LETTER pubs.acs.org/NanoLett
Measuring Carbon Nanotube Band Gaps through Leakage Current and Excitonic Transitions of Nanotube Diodes Argyrios Malapanis, David A. Jones, Everett Comfort, and Ji Ung Lee* College of Nanoscale Science and Engineering, University at Albany, State University of New York, Albany, New York 12203, United States ABSTRACT: The band gap of a semiconductor is one of its most fundamental properties. It is one of the defining parameters for applications, including nanoelectronic and nanophotonic devices. Measuring the band gap, however, has received little attention for quasi-one-dimensional materials, including single-walled carbon nanotubes. Here we show that the current voltage characteristics of p-n diodes fabricated with semiconducting carbon nanotubes can be used along with the excitonic transitions of the nanotubes to measure both the fundamental (intrinsic) and renormalized nanotube band-gaps. KEYWORDS: Nanotube band-gap, p-n diode, band-gap renormalization, excitons
T
he quasi-one-dimensional (1D) nature of single-walled carbon nanotubes (SWNT) offers enhanced device properties for future applications.17 These properties include reduced carrier scattering,1 enhanced optical absorption,8 and band gaps tunable with both tube diameter9 and electrostatic doping.10 Researchers have developed a number of techniques to characterize individual single-walled carbon nanotubes.1114 One of the most important parameters for device applications, however, the electronic (free carrier) band gap, is among the most difficult to measure in quasi-one-dimensional semiconductors.1520 While some of the earlier confusion concerning the excitonic nature of optical transitions in nanotubes has been resolved,3 little work has addressed the measurement of the band gap. Additional complications arise in 1D semiconductors when doping is considered because the band gap is a strong function of doping density. Here we report on the strong correlation between the carbon nanotube band gap and the currentvoltage charactersistics of nanotube p-n diodes. We show that the reversebias saturation (leakage) current of p-n junction diodes formed along individual single-walled carbon nanotubes scales with both the fundamental (intrinsic) and renormalized band-gaps. We estimate the band gap shrinkage in the doped regions of the nanotube, which arises from band gap renormalization (BGR).10 Specifically, we show that the leakage current of nanotube p-n diodes scales with the lowest exciton resonance E11, which, as we discuss later, is largely doping independent. Using this result, we provide scaling of the band gap with the diode leakage current. We also show that this leakage current is tunable to a large degree by controlling how we deposit the catalyst used to grow the nanotubes through chemical vapor deposition (CVD). In the process, we make an addition to the Kataura diagram21 (which plots the nanotube exciton transitions with tube diameter, or radial breathing mode frequency22) in a diameter range that until now has not been confirmed experimentally.23 r 2011 American Chemical Society
We draw these conclusions in experiments with nearly ideal SWNT p-n diodes.15 By varying the spin-coating speed, we control the nanoparticle catalyst deposition and study the resulting effect on diode electronic properties. We use transport measurements, photocurrent (PC) spectroscopy, and Raman spectroscopy to make our analysis. We take all transport measurements in air at constant temperature T = 300 K. All PC and Raman spectroscopy measurements are taken in air at room temperature. Figure 1a shows an idealized sketch of our SWNT diode device. We use standard lithography and etch techniques in the fabrication process. Briefly, we deposit a 100 nm oxide (SiO2) on a heavily doped 300 mm silicon wafer. Using standard deposition, ion implantation, and lithography methods, we form doped polysilicon split gates with spacing ranging from 0.5 to 2 μm. We subsequently deposit a thick layer of SiO2 and planarize it through chemicalmechanical polishing to form a 25 nm gate dielectric above the split gates. We then deposit TiN and pattern it to form source (S) and drain (D) contacts. To suspend the nanotubes, we etch a trench into the SiO2 between the split gates. It has been shown that suspending the nanotubes, rather than growing them directly on a substrate, makes the diodes nearly ideal.7 The trench width (L) is 200 nm less than the split-gate spacing. Finally, we grow nanotubes on top of the S and D contacts through catalytic chemical vapor deposition. Prior to the CVD growth, we pattern micrometer-scale wells in a layer of PMMA covering the wafer to delineate catalyst regions. Catalyst nanoparticles suspended in solution are then spin-coated onto the wafer. The catalyst composition and method of preparation are the same as described in ref 24. As a last step before the CVD process, we lift off the PMMA, leaving behind well-defined catalyst islands on the source and drain contacts. During Received: January 14, 2011 Revised: March 31, 2011 Published: April 06, 2011 1946
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Figure 1. (a) Schematic of SWNT p-n diode device. The two buried gates Vg1,2 are biased with opposite voltages to create p- and n-doped regions along the nanotube. (b) SEM image of suspended SWNT in a p-n diode device. (c) Two IV curves of p-n diode devices. Open circles are data points; solid lines are fits to eq 1, the diode equation given in the text with a series resistance. Fitting parameters are I0 = 42 fA, n = 1.1, Rs = 20 MΩ (bottom) and I0 = 2.7 pA, n = 1.24, Rs =120 MΩ (top). (d) Band diagram of p-n diode showing regions doped from split gate biases (red solid circles are electrons, blue are holes), and formation of heterointerfaces between doped and suspended (undoped) portion L of a SWNT. For a symmetrically doped diode, each doped region contributes I0/2 to leakage current due to diffusion of minority carriers, np and pn. In region L, the optical transition E11 creates the lowest excitons with binding energy EB. Band bending at CNT interface with source and drain is due to Schottky contact between nanotube and metal leads. Ea is the activation energy, measured by heating the diode in increments. Eg is the intrinsic nanotube band gap and EBGR is the renormalized band gap. Δ denotes the band gap shrinkage in the doped regions, compared to the undoped region, due to band gap renormalization. EFp and EFn are the quasi-Fermi levels in the p- and n-doped regions, respectively.
