Evaluating Bandgap Distributions of Carbon Nanotubes via Scanning

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Letter pubs.acs.org/NanoLett

Evaluating Bandgap Distributions of Carbon Nanotubes via Scanning Electron Microscopy Imaging of the Schottky Barriers Yujun He, Jin Zhang, Dongqi Li, Jiangtao Wang, Qiong Wu, Yang Wei, Lina Zhang, Jiaping Wang, Peng Liu, Qunqing Li, Shoushan Fan, and Kaili Jiang* State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: We show that the Schottky barrier at the metalsingle walled carbon nanotube (SWCNT) contact can be clearly observed in scanning electron microscopy (SEM) images as a bright contrast segment with length up to micrometers due to the space charge distribution in the depletion region. The lengths of the charge depletion increase with the diameters of semiconducting SWCNTs (s-SWCNTs) when connected to one metal electrode, which enables direct and efficient evaluation of the bandgap distributions of sSWCNTs. Moreover, this approach can also be applied for a wide variety of semiconducting nanomaterials, adding a new function to conventional SEM. KEYWORDS: Carbon nanotube, bandgap, Schottky barrier, scanning electron microscopy

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electronic and optoelectronic devices.42−49 The p-type ballistic conduction4 as well as n-type conduction6 has been achieved by tuning the Schottky barrier in SWCNT FETs. Imaging of the Schottky barrier will not only directly prove its existence, but also deepen the understanding of its role in real device. Some pioneer works have been carried out in this direction either by scanning gate microcopy50 or photoelectronic transport imaging.51,52 However, both methods suffer from a low efficiency. A direct and rapid imaging method is therefore expected. We show that the Schottky barrier at the metal-SWCNT contact can be clearly observed in scanning electron microscopy (SEM) images as a bright contrast segment with length up to micrometers, due to the space charge distribution in the depletion region. The lengths of the charge depletion increase with the diameters of s-SWCNTs when connected to one metal electrode, which enables direct and efficient evaluation of the bandgap distributions of s-SWCNTs. Moreover, this approach can also be applied for a wide variety of semiconducting nanomaterials, such as Si nanowires or graphene-like (including graphene or MoS2 etc.) nanoribbons, adding a new function to conventional SEM. SWCNTs were first synthesized on a quartz substrate via chemical vapor deposition (CVD)53 and then transferred onto a SiO2/Si (thickness of the SiO2 layer: 300 nm) substrate.54 The metal electrodes were patterned and formed via electron beam lithography (EBL) process using double layer resist,

emiconducting single walled carbon nanotube (s-SWCNT) is a promising material for next generation electronic and optoelectronic devices1−3 due to its excellent properties such as high mobility and ballistic transport of charge carriers,4−6 high ON/OFF ratio,7 and direct bandgap electronic structure,8 and so forth. Unlike bulk semiconducting materials such as Si, Ge, and so forth., s-SWCNTs possess bandbaps which are strongly dependent on their diameters.8 For an ensemble of as-grown SWCNTs, the existing diameter distribution always leads to a bandgap distribution. Thus “the key challenges for carbon nanotubes to be viable in high-performance field effect transistors (FETs) is the requirement of a process that provide a tight distribution of semiconductor bandgaps...”, according to the International Technology Roadmap for Semiconductors (Emerging Research Materials, 2011 edition). Much effort has been put to separation,9−17 sorting,18 selective growth,19−28 and “cloning”29−33 of SWCNTs, aiming at harvesting SWCNTs with single chiral index. At the same time, several methods have been developed to assign the chiral index of SWCNT, including Raman scattering,34 excitation−emission spectroscopy,35 Rayleigh scattering,36,37 and TEM diffraction.38−41 Among these methods, the excitation−emission approach is the only one suitable for an ensemble evaluation, but restricted to liquid phase SWCNTs wrapped by unwanted surfactant.35 Also, it does not work for metallic SWCNTs (m-SWCNTs) and large diameter s-SWCNTs. Hence the new challenge posed by real device applications is how to evaluate the percentage of sSWCNTs as well as the bandgap distributions for an ensemble of clean SWCNTs. On the other hand, Schottky barrier formed at the metalSWCNT contact plays a key role in the performance of © 2013 American Chemical Society

