전기영동과 열영동을 고려한 수평기류에서의 입자 침착 속도 연구

Abstract

반도체 생산 공정에서 입자 오염은 생산 수율을 감소시키고 신뢰성, 성능 저하를 가져온다. 이러한 입자 오염을 제어하기 위해서는 입자 침착에 관한 정보를 빠르고 정확하게 예측할 수 있어야 한다. 본 연구는 전기영동과 열영동의 복합적인 영향을 고려하여 수평기류에 놓인 평판으로의 입자 침착 속도를 예측할 수 있는 방법을 개발하고, 이 방법을 이용하여 수평기류에 놓인 침착면으로의 침착 특성을 분석한다. 가우스 확산구 모델은 무작위 거동인 확산을 통계적 기법으로 처리하고, 궤적을 추적하여 평균 입자 침착 속도를 예측한다. 이 논문의 가우스 확산구 모델은 대류, 브라운 확산, 중력 침강, 열영동, 전기영동의 입자 이동 메커니즘을 고려할 수 있으며, 빠른 계산 속도와 정확한 예측 성능을 가진다. 전기영동은 입자의 하전 극성 양쪽을 고려하여, 인력과 척력 모두를 분석한다. 전기영동 유무에 따른 차이는 입자 크기가 작을수록 크다. 인력의 전기영동에서 전기장 크기에 증가에 따른 변화는 정확히 비례한다. 입자 지름이 1 nm의 경우, 전기장 세기가 10 V/cm이면 전기영동이 없을 때와 비교해 침착 속도가 100배 크고, 100 V/cm이면 이보다 10배 더 크다. 척력의 전기영동은 침착 속도 감소를 유발하며, 그 변화의 정도는 인력의 경우에 비해 크다. 이는 브라운 확산의 감소가 결합되기 때문이다. 전기장 크기가 10 V/cm일 때, 크기가 0.04 μm보다 작은 입자의 침착 속도는 5×10^(−4) cm/s으로 침착 속도가 일정하다. 자유 유동 속도가 침착 속도에 미치는 영향도 분석하였다. 인력의 전기영동은 유동 속도는 침착 속도에 영향을 미치지 못하고, 척력의 전기영동은 현저한 영향을 준다. 복합 메커니즘의 경우는 각 메커니즘 별로 크기 인자의 영향의 차이를 분석한다. 중력과 정전력이 지배적이고 입자를 침착면으로 움직이게 하는 경우는 평균 침착 속도는 침착면 크기에 영향을 받지 않는다. 반면에 입자가 멀어지는 경우는 평균 침착 속도는 침착면이 커질수록 작아진다. 이는 입자 침착의 국소적 분포와 관련이 있다. 열영동에 의한 침착은 경계층 성장의 영향을 받는다. 침착면이 커질수록 열영동에 의한 침착 속도 증가나 감소 효과가 줄어든다. 차기 웨이퍼 지름인 450-mm를 길이로 가진 침착면이 온도차 40K로 가열된 경우를 열영동과 전기영동을 고려하여 분석한다. 열영동만 있는 경우는 상면의 경우는 입자 지름 0.02 μm부터 2 μm까지, 하면은 0.02 μm보다 작은 입자의 범위에서 입자 침착 속도는 10^(−5) cm/s 보다 작으며, 이것은 이 크기 범위의 입자는 열영동을 이용하여 침착을 방지할 수 있음을 의미한다. 하지만 이 상태에 인력의 전기영동이 추가로 작용하면 그 범위가 줄어들고, 전기장 크기가 1000 V/cm이면 모든 입자 크기에서 열영동에 의한 침착 방지 효과가 소멸됨을 예측할 수 있다. |Particulate contamination during the semiconductor manufacturing process leads to a decrease in production yield and a resultant deterioration in reliability and performance. Rapid and accurate prediction of particle deposition behavior is required in order to control particle contamination. In this study, a prediction model for deposition velocity in parallel flow under the combined effects of electrophoresis and thermophoresis is proposed. Using this model, the characteristics of the particle deposition under various electrophoretic and thermophoretic conditions are analyzed.. The Gaussian diffusion sphere model (GDSM) treats particle diffusion, i.e., a random behavior of airborne particles, as a statistical technique, and calculates the particle trajectories in order to predict average particle deposition velocities. This model can account for convection, Brownian diffusion, gravitational settling, electrophoresis, and thermophoresis, and it provides fast calculation times and accurate predictions. Both electrical polarities, i.e., attractive and repulsive electrophoresis, are considered. As particle size decreases, the deposition velocity difference between cases with and without electrophoresis increases. In the case of attractive electrophoresis, the particle deposition velocities indicate a proportional increase relative to the electric field strength. For a particle diameter of 1 nm, the deposition velocity at an electric field strength of 10 V/cm is 100 times greater than in the case with no electrophoresis, while the deposition velocity with an electric field strength of 100 V/cm is 10 times greater than that value. Repulsive electrophoresis causes the deposition velocity to decrease and the degree of change is greater than that of attractive electrophoresis. This is because a reduction in Brownian diffusion also occurs. With an electric field strength of 10 V/cm, the deposition velocities of particles having a size < 0.04 μm are constant at 5 × 10^(−4) cm/s. The effects of the freestream velocity on the deposition velocity are also analyzed. The influence of the freestream velocity is negligible in the case of attractive electrophoresis, whereas it is significant in the case of repulsive electrophoresis. Considering the combined deposition mechanisms, the effects of the deposition surface size parameters on the deposition velocity are analyzed. When gravitational settling and electrophoresis are dominant for the deposition velocity and the particles move toward the surface as a result of these mechanisms, the deposition velocities are unaffected by plate size variation. However, when particles move away from the surface under the effects of gravitational settling and electrophoresis, larger deposition surface lengths correspond to smaller average deposition velocities. These characteristics are related to the local particle deposition distribution. Deposition under the influence of thermophoresis is dependent on the deposition surface size because of the development of a thermal boundary layer. The thermophoretic effects on