Letter pubs.acs.org/NanoLett
Length Scaling of Carbon Nanotube Electric and Photo Diodes down to Sub-50 nm Haitao Xu, Sheng Wang, Zhiyong Zhang, and Lian-Mao Peng* Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China S Supporting Information *
ABSTRACT: Carbon nanotubes (CNTs) are promising candidates for future optoelectronics and logic circuits.1−3 Sub-10 nm channel length CNT transistors have been demonstrated with superb performance.4 Yet, the scaling of CNT p−n diodes or photodiodes, basic elements for most optoelectronic devices, is held back on a scale of micrometers.5−8 Here, we demonstrate that CNT diodes fabricated via a dopant-free technique show good rectifying characteristics and photovoltaic response even when the channel length is scaled to sub-50 nm. By making a trade-off between performance and size, a diode with both channel length and contact width around 100 nm, fabricated on a CNT with a small diameter (d ∼ 1.2 nm), shows a photovoltage of 0.24 V and a fill factor of up to 60%. Study on the dependence of turn-on voltage on scaled channel length reveals transferred charges induced potential barrier at the contact in long channel diodes and the effect of self-adjusting charge distribution. This effect could be utilized for realizing stable and high performance sub-100 nm pitch CNT diodes. As elementary building blocks, such tiny electric and photodiodes could be used in nanoscale rectifiers, photodetectors, light sources, and high-efficiency photovoltaic devices. KEYWORDS: carbon nanotube, diode, photodiode, nanophotonics
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Figure 1a, where Sc and Pd electrodes are asymmetrically contacted to a semiconducting single-wall CNT (SWNT) grown on an n+ silicon/SiO2 substrate using chemical vapor deposition (CVD) method.18 Here, p-region and n-region are formed automatically by charge transfer from the metal contacts, with the region near the Pd contact being hole-rich and the region near the Sc contact being electron rich. Ohmic contacts are achieved for both Pd and Sc contacts with a semiconducting SWNT of moderate diameter, which is crucial for the high performance of the device.15 In addition, the intrinsic properties of the semiconducting SWNT are little compromised in this relatively simple fabrication process, during which no dopants or scatters are intentionally introduced into the systems. The scanning electron microscope (SEM) image of Figure 1b shows a typical 100 nm pitch diode, with both channel length and contact width being about 50 nm. A typical rectifying diode current−voltage (I−V) characteristic is observed in dark at room temperature (Figure 1c). The diameter of the SWNT used here is about 1.5 nm with a bandgap of about 0.47 eV (Figure S1c, Supporting Information). No sign of reverse bias breakdown is observed at an electric field around105 V/cm. Considering the high
ransistors and p−n diodes are the most elementary building blocks for modern information processing and communication systems. The miniaturization of the diodes, however, falls far behind that of transistors, becoming a bottleneck in miniaturizing optoelectronic devices, such as light emitting diodes (LEDs), photodetectors, and solar cells, and remains a challenge for integrated electronic and photonic circuits.9,10 Emerging nanomaterials such as carbon nanotubes (CNTs), raise the hope of solving this dilemma, breaking the limit set by conventional semiconductors. CNTs are not only excellent electronic materials for logic applications11,12 but also promising for applications in photonics and optoelectronics.3 In particular, CNTs offer a perfect platform where electronic and optoelectronic technology may be most conveniently combined together to form a more efficient integrated system. To date, though theoretical work forecasted nanoscale channel length nanotube p−n diodes,13,14 experimentally fabricated devices either through split-gate modulation5 or chemical doping7 generally have a channel of micrometers long, showing no advantage over silicon diodes on size scaling. In this work, sub-100 nm pitch CNT diodes with scaled channel length and contact width are fabricated via a dopingfree technique.15 Although high-performance LEDs and room temperature infrared photodetectors were fabricated previously using this technique,16,17 demonstrated device size was typically of the order of micrometer and scaling behavior of the CNT diodes was not explored. The device structure is depicted in © XXXX American Chemical Society
Received: July 6, 2014 Revised: July 31, 2014
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Figure 1. SWNT photodiodes with 100 nm pitch. (a) Schematic device structure of a SWNT photodiode with asymmetric contacts. PMMA is coated as a protective layer to improve its stability. (b) False-colored scanning electron microscope image showing a 100 nm pitch CNT diode with L ≈ Lc ≈ 50 nm. The scale bar is 200 nm. (c) Experimental and fitted I−V rectifying characteristics of the 100 nm pitch diode in the dark and (d) I− V characteristic under illumination at room temperature with a light intensity of 25 KW/cm2. The wavelength of the laser is 785 nm.