Received: August 22, 2013 Revised: October 11, 2013 Published: October 17, 2013 5556

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Figure 1. Fabrication process and SEM images of the metal-SWCNT contacts. (a) Schematic illustration of the fabrication process for the clean metal-SWCNT contacts. After transferring SWCNTs onto SiO2/Si (thickness of SiO2: 300 nm) substrate, the metal electrodes were patterned and formed via EBL process using double layer resist, followed by deposition of a 50 nm thick metal film and a standard lift-off process. (b) Lowmagnification and (c) high-magnification SEM images of the as-fabricated Ti electrodes connected to SWCNTs. The m-SWCNTs and s-SWCNTs clearly show different contrast and s-SWCNTs have distinct bright segments with various lengths.

followed by deposition of a 50 nm thick metal film and a standard lift-off process, as illustrated in Figure 1a. This fabrication process guarantees a clean metal-SWCNT contact without the disturbance from residue photoresist. Figure 1b,c shows the low voltage (1 kV) SEM images of the as-fabricated titanium (Ti) electrodes connected to SWCNTs. As usual, m-SWCNTs appear bright and s-SWCNTs appear dark due to their different conductivity, which is consistent with our previous results.55 What is unusual is that there are always distinct bright segments at the metal-SWCNT contact for the dark s-SWCNTs. Moreover, the lengths of the bright segments (LBS) are notably different for various s-SWCNTs and roughly the darker s-SWCNTs display shorter bright segments. Considering these segments exist at the metal contact for every s-SWCNT, we speculate that it might originate from the Schottky barrier formed at the metal-SWCNT contact. As is well-known, the Schottky barrier formed at metalsemiconductor contact is determined by both the work function of the metal and the band structure of the semiconductor.56 In case of s-SWCNT, its bandgap is inversely proportional to its diameter.8 We therefore tried to find the relation between LBS and the diameter. As shown in Figure 2a,b, one m-SWCNT and three neighboring s-SWCNTs with different LBS were selected for further atomic force microscopy

(AFM) imaging (Figure 2c). The gray level along the tube axis near the contact was extracted from the higher-magnification SEM image (Figure 2b) and was plotted in Figure 2d. It clearly shows two distinct groups of curves. The gray level of mSWCNT varies slowly along the tube axis and keeps a high value, while that of s-SWCNTs has a plateau near the contact and then drops to a low level abruptly. The average AFM height, which is obtained by executing “step analysis” function within the white rectangle of Figure 2c, is plotted against the lateral position of SWCNTs (Figure 2e). It is clear that Figure 2e resembles Figure 2b, except for the m-SWCNT, indicating that LBS qualitatively increases with the height of s-SWCNT. To be quantitative, LBS is defined as the length measured from the interface of metal and s-SWCNTs to the location where the gray level difference (defined as the value of gray level minus the averaged value far away from the contact) decays to 1/e of its maximum value (Figure 2d). The diameter of s-SWCNT is defined as the average AFM height along the tube axis. Here we chose more than 100 lines close to the metal electrode and perpendicularly intersecting the s-SWCNTs, avoiding any parts that s-SWCNT bends or is contaminated by particles, to obtain the average height from the AFM image. The quantitatively measured data are displayed in Figure 2f, showing a linear relationship between LBS and the diameter of 5557

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Figure 2. Linear relationship between the length of bright segment (LBS) and the diameter of s-SWCNT. (a) Low-magnification and (b) highmagnification SEM images of Ti electrodes connected to SWCNTs. (c) AFM image of the SWCNTs shown in panel b. (d) Grayscale curves of SWCNTs extracted from panel b; the black, red, green, and cyan curves correspond to SWCNTs from left to right in panel b. Inset: Schematic illustration of the SWCNTs in panel b. (e) AFM height value averaged within the white rectangle of panel c, plotted against the lateral position. (f) Linear relationship between LBS and the diameter of s-SWCNT. (g) The diameter−LBS plot of nine groups of data, showing the linear relationship with nearly identical slopes.

