Semiconducting Carbon Nanotubes Research Articles

Interface States in Gate Stack of Carbon Nanotube Array Transistors.

A deep understanding of the interface states in metal-oxide-semiconductor (MOS) structures is the premise of improving the gate stack quality, which sets the foundation for building field-effect transistors (FETs) with high performance and high reliability. Although MOSFETs built on aligned semiconducting carbon nanotube (A-CNT) arrays have been considered ideal energy-efficient successors to commercial silicon (Si) transistors, research on the interface states of A-CNT MOS devices, let alone their optimization, is lacking. Here, we fabricate MOS capacitors based on an A-CNT array with a well-designed layout and accurately measure the capacitance-voltage and conductance-voltage (C-V and G-V) data. Then, the gate electrostatics and the physical origins of interface states are systematically analyzed and revealed. In particular, targeted improvement of gate dielectric growth in the A-CNT MOS device contributes to suppressing the interface state density (Dit) to 6.1 × 1011 cm-2 eV-1, which is a record for CNT- or low-dimensional semiconductors-based MOSFETs, boosting a record transconductance (gm) of 2.42 mS/μm and an on-off ratio of 105. Further decreasing Dit below 1 × 1011 cm-2 eV-1 is necessary for A-CNT MOSFETs to achieve the expected high energy efficiency.

Interface States in Gate Stack of Carbon Nanotube Array Transistors.

A deep understanding of the interface states in metal-oxide-semiconductor (MOS) structures is the premise of improving the gate stack quality, which sets the foundation for building field-effect transistors (FETs) with high performance and high reliability. Although MOSFETs built on aligned semiconducting carbon nanotube (A-CNT) arrays have been considered ideal energy-efficient successors to commercial silicon (Si) transistors, research on the interface states of A-CNT MOS devices, let alone their optimization, is lacking. Here, we fabricate MOS capacitors based on an A-CNT array with a well-designed layout and accurately measure the capacitance-voltage and conductance-voltage (C-V and G-V) data. Then, the gate electrostatics and the physical origins of interface states are systematically analyzed and revealed. In particular, targeted improvement of gate dielectric growth in the A-CNT MOS device contributes to suppressing the interface state density (Dit) to 6.1 × 1011 cm-2 eV-1, which is a record for CNT- or low-dimensional semiconductors-based MOSFETs, boosting a record transconductance (gm) of 2.42 mS/μm and an on-off ratio of 105. Further decreasing Dit below 1 × 1011 cm-2 eV-1 is necessary for A-CNT MOSFETs to achieve the expected high energy efficiency.

Label-Free and Ultrasensitive Detection of Cartilage Acidic Protein 1 in Osteoarthritis Using a Single-Walled Carbon Nanotube Field-Effect Transistor Biosensor.

Osteoarthritis (OA), a prevalent degenerative joint disease, significantly affects the well-being of afflicted individuals and compromises the standard functionality of human joints. The emerging biomarker, Cartilage acidic protein 1 (CRTAC1), intricately associates with OA initiation and serves as a prognostic indicator for the trajectory toward joint replacement. However, existing diagnostic methods for CRTAC1 are hampered by the limited abundance, thus restricting the precision and specificity. Herein, a novel approach utilizing a single-walled carbon nanotube field-effect transistor (SWCNTs FET) biosensor is reported for the direct label-free detection of CRTAC1. High-purity semiconducting carbon nanotube films, functionalized with antibodies of CRTAC1, provide excellent electrical and sensing properties. The SWCNTs FET biosensor exhibits high sensitivity, notable reproducibility, and a wide linear detection range (1 fg/mL to 100 ng/mL) for CRTAC1 with a theoretical limit of detection (LOD) of 0.2 fg/mL. Moreover, the SWCNTs FET biosensor is capable of directly detecting human serum samples, showing excellent sensing performance in differentiating clinical samples from OA patients and healthy populations. Comparative analysis with traditional enzyme-linked immunosorbent assay (ELISA) reveals that the proposed biosensor demonstrates faster detection speeds, higher sensitivity/accuracy, and lower errors, indicating high potential for the early OA diagnosis. Furthermore, the SWCNTs FET biosensor has good scalability for the combined diagnosis and measurement of multiple disease markers, thereby significantly expanding the application of SWCNTs FETs in biosensing and clinical diagnostics.

Molecular transport enhancement in pure metallic carbon nanotube porins.