current carrying capacity and thermal conductivity of CNTs,19 such doping free CNT diodes are expected to be excellent nanoscale rectifiers, capable of enduring larger forward current (either maximum average forward current or peak recurrent forward current) and reduced irreversible reverse breakdown caused by excessive heat compared to conventional diodes. This type of diode is also a good choice for high frequency applications due to its high carrier mobility and dopant free channel. The I−V characteristic of the diode may be described by a modified diode equation I=
⎧ ⎡ q(V − IR ) ⎤ ⎫ V − IR s s + Is⎨exp⎢ ⎥ − 1⎬ ⎦ R sh nkT ⎩ ⎣ ⎭
causes reverse breakdown and introduces defects that lead to undesirable scattering and recombination in transport and photoelectric processes. A similar situation also exists in semiconducting nanowire based photovoltaic devices, where additional surface states induced scattering and recombination makes the situation even more complex.21,22 One promising application of CNT photodiodes would be in complementary metal oxide semiconductor (CMOS) image sensors. Compared to charge-coupled device (CCD), CMOS image sensors offer many advantages, such as low power consumption, low cost, on-chip circuitry, and miniaturization, mostly benefiting from their compatibility with standard CMOS technology and scaling behavior.23 Thus, shrinking of the pixel size is crucial to the further development of CMOS image sensors as well as to achieve high spatial resolution. However, in silicon CMOS image sensors, smaller pixels typically result in larger pixel cross-talk, smaller dynamic range and lower pixel sensitivity, which put a lower limit of the pixel size.24−26 CNT photodiodes may have advantages in these aspects. The pixel cross talk is a phenomenon wherein the photons intended to be detected for one pixel get detected by another pixel nearby. The primary pixel cross-talk in silicon CMOS image sensors results from the fact that photogenerated carriers may diffuse in the silicon layer (with respect to the wavelength of incident photons, the carriers are generated with different depth) and get collected by neighboring pixel.25,27 However, in CNT photodiodes, because of the ultrathin body of the CNT and the doping-free fabrication technique used, such pixel cross-talk will not happen. The small diameter of SWNTs will also contributes to the high spatial resolution of the image sensors.28,29
(1)
where Is is the reverse saturation current, Rs is the effective series resistance of the device, Rsh is the shunt resistance, q is the electron charge, k is the Boltzmann constant, T is temperature, and n denotes the ideality factor of the diode. By fitting Figure 1c using eq 1, an ideality factor of n = 1.14 is obtained, which is very close to the ideal value n = 1, indicating little defect and negligible recombination in the channel.20 When illuminated, the device shown in Figure 1b yields an evident photocurrent of 1.12 nA and photovoltage of 0.15 V (Figure 1d), and to our knowledge, this is the smallest photodiode (with a pitch size of 100 nm) reported to date. This small diode can be fabricated in a controllable and repeatable manner. For conventional semiconductors and usual fabrication procedure, such a small photodiode size is impossible to realize. This is because the size of a conventional p−n diode is largely limited by the depletion width which is typically of the size of micrometer in a semiconductor. Although heavy doping may reduce the depletion region width and thus diode size, it also B
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Figure 2. Contact width and channel length scaling of CNT diodes. (a) I−V characteristics of illuminated carbon nanotube diodes with contact width of 60 nm (blue), 100 nm (orange), and 200 nm (green). The channel length is fixed to be around 100 nm. (b) I−V characteristics of illuminated carbon nanotube diodes with channel length of 50 nm (blue), 100 nm (orange), and 200 nm (green). The contact width is fixed to be around 500 nm. (c) I−V characteristic of a carbon nanotube diode with L ≈ Lc ≈ 100 nm under illumination. The incident power is about 25 KW/ cm2. (d) I−V characteristics of a single photovoltaic cell and a photovoltaic module consisting of three cells connected in series via virtual contacts. The channel length of the single cell is about 50 nm. In the inset is a false-colored SEM image showing the CNT triple cells. The scale bar is 200 nm.