chemical vapor deposition with methane as the precursor carbon nanotubes grow out of the catalyst nanoclusters on these islands. As Kong et al. have shown, the large majority of nanotubes synthesized by this approach are individual SWNT with some of them bridging the islands where catalyst nanoparticles had been deposited.24 We similarly find that a number of nanotubes grown in this fashion bridge the S and D contacts to form devices like the one sketched in Figure 1a. As previously demonstrated, electrostatic doping of the nanotubes produces p-n junction diodes.7 We fabricate many devices this way, a portion with a single semiconducting SWNT bridging S and D. Figure 1b shows a scanning electron microscopy (SEM) image of such a device. Figure 1c shows typical IV curves with the split gates biased in a diode configuration (Vg1 = Vg2 = þ5 V) along with a fit to the diode equation25 IDS ¼ I0 ðeqVDS =nkB T 1Þ
ð1Þ
where IDS and VDS are the current and voltage across the junction, respectively, I0 is the reverse-bias saturation current, q is the electron charge, n is the ideality factor, kB is Boltzman’s constant, and T is the absolute temperature. For an ideal diode n is precisely 1, but it can be as large as 2. The value of the ideality factor depends on the nature of the electronhole generation and recombination mechanism and can depend on voltage.25 In fitting the data to eq 1, we include a series resistance (Rs) to
account for the contact resistance between the nanotube and the source and drain metals. As Figure 1c shows, contact resistance for our devices can be relatively high, for example, 20 and 120 MΩ for each of the two devices, respectively, whose IV curves are depicted in that graph. Variations in contact resistance, however, have no impact on our conclusions since Rs affects the bending of the IV curve in the forward bias region for high bias. We measure the diode leakage current I0 by fitting our data to eq 1 in the reverse bias region for low bias. Thus the value of I0 is independent of the magnitude of Rs. Variations in contact resistance have no impact on the positions of the SWNT exciton peaks, either, which we discuss later. The origin of the ideal diode behavior in carbon nanotube p-n structures has been previously described.26 Briefly, the reversebias characteristics of an ideal diode are either the result of direct band-to-band generation of electronhole pairs in the field region L, or of diffusion of minority carriers (np and pn) from the doped p and n regions as shown in Figure 1d. The first mechanism would require a dependence of the reverse-bias saturation current on the value of L. As Figure 3c shows, however, the leakage current in our diodes with n 1.2. Green solid line shows typical values of the band gap Eg calculated using the reported scaling (Eg = 1.53 E11) for the E11 range measured in our devices. Arrows indicate y-axis that corresponds to each curve. (b) E11 resonances of four different nanotubes. E11 peak shifts to larger values as I0 is reduced. For clarity of comparison, photocurrent IPC here is normalized to incident photon flux and to IPC value at E11 peak. The leakage current of each diode that showed the indicated E11 transition is noted on top of each peak. (c) Diode leakage current as a function of length of suspended (undoped) portion L of the nanotube for all devices in (a) with n < 1.2. Data, grouped by similar I0, show there is no dependence of I0 on L. (d) Kataura plot shows first two excitonic transitions for semiconducting nanotubes. It includes theoretical data (green solid circles) and experimental data (black open circles) previously reported.23 It also includes experimental data added from our results (red open circles); the rectangle highlights the diameter range with the new data.