Nanofluidic channels impose extreme confinement on water and ions, giving rise to unusual transport phenomena strongly dependent on the interactions at the channel-wall interface. Yet how the electronic properties of the nanofluidic channels influence transport efficiency remains largely unexplored. Here we measure transport through the inner pores of sub-1 nm metallic and semiconducting carbon nanotube porins. We find that water and proton transport are enhanced in metallic nanotubes over semiconducting nanotubes, whereas ion transport is largely insensitive to the nanotube bandgap value. Molecular simulations using polarizable force fields highlight the contributions of the anisotropic polarizability tensor of the carbon nanotubes to the ion-nanotube interactions and the water friction coefficient. We also describe the origin of the proton transport enhancement in metallic nanotubes using deep neural network molecular dynamics simulations. These results emphasize the complex role of the electronic properties of nanofluidic channels in modulating transport under extreme nanoscale confinement.

Onset of spin entanglement in doped carbon nanotubes studied by EPR.

Nanoscale semiconductors with isolated spin impurities have been touted as promising materials for their potential use at the intersection of quantum, spin, and information technologies. Electron paramagnetic resonance (EPR) studies of spins in semiconducting carbon nanotubes have overwhelmingly focused on spins more strongly localized by sp3-type lattice defects. However, the creation of such impurities is irreversible and requires specific reactions to generate them. Shallow charge impurities, on the other hand, are more readily and widely produced by simple redox chemistry, but have not yet been investigated for their spin properties. Here, we use EPR to study p-doped (6,5) semiconducting single-wall carbon nanotubes (s-SWNTs) and elucidate the role of impurity-impurity interactions in conjunction with exchange and correlation effects for the spin behavior of this material. A quantitative comparison of the EPR signals with phenomenological modeling combined with configuration interaction electronic structure calculations of impurity pairs shows that orbital overlap, combined with exchange and correlation effects, causes the EPR signal to disappear due to spin entanglement for doping levels corresponding to impurity spacings of 14nm (at 30K). This transition is predicted to shift to higher doping levels with increasing temperature and to lower levels with increasing screening, providing an opportunity for improved spin control in doped s-SWNTs.

System of metastable volume-localized electronic states in positively charged semiconductor single-wall carbon nanotubes

The volume-localized electronic states (SAMOs) with a maximum of their electron wave functions located in the cavity of nanomaterials have been experimentally and theoretically demonstrated in a fullerene. The existence of SAMOs in single-wall carbon nanotubes (SWCNTs) was also predicted theoretically. In the present paper, these volume states in semiconductor SWCNTs were theoretically investigated using numerical quantum modeling based on density functional theory (DFT). It is shown that the well appears in the center of the tube, whose depth increases with increasing positive charge, since the total potential of a positively charged structure can be represented as the sum of the Coulomb potential and the potential of the atoms of the tube wall. In this context, in addition to the well-studied surface-localized states, states localized in the volume of the cylinder also occur. Using the components of the electric transition dipole moment, the lifetime of the volume states was preliminarily estimated in comparison to the lifetime of the ordinary surface states.

Diagnostics of Tuberculosis with Single-Walled Carbon Nanotube-Based Field-Effect Transistors.

Tuberculosis (TB) is still threatening millions of people's lives, especially in developing countries. One of the major factors contributing to the ongoing epidemic of TB is the lack of a fast, efficient, and inexpensive diagnostic strategy. In this work, we developed a semiconducting single-walled carbon nanotube (SWCNT)-based field-effect transistor (FET) device functionalized with anti-Mycobacterium tuberculosis antigen 85B antibody (Ab85B) to detect the major M. tuberculosis-secreted antigen 85B (Ag85B). Through optimizing the device fabrication process by evaluating the mass of the antibody and the concentration of the gating electrolyte, our Ab85B-SWCNT FET devices achieved the detection of the Ag85B spiked in phosphate-buffered saline (calibration samples) with a limit of detection (LOD) of 0.05 fg/mL. This SWCNT FET biosensor also showed good sensing performance in biological matrices including artificial sputum and can identify Ag85B in serum after introducing bovine serum albumin (BSA) into the blocking layer. Furthermore, our BSA-blocked Ab85B-SWCNT FET devices can distinguish between TB-positive and -negative clinical samples, promising the application of SWCNT FET devices in point-of-care TB diagnostics. Moreover, the robustness of this SWCNT-based biosensor to the TB diagnosis in blood serum was enhanced by blocking SWCNT devices directly with a glutaraldehyde cross-linked BSA layer, enabling future applications of these SWCNT-based biosensors in clinical testing.