To answer these questions, the schematic band diagrams are plotted in Figure 3a for two identical p-type SWCNTs connected to metal electrodes with different work functions. Here we note that the as grown SWCNTs are all p-doped due to oxygen adsorption. It is assumed here that before contact, the work function of the metal is smaller than the Fermi level of the oxygen doped (p-type) SWCNT, which applies for most metals including palladium (Pd 5.1 eV), Ti (4.3 eV), aluminum (Al 4.1 eV), gold (Au 5.1 eV), and scandium (Sc 3.3 eV) electrodes.6,44 The difference in Fermi levels on both sides of the contact will drive electrons to flow into SWCNT until the line-up of their Fermi levels, creating a charge depletion region in which negative space charges are uniformly distributed (Figure 3b). The charge density distribution curve is very similar to the gray level curve of s-SWCNT shown in Figure 2d. We therefore conjecture that the bright segment is probably the

s-SWCNT. We have randomly selected nine groups of sSWCNTs for the aforementioned imaging and measurement, and the details are shown in Supporting Information Figures S1−S8. All the nine groups of data are displayed in the diameter−length plot (Figure 2g), showing that the linear relationship still exists with nearly identical slope but different intercept. We note here that the fluctuation of intercepts is limited by the accuracy of AFM (0.25 nm in our case), which can be clearly seen from the results of nine independent measurements on the same group of SWCNTs (Supporting Information Figure S9). The aforementioned experimental results indicate that the distinct bright segment at the metal-SWCNT contact might originate from the Schottky barrier, and LBS is likely proportional to the diameter of s-SWCNT. Now the questions are what the bright segment is and why its length increases with the diameter. 5558

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Figure 3. Schematic illustrations of band diagrams for various metal-SWCNT contacts. (a) Schematic band diagram depicts the Schottky barrier and the depletion region for one SWCNT connected to two different metal electrodes. (b) Schematic illustration of the space charge distribution along SWCNT. The green and blue curves correspond to the SWCNT connected to metals with smaller and larger work functions, respectively. (c) Schematic illustration of the bright segments near the SWCNT-metal contact. (d) Schematic band diagram depicts the Schottky barrier and the depletion region for two SWCNTs connected to one metal electrode. (e) Schematic illustration of the space charge distribution along SWCNTs. The red and purples curves correspond to the SWCNT with smaller and larger bandgap, respectively. (f) Schematic illustration of the bright segments near the SWCNT-metal contact.

Figure 4. Various metal-SWCNT contacts. (a) SEM images of SWCNTs connected to Ti (50 nm) and Pd (50 nm). (b) LBS(Pd) versus LBS(Ti), and the slope of the fitted line is 0.5. (c) SEM images of SWCNTs connected to Ti/Au (1 nm/49 nm) and Au (50 nm). (d) LBS(Au) versus LBS(Ti/Au), and the slope of the fitted line is 0.83. (e) SEM images of SWCNTs connected to Pd (50 nm) and Sc (50 nm). (f) LBS(Sc) versus LBS(Pd), and the slope of the fitted line is 0.84.

charge depletion region (Figure 3c), and LBS is equal to the length of the depletion region (LD). It has been shown that SEM working at 1 kV will lead to a positive charging at the surface of insulators such as SiO2.55 Thus the negative space charge will show a distinct bright

contrast when s-SWCNT is lying on the surface of SiO2. It is therefore reasonable that the observed bright segment is the charge depletion region (Figure 3c). Unlike the conventional planar bulk junction, the length of the charge depletion region approximately follows LD ∼ R 5559