As Figure 3a,b shows, we find a strong correlation between the leakage current of our p-n diodes and the E11 peak. For the devices with ideality factor n < 1.2, our data show that the diode leakage current decreases exponentially with E11. (We discuss later why the devices with n > 1.2 do not follow this trend.) This trend is expected since both E11 and the band gap energy (Eg) are inversely proportional to nanotube diameter.18,34 In Figure 1d, Eg is defined as the sum of E11 and the exciton binding energy (EB). Comparing our data relating I0 to E11 and our doping density to those previously reported in refs 15 and 26 leads us to adopt the scaling for E11 and Eg quoted in that previous work. As that earlier work shows, these scaling relations are empirically derived as the best fits for a wide range of experimental data relating nanotube diameter (in the 12 nm range) to Eg and E11. Eg was obtained by measuring the onset of the continuum, and nanotube diameter was assigned using a Kataura plot based on measured E11 and E22 transitions. These values refer to the intrinsic (undoped) region of the nanotube, which we relate to I0. For the diameter range of the nanotubes we grow, these values are E11 = γ/dt and Eg= δ/dt, (dt in nm) with γ = 1.01 eV and δ = 1.55 eV,15 which are close to theoretical calculations.1620 This also implies the following relationship between the band gap and the first exciton level Eg = (δ/γ)E11.
From fitting our data for devices with n < 1.2 (Figure 3a), we obtain the following relationship between the diode leakage current and E11 I0 ¼ ReβE11
ð2Þ
where R and β are fitting parameters with R = 1.8 103 Å and β = 33.89 eV1. As we will see later, β depends on doping and temperature and is related to the renormalized band gap. It is related to temperature in the usual way: β = χ/kBT where χ = 0.88. Thus the leakage current scales with an activation energy that is less than the lowest exciton level E11 by the factor χ. This is consistent with the conclusions of ref 26 but it is examined differently here by relating the activation energy to E11. Later in this article we relate χ to a more fundamental parameter, the band gap shrinkage. Now from eq 2 and the scaling of E11 we reported earlier, we arrive at the following empirically derived relationship between the diode leakage current and nanotube diameter dt = βγ/ln(I0/R) To test our result, we calculated the nanotube diameters for six devices using the equation above and compared them with the diameters we had previously assigned using the measured E11 and E22 peaks from the photocurrent spectra and the Kataura plot. 1949
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Table 1. Nanotube Diameter Dependence on Diode Leakage Current device
I0 (A)
E11 (eV)
E22 (eV)
1
7.98 1012
0.599
1.027
2
2.92 1012
0.595
1.150
3
1.76 1012
0.628
1.146
4
8.17 1013
0.699
1.226
5
4.68 1014
0.663
6
4.46 1014
0.697
ωRBM (cm-1)
1.9 ( 0.1 136.24
154.07 1.145
The measured (assigned) and calculated diameters matched within (2 Å. The deviation between assigned and calculated diameters tends to be larger for smaller nanotubes because we do not account for family corrections.34 The results are summarized in Table 1. As the table shows, in two cases we were able to obtain the nanotube radial breathing mode in the Raman spectra and to corroborate the dt we had assigned (using the PC spectra) by crosschecking it against the measured ωRBM. For these two nanotubes, we observed ωRBM only when we resonantly excited them with a 633 nm laser within about 1 μm of the SWNT location. We used the relation provided in ref 22 for similar suspended nanotubes in air to relate ωRBM to nanotube diameter: ωRBM = 204/dt þ 27 cm1. The assigned diameters using ωRBM are given in the table in parentheses; the additional significant figures in this case are intended to further distinguish these values for dt from those where no ωRBM was obtained. We also want to note here that the most recent version of the Kataura plot23 does not include measurements in the nanotube diameter range of our devices. As Figure 3d shows, our measurements make an addition to the experimental data included in the Kataura diagram. Similarly, using the scaling quoted earlier for Eg, we arrive at the following relation between I0 and the nanotube band gap: Eg = (δ/βγ)ln(I0/R). This leads us to the conclusion that the diode leakage current of SWNT p-n structures is a measure of the intrisinc nanotube band gap. Figure 3a shows typical values of the band gap for the range of E11 values measured in our experiments. As we already pointed out, our data show that devices with an ideality factor n > 1.2 do not follow the trend eq 2 describes. On the basis of the SchockleyHallRead phenomenological theory,35,36 even with a significant BGR as we include here, we expect that the diode characteristics can be altered by localized states within the energy band gap