Removal of conjugated polymer on carbon nanotube array by dry process

With the progress in the purity and alignment of semiconductor carbon nanotubes (CNTs), how to efficiently remove the conjugated polymers twining round CNTs has become an important and urgent matter for the further development of CNT electronics. The removal of conjugated polymers (CPs) by wet cleaning will inevitably lead to the destruction of the morphology of aligned CNT array films, which will cause the monolayered CNTs to form agglomeration or stacking. Therefore, it is necessary to develop a dry method to remove CPs on the aligned CNT films. In this work, we studied the thermal decomposition characteristics of CNTs and CPs in detail, and found that the ratio of the oxidative decomposition rate of CNTs and CPs could reach up to 35.7 in the oxygen environment at 450 °C. The transmission electron microscopes (TEMs) show that such a dry treatment process can effectively remove the polymer on CNTs without affecting the morphology of CNT arrays. The Raman spectrum show that ratio of G/D of the annealed sample is as high as 41.8, which indicates that the CNTs are not detectable damaged during the annealed process. The fabricated field-effect transistors (FETs) with a length of 2 μm exhibit a current on/off ratio higher than 104 and a current density higher than 660 μA/μm, which further justifies that the CNT arrays treated by the dry method exhibit high quality.

Improving Carbon Nanotube-Based Radiofrequency Field-Effect Transistors by the Device Architecture and Doping Process.

The semiconducting carbon nanotube (CNT) has been considered a promising candidate for future radiofrequency (RF) electronics due to its excellent electrical properties of high mobility and small capacitance. After decades of development, great progress has been achieved on CNT-based RF field-effect transistors (FETs). However, almost all elevations are owing to advancement of the CNT materials and fabrication process, while the study of device architecture is seldom considered and reported. In this work, we innovatively combined device architecture and related doping processes to further optimize CNT-based RF FETs by guiding process or materials with collaborative optimization for the first time and explore their effect on device performance carefully and statistically. Based on more mature random-oriented CNT materials, we fabricated CNT-based RF FETs having three different gate positions of device architecture variation accompanied by suitable doping schemes. The optimized FETs obtained 2-3 times of current density (transconductance) and 1.3 times the cutoff frequency and maximum oscillation frequency compared with unoptimized devices at the same channel length. After transistor-level verification of effect, we further built a CNT RF amplifier and demonstrated almost 10 dB of transducer gain improvement operating at 8 GHz for X-band application. The achieved results from this work would help further improve CNT RF performance beyond the materials and process point of view.

Assembly and Alignment of High Packing Density Carbon Nanotube Arrays Using Lithographically Defined Microscopic Water Features.

High packing density aligned arrays of semiconducting carbon nanotubes (CNTs) are required for many electronics applications. Past work has shown that the accumulation of CNTs at a water-solvent interface can drive array self-assembly. Previously, the confining interface was a large-area, macroscopic feature. Here, we report on the CNT assembly on microscopic water features. Water microdroplets are formed on 10-100 μm wide hydrophilic stripes patterned on a substrate. Exposure to CNTs dispersed in solvent accumulates CNTs at the microdroplet-solvent interface, driving their alignment and deposition at the microdroplet-solvent-substrate contact line. Compared with macroscopic methods in which the contact line uncontrollably moves across the substrate as it is pulled out of the liquids, the hydrophilic patterns and microdroplets allow pinning of the contact line. As CNTs deposit, the contact line self-translates, allowing for dense CNT packing. We realize monolayer CNT arrays aligned within ±3.9° at density of 250 μm-1 and field effect transistors with a high current density of 1.9 mA μm-1 and transconductance of 1.2 mS μm-1 at -0.6 V drain bias and 60 nm channel length.

