以脈衝式電源驅動的軸對稱均勻氙氣電漿產生真空紫外光輻射之數值模擬研究

Abstract

近年來，準分子紫外光(Excimer UV; EUV)燈管放光技術在工業方面有著廣泛的應用，例如臭氧的生成及半導體矽晶圓的表面清潔等。準分子的產生是透過電漿內部複雜的化學反應機制例如解離、激發等碰撞過程，而真空紫外光的發生則是在準分子由受激態掉回基態時所釋放出的能量所致。由於此類電漿反應機制相當複雜，以致於燈管的設計通常靠試誤法，需付出高額的時間及成本。因此本論文的主要目的是藉由流體模式模擬工具了解EUV燈管的氣體放電機制。如此，在使用不同的參數時，我們可以先預測難以在實驗下量測到的電漿特性。這樣不但可以縮短EUV燈管的設計時程而且可能得到更好的燈管設計。 本論文使用一維軸對稱流體模式進行kHz等級電源驅動的氙氣準分子燈管電漿模擬。此程式以有限差分法進行數值離散，考慮 local mean energy approximation (LMEA)及簡化氙氣化學反應機制。由於電子質量很輕，可立即反應電場變化，以電子在一個週期內隨時間的變化量可分為三個主要階段: pre-breakdown(前放電區)、breakdown (放電區；172 nm真空紫外光放光最強烈階段) 及 post-breakdown (後放電區) 階段。結果顯示真空紫外光放射效率在使用distorted bipolar 方形波形的表現比使用正弦波波形為佳。主要歸因於以下兩種主要的機制: 第一、在distorted bipolar 方形波形下外加電壓迅速抬升，電子在沒有彈性碰撞損失下可以吸收更多能量進行解離、激發等碰撞反應產生更高濃度的激發態原子進而增加172 nm紫外光所放出的量。第二、在正弦波形下，外加電壓的緩慢下降促進離子透過歐姆加熱方式吸收外加電場能量，而離子所吸收的能量並不會用於解離、激發等碰撞反應，對整個放電系統而言是一種能量的浪費。 為了瞭解控制準分子紫外光燈放電的真空紫外光輻射效率，我們在distorted bipolar 方形波形電源驅動下變化四種參數包括外加電壓頻率、背景氣體壓力、燈管的寬度及介電層的數量。結果顯示強烈的172 nm紫外光放射均在放電區前期發生，這與電子吸收能量的階段相當吻合;另外離子的能量吸收主要發生在放電區的後期。令人驚訝的是，當調高頻率時，燈管的效率只有些微的增加;而隨著燈管電極間寬度的增加，燈管的效率也大幅的增加。此外，172 nm紫外光的放射效率在600 torr 下有最大值。而只放置一個介電層的燈管效率的表現比兩端都放置介電層的燈管為佳。 最後，在本論文中也進行背景氣體的加熱影響的研究。加入氣體加熱影響的模擬結果可合理解釋電漿產生的真空紫外光輻射與背景氣體壓力的關連而在超過某各臨界壓力電漿無法被點燃的現象的實驗結果。這主要歸因於兩個主要機制，第一、在高壓 (P = 510 torr) 下，由於氣體加熱引起背景氣體不均勻分佈導致離子轉換反應(2Xe+Xe+沦 Xe2+)更為活躍進而增進與電子的合併反應，最終使得電子數量無法維持電漿生成;第二、隨背景氣壓增加，電子彈性碰撞的能量損失亦隨著增加，造成整體電子能量(溫度)下降，進而使得電漿強度減弱，這反應機制在高氣壓下對電漿造成的影響更為顯著。

Recently, the excimer UV (EUV) lamp has found a wide range of applications in industry, for example, in ozone generation and surface cleaning for Si wafer in semiconductor fabrication process. The generation of EUV results from the reaction mechanism like ionization or excitation and other collision processes in the plasma. The occurrence of VUV is due to the process that excimer falls from various excited states to a ground state. However, its design was mostly based on the trial-and-error method, which is time-consuming and cost ineffective. Thus, the goal of this thesis is to predict and understand the plasma physics and chemistry inside an homogeneous EUV discharge through fluid modeling technique. In this thesis, a self-consistent radial one-dimensional fluid model, considering local mean energy approximation (LMEA), along with a set of simplified xenon plasma chemistry is employed to simulate the discharge physics and chemistry. The discharge is divided into three-period regions; these include: the pre-breakdown, the breakdown (most intense at 172 nm VUV emission) and the post-breakdown periods. The results show that the efficiency of VUV emission using the distorted bipolar square voltages is much greater than that using sinusoidal voltages, which is attributed to two major mechanisms. The first is the much larger rate of change of the voltage in bipolar square voltages, in which only the electrons can efficiently absorb the power from the applied electric field in a very short period of time. Energetic electrons then generate a higher concentration of metastable (and also excited dimer) xenon that is distributed more uniformly across the gap, for a longer period of time during the breakdown process. The second is the comparably smaller amount of “wasted” power deposition by in the post-breakdown period, as driven by distorted bipolar square voltages, because of the nearly vanishing gap voltage caused by the shielding effect resulting from accumulated charges on both dielectric surfaces. Emitted powers of EUV light and deposited powers to the charged species of a homogeneous coaxial xenon discharge driven by the distorted bipolar square voltages are simulated by varying the test conditions of four key parameters, which include the driving frequency, gas pressure, gap distance and number of dielectric layers. Results show that there are three distinct periods that include pre-breakdown, breakdown and post-breakdown ones. It is found that intensive EUV (172 nm) emission occurs during the early part of the breakdown period, which correlates very well in time with the power deposition through electrons. In addition, power deposition through and occurs mainly in the breakdown period and later part of breakdown period, respectively. Surprisingly, the emission efficiency of 172 nm increases only slightly with increasing driving frequency of power source, while it increases dramatically with increasing gap distance. In addition, the maximum emission efficiency is found to take place at gas pressure of 600 torr. The emission efficiency of one-dielectric case is found to be better than that of two-dielectric one. The underlying mechanisms in the above observations are discussed in detail in the paper. Finally, gas heating is included in the fluid modeling by a heat conduction equation for xenon. With this consideration, one can explain reasonably well the experimentally observed VUV emission at various background pressures, especially the extinguishment of the discharge as pressure exceeds some threshold value. The major mechanisms of the above phenomena are described as follows: 1) Increasing pressure leads to higher gas heating because of increasing electron energy loss through the elastic collision with xenon atoms in the bulk region; and 2) The above leads to higher gas density at outer region of the gap (r绌 1.1~1.16 cm), because of heat conduction and assumed uniform pressure distribution, as compared to the case without gas heating which promotes the three-body Xe+-to-Xe2+ ion conversion and e-Xe2+ recombination that greatly reduces the plasma density as pressure exceeds some threshold.