紅外光入射於不同厚度金薄膜和光柵穿透率之研究

Abstract

金屬薄膜的研究一直沒有被中斷過，它有很高的反射係數，因此常被作來反射鏡使用，但在金屬薄膜厚度小於集膚深度時，電磁波即可穿透過去，所以穿透率與薄膜的厚度息息相關，因此我們想知道在金屬薄厚度多厚時，電磁波可以將其視為一透明層，之後再利用薄膜矩陣理論，利用穿透率來反推我們金屬薄膜的介電常數，來與Drude Model所提出的理論介電常數做個比較。 Drude Model在1900年時被提出，一直以來它是在探討金屬內部自由導電載子如何影響介電常數的變化的最佳模型，許多理論上的介電常數值都經由它計算所得到，但也有許多人提出在短波長時，金屬材料的介電係數實部項已由負數轉為正數，因此拿來描述金屬的作用已不正確，不過在紅外光波段時被認為仍是適用的，但卻與我們實驗的結果有很大的差異性，我們發現在金屬厚度在非常薄的情形時，金屬介電常數將與Drude Model的理論值有明顯的不同，因此認為Drude Model在金屬非常薄時，將會不再適用。 我們利用電子束微影系統做出金屬光柵結構，來幫助我們改變金屬薄膜的比例，進而去討論不同金屬比例所得到的等效介電常數，但光柵厚度在大於集膚深度跟小於集膚深度時所表現出來的穿透率截然不同，我們將入射光分成TE和TM模態，並且找出在5nm時為紅外光可看到金屬光柵的臨界厚度，此為紅外光與金屬光柵間耦合消失之厚度。 我們也去討論在不同角度下時入射金屬光柵的結果，在斜向入射時，由於入射波本身有水平分量，再加上電子在週期性金屬光柵所造成的水平波向量，因此在發生異常穿透波長的位置會改變，且由於水平波向量會對入射波的水平分量造成增加或損耗的結果，因此異常穿透現象波長發生的位置並不同於正向入射時只發生在單一波長，而是會在不同波長的位置發生，且是與入射角有關的函數。 我們利用光動量守恆和色射關係式，推出在不同角度下異常穿透現象發生的波長位置，不管是在正向入射或是斜向入射的情形與實驗結果皆是符合的，所以可以確定異常穿透現象發生的波長位置與光柵的倒晶格向量是相關的。

Scientist never stops studying the researches of metal thin film. And metal thin film is often used as a reflection mirror because it has high reflective coefficient. When the thickness of metal thin film is thinner than the skin depth, EM wave can transmit through it. In this study, we would like to know whether EM wave could consider metal thin film as an invisible layer, and use the thin film theorem to calculate the dielectric constant of metal thin film to compare with the theoretical dielectric constant in Drude Model. Drude Model was mentioned in 1900.Acordding to recent study, Drude Model is the best model to confer the free electron inside metal that how to affect the dielectric constant. Most of the theoretical dielectric constant is calculate by Drude Model, but there are some scientist mentioned that on short wavelength, the real part of dielectric constant in metal material is changed from negative value to positive value. Therefore the Drude Model is not correct in short wavelength region. We consider it is suitable for using in infrared region, but the dielectric constant has a lot of differences between the Drude Model and the value from experiment when metal is thin enough. For this reason, we think Drude Model is not suitable under the condition that thickness is thinner than skin depth. We used E-beam lithography system to make the structure of metal grating that helped us change the percentage of metal in thin film. Then we calculated the dielectric constant of metal thin film in different percentage. The transmission of thin film was different between thicker and thinner. We find out that when thickness of grating is 5nm, it is the critical thickness that infrared could see the grating structure. And 5nm is the thickness that the coupling between EM wave and grating disappears. We also discuss the results of incidence through metal grating with different angles. In oblique incidence, incident wave has horizontal wave vector and affected by the horizontal vector caused by the electron on periodic metal grating. Due to the grating wave vector which enhance or reduce horizontal wave vector of incident wave, the position of wavelength in transmission anomaly would change. Therefore comparing to the normal incidence, the position of wavelength in transmission anomaly was not only on single wavelength in oblique incidence. It will occur on different wavelength and is the function of incident angle. We used momentum conservation and dispersion relation to derive the position of wavelength that transmission anomaly occurs. Both normal incidence and oblique incidence were identical with the results. Hence, we could confirm the position of wavelength in transmission anomaly was related to the reciprocal lattice vector of metal grating.