title: SEM Charging Effect Model for Chromium/Quartz Photolithography Masks authors: Adam Seeger, Alessandro Duci, Horst Haussecker

Transcription

1 1 ttle: SEM Chargng Effect Model for Chromum/Quartz Photolthography Masks authors: Adam Seeger, Alessandro Duc, Horst Haussecker department/nsttuton: Computatonal Nano-Vson Group, Intel Corporaton address for correspondence: Adam Seeger, Intel Corporaton, SC12-303, 2200 Msson College Blvd., Santa Clara, CA 95054; emal: key words: SEM, chargng, smulaton, mage analyss, lthography masks PACS Code: Hp, Hk, Tp, c, Va

2 2 Summary: We propose a new model to descrbe the effect of specmen chargng on SEM mages. Chargng effects cause errors when one attempts to nfer the sze or shape of a specmen from an mage. The goal of ths model s to enable mage analyss algorthms for measurement, segmentaton and 3D reconstructon that would otherwse fal on mages contanng chargng effects. Ths model s appled to mages of chromum/quartz photolthography masks and may also work n the more general case of solated metal slands on a flat nsulatng substrate. It does not handle more general topographes, as n [1], [2] or specmens composed entrely of an nsulator and t s a severe approxmaton to the actual physcal chargng process descrbed n more detal by [3], but can be ft wth quanttatve accuracy to real SEM mages. We only consder changes n ntensty and do not model chargng-nduced dstorton of mage coordnates. Our approach has the advantage over exstng methods of enablng fast predcton of chargng effects so t may be more practcal for mage analyss applcatons. Introducton: Specmen chargng s an mportant ssue n electron mcroscopy because t causes dstorton of mage coordnates and contrast. The electrc feld around a specmen exerts a force on electrons and affects where ncdent electrons ht the specmen (dstorton of mage coordnates), and the detecton of escapng electrons (dstorton of ntensty sgnal). Chargng wll result n errors when one attempts to nfer the sze or shape of a specmen from an mage. Also, when an SEM s used for a controlled exposure n electron-beam lthography, chargng can dstort the regon of exposure creatng defects n the fnal product. Gven a specmen composed of an nsulator or electrcally solated conductor, the dfference between the number of ncdent electrons and the number of backscattered electrons (ncludng secondary electrons) results n ether a postve or negatve charge n the specmen. Ths fact allows the sgn of the charge to be determned from models of secondary and backscattered electron emsson (Monte Carlo smulaton or emprcal formulas). In the case of an nsulator, a more complete pcture s provded by the dynamc double layer model descrbed n [Melchnger95]. In ths model, the numerous secondary electrons whch escape very close to the surface of the specmen result n a postvely charged layer about 5 nm thck at the surface. Some of the prmary electrons become trapped deep n the specmen formng a negatvely charged layer at a depth approxmately equal to the maxmum range of electrons n the materal. In between these two layers, there s an electron beam-nduced conducton (EBIC) or radaton nduced conducton (RIC) layer that allows charge to conduct manly n a vertcal drecton. The combnaton of secondary electrons escapng near the surface and a relaxaton current that transports electrons from the lower layer up to the surface helps to explan tme dependent chargng behavor [Melchnger95]. Because the nduced conducton lasts only for a short tme after the beam s scanned to a new locaton, ths only allows charge to mgrate wthn a small volume at each beam poston. The total electron yeld (rato between total emtted and ncdent electrons) s a functon of the ncdent energy. Typcally there are two crossover ponts at energes E1 and E 2 where the electron yeld s 1. Ths s llustrated n Fgure 1.

