TY - JOUR
T1 - Modeling of protection schemes for critical surfaces under low pressure conditions
T2 - Comparison between analytical and numerical approach
AU - Asbach, Christof
AU - Pui, David Y.H.
AU - Kim, Jung Hyeun
AU - Yook, Se Jin
AU - Fissan, Heinz
PY - 2005/11
Y1 - 2005/11
N2 - Nanoparticle contamination is one of the crucial issues for the semiconductor industry on the move towards structure sizes of 50 nm and below. In extreme ultraviolet lithography (EUVL), a likely successor to optical lithography, the masks cannot be protected by common pellicles. Different protection methods, such as a "thermophoretic pellicle" [L. Klebanoff and D. J. Rader, US Patent No. 6,153,044 (2000) and US Patent No. 6,253,464 B1 (2001)] have therefore been proposed to protect a face-down mask in an EUV scanner, which might be operated at 50 mTorr (6.7 Pa). In order to quantify the effectiveness of such protection schemes, we developed an analytical model that allows simple determination of the particle stopping distance as a function of particle and gas properties as well as a thermal gradient that might be employed to make use of a thermophoretic force in order to protect the mask. The analytical results indicate that drag force is most effective in slowing down particles, traveling at high initial velocities. Thermophoresis can add effective protection to particles traveling at low velocities and therefore decrease diffusional deposition. The results from the analytical model were used to check the accuracy of the discrete phase model in FLUENT for particle diameters between 100 and 500 nm and pressure levels between 10 mTorr (1.3 Pa) and 500 mTorr (66.7 Pa) (corresponding Knudsen numbers 407≤Kn≤102 000). The comparison results indicate that with no thermal gradient, the results agree very well with less than 2% deviation. If thermophoresis is included, the absolute deviation generally increases with increasing Knudsen number and with increasing temperature gradient. For a temperature gradient of 10 Kcm and a Knudsen number of 102 000 (p=10 mTorr, dp =100 nm), the deviation reaches almost 50% for 2 ms initial particle velocity.
AB - Nanoparticle contamination is one of the crucial issues for the semiconductor industry on the move towards structure sizes of 50 nm and below. In extreme ultraviolet lithography (EUVL), a likely successor to optical lithography, the masks cannot be protected by common pellicles. Different protection methods, such as a "thermophoretic pellicle" [L. Klebanoff and D. J. Rader, US Patent No. 6,153,044 (2000) and US Patent No. 6,253,464 B1 (2001)] have therefore been proposed to protect a face-down mask in an EUV scanner, which might be operated at 50 mTorr (6.7 Pa). In order to quantify the effectiveness of such protection schemes, we developed an analytical model that allows simple determination of the particle stopping distance as a function of particle and gas properties as well as a thermal gradient that might be employed to make use of a thermophoretic force in order to protect the mask. The analytical results indicate that drag force is most effective in slowing down particles, traveling at high initial velocities. Thermophoresis can add effective protection to particles traveling at low velocities and therefore decrease diffusional deposition. The results from the analytical model were used to check the accuracy of the discrete phase model in FLUENT for particle diameters between 100 and 500 nm and pressure levels between 10 mTorr (1.3 Pa) and 500 mTorr (66.7 Pa) (corresponding Knudsen numbers 407≤Kn≤102 000). The comparison results indicate that with no thermal gradient, the results agree very well with less than 2% deviation. If thermophoresis is included, the absolute deviation generally increases with increasing Knudsen number and with increasing temperature gradient. For a temperature gradient of 10 Kcm and a Knudsen number of 102 000 (p=10 mTorr, dp =100 nm), the deviation reaches almost 50% for 2 ms initial particle velocity.
UR - http://www.scopus.com/inward/record.url?scp=29044440754&partnerID=8YFLogxK
U2 - 10.1116/1.2122927
DO - 10.1116/1.2122927
M3 - Article
AN - SCOPUS:29044440754
SN - 1071-1023
VL - 23
SP - 2419
EP - 2426
JO - Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures
JF - Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures
IS - 6
ER -