resistance has a very weak influence on both the photocurrent and photovoltage until it is very large.33,34 The extracted series resistance of CNT diodes with Lc = 60 nm and Lc = 100 nm are around 92 and 211 KΩ, respectively. The fill factor is found to sensitively depend on the series resistance, which increased from 49% to 60% when the contact width is increased from 60 to 100 nm (Table 1).33,34
Wide dynamic range is another merit of CNT photodiodes. Dynamic range characterize the ability of light sensors to work under low illumination up to high illumination. Carbon− carbon bonds in CNTs are the most stable covalent bond in nature, which could sustain high illumination and high temperature. On the other hand, CNT diodes have very small dark current and therefore a low noise level.30 The absence of dopants in the channel further improves the stability and signal to noise ratio of CNT diodes. Experimentally, a wide dynamic range of 80 dB has been observed and CNT photodiodes have been shown to work well under a light intensity of 90 KW/cm2 with good linearity and no sign of saturation.17,31 Pixel sensitivity is crucial for image quality in CMOS image sensors. The basic parameter for characterizing pixel sensitivity is the product of pixel fill factor and quantum efficiency, which could be reflected in the photocurrent.23 In silicon CMOS image sensors, smaller absorption area generally results in weaker signal and lower pixel sensitivity. The dependence of photocurrent and photovoltage on the diode size, in fact, is not obvious in CNT photodiodes, and a careful study is carried out here with varying contact width Lc and channel length L (as defined in Figure 1a). The effect of contact width is mainly manifested as the contact resistance. When scaled below the transfer length (typically around 100 nm for Pd contact), a reduction of contact width would remarkably increase the contact resistance.32 In the short channel CNT diode, the contact resistance is roughly the series resistance. The I−V characteristics of illuminated CNT photodiodes with scaled contact width are shown in Figure 2a. By increasing the contact width from 60 to 100 and 200 nm, the photocurrent and photovoltage are little changed. This is because the series
Table 1. Performance of CNT Diodes with Varying Contact Widtha
a
Lc (nm)
Iph (nA)
Voc (V)
FF
60 nm 100 nm 200 nm
1.41 1.08 1.49
0.244 0.238 0.246
0.49 0.60 0.56
dCNT ∼ 1.2 nm.
A weak dependence of the photocurrent on channel length is also observed. In principle, the longer the diode, the more photons would be absorbed. But for a longer channel, the separation of photogenerated carriers would be less effective than in a short channel because the build-in field is reduced. The exciton interactions will also be enhanced in shorter channel devices, which in turn would contribute to an increase of photocurrent.35 In addition, recombination in the contact region by minority carriers also affects the photocurrent and photovoltage. This recombination rate is largely determined by charge distribution near the contact, where a bandgap narrowing effect would play an important role and ultimately determine the photovoltage obtained.36−38 Although intrinsic processes are complicated, the experimentally obtained photocurrent and photovoltage do not depend sensitively on the C
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Figure 3. Scaling behavior of CNT diodes. (a) I−V rectifying characteristics of scaled CNT diodes with channel length scaling from 400 to 50 nm. The contact width is fixed to be 500 nm. The diameter of the SWNT used is around 1.2 nm. (b) I−V rectifying characteristic of a long channel diode with a channel length L = 400 nm, as shown in (a). A turn-on voltage of about 0.83 V is observed. (c) Dependence of the turn-on voltages on channel length. (d) Turn-on voltages for short channel diodes with 50 nm < L < 100 nm. (e) Depicted energy band diagrams for long channel diodes under different gate voltages and with a large forward bias being applied. (f) Corresponding transfer characteristics of the carbon nanotube diodes as in (a).