3 3 total electron yeld 1.0 E 1 E 2 beam energy Fgure 1: Qualtatve graph of total electron yeld as a functon of energy showng the two crossover ponts at energy E 1 and E 2. The crossover ponts are sgnfcant because when the SEM acceleratng voltage s set to the crossover energy where the numbers of ncdent and emtted electrons are equal, no chargng wll occur. Because of the dependence on topography and materal, for many specmens t s mpossble to fnd a sngle acceleratng voltage that makes the electron yeld 1 at all ponts. It s very dffcult to measure the E 1 crossover pont because t s unstable and Monte Carlo smulatons tend to be very naccurate n ths energy regme but there s relatvely relable data for the E 2 crossover pont. The expermental data for quartz and chrome are shown n Fgure 2. Ths data s for a flat surface and the yeld wll vary sgnfcantly dependng on the topography. The plots n Fgure 2 show that the E 2 crossover pont occurs at 2keV for Chromum and 3keV for SO 2. Chromum Slcon Doxde (quartz) electron emsson yeld ncdent energy [kev] electron emsson yeld ncdent energy [kev] Fgure 2: Expermental data for total electron yeld from a flat surface [Joy01]. When the electron emsson yeld s 1.0 the njected and emtted electrons are equal (around 2 kev for Chromum and 3 kev for SO2). In our experments the specmen s composed of nearly flat chrome slands on top of a nearly flat SO 2 substrate. The man topographc feature s the step edge at the boundary of the chrome regons. Images are acqured wth a 1keV acceleratng voltage. At ths voltage, both the chrome and SO 2 wll become charged postvely. As the surfaces become more postvely charged, the potental dfference between the electron gun and specmen wll tend to ncrease and electrons wll strke the surface wth more energy. Allowng the beam to st

4 4 on a chrome regon, the energy wll reach a stable equlbrum at the E 2 energy of 2keV and on a SO 2 regon, the energy wll reach a stable equlbrum of 3keV (see Fgure 3). -1kV Intal state (A) total electron yeld 1.0 A B -1kV Charged state (B) E 1 E 2 beam energy SO2 Cr sland 2kV Cr sland 1kV SO2 2kV Fgure 3: For an ntal acceleratng voltage of 1kV, we expect the chrome to become postvely charged by a net loss of secondary electrons untl ts potental s approxmately +2kV relatve to the electron gun. The quartz should smlarly reach a potental that s approxmately +3kV relatve to the electron gun. Model Descrpton: When a chrome regon s electrcally solated, there s a lmted pool of charge that can be pulled out before the regon reaches the equlbrum voltage and we consder the chrome chargng n ths case as analogous to the chargng of a capactor. Our model descrbes the chargng of the chrome usng a resstor-capactor crcut analogy. We assocate wth every chrome regon a voltage that descrbes the chargng state of the surface. These voltages change wth tme dependng on the poston of the beam. When the beam s ncdent on a chrome regon, that regon wll become more postvely charged tendng towards an equlbrum postve voltage relatve to ground and all other regons wll gradually reduce towards the ground voltage as they capture backscattered and secondary electrons. When the beam s on the quartz all the chrome regons wll also recapture secondary electrons and ther voltages wll reduce gradually down to the ground voltage (see Fgure 4).

5 5 chargng of chrome dschargng of chrome V gun V gun Cr sland V chrome Cr sland V chrome SO2 SO2 V ground Fgure 4: Secondary electrons emtted from the quartz and scattered by the specmen chamber may help to restore the chrome slands back to a ground potental. V chrome E 2 +V gun chargng dschargng tme V ground Fgure 5: We expect an asymptotc behavor of the chrome voltage as a functon of tme when the beam hts the chrome (chargng) and when t hts the quartz (dschargng). The voltage of the th chrome regon s represented by V. The th chrome regon charges (dscharges) wth a tme constant µ ( µ ). The change n voltage when the beam s on the regon R ( t ) s descrbed by c d ( c ( )) ( ) ( ) dv µ c V V t f R t =, ( t ) = dt µ d ( Vd V t ) f R( t ) ; where V c s the maxmum possble voltage for the chrome and V d s the mnmum possble voltage for the chrome. We ntegrate ths formula dscretely usng the pxel dwell tme as a tme step to compute the voltages for each chrome regon as a functon of tme. We approxmate the observed SEM ntensty I(t) for a chrome regon wth a lnear functon of the voltage V. The ntensty for the quartz s nstead descrbed by a lnear functon of the maxmum voltage among all V.

