Effects of Plasma Properties on Plasma Recovery in Plasma Source Ion Implantation 2007 IEEE Pulsed Power and Plasma Science Conference Albuquerque, New Mexico, June 17-22, 2007 본 연구는 플라즈마 소스 이온 임플란테이션에 있어서 쉬스 다이나믹스와 펄스 폴타임 동안에 일어나는 플라즈마의 리커버리에 관한 것이다. K. J. Chung, S. W. Jung, J. M. Choe, G. H. Kim, and Y. S. Hwang Department of Nuclear Engineering, Seoul National University, Seoul 151-742, Korea

Abstract Both numerical and experimental investigations of the sheath dynamics and plasma recovery during the pulse-off time have been carried out in low-pressure plasma in order to give more deep understandings on those phenomena and examine the effects of the plasma properties on the plasma recovery process. Experimental and numerical results reveal that the plasma recovery process is an inherent characteristic of the plasma itself and therefore it is not affected by the external pulse characteristics. The recovery process is deeply related to a rarefaction wave and ion flow because the ion flux to refill the depleted region is supplied by the excavation of the bulk plasma by the rarefaction wave and the incoming flux from the source plasma. Furthermore, it is also found that the characteristic time for the plasma recovery process can be simply expressed as a function of s/uB , where s and uB is the sheath thickness at the pulse-off time and the Bohm speed, respectively. The numerical simulation predicts that increasing the ion flow velocity up to or above the Bohm speed can effectively reduce the plasma recovery time for a given operating condition. Consequently, it is recognized that for the effective use of the highly repetitive PSII process, the plasma recovery process during the pulse-off time which is independent of the external operating conditions needs to be considered together with the ability of the pulse power system itself. 발표순서는, 우선 플라즈마 소스 이온 임플란테이션 기술에 대한 소개와 기술의 특징 및 장단점, 또한 여러 분야에의 응용에 대하여 말씀드린 후, 본 연구를 하게 된 동기와 연구의 목적에 대하여 말씀드리겠다. 기존의 다이나믹 쉬스에 대한 어낼러틱 모델과 리커버리에 관한 모델에 대한 소개를 한 후, 본 연구에서 개발된 셀프-컨시스턴트한 회로모델에 대하여 설명을 한 후, 실험 셋업과 플라즈마의 진단법에 대하여 논하고, 실험결과와 계산결과에 대한 논의를 통하여 쉬스의 동역학 및 플라즈마의 리커버리 프로세스에 대하여 논하도록 한다. 결론과 퓨쳐웍에 대하여 말씀드리겠다.

Plasma Source Ion Implantation (PSII) Conventional Beamline Ion Implantation Pros. - Easy to control ion beam energy and dose - Easy to determine total dose - Clean & well-established Cons. - Line-of-sight process - Complex due to target manipulation - High cost & low dose-rate - Low energy implantation is difficult due to ion beam optics PSII (Plasma Source Ion Implantation) or PIII (Plasma Immersion Ion Implantation) Invention - J. Conrad et al. at the UW at Madison in the mid-1980s* - To overcome the line-of-sight restriction inherent in conventional method - To improve the dose-rate and process efficiency Idea - A substrate to be implanted is immersed in plasma - A negative, high-voltage pulse is applied to the substrate - Ions are accelerated across the sheath and implanted to the substrate 기존의 문제점… * J. R. Conrad et al., J. Appl. Phys. 62, 4591 (1987)

Typical Characteristics of PSII Use of the pulsed power*  Pulsed sheath dynamics is most important in PSII To avoid arcing on the substrate. To limit the sheath size when operating with very high voltage (>10 kV) and low-density plasmas. To allow the near-substrate region to be refilled with fresh ions during the pulse-off time for the next pulse. To avoid surface charging for the treatment of insulating materials. To have additional degrees of freedom such as pulse length and duty cycle for the design of process. Advantages and limitations** Advantages Limitations - Non-line-of-sight: can treat large, heavy, and complicated shapes - Process time independent of surface area - Compatible with traditional plasma-enhanced chemical vapor deposition and semiconductor tools - Low-temperature process - Charge buildup in insulating workpieces neutralized by plasma - No mass separation - Minimum feature size ~ sheath width - Inhomogeneous implant energy distribution - Secondary electron limits efficiency and generates X-rays - Limited practical working voltage - Accurate in situ dose monitoring is difficult 펄스를 이용하기 때문에 쉬스의 다이나믹스와 그에 따른 이온의 거동이 가장 중요하다. 물론 펄스를 이용하지 않는 dc-PIII라는 개념도 있으나, 여기서는 그 이야기는 제외한다. 장점으로는 라인-오브-사이트 문제, 복잡한 3차원 형상 가능, 보어 홀 가능 차지빌드업 해결 등이 있는 반면, 단점으로는 매쓰 셀렉션이 불가능하고 너무 작은 부분은 힘이 들다는 점, 에너지가 인호모지니어스하고 이차전자 문제, 도즈 모니터링이 힘들다는 점 등이 있다. * A. Anders, Surf. Coat. Technol. 156, 3 (2002), Z. L. Dai et al., J. Appl. Phys. 92, 6428 (2002) ** A. Anders, Handbook of Plasma Immersion Ion Implantation and Deposition, John Wiley & Sons (2000)