channel length. A sub-50 nm photodiode still maintains its performance when compared to that of longer diodes, with an acceptable small photovoltage drop (Figure 2b). To better understand the intrinsic behavior of the diodes, a careful study on the dark I−V characteristics is carried out (see Supporting Information). The extracted shunt resistance is reduced when the channel length is reduced to 50 nm (Supporting Information Figure S12 and Table S3), which would cause a photovoltage drop. By making a trade-off between the photovoltaic performance and diode size, an optimized photodiode would be with both channel length and contact width of about 100 nm, and fabricated on a SWNT with a small diameter39 (Figure 2c). The diameter of the SWNT is about 1.2 nm (Figure S1a and S1b, Supporting Information). A photovoltage of 0.24 V is obtained (which is a large value for typical CNT diodes), and the corresponding fill factor of the diode is as high as 0.60. In an ideal case, the fill factor (FF) of a photodiode depends only on its open circuit voltage (Voc) via the relation33,34
FF =
Uoc − ln(Uoc + 0.72) Uoc + 1
(2)
where Uoc = Voc(q/nkT) and k, T, n, and q have their usual meaning as in eq 1. For Voc = 0.24 V and n = 1, the ideal fill factor is 0.68, which is very close to our experimental value of 0.60. The small deviation from the theoretical value is a result of the relatively large contact resistance for a single nanotube (limited by quantum resistance). The theoretical maximum open circuit voltage across the junction is about 0.28 V (see Supporting Information, Figure S13), just a little larger than the experimentally obtained 0.24 V. The power conversion efficiency η of this photodiode is about 0.48%, derived from the definition: η = (FF × ISc × VOC)/Pin, where Pin is the incident power. This value is comparable and somewhat larger than that obtained from single SWNT based diodes in previous work.31,36 The low value of η is a result of limited absorption of SWNT within this nanometer scale. By replacing the single SWNT with an aligned SWNT arrays of high density, both the D
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Figure 4. Self-adjusting charge distribution and effect on CNT diodes. (a) I−V characteristics of CNT diodes with scaled channel length: L = 50, 100, and 400 nm. The contact width is fixed to be 500 nm. In the inset is a schematic diagram illustrating charge transfer from metal contacts into CNT channel, forming an electron-rich region at the Sc contact and hole-rich region at the Pd contact. (b) Simulation results based on a simple model on profiles of charge distribution, built-in electric field, and built-in potential along the CNT diode channel with asymmetric contacts. (c) Simulated built-in electric field along the channel for scaled channel lengths. (d) Simulation derived built-in potential (Vbi) and experimentally obtained turn-on voltage versus channel length (L). The dashed line of the simulated Vbi indicates that for L < 50 nm, the model used is not valid.
fill factor and the efficiency could be improved due to reduced contact resistance and enhanced light absorption. Although the photovoltage of a single diode is not large, efficient photovoltage multiplication can be achieved by using virtual contacts.31 The inset of Figure 2d shows a SEM image of a triple cell with two virtual contacts (L = 1000 nm). As a result, the photovoltage is increased from 0.14 V for a single cell (L = 50 nm) without virtual contact to 0.56 V for the triple cell, and the fill factor sequentially increases from 0.40 to 0.47. In principle, the size of the cascade module could be further scaled, so that more cells could be connected in series to obtain larger photovoltage within limited size. This is appreciated both in solar cell and photodetector applications. Additionally, efficient multiple electron−hole pair generation was demonstrated in CNT devices,6 and photothermal-electric effect was shown to be prominent,29,40 which might be utilized to capture hot electrons to further improve the solar cell efficiency, with a possibility of pushing it beyond the Shockley−Queisser limit. So far, CNT photodiodes fabricated via the doping-free approach have demonstrated remarkable performance, but some important questions remain unanswered. These questions include what is the intrinsic behavior for these diodes, and what is their experimental scaling limit. To clarify these issues, study on channel length scaling is performed on a single semiconducting SWNT, the same one as that used in Figure 2c, with channel length being scaled from 400 nm down to 50 nm (Figure 3a). The turn-on voltage of the device shows a strong dependence on the channel length for long channel diodes (with L > 100 nm) but approaches a stable value around 0.53 V when L < 100 nm (Figures 3c and 3d). Note that for the long channel diode with L = 400 nm, the turn-on voltage is about 0.83 V (Figure 3b). This value is indeed much larger than that