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exp(∈||∈0Eg/e2RNf) in which R is the radius of s-SWCNT, ∈|| is the static relative dielectric constant in the axial direction of SWCNT, ∈0 is the permittivity of free space, Eg is the bandgap of s-SWCNT, e is the unit charge, N is the number of carbon atoms per unit area, and f is the doping fraction.57 This formula is valid when LD ≫R, thus applicable for our situation. In general, the low-frequency dielectric constant depends on the average bandgap E̅g of semiconducting materials, ∈ = 1 + (ℏωp/E̅g)2 in which ℏωp is the plasma energy according to the linear-response theory.58 Both tight-binding and first principle calculations have confirmed that ∈|| = 1 + A/Eg2 for s-SWCNTs in which A is a constant value.58,59 Since experimental results suggest that ∈|| ≥ 18 even for large bandgap s-SWCNTs,59 a good approximation is ∈|| ≈ A/Eg2. Hence LD ∼ R exp(A∈0/ EgRe2Nf). For s-SWCNTs, Eg ∝ 1/R and EgR is a constant. Given B as a constant for all s-SWCNTs, LD ∼ R exp(B/f), which shows that the length of charge depletion LD is proportional to the diameters, or equally the inverse of the bandgap, and decreases with doping fraction. The schematic band diagrams for two SWCNTs with different diameter are illustrated in Figure 3d, showing that LD is proportional to the diameter (Figure 3e,f), which agrees well with our experimental results that LBS is proportional to diameter shown in Figure 2f,g. We therefore reach a conclusion that the bright segment is the charge depletion region (Figure 3c), and LBS is equal to LD. It is well-known that the Schottky barrier strongly depends on the work function of metal, although it is not included in the expression of LD by Leonard and Tersoff.57 The schematic band diagrams shown in Figure 3a clearly indicate that smaller work function will lead to a larger LD. To verify this point, we fabricated several kinds of metal-SWCNT contacts for further investigation. Typically we deposited several kinds of metal to contact with the same group of SWCNTs for direct comparison, keeping constant thickness of the metal electrodes at 50 nm. Figure 4a shows the same groups of SWCNTs connected to both Ti and Pd electrodes, which were chosen because of their good wetting with SWCNTs.60 It is clear that LBS for the Ti (4.3 eV) electrode is notably longer than that for the Pd (5.1 eV) electrode, which agrees well with the aforementioned qualitative analysis. From the SEM image (Figure 4a), LBS is measured for each s-SWCNTs connected to both Pd and Ti and is displayed in Figure 4b as a data point (LBS(Pd), LBS(Ti)). The good linearity implies the same linear diameter dependence of LBS(Pd) as LBS(Ti). Au (5.1 eV) is also one of the most popular electrode material with nearly the same work function as Pd (5.1 eV), and usually a thin layer of Ti was predeposited as both adhesion layer for Si substrate and wetting layer for SWCNTs. We also fabricated Au and Ti/Au (1 nm/49 nm) electrodes as shown in Figure 4c. LBS(Au) is as short as LBS(Pd) as expected. An interesting phenomenon is that a wetting layer of 1 nm thick Ti between s-SWCNT and Au electrode does not alter the work function of Au very much and gives rise to a little bit larger depletion length than pure Au (Figure 4d). Another interesting material is scandium (Sc) that possesses a low work function and recently was employed as electrodes for n-type conduction of s-SWCNTs.6 We therefore fabricated Sc and Pd electrodes for direct comparison, since Pd usually served as electrodes for p-type conduction (Figure 4e). As a low work function metal, Sc (3.3 eV) is expected to give rise to a longer depletion length than Ti (4.3 eV). On the contrary, the experimental results show a notably shorter LBS than Ti, similar

with Pd (Figure 4a,e), indicating some deviation from the qualitative analysis. Considering Sc is a substance susceptible to oxidation, and oxidation will lead to larger doping fraction f than oxygen adsorption, we expect a shorter LD according to LD ∼ R exp(B/f). Details will be discussed in Supporting Information. However, LBS(Sc) still follows a linear relation with LBS(Pd) (Figure 4f), implying the linear diameter dependence still holds for LBS(Sc). So far, we have established the linear relationship between LBS and the diameter of s-SWCNT. Since the bandgap of sSWCNT is proportional to the inverse of its diameter, the relationship between the bandgap and LBS is therefore determined, which enables the evaluation of the bandgap distribution of as-synthesized SWCNTs (Figure 5). It follows Gaussian distribution with center bandgap of 0.50 eV and standard deviation of 0.06 eV.

Figure 5. Bandgap distributions of SWCNTs synthesized in a typical growth run: it follows Gaussian distribution with center bandgap of 0.50 eV and standard deviation of 0.06 eV. The bandgaps (eV) were derived from the length of bright segment (LBS, μm) according to the following expression Eg = 0.83/(0.31 × LBS + 0.88) (details are shown in Supporting Information).

