直接和间接EBSD探测器对比

There is a growing interest in the use of direct electron detection (DeD) for electron backscatter diffraction (EBSD), where the diffraction pattern is acquired directly via a pixelated semiconductor image sensor. This contrasts with the conventional approach of indirect electron detection (IeD), where incident electrons strike a scintillator (e.g. a phosphor screen), generating photons that are subsequently imaged using an optical camera system. Given that, in IeDs, both the conversion of electrons to photons and the detection of the photons using an optical camera can be relatively inefficient processes, and that some electron-counting DeD systems offer “single electron sensitivity” (i.e. detecting individual electrons as discrete particles so that the signal is completely free of any system noise), it would seem intuitive that DeD systems must offer the ultimate sensitivity for EBSD. However, reported results to date, using sensors such as Timepix and Timepix3, have not demonstrated any quantified improvement to sensitivity compared to the most sensitive IeD EBSD cameras such as the Symmetry S3 detector.

Having examined the topic of sensitivity already (see “fibre optics and sensitivity”), here we take a brief look at the physics of electron detection to understand better the sensitivities of an optimised IeD, such as the Symmetry S3 detector, and an electron-counting (EC) DeD. The results indicate that, contrary to popular belief, the indiscriminate detection of backscattered electrons of all energies using an EC-DeD actually results in a lower sensitivity than is possible with the Symmetry S3 IeD. This surprising result explains the lack of any sensitivity benefit from the use of DeD technology in EBSD applications to date.

所有EBSD分析,都需要首先从采集的EBSD花样中,将微弱的、低衬度衍射花样,从嘈杂的背底中区分出来。增加采集EBSD花样的电子剂量会提高信噪比(SNR),使衍射花样更易从背底噪声中区分开来。电子剂量增加到一定程度(检测限),SNR达到一定的阈值,那么就可以成功分析衍射花样。花样的解析策略也会影响检测限,使用离线的图像增强或花样相关性等方法的检测限,低于常用的实时、基于霍夫变换的标定方法。

在EBSD实验过程中,有大量背散射电子(BSE)轰击到EBSD探测器上,其中只有很小一部分电子形成了衍射花样,成为有效的信号。众所周知,这些衍射电子的能量,仅比入射电子能量E0[1]小约1-2 keV。剩下大部分BSE,平均能量较低,形成漫散的背底,对衍射花样没有贡献。如果探测了这些电子,它们只贡献了衍射花样的噪声,降低了整体的信噪比。因此,为了提高信噪比,有研究尝试在EBSD探测器中,仅提取某个能量段的电子来采集花样[2-4]。这里,我们将通过对EBSD花样中BSE的能量分布建模,分析不同类型探测器对不同能量的响应函数,来量化IeD和DeD的相对灵敏度。

EBSD探测器接收到的电子能量分布

下图是利用蒙特卡罗模拟[5],对EBSD花样中BSE的能量分布P(E)建模的结果。入射电子束被样品散射后,轰击到EBSD探测器上,设能量为E,P(E)描述了背散射电子的能量分布概率。理论上讲,探测器上不同的位置也会影响能量的分布,但这个差异对本分析影响很小,因此这里仅考虑整个花样的平均能量值。

除此之外,所有能量为E的BSE中,发生衍射、贡献花样的部分[6]也可以估算出来,这部分为D(E)。衍射电子的确切能量分布仍然存在一些争议,但为了方便比较不同探测器类型对所有能量段背散射电子的响应,这里采用的D(E)近似值适用于强衍射和弱衍射样品。图中的红色曲线代表了发生衍射的电子的能量分布,主要集中在略低于入射电子能量值(这里为20 keV)范围内,图中的黑色曲线是所有BSE的能量分布,分布在整个能量段范围内。

贡献了衍射衬度的电子剂量,可以通过以下公式进行计算:入射电子剂量·P(E)·D(E)有效的信号在图中表示为红色曲线下的总面积。

在SEM电子束能量E0 = 20 keV条件下,蒙特卡罗模拟Si样品倾转70°时,背散射电子能量分布P(E),P(E)·D(E)将用来计算SNR。

除此之外,探测器系统具有本征的散粒噪声,其与BSE电子总数相关,且服从泊松统计关系[7]。探测器的输入SNR,即为输入的有效信号与散粒噪声之间的比率。然而更重要的是,衍射花样自身的SNR,这主要取决于探测器对不同能量的电子的响应,即:探测器的能量响应函数。

参考文献

[1] A. Winkelmann, T. Ben Britton, and G. Nolze (2019), “Constraints on the effective electron energy spectrum in backscatter Kikuchi diffraction.” Phys. Rev. B, vol. 99, no. 6, p. 064115.

[2] Abhishek Bhattacharyya, John A. Eades (2009), “Use of an Energy Filter to Improve Spatial Resolution of Electron Backscatter Diffraction.” Scanning, vol. 31, 114-121.

[3] US Patent US8890065B2:  Apparatus and method for performing microdiffraction analysis

[4] Vespucci, S., Winkelmann, A., Naresh-Kumar, G., Mingard, K., Maneuski, D., Edwards, P., Day, A., O’Shea, V., Trager-Cowan, C.  (2015).  “Digital direct electron imaging of energy-filtered electron backscatter diffraction patterns.” Physical Review B 92, 205301

[5] X. Llovet and F. Salvat-Pujol (2016), “PENEPMA: a Monte Carlo programme for the simulation of X-ray emission in EPMA.” IOP Conf. Ser. Mater. Sci. Eng., vol. 109, p. 012009.