the deposition velocity are weaker for larger values of the deposition surface length. Finally, deposition velocities for a 450-mm-long surface heated at a temperature difference of 40 K are studied, taking both thermophoresis and electrophoresis into account. Under the effects of thermophoresis alone, the particle deposition velocity is less than 10^(−5) cm/s in the range of particle diameters from 0.02 μm to 2 μm for the face-up surface, and for sizes larger than 0.02 μm for the face-down surface. Heating the surface can prevent deposition of particles of these sizes. However, under the influence of attractive electrophoresis at 1000 V/cm, thermophoresis cannot prevent the deposition of particles of all tested sizes.; Particulate contamination during the semiconductor manufacturing process leads to a decrease in production yield and a resultant deterioration in reliability and performance. Rapid and accurate prediction of particle deposition behavior is required in order to control particle contamination. In this study, a prediction model for deposition velocity in parallel flow under the combined effects of electrophoresis and thermophoresis is proposed. Using this model, the characteristics of the particle deposition under various electrophoretic and thermophoretic conditions are analyzed.. The Gaussian diffusion sphere model (GDSM) treats particle diffusion, i.e., a random behavior of airborne particles, as a statistical technique, and calculates the particle trajectories in order to predict average particle deposition velocities. This model can account for convection, Brownian diffusion, gravitational settling, electrophoresis, and thermophoresis, and it provides fast calculation times and accurate predictions. Both electrical polarities, i.e., attractive and repulsive electrophoresis, are considered. As particle size decreases, the deposition velocity difference between cases with and without electrophoresis increases. In the case of attractive electrophoresis, the particle deposition velocities indicate a proportional increase relative to the electric field strength. For a particle diameter of 1 nm, the deposition velocity at an electric field strength of 10 V/cm is 100 times greater than in the case with no electrophoresis, while the deposition velocity with an electric field strength of 100 V/cm is 10 times greater than that value. Repulsive electrophoresis causes the deposition velocity to decrease and the degree of change is greater than that of attractive electrophoresis. This is because a reduction in Brownian diffusion also occurs. With an electric field strength of 10 V/cm, the deposition velocities of particles having a size < 0.04 μm are constant at 5 × 10^(−4) cm/s. The effects of the freestream velocity on the deposition velocity are also analyzed. The influence of the freestream velocity is negligible in the case of attractive electrophoresis, whereas it is significant in the case of repulsive electrophoresis. Considering the combined deposition mechanisms, the effects of the deposition surface size parameters on the deposition velocity are analyzed. When gravitational settling and electrophoresis are dominant for the deposition velocity and the particles move toward the surface as a result of these mechanisms, the deposition velocities are unaffected by plate size variation. However, when particles move away from the surface under the effects of gravitational settling and electrophoresis, larger deposition surface lengths correspond to smaller average deposition velocities. These characteristics are related to the local particle deposition distribution. Deposition under the influence of thermophoresis is dependent on the deposition surface size because of the development of a thermal boundary layer. The thermophoretic effects on the deposition velocity are weaker for larger values of the deposition surface length. Finally, deposition velocities for a 450-mm-long surface heated at a temperature difference of 40 K are studied, taking both thermophoresis and electrophoresis into account. Under the effects of thermophoresis alone, the particle deposition velocity is less than 10^(−5) cm/s in the range of particle diameters from 0.02 μm to 2 μm for the face-up surface, and for sizes larger than 0.02 μm for the face-down surface. Heating the surface can prevent deposition of particles of these sizes. However, under the influence of attractive electrophoresis at 1000 V/cm, thermophoresis cannot prevent the deposition of particles of all tested sizes.