In summary, we have discovered that the Schottky barrier and charge depletion region between s-SWCNT and metal electrode can be directly and clearly identified as a bright segment in SEM image. The length of depletion region shows a linear dependence on the diameter or the inverse of the bandgap of s-SWCNT, which enables direct and efficient evaluation of the bandgap distribution of an ensemble of SWCNTs. This approach will play key roles on the road toward implementing narrow bandgap-distribution, or even single bandgap (single chirality) SWCNT integrated circuits. Furthermore it might also be applied for a wide variety of semiconducting nanomaterials, such as Si nanowires or graphene-like (including graphene or MoS2 etc.) nanoribbons. Finally, we need to point out that there are some inadequacies and limitations in the present work, which might be the start point of future investigations. First, the current approach provides a relative measurement of the bandgap, which clearly shows the bandgap difference between SWCNTs. But currently it cannot give the absolute value of the bandgap. The limitation lies in the inaccurate methods used here to determine the LBS-diameter relation. Second, this approach will fail if two SWCNTs are too close to each other, which is primarily limited by the resolution of low voltage SEM. Despite these inadequacies and limitations, the approach we demonstrated here provides a new and general method to 5560

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Author Contributions

evaluate the bandgap distribution of nanomaterials, adding another function to conventional SEM. Methods. Horizontally aligned SWCNTs were synthesized on stable temperature-cut (ST-cut) quartz wafers by chemical vapor deposition. Details of the synthesis can be found in our previous paper.55 SWCNTs grown on the quartz substrate were then transferred onto silicon wafers (thickness of SiO2: 300 nm) using poly(methyl methacrylate) (PMMA).54 After removal of the PMMA in acetone, a double-layer resists of methyl methacrylate (MMA) and PMMA were spin-coated onto the silicon wafers. Electrodes were patterned and formed via EBL, followed by deposition of a 50 nm thick metal film and a standard lift-off process. Conventional UV lithography was also used to define the electrodes but it is not very convenient for small samples. Also, it is not easy to totally remove the UV photoresist from SWCNTs, which hinders the accurate measurement of LBS. We therefore use EBL in the current study. Silicon wafers with 500 nm SiO2 layer were also tested, almost the same as silicon wafers with 300 nm SiO2 layer. Metal electrodes can also be deposited on quartz substrate by using UV lithography (EBL does not work on quartz substrate due to the insulating property), and bright segments can also be identified. But the residue photoresist hinders the accurate measurement of both LBS and the diameter of SWCNT. We therefore choose silicon wafers with 300 nm SiO2 layer for the current study. The SEM (FEI Sirion 200) was operated at 1 kV with a working distance of 6.5 mm, a line scan time of 20 ms, 1936 lines per frame, a spot size of 4, a final lens strip aperture size of 100 μm, and a beam current of 250 μA. The low-voltage SEM imaging approach used here relies on the voltage contrast mechanism.55 The operation voltage window is from several hundred volts to less than 3 kV within which the total secondary electron emission coefficient is larger than one, and the substrate is positively charged. When connected to electrodes, m-SWCNTs appear bright and sSWCNTs appear dark due to the voltage contrast. Details can be found in ref 55 and references therein. The AFM (Nanosope 5) was operated in a tapping mode with a scan size of 2−5 μm, a scan rate of 0.5 Hz (0.25 Hz for Supporting Information Figure S4), sample/line 512 (1024 for Supporting Information Figure S4), and an amplitude set point of feedback 180−220 mV.

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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Professor Zhiping Yu for helpful discussion. This work was supported by the National Basic Research Program of China (2012CB932301) and NSFC (90921012, 51102144, 11274190, 51102147).

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ABBREVIATIONS SWCNT, single walled carbon nanotube; SEM, scanning electron microscopy; s-SWCNT, semiconducting SWCNT; FET, field effect transistor; TEM, transmission electron microscopy; CVD, chemical vapor deposition; LBS, the lengths of the bright segments; AFM, atomic force microscopy

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ASSOCIATED CONTENT

S Supporting Information *

Part I: Linear relationship between the length of bright segments (LBS) and the diameter for randomly selected eight groups of s-SWCNTs for SEM imaging and AFM measurement. Part II: The accuracy of AFM measurement. Part III: Oxidation mechanism for the shortening of depletion width. Part IV: The relation between the bandgap Eg and the length of bright segment (LBS). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 5561

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dx.doi.org/10.1021/nl403158x | Nano Lett. 2013, 13, 5556−5562