×10 -4 3.5×10 -4 4.0×10 -4Current [A]Fig. 5: Histograms of on-current distributions in 20030×50 nm MOSFETs for 3 different values of correlationlength Λ and ∆=2nm The slight skew in the distributions isattributed to increased short channel effects in shorterelements of the ensemble when effective channel length isshortened by LER.Source50nmSource50nmFig. 6: Two extreme cases of actual source/drain junctionprofiles in an ensemble of 200 50×50 nm MOSFETs with∆=3nm and Λ=20nm. Simulation experiments verify that thedrain current is maximum for the device on the left andminimum for the one on the right.

12080V D= 1.0VV D= 0.1V4030V D= 1.0VV D= 0.1VσI D[%]40I offI onσI D[%]2010I offI on0001 2 3 0 5 10 15 20rms fluctuations, ∆ [nm]Correlation length, Λ [nm]Fig. 7: Dependence of the standard deviation of the draincurrent, σI D , on the LER rms amplitude, ∆, for 30×50nmMOSFETs with Λ = 20nm. Results for on- and off-currentat two drain bias conditions are presented.Fig. 8: Dependence of the standard deviation of the draincurrent fluctuations, σI D , on the LER correlation length, Λ, for30×50nm MOSFETs with ∆ = 2nm. Results for on- and offcurrentat two drain bias conditions are presented.σV T[mV]201510500V Tlowering [mv]10864200 1 2 3∆ [nm]L=30 nmL=50 nm1 2 3rms fluctuations, ∆ [nm]Fig.9:Dependence of the standard deviation of the thresholdvoltage fluctuations, σV T , on the LER rms amplitude, ∆, for30×50nm and 50×50nm MOSFETs with Λ = 20nm and atthe same drain biases as in Fig.7. Note that the averagethreshold voltage also exhibits a slight lowering. Results fortwo drain biases are presented.σI D[%]100010010off currenton current / 10 -410 -510 -610 -710 -820 40 60 80 100120 40 60 80 100Channel Length [nm]Fig. 10: Dependence of the standard deviation of the draincurrent , σI D , on the effective gate length in sub-100 nmMOSFETs. The inset shows ratio of average off- and oncurrents.V D =1.0 V, W eff =50 nm, ∆=2 nm and Λ=20 nm. Notethat the leakage current is exceedingly large below 50 nm.σI D[%]10010off currenton current / 2.2×10 -72.0×10 -71.8×10 -71.6×10 -750 100 150 200150 100 150 200Channel Width [nm]Fig.11: Dependence of the standard deviation of current,σI D , on the effective channel width. The inset shows theratio of average off- and on-currents. V D =1.0 V, L eff =50 nm,∆=2 nm and Λ=20 nm.Fig.12: Potential distribution in a 50×50 nm MOSFET, whichincludes both random doping and LER effects. Average dopingis N A =5×10 18 cm -3 in the bulk and N D =1×10 20 cm -3 in the sourceand drain regions, ∆=3 nm, Λ=10 nm.