[6] F. Ram and M. De Graef (2018), “Energy dependence of the spatial distribution of inelastically scattered electrons in backscatter electron diffraction” Phys. Rev. B, vol. 97, no. 13, pp. 1–5.

[7] L. Reimer (1998), Scanning Electron Microscopy, vol. 45. Berlin, Heidelberg: Springer Berlin Heidelberg.

电子计数器DeD


电子计数器DeD系统具有很高的电子增益,因此单个电子产生的信号远大于系统噪声。而且,它可以通过像素上的电子电路,快速区分信号和噪声(通过适当地设置低能阈值),在下一个电子到达之前,生成每个单电子事件的数字计数。虽然这能消除系统噪声,但是低能阈值意味着,包含衍射信号的高能电子和构成背底的低能电子无法区分。每个探测到的电子将具有相同的权重,因此电子对花样的有效贡献与所有BSE的能量分布相似(参见“EBSD电子能量分布”标签页的图),在下图中显示为黑色曲线:




电荷积分IeD

不同入射电子能量对EBSD花样的有效贡献
对比用优化的IeD和EC-DeD传感器探测有效BSE能量分布谱图,谱图是关于入射电子能量的函数(已按纵坐标最大值归一化)。

Indirect electron detectors are typically not suitable for electron counting; rather than producing a noise-free, digital count of incident electrons, their output is formed from an analogue integration of the total charge induced by the incident electrons, and they are referred to as Charge-Integrating (CI) detectors. CI-DeD cameras are also available and are commonly used in transmission electron microscopy, with limited investigation into their potential for EBSD applications [See reference 1]. CI detectors are not free from system noise, but for optimised high-gain systems (as exemplified by the Symmetry S3 detector) the system noise is insignificant except at very low electron doses. This is detailed in a separate technical note “High Sensitivity EBSD Detectors” available here.

Importantly, in CI detectors, the output is proportional to the energy of the incident electrons (with the constant of proportionality being the electron gain, G). This linear relationship means that the higher-energy part of the measured spectrum is preferentially weighted compared to the lower-energy electrons, as shown by the red curve in the figure above. Given that most diffracted electrons have an energy close to the incident energy, this means that a high-gain charge-integrating IeD will have a superior SNR for diffracted electrons compared to a simple, low-threshold electron-counting DeD.

灵敏度对比:电子计数DeD与电荷积分IeD

接下来,通过上述的模型,就可以定量计算,比较电子计数DeD和电荷积分IeD EBSD探测器各自的灵敏度了。当样品及实验条件一定时,探测器的灵敏度(SEC-DeD和SIeD)也是确定的,并具有以下关系:

SIeD / SEC-DeD = 1.4

这意味着,优化的高增益IeD(如Symmetry S2 EBSD探测器)的灵敏度,约为简单的低能阈值EC-DeD的1.4倍。

当然,在非常低的剂量(此时系统噪声的影响变大)和非常低的电压(此时荧光屏的光子产生效率下降)时, IeD的灵敏度优势将减弱。

参考文献

[1] A. J. Wilkinson, G. Moldovan, T. B. Britton, A. Bewick, R. Clough, and A. I. Kirkland (2013), “Direct detection of electron backscatter diffraction patterns,” Phys. Rev. Lett., vol. 111, no. 6, pp. 1–5.

在讨论探测器技术时,有许多不同的术语,尤其是不同类型的直接电子探测器。此表将帮助您区分混合像素检测器和单片有源像素传感器!

CMOS:互补金属氧化物半导体,应用最广泛的传感器技术。

Monolithic Active Pixel Sensor (MAPS):单片有源像素传感器,基于CMOS技术。这种传感器每个有源像素上都有一个或多个放大器,传感器整个集成在一层Si上,像素尺寸相对较小,因此像素数量较多,但动态范围较低。

Hybrid Pixel Detector:混合像素检测器。这一类型检测器包括半导体传感器层和CMOS电路层,两部分通过凸点封装连接。其像素尺寸通常较大,限制了整体像素数量,但支持更高的动态范围。

Pixel Array Detector (PAD):像素阵列检测器,同混合像素检测器。

Electron-Counting Direct Electron Detector (EC-DeD):电子计数直接电子探测器,一种能够对单个电子进行计数的探测器,在以极低剂量成像时可过滤系统噪声。

Charge-Integrating (CI) Detectors:电荷积分探测器,一种在传感器上,对由入射电子产生的电荷,进行连续积分的探测器类型。最常见于高剂量应用,使用直接和间接电子探测器技术。

SNR:信噪比,输出的信号与噪声之间的比率,通常代表着传感器在特定条件下,对电子的响应性能。

Dynamic Range(DNR):动态范围,指最大输出信号水平与最小放大时的本底噪声之间的比率。它决定了探测器可以解析的信号水平的数量。

Shot Noise:散粒噪声,也称为“泊松噪声”。这是由单电子离散性引起的信号波动,它会影响高信号水平下的信噪比。

Read Noise:读出噪声,传感器电子元件引起的噪声,这将确定传感器能够检测到的最低电子数,有时也被称为“系统噪声”。

Dark Noise:暗噪声,是传感器内部产生的电流,与探测电子无关。暗噪声高度依赖于工作温度,但通常在EBSD工作的短时间曝光中可以忽略。

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