expected from the bandgap of the SWNT (Eg ∼ (0.7/d) eV ∼ 0.58 eV), and this is unexpected. For a conventional semiconductor based p−n junction diode, the turn-on voltage is smaller than its built-in potential, which in turn is smaller than that related to the band gap. This unexpected large turnon voltage may be attributed to an extra potential barrier at the contact region, which may in turn be ascribed to the band bending caused by the transferred electrons and holes-induced electric field (Figure 3e). It should be noted that when subjected to a bias on the back-gate, this potential barrier may be easily tuned by the gate voltage. The turn-on voltage therefore depends sensitively on gate voltages for long channel diodes as shown in Supporting Information Figure S3a. In general, we may divide the transfer characteristic of a diode into three regimes: the off-state region, the transition region and the on state region (Supporting Information Figure S3b). In an ideal situation, a long channel diode should be biased slightly off the transition region into the on state region (e.g., with Vg > Vth) so that the barrier, for example, Φn near the Sc contact, for the injection of electrons into the channel is reduced below zero. The height of the extra potential barrier (ϕn and ϕp, as depicted in Figure 3e) is in the range between 80 to 95 meV for the CNT used here, with a detailed discussion presented in Supporting Information (Figure S2). Although the turn-on voltage reduces with decreasing channel length, the minimum current (the off-state current, see Figure 3f) in the transfer characteristics increases by orders of magnitude when the channel length is scaled from 400 nm to 50 nm. This observation suggests that the potential barrier for carrier injection into the channel is significantly lowered when the diodes is shorted to, say L < 100 nm for this nanotube. This phenomenon may be attributed to the redistribution of E
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For long channel diodes with L ≫ 1/k, the Coulomb interaction between the electrons transferred from the Sc contact and holes from the Pd contact is weak and has little influence on the charge distribution profile near these contacts. But when the channel is short enough with L ∼ 1/k, the electrons and holes in each end of the diode begin to be attracted toward each other by the Coulomb interaction. As a result, more charges will be transferred to the carbon nanotube channel, resulting in a strengthened “doping”, and broadened distribution width. In other words, both Np and w are tend to increase significantly when the channel length is aggressively scaled down. To a good approximation, the relation may be expressed as Np ∼ (1/ln(1 + 10d)), w ∼ (1/350√d) (Supporting Information Figure S5a and S5b). On the contrary, with symmetric contacts, charges transferred from the contacts are of the same type and exclude each other when extremely scaled. As a result, “doping” in the channel would be weakened, and a lower inverse subthreshold slope than expected would be obtained.4 Figure 4b shows in arbitrary units resulting charge distribution, electric field and built-in potential profiles from our model calculations. With decreased channel length, the built-in electric field is greatly enhanced in the channel (Figure 4c). What we are most concerned with is the dependence of built-in potential on scaled channel length, as shown in Figure 4d. The simulated built-in potential does not change much for L > 50 nm, and this is consistent with experimentally obtained turn-on voltage dependence on scaled channel length (Figure 4d). It appears that this simplified model describes the intrinsic behavior of such dopant-free diodes quite well (more experimental results are presented in Supporting Information Figure S6). Further scaling down causes a dramatic reduction of the built-in potential and tunneling would easily occur, resulting in reverse breakdown. Supporting Information Figure S8e shows a set of CNT diodes with channel lengths scaled below 50 nm. The 50 nm diode still maintains a good rectifying characteristic. Then, reverse breakdown happens when scaled to 30 nm, as a result of strengthened tunneling at the compressed and thinned band structure. Further scaling to 20 nm, the diode fails to establish a solid built-in potential any more. In such short diodes, transferred electrons and