Semiconducting Carbon Nanotubes with Light‐Driven Gating Behaviors in Phototransistor Memory Utilizing an N‐Type Conjugated Polymer Sorting

Semiconducting single‐walled carbon nanotubes (s‐SWNTs) have arisen a growing interest in field‐effect transistors (FETs) due to their advantages, such as lower fabrication temperature, flexibility, and solution processing applicability, compared to traditional silicon‐based FETs. In this study, diversifying the functionality of s‐SWNT‐based FETs is focused on, particularly emphasizing their use in nonvolatile photomemory applications. By selectively wrapping s‐SWNT with n‐type conjugated polymers (CPs), electron‐trapping and photoresponsive capabilities are endowed in the device. After optimizing the structure and aggregating behavior of n‐type CPs, a favorable supramolecular network comprising s‐SWNT and CPs is formed and applied in phototransistor memory. Accordingly, the device exhibits a high memory ratio and window of 105 and 75.7 V, representing its remarkable charge‐storage capabilities. In addition, the device demonstrates decent long‐term stability over 104 s and multilevel memory behavior driven by the varied gate bias or accumulated light‐gating periods. The proposed memory mechanism involves electrical writing and photoerasing processes with the existence of n‐type CPs on s‐SWNT, revealing the underlying principles of charge transfer between their heterojunction interfaces. Herein, this research contributes to developing advanced phototransistor memory, offering a promising avenue for future electronic applications.

Femtosecond pulse shaper built into a prism compressor.

We present a frequency domain, AOM-based pulse shaper that utilizes Brewster prisms rather than the current standard of gratings. In doing so, we demonstrate a three-fold increase in efficiency and the ability to compensate for temporal dispersion created by the acousto-optic modulator that filters the pulse spectrum. The shaper is tested between the wavelengths of 520-660 and 840-1170 nm, creating sub-50 fs pulses for each, and used to collect a 2D white-light spectrum of a thin film of semiconducting carbon nanotubes.

Excitation Energy Transfer via Electron Transfer between a Semi‐Conducting Single Walled‐Carbon Nanotube and Encapsulated Zinc Porphyrin or Photovoltaic Application

AbstractIn this paper, the encapsulating effect of single molecule of zinc porphyrin (Zn−P) inside semiconducting single walled carbon nanotubes (NT17) on the stability and optoelectronic properties of organic solar cells is investigated, assuming that this nano‐hybrid system will serve as the active layer in solar cell device. Making use of density functional theory (DFT), we looked at the optoelectronic characteristics of the isolated Zn−P molecules as well as two different configurations of the hybrid system that has a single Zn−P molecule inserted into NT17 (Zn−P@NT17 and Zn−P2@NT17). The addition of a zinc atom at the core of a porphyrin molecule results in the emergence of novel electronic and chemical characteristics, leading to distinct behavior compared to a free‐base porphyrin. These distinctions hold substantial implications for a range of applications, encompassing catalysis, sensing, and energy conversion processes. According to the study's outcomes, a charge transfer (CT) between the Zn−P molecules and the NT17 nanotube caused the structure to remain stable, and assuming to the electronic and optical computations the CT in Zn−P@NT17 hybrid nanosystems has been identified, along with its orientation. The results show that type II heterojunctions on filled semiconducting carbon nanotubes are likely to make them a viable choice for charge and light transport in the active layer, which can help create filled NT‐based OSCs that are extremely efficient.

(Invited) Aligning Dense Arrays of Semiconducting Carbon Nanotubes for Logic and RF Technologies

Semiconductors are materials with electrical conductivity that can be switched on and off, that have allowed for nearly all electronics. However, most semiconductor devices utilize silicon, a microelectronics technology more half a century old. Silicon is now being extended to its limit and cannot meet the needs of next-generation devices.Carbon nanotubes are nanoscale semiconducting wires that conduct more electricity per area than silicon and more rapidly switch between on and off states with less voltage, making them ideal for next-generation fast, low-energy logic and high-speed, linear RF devices. However, no one has yet been able create a process for employing nanotubes commercially. In raw form, nanotubes are disordered and tangled and thus do not conduct electricity well. For nanotubes to be most useful, they must be lined up in the same direction in a single layer so that electricity can rapidly and efficiently travel through them. This has been a long-standing roadblock.This talk will present recent discoveries at the University of Wisconsin on (1) purifying and aligning semiconducting nanotubes into massively parallel arrays and (2) the research and development of semiconducting carbon nanotubes for logic and radio frequency technologies. We have pioneered nanotube array fabrication technologies that enable the (a) partial alignment of nanotubes (±30˚) via shear (demonstrated 100 mm wafer-scale); (b) finer alignment (±6˚) at liquid-liquid interfaces (demonstrated 100 mm size-scale); and, (c) the selected-area deposition of nanotube arrays (±7˚) in lithographically-defined patterns combining topographical and chemical features (demonstrated 25 mm size-scale). Most recently, we have discovered a powerful new mechanism for driving the self-assembly of nanotubes into aligned arrays, by coaxing them to form two-dimensional liquid-crystals. We have uncovered that when nanotubes are segregated to liquid-liquid interfaces, mesogenic interactions cause them to self-align (within +/-5.7 degrees so far) and self-assemble into dense arrays (> 100 per micron) like those needed for microelectronics. The assembled nanotubes are easily integrated on silicon substrates at room-temperature and integrated into high-performance devices.APL (2014); ACS Nano (2014); Science Advances (2016); Langmuir (2017); Adv Elect Materials (2019); Science Advances (2021); Nanoscale Advances (2021); JAP (2022). Highlights by Bloomberg News https://youtu.be/VsUF_CBJq50 (2022); US Patent 10,873,026; US Patent 10,074,819; US Patent 9,673,399.

