Image formation mechanisms in scanning electron microscopy of carbon nanotubes, and retrieval of their intrinsic dimensions.

TL;DR: It is shown how SEM images can be modelled by accounting for surface enhancement effects together with the absorption coefficient for secondary electrons, and the electron-probe shape, enabling retrieval of the intrinsic nanotube dimensions.

About: This article is published in Ultramicroscopy.The article was published on 2013-01-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Scanning confocal electron microscopy & Energy filtered transmission electron microscopy.

Summary

1. Introduction

• The development of scanning probe microscopy (SPM) instruments combined with scanning electron microscopy (SEM) and transmission electron microscopy (TEM) enables free standing nanostructures (such as carbon nanotubes) to be studied in terms of their mechanical and electrical properties.
• The space available inside SEM instruments is comparatively large and several probes can be used [2] .
• One route is then to combine the SEM in-situ analysis with regular TEM imaging [4, 5] .
• The material testing would then first be performed inside an SEM, and the sample of interest subsequently transferred into a TEM to obtain the detailed structural information.

2.1. Sample preparation

• Two types of commercial CNTs have been studied: NC2100 and NC2101, obtained from Nanocyl.
• Both types were produced by catalytic chemical vapor deposition (CCVD) with the difference being that NC2101 was functionalized with a carboxyl group (-COOH) to reduce bundling.
• The CNTs are marketed as double-walled with an average diameter of 3.5 nm and lengths varying between 1-10 µm.
• Sonication for longer periods of time can introduce defects so that the concentric cylinder structure is broken [8] .
• The solution containing the CNTs was drop-casted onto a holey carbon support film for TEM (R 2/1 produced by Quantifoil) and then allowed to dry.

2.2. Microscopy

• The samples were first studied in a JEOL (JEM 2100) TEM equipped with a LaB 6 cathode and a digital camera from Gatan (SC1000 Orius).
• The best performance of the TEM is obtained at the Scherzer defocus [10] .
• The error when estimating the diameter of a CNT from TEM images is less than 10% for diameters larger than 1 nm [11] .
• An acceleration voltage of 12 kV was found to be a good tradeoff between resolution and signal-to-noise ratio and was used when acquiring all images in this study.
• Electron beam-induced deposition (EBID) can be a problem during SEM analysis and it will increase the diameter of the CNTs [12] .

2.3. Modelling

• This can be described as a convolution of the SE yield at each sample position, δ(r), with the electron-probe shape, i(r): EQUATION.
• In these intensity profiles, a radial symmetric i(r) can be described as one dimensional and Gaussian and Lorentzian functions can be used to describe i(r).
• The SE yield from a homogeneous material depends on the generation and scattering of SE.
• Φ will vary across its surface and δ increases with increasing φ.
• Pair of elements were multiplied and the products summed together in each step.

3. Results and Discussion

• The inner and outer diameter of the CNTs obtained from the TEM images was used as parameters when simulating intensity profiles, I sim .
• One reason that the deconvolution cannot fully retrieve the underlying structures, is the image noise in the shape of streaks.
• The authors have previously shown, from empirical studies, that the width of the SEM profile can be used to estimate the outer diameter of the nanotubes [6] .
• Δ only has a slow decrease after the step, and the second derivative should still give a good measure of the diameter.
• When fitting the experimentally obtained SEM intensity profiles by simulations, the best results were obtained in their case when using i(r) in Eq. 9 with Γ = 2.05 nm.

4. Conclusions

• A method for reproducing SEM intensity profiles of CNTs has been presented.
• The intensity profile is modelled as the convolution of the electron-probe shape and the secondary electron yield, [δ * i](r).
• Information regarding the true sample structure can thus be obtained and SEM-images can be deconvoluted to improve the resolution.
• A simple method for estimating the outer diameter is also proposed, where the distance between the two zero points of the intensity profile's second derivative is used.
• The theory described should also be applicable to other homogeneous nanofibers and can aid the analysis of in situ SEM experiments.

Figures

Figure 1: Images of the same CNT acquired by (a) SEM and (b) TEM. (c) Shows the integrated intensity profiles from the two rectangles in (a) and (b), and the diameter estimated from the TEM profile is indicated.

Figure 4: SEM images of a CNT showing (a) a raw-image and (b) a deconvoluted image. The integrated intensity profiles from the boxes in (a) and (b) are plotted in (c).

Figure 5: (a) TEM and SEM profiles, from images in Fig. 3 (a) and (b), together with a polynomial fit of ISEM(r), and the second derivative of this fit(the zero points are indicated). (b) Diameters estimated from SEM images using the second derivative versus the diameter measured in TEM. The predicted diameter from simulations (using ΓG = ΓL = 2.0 nm) is shown as a grey line. (c) The robustness is tested with five prediction curves (obtained using isim = 1 2 iL + 1 2 iG and ΓG = ΓL).

Figure 2: (a) The total SE yield, δsim, for two different α-values (solid lines), calculated for the CNT dimensions indicated by the dashed lines. (b) Two simulated intensity profiles, Isim, for the CNT dimensions in (a) using isim = iG and isim = iL with ΓG = ΓL = 2.1 nm (for α = 1/20 nm−1).

Frequently asked questions

Q1. What have the authors contributed in "Image formation mechanisms in scanning electron microscopy of carbon nanotubes, and retrieval of their intrinsic dimensions" ?

The authors present a detailed analysis of the image formation mechanisms that are involved in the imaging of carbon nanotubes with scanning electron microscopy ( SEM ). The authors show how SEM images can be modelled by accounting for surface enhancement effects together with the absorption coefficient for secondary electrons, and the electron-probe shape. The authors also present a simple and robust model for obtaining the outer diameter of nanotubes without any detailed knowledge about the electron-probe shape. 

Q2. How did the model reproduce the intensity profiles of CNTs?

The model reproduced experimental intensity profiles well when a combination of a Gaussian and a Lorentzian function for the probe shape was used. 

Q3. How much voltage was used to acquire all images in this study?

An acceleration voltage of 12 kV was found to be a good tradeoff between resolution and signal-to-noise ratio and was used when acquiring all images in this study. 

Q4. What was used as a parameter when simulating intensity profiles?

The inner and outer diameter of the CNTs obtained from the TEM images was used as parameters when simulating intensity profiles, Isim. 

Q5. How many CNTs were used in this study?

Since all CNTs used in this study had d > 1 nm, the diameters measured in the TEM should deviate less than 10% from the true diameter. 

Q6. What was the integration in Eq. 8?

The integration in Eq. 8 was performed numerically in MATLAB, were both isim(r− r′) and δsim(r′) were divided into small elements. 

Q7. What was the solution containing the CNTs?

The solution containing the CNTs was drop-casted onto a holey carbon support film for TEM (R 2/1 produced by Quantifoil) and then allowed to dry. 

Q8. What is the way to deconvolute a full SEM image?

Knowing the exact probe shape, one can deconvolute a full SEM image to obtain the SE yield, and in turn from that retrieve the intrinsic nanotube dimensions. 

Q9. What is the probability of escaping a specimen?

The probability of escaping a specimen decreases exponentially with the distance travelled in the solid, z:Pescape ∝ e−αz (4)with α being the absorption coefficient for SE of the specimen material. 

Q10. What is the simplest way to deconvolute a SEM image?

The authors have used the two dimensional version of Eq. 9 as the input point spread function in the MATLAB-function deconvblind to deconvolute SEM images.