holes might encounter and recombine in the channel. It becomes even more complicated when taking into account the bandgap narrowing effect, which may play a more important or even dominating role in this case. A modified model is needed to better describe this situation. It should also be noted that a quasiballistic transport is approached for the 50 nm CNT channel shown in Figure 4a, where a current of larger than 25 μA is observed which is higher than the maximum current limited by optical-phonon scattering in CNTs. Simple calculation reveals that the series resistance of the diode is about 19.8 kΩ at room temperature which is about three times the quantum resistance (6.5 kΩ). Such efficient carrier injection and quasiballistic transport would be greatly appreciated in high efficiency optoelectronic devices. In summary, excellent photovoltaic characteristics are observed in SWNT diodes with sub-100 nm pitch. Optimized photovoltaic characteristics are realized with a fill factor of 0.6 for a diode fabricated on a SWNT with a small diameter d ≈ 1.2 nm, and the same contact width and channel length of 100 nm. By introducing virtual contacts, both open circuit voltage and fill factor can be improved. For a triple cell, the photovoltage is increased from 0.14 to 0.56 V and the fill factor from 0.40 to 0.47. In principle, the performance of the diode may be further
transferred electrons and holes from contacts in the channel, which in a way is similar to the effect of gate tuning (e.g., comparing Figure 3a and Supporting Information Figure S3a). This charge redistribution also leads to a compressed band profile for short channel diodes which leads to enhanced tunneling in the off-state region and reduced turn-on voltage. Figure 3d shows some statistical results on the turn-on voltage for six short channel diodes with 50 nm < L < 100 nm, and all these devices are fabricated on the same CNT. The corresponding rectifying I−V characteristics and transfer characteristics are shown in Supporting Information Figure S4. For all these short channel devices with very different transfer characteristics, the turn-on voltage is seen to remain a constant, which are not affected easily by gate voltage or other external factors, demonstrating better performance stability against long channel diodes. Under certain favorable conditions, the turn-on voltage of the CNT diode is largely determined by the built-in potential. Scaling behavior in this case is very different from that dominated by the extra potential barrier as discussed earlier. To demonstrate the difference, a new set of diodes is fabricated on a SWNT with a larger diameter than that shown in Figure 3 (the corresponding electronic characterizations are shown in Supporting Information Figure S1). Here, the long channel diodes work under an ideal condition, that is, off the current minimum region. Unlike that shown in Figure 3, the turn-on voltage of the CNT diodes shown in Figure 4a are hardly affected by the extra potential barrier for 50 nm < L < 400 nm (Figure 4a). Although in conventional silicon p−n diodes, the turn-on voltagedetermined by the built-in potentialhas a close connection with the depletion region width, both greatly depend on the doping level. This unexpected result for CNT diodes is attributed to the self-adjusting charge distribution effect in this type of dopant-free diodes, which is quite different from conventional p−n diodes where dopants are position and density fixed. Here, electron-rich and hole-rich regions are created near the contacts via charge transfer from the contacts instead of from thermal excitations of dopants in the channel. Using the Tomas−Fermi screening model, the distribution of the electrons or holes may be approximated as exponential profiles near the contact. The screened coulomb potential then follows the expression: ϕ(r) = (Q/4πεr)e−kr, where 1/k is defined as a characteristic screening length. In CNT, such screening effect is weakened for its reduced dimensionality. Considering the symmetric characteristics of electrons and holes in CNT, we consider only the p region for simplicity. The distribution of holes may be expressed as ρ(x) = Np exp (−(x + d/w)), −d < x < 0, as depicted in the inset in Figure 4a. Here, Np characterizes the “doping level”, that is, how many holes are transferred into the channel, w represents the distribution width of the transferred carriers, and d denotes half of the channel length. The boundary condition is set to be E(−d) = 0, V(−d) = 0. By solving the Poisson equation, we obtain the electric field and the built-in potential profiles in the channel E (x ) = −
Npw ⎛ ⎛ x + d ⎞ ⎞ ⎟ − 1⎟ ⎜exp⎜ − ⎠ w ⎠ εε0 ⎝ ⎝
−d
