材料分析Part B-4-4 TEM明場像中常見的共同特徵影像 – 2/2 弗瑞斯聶爾條與莫瑞條紋

弗瑞斯聶爾條紋(Fresnel fringes)

顯微鏡影像一般都在正聚焦(in-focus)條件下拍攝，唯獨TEM明場像試在欠焦(under focus)條件下拍攝，旨在補償一些球面像差，同時使邊界位置或界面更清楚，更容易辨識。如圖B-39明場像所示，圖B-39(a)是正聚焦影像，圖B-39(b)欠焦影像，而圖B-39(c)則是過焦影像。相比之下，可以看出圖B-39(a)中物體的邊界沒有圖B-39(b)中的清晰明確，欠焦的TEM明場像沿物體輪廓邊緣多出一白線，使物體的輪廓邊緣更清晰，過焦的影像則在物體輪廓邊緣多出一條黑線。這些白線和黑線都叫弗瑞斯聶爾條紋。

Images taken by microscopes are usually photographed at in-focus condition, except TEM BF images. TEM BF images are usually photographed at under focus conditions, which can compensate some spherical aberration and highlight positions of boundaries or interfaces. Fig. B-39 shows images taken at in-focus, under focus, and over focus respectively. Apparently, the boundaries in the image in Fig. B-39(b) are more clearly than that in Fig.B-39(a). Those while lines along boundaries in under focus TEM BF images make boundaries more definitely. There are black lines along the boundaries when TEM images are photographed at over focus conditions. Both white and black lines are Fresnel fringes。

圖B-39弗瑞斯聶爾條紋(Fresnel fringes)。(a)正聚焦，Δf = 0 nm；(b)欠焦，Δf = -200 nm；(c) 過焦，Δf = +200 nm。[1]

在大多數狀況下，適當欠焦的明場像強調出邊界的位置，是一般TEM工程師拍攝TEM明場像的慣用條件。但是有時候這一層很薄的白色層次會造成顯微結構上的誤解。在半導體業界，弗瑞斯聶爾條紋最普遍被工程師誤認為矽原生氧化層，有時候連製程上的專家都會陷入此種迷惘。圖B-40展現此典型的例子，第一層多晶矽和第二層多晶矽之間的弗瑞斯聶爾條紋被誤判為矽原生氧化層，導致TEM顯微結構分析和該元件的電性不符。

Generally, the boundaries of phases are highlighted by a suitable under focus which is used for almost all TEM engineers to take TEM BF images. However, these white lines can be mistaken to be thin layers in the microstructure sometimes. Fresnel fringes are easy to be confused with Si native oxide layers for process engineers, even some process experts were puzzled, in semiconductor industry. Fig. B-40 shows a typical case, the Fresnel fringe between poly 1 and poly 2 was mis-judged to be a Si native oxide layer. This mistake resulted in a contradictory between the microstructure and the resistance measured.

圖B-40弗瑞斯聶爾條紋造成第一層多晶矽和第二層多晶矽之間有原生氧化層的誤判。[1]

莫瑞條紋(Moirè fringes)

在TEM試片厚度內，電子束前進的路徑如果通過二個晶粒，而這二個晶粒有某種晶向關係的時候，就有可能產生莫瑞條紋。圖B-41內的示意圖解說產生莫瑞條紋的二種主要型式[2]：(1)上下二個晶體不同相，但是某一組晶格面互相平行，而且晶格面間距大小很接近；(2)上下二個晶體同相，同組晶格面相對旋轉一個小角度。第一類型的條紋走向和原來的晶格面平行，間距則為晶格面間距的數倍到數十倍，視二組晶格面間距的差而定。第二類型的條紋走向和原來二組晶格面的伯格向量差垂直，間距約為晶格面間距除以旋轉角度(徑度)。圖B-42顯示氮化鎵柱狀晶重疊產生的第二類型莫瑞條紋。

Moirè fringes are possible to be observed when the incident electron beam passes through two crystals with a special relationship in crystal orientation. Fig. B-41 explains how Moirè fringes are formed schematically [2]. For the first type, two crystal are different phase, (h₁ k₁ l₁) and (h₂ k₂ l₂) are crystal planes parallel to each other and the difference in d-spacings is small. For the second type, two crystals are same phase, the (h_i k_i l_i) crystal planes of one crystal rotates a small angle related to the same (h_i k_i l_i) crystal planes of the other crystal. The direction of Moirè fringes of the first type run parallel to the (h k l) planes and their spacing is about several to more than ten times of the d-spacing of (h k l) planes. Fig. B-42 shows a second type of Moirè fringes of GaN columnar crystals.

圖B-41莫瑞條紋的形成的機構。(a)電子束與試片關係示意圖；(b)第一類型莫瑞條紋產生機構的示意圖；(c)第二類型莫瑞條紋產生機構的示意圖。[2]

圖B-42氮化鎵柱狀晶重疊產生的莫瑞條紋。

參考文獻

1] 鮑忠興和劉思謙，近代電子顯微鏡實務，第二版，滄海書局，台中 (2012)。

2] Practical Electron Microscopy in Materials Science, edited by J. W. Edington, Van Nostrand Reinhold Company (1976).