6 6 ( ) m ( ) ( ) R( t ) gmv t + d f R t > 0, I ( t ) = gs max V ( t) + ds f R t = 0; = 1... N where gm, dm, gs, d s are constants such that gm < 0, gs < 0. These functons approxmately descrbe the effect of the chrome voltage on the recapturng of electrons whch reduces the observed sgnal. The functon determnng ntensty on the quartz was nspred by the dea that secondary electrons leavng the quartz would tend to be most nfluenced by the chrome regon that s maxmally charged but ths choce was somewhat arbtrary and may gnore mportant effects of geometry. For the purpose of predctng mage contrast, the parameters V c and V d are redundant because they ntroduce a scale and offset that can just as well be determned by the parameters gm, dm, g s and d s. Therefore, wthout loss of generalty we let V c =1 and V d =0. Ths model predcts that the mage ntensty wll converge n an approxmate sense to an ntensty that depends on the fracton of chrome wthn a scanlne of the mage. In general, the fracton of chrome wll vary dependng on the specmen shape but ths behavor s shown usng synthetc examples where the fracton of chrome s set to dfferent constant values n Fgure 6. 25% tme [pxels] chrome voltage 50% tme [pxels] chrome voltage 75% tme [pxels] chrome voltage Fgure 6: Voltage of the chrome, and the related sgnal modulaton converge to dfferent values dependng on the fracton of chrome n a scanlne. Synthetc Examples: The nput to a 2D smulaton s a bnary mage of a specmen where 1 represents chrome and 0 represents quartz and a descrpton of the order n whch the beam vsts the pxels n the mage. We perform a connected components analyss to determne the number of dstnct chrome regons. Fgure 7 shows an example nput mage and the resultng smulated ntensty

7 7 usng arbtrary parameters values ( gm, dm, gs, d s ) = (-1.6, 5, -1.34, 4) and ( µ c, µ d )=(0.0009, ) and a raster scan pattern. a b Fgure 7: The chargng smulaton shows a characterstc bandng pattern related to the amount of chrome n a scanlne. Fgure 8 shows an example wth two separate chrome slands. In ths case the chargng state of the specmen s descrbed by two voltage values. In Fgure 9 we show an example of how our smulaton predcts a change n the chargng effect when a small connecton s ntroduced between two separated chrome regons. Ths suggests that even a qualtatve understandng of the chargng effects may be useful n detectng the presence of a conductng path between two parts of a surface. a b Fgure 8: Multple chrome slands requre modelng a dfferent voltage for each sland.

8 8 a b connected separate Fgure 9: The chargng model predcts a change n appearance between separated and connected chrome regons. In comparson wth actual mages, ths could be useful n determnng electrcal connectvty for a real specmen. Model Fttng Algorthm: To ft our model to an expermental SEM mage we requre a segmentaton of the scanned regon nto quartz and chrome regons. After algnment of ths segmentaton to the SEM data, we ft the parameters of our model usng a gradent descent optmzaton. A dataflow dagram for the model fttng and smulaton along wth example mages s shown n Fgure 10.

9 9 SEM optmzaton algorthm smulaton CAD or AFM model µ, µ, g, d, g, d c d m m s s Fgure 10: Gven an actual SEM mage and the 2D shape of the specmen, we estmate optmal chargng parameters. Results: We tested the model by fttng t to several expermental SEM mages. We compared the output of our model to a pecewse constant model and we found that our model was sgnfcantly more accurate. Two examples of the fttng results and comparson wth a pecewse constant ntensty model are shown n Fgure 11 and Fgure 12. data smulaton absolute dfference (x2) pecewse constant ft for comparson Fgure 11: Though our smulaton contans some resdual systematc error, t s sgnfcantly more accurate than an optmal pecewse constant ft to the mage.

10 10 data smulaton absolute dfference (x2) pecewse constant ft for comparson Fgure 12: Second example comparng resdual error n the model wth that for a pecewse constant ft. Acknowledgements: We would lke to thank Saghr Munr at Intel Mask Operatons for provdng us wth combnaton AFM/SEM data that nspred ths approach and allowed us to test t. References: [1] Davdson, M. and N. T. Sullvan (1997). An Investgaton of the Effects of Chargng n SEM based CD Metrology. SPIE 3050: [2] Ko, Y.-U., S.-W. Km, et al. (1998). Monte Carlo Smulaton of Chargng Effects on Lnewdth Metrology. Scannng 20: [3] Melchnger, A. and S. Hofmann (1995). Dynamc double layer model: Descrpton of tme dependent chargng phenomena n nsulators under electron beam rradaton. J. Appl. Phys. 78(10):