Objective and Scope of Study Development of a self-consistent circuit model for the PSII system Effects of plasma properties on sheath dynamics and plasma recovery Experiment Simulation Analytic Model Sheath Dynamics Plasma Recovery Characterizations of sheath dynamics and plasma recovery / Systematic understanding of PSII system

Collisionless Dynamic Sheath Model* Assumptions: - Collisionless - Cold, singly-charged ion - Massless electron - Instantaneous high-voltage buildup - Quasi-static Child law sheath forms - Ion transit time is neglected * Lieberman, J. Appl. Phys. 66, 2926 (1989) Scheuer et al., J. Appl. Phys. 67, 1241 (1990) Uncovering of ions at the moving sheath edge = Child law current density 이외에도 매트릭스 쉬스 내의 이온에 관한 이론, 펄스 라이즈와 폴타임이 존재하는 경우에 대한 이론, 콜리젼의 영향 등에 관한 이론 등이 있다.

Models for Plasma Recovery Process 1. Ambipolar Diffusion Model (Wood, J. Appl. Phys. 73, 4770 (1993)) 2. Bohm Current Recovery Model (Briehl & Urbassek, J. Phys. D 35, 462 (2002)) 두 모델의 공통점은 샤프 바운더리 및 디플리티드 영역 내에 균일 플라즈마, 벌크 부분의 영향없음이다. Briehl & Urbassek pointed out that the ambipolar diffusion model gives too short recovery time to explain their PIC simulation results because the strength of the ambipolar diffusion current is reduced considerably by the floating potential repelling electrons from the wall.

Experimental Setup Solid-state Switch (Behlke, 651-03-LC) f18 cm 2kW 0.1 mF f18 cm Measurement Region 10 cm Plasma Flow +50 V 이 그림은 본 연구에 사용한 실험 장치의 개념도이다. 펄스 파워시스템은 붉은 점선 안과 같이 등가적으로 그릴 수 있는데, 여기서 C1은 에너지 스토리지 캐패시터이다. 여기에 저장된 에너지는 스위치의 개폐에 따라 플라즈마와 맞닿아 있는 타겟 전극에 인가하게 된다. 이 때, 사용된 스위치는 그림과 같은 솔리드-스테이트 스위치인데, 이 스위치는 다음과 같은 등가회로로서 표현이 가능하다. 펄스시스템의 로드로써의 플라즈마는 그림과 같이 RF에 의하여 발생한 플라즈마를 타겟쪽으로 확산시켜 사용하였다. 펄스 인가시 타겟의 전압과 전류를 측정하였으며, 플라즈마 쉬스의 거동을 관찰하기 위하여 +50V로 바이어스된 랑뮤어 프로브를 사용하였다. Source Plasma 100 W

Detailed Specifications of a Pulse Modulator Component Specification Model/ Manufacturer High-voltage DC Power Supply Max. voltage: 50 kV Max. current: 80 mA Power rating: 4 kW PK50R80/ Glassman Energy-storage Capacitor Capacitance: 100 nF Voltage rating: 50 kV Max. peak current: 50 kA Max. RMS current: 45 A Internal inductance: 15 nH Lifetime: 1108 shots (20% VR) 37330/ General Atomics Solid-state Switch Max. voltage: 65 kV Peak current: 30 A (Duty < 1%) Max. continuous current: 0.33 A Turn-on delay time: 180 ns Switch recovery time: 500 ns Max. switching frequency: 2.5 kHz Natural capacitance: 30 pF Coupling capacitance: 48 pF HTS 651-03-LC/ Behlke Current-limiting Resistor Thick-film non-inductive resistor Resistance: 2 k Power rating: 200 W UT100/ 3RLab Trigger Pulse Generator 4 channel Resolution: 1 ns Maximum trigger rate: 1 MHz 555-4C/ BNC

1-D Fluid Model in Planar Geometry Assumptions: - Collisionless, cold, singly-charged ion - Massless electron: Boltzmann relation - 1-D, planar geometry Target current: Governing equations: Solving methods: - Thomas algorithm for linearized Poisson’s eq. - MacCormack’s explicit scheme for momentum eq. - Low-order upwind scheme for continuity eq.