that serve as generation and recombination centers. We can only speculate about the origin of such trap states, noting that adsorbents onto the nanotube surface can be one reason for their appearance.27,28 Such band gap states cause n to be much larger than its ideal value of 1, and for the diode characteristics, including the leakage current, to substantially diverge from ideal behavior. For example, we calculate n = 2 when the electronhole generation and recombination mechanism is completely mediated by states near the middle of the band gap.25 In our diodes, the ideality factor can be as large as 2. Figure 3a shows that for nanotubes with similar band gap, that is, nanotubes with similar E11 energy, those with n > 1.2 show greater I0 than expected for nearly ideal diode behavior due to enhanced generation and recombination of carriers from band gap states. Now we need to address the following point. How is it possible for the diode leakage current, which depends on the diffusion of minority carriers from the doped regions of the nanotube, to
dt assigned (nm)
dt calculated (nm) 1.8
1.8 ( 0.1 (1.758)
1.7
1.7 ( 0.1
1.6
1.5 ( 0.1
1.6
1.6 ( 0.1 (1.606)
1.4
1.6 ( 0.1
1.4
be a measure of the fundamental band gap of the nanotube, that is, of the band gap in the undoped area? In an ideal diode we would expect I0 to be a measure of the renormalized band gap (EBGR), the band gap in the doped regions, which, as we pointed out earlier, is much smaller than the fundamental band gap, due to BGR. According to ref 37, however, the E11 peak in a quasi 1D semiconducting wire, like a carbon nanotube, is expected to be nearly constant with carrier density. This is true because the renormalization of the fundamental band gap is of the same order as, or it is canceled by, the renormalization of the exciton binding energy (since E11 = Eg EB). A similar inference can be made from ref 10. Therefore, we conclude that I0 scales not only with the renormalized band gap but also with the fundamental band gap, the central result of our work. In fact, the scaling of I0 with E11, expressed by eq 2, which we derived by analyzing our experimental data, can be inferred qualitatively by using the results of first-principles calculations examining BGR in 1D quantum wires.37,38 According to ref 38, the band gap shrinkage (Δ) can be normalized to E11 to give a doping-dependent but diameter-independent parameter (Δ/E11 = η). From Figure 1d, we can see that the activation energy Ea can be written as Ea = EBGRþ (EV EFp). Using the scaling of Eg with E11 reported earlier, and the fact that EBGR = Eg Δ, we can rewrite the last equation as Ea = [(δ/γ) η]E11 þ (EV EFp). Now the diode leakage current scales with Ea through an Arrheneous relationship.25 Therefore, I0 ∼ eEa/kBT = e(EV EFp)/kBTe{[δ/γ) η]/kBT} 3 E11. This is qualitatively the same scaling relationship as that expressed by eq 2, assuming the term e(EV EFp)/kBT has a very small dependence on nanotube diameter, which would also explain the scatter of our data shown in Figure 3a. If we then compare the scaling of I0 that we just derived with eq 2, we find η = 0.65((0.03). This means that the band gap shrinkage is Δ = η(δ/γ1)Eg = 0.43((0.03)Eg, confirming the significant band gap renormalization we expect from both theoretical calculations and experimental results. When we normalize the band gap shrinkage to the exciton binding energy we find Δ/EB = 1.23((0.03), a value similar to that reported in ref 10 and 37 for the same doping density. This ratio is directly related to η and is an additional confirmation of the large band gap shrinkage we expect. We note that a different doping density would produce a different set of data relating I0 to E11 and a different scaling behavior because BGR depends on doping density. To summarize, we have shown that the leakage current I0 of nearly ideal p-n diodes formed with semiconducting singlewalled carbon nanotubes can be tuned to a large degree in the fabrication process. We have also demonstrated that I0, a directly measurable parameter, can be used to measure the nanotube band gap by relating it to the first exciton level. Relating I0 to both the fundamental and renormalized band gaps is the central result of our work. Our conclusions have confirmed the large band gap 1950
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Nano Letters reduction due to band gap renormalization that theoretical calculations predict, and our analysis has provided an estimate of that band gap shrinkage. In the process, we have also made an addition to the Kataura plot in a nanotube diameter range where until now no experimental data had been reported to our knowledge.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by a National Science Foundation Grant (EPDT-0823715) and a Defense Threat Reduction Agency Grant (HDTRA1-10-1-0016). ’ REFERENCES
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