Advances in separation of monochiral semiconducting carbon nanotubes and the application in electronics

For over half a century, traditional silicon-based integrated circuits (ICs) have been the basis of computational electronics and are widely used in computers, cell phones, and other fields. With the rapid development of human society, silicon-based semiconductor technology is approaching its physical and engineering limits. Our increasing diversity of non-traditional computing needs, such as ultra-small, ultra-fast, ultra-low-power wearables, and space radiation protection, is driving the search for new electronic materials. Semiconducting single-walled carbon nanotubes (s-SWCNTs) have many excellent electrical properties, such as high carrier mobility and high ballistic transport, making them strong candidates for new semiconductor materials in the post-Moore era. Carbon-based electronic technology has been developed for over 20 years, and the fundamental issues such as the material purification of s-SWCNTs, preparation prospects of s-SWCNT-based field-effect transistors (CNT FETs), and device physics based on CNT FETs have been basically solved. However, the chiral diversity of s-SWCNTs may lead to problems such as fluctuations in the electrical performance of CNT FETs, limiting the application of s-SWCNTs in high-end ICs. Monochiral s-SWCNTs not only have excellent electrical properties but also have a controllable structure and uniformity, which are crucial for the high-end IC of CNTs. However, some problems exist in the purity and yield of monochiral s-SWCNT preparation and the optimization of monochiral CNT FETs. Therefore, the chiral sorting of CNTs is reviewed in this paper, and the progress of polymer reprocessing in chiral separation is highlighted. Then, the research progress of monochiral CNT FETs is introduced, and possible development directions are summarized and analyzed. Finally, the application prospects of chiral-enriched s-SWCNTs include challenges and future opportunities.

High-performance thin-film transistors based on aligned carbon nanotubes for mini- and micro-LED displays

Inorganic mini-LEDs (mLEDs) and micro-LEDs (μLEDs) have ultrahigh luminance and long lifetimes, and are challenging liquid crystal displays (LCDs) and organic light-emitting diode (OLED) displays for next-generation displays. Backplane thin-film transistors (TFTs) for mLED/μLED displays with high mobility and large driving current are under development as currently widely used backplane active materials such as crystalline silicon (CMOS Si), amorphous silicon (a-Si), low-temperature polycrystalline silicon (LTPS), and metal oxides are facing difficulties to meet the requirements. Semiconducting carbon nanotubes (s-CNTs) have long been considered as promising materials for TFTs because of their unique electronic properties. However, TFTs based on s-CNT random networks show inadequate performance due to large amounts of inter-tube junctions. Here, we report high performance TFTs based on wafer-scale, high-density aligned s-CNT array (A-CNT) for mLED/μLED driving backplanes. These A-CNT TFTs with micrometer scale channel length were fabricated using standard semiconductor manufacturing process, and exhibited mobility as high as 160 cm2/Vs and driving current as large as 417 μA/μm at operation voltage of ∼3 V, exceeding commercially available TFTs with similar device sizes. In addition, these A-CNT TFTs have demonstrated good driving capability for commercial mLEDs in a one-transistor-one-diode (1T1D) pixel circuit configuration, and been capable of driving commercially available mLED/μLED displays. Moreover, a prototype display with 2 × 2 mLED array have been demonstrated with full control of each pixel, manifesting the great potential for A-CNT TFT technology for backplane of mLED/μLED displays.

Current density in a nonlinear medium of carbon nanotubes under the action of diffraction free laser pulses

Based on the spatial distribution of the electric field strength of diffraction-free extremely short Bessel and Airy–Bessel optical pulses, patterns of the temporal evolution of