Equivalent Circuit Model of a PSII Pulse System Main switch Control of two switches by delayed trigger signals to the gates Voltage-controlled current source function [sheath, Ii, Ie, Is, Id] = fcn(t, V) persistent x phi ni u… ; solve Poisson’s equation solve momentum equation solve continuity equation Calculate Ii, Ie, Is, Id, sheath position, etc Pulse Modulator Circuit Dynamic Sheath Pull-down switch

Diagnostics of Plasma and Sheath Upstream Measurement region Typical operating conditions Target - Gas pressure: 0.4 mTorr (0.05 Pa) Ar - RF power: 120 W - Pulse: 10 s, single or repetitive - Charging voltage: -1 ~ -10 kV Plasma flow Bulk Plasma  18 cm Probe Downstream Excitation grid (x=14 cm) x Measurements of initial steady-state plasma properties 10 cm Plasma Density Electron Temperature Ion Flow Velocity Plasma Potential Langmuir Probe Ion Acoustic Wave Mach Probe Measurements of dynamic motions of sheath edge and rarefaction wave - Standard method: a biased cylindrical Langmuir probe* - Measuring the perturbation in electron saturation current - Bias voltage > plasma potential * Shamim et al., J. Appl. Phys. 69, 2904 (1991)

Measurements of Initial Plasma Properties (1/3) I. Langmuir probe Density profile along a distance from a target Radial density profiles at various axial positions Construction - Cylindrical probe - Tungsten tip with  0.3 mm diameter and 5 mm length - Uncompensated OML ion current F. Iza and J. K. Lee, J. Vac. Sci. Technol. A 24(4), 1366 (2006)

Measurements of Initial Plasma Properties (2/3) II. Mach probe Construction - Probe diameter:  6.35 mm (Tantalum sheet (0.2t)) - Insulator thickness: 4 mm L. Oksuz and N. Hershkowitz, Plasma Sources Sci. Technol. 13, 263 (2004)

Measurements of Initial Plasma Properties (3/3) III. Ion Acoustic Wave - Constant electron temperature (Te) - Cold ion (Ti = 0) - Constant ion flow velocity (ui) at x = 6 cm : similar to Mach probe measurement : ~ 16% lower than the Langmuir probe measurement (~5 eV)

Summary of Initial Plasma Properties Initial conditions in simulation: Initial floating sheath is ignored

Measurements of Dynamic Sheath Motion 10% of initial electron current Displacement current Point A: leading edge of rarefaction wave Point B: expanding sheath edge Point C: collapsing sheath edge Biased Langmuir probe - Cylindrical probe - Uncompensated - Bias voltage: +50 V > plasma potential - Measuring resistor: 100 

Evolution of Sheath Edge & Propagation of Rarefaction Wave Long pulse application > 100 s Slight increase in the propagation speed of a rarefaction wave is caused by the decrease of ion flow velocity with propagation Separation of a rarefaction wave from the sheath edge

Sheath Dynamics in Rapidly-decaying Pulse Charging voltage = -5 kV Pulse width = 10 s Pulse fall time < 1 s Sheath collapse time < 2 s Floating sheath The plasma density in the depleted region is refilled by the excavation of bulk plasma by the rarefaction wave and initial ion flux from the bulk plasma

Long Time Behaviors of Plasma Recovery Besides the rarefaction wave, we can observe a restoring compression wave produced by a plasma recovery process According to the characteristics of the two waves, we can divide x-t space into three different regions: unperturbed, perturbed, and recovered regions Unlike the sheath dynamics, the plasma recovery is recognized to a long time process order of several tens of microseconds irrespective of the speed of the pulse-off

Comparison of Plasma Recovery Time with Experiments Affected by a source plasma due to large sheath sizes The Bohm current recovery model explains the simulation results well in spite of its simplicity when the offset of 5 s is added to it Discrepancy between experiment and simulation is thought to be caused by (a) a finite size of the experimental apparatus and (b) a limitation of the fluid model The characteristic time for the plasma recovery process can be simply expressed as a function of s/uB , where the s is the sheath thickness at the pulse-off time

Effects of Plasma Properties on Plasma Recovery Effect of the electron temperature Effects of plasma density and ion flow velocity With increasing the electron temperature, the plasma recovery time is reduced according to a function of s/uB because the Bohm speed uB is proportional to the square root of the electron temperature The plasma recovery time has nearly nothing to do with the pulse characteristics such as pulse width and voltage for a given electron temperature Increasing the ion flow velocity sufficiently up to or above the Bohm speed can effectively reduce the plasma recovery time even though it is currently not clear how to realize that

Conclusions and Future Work The sheath motion after the pulse-off is governed by the more mobile electron species because they respond instantaneously to the time-varying electric potential. To the contrary, the plasma recovery process is a long time process because it is governed by the immobile positive ion species. The plasma recovery process is an inherent characteristic of the plasma itself and it is deeply related to a rarefaction wave and ion flow. Hence the external pulse characteristics cannot affect the plasma recovery process. The characteristic time for the plasma recovery process can be simply expressed as a function of s/uB . Therefore, in order to enhance the plasma recovery process, one should increase the electron temperature or the sheath size. Another way to reduce the recovery time is to increase the ion flow velocity up to or above the Bohm speed by any means. Future Work The circuit model developed in this study should be extended to two-dimension in order to explain the experimental observations more precisely and apply the model to a real PSII process. The density enhancement in the unperturbed region which seems to be caused by the energetic secondary electrons or the expelled electrons by initial sheath expansion needs to be thoroughly investigated both experimentally and numerically. LIF system will be introduced to measure the ion flow velocity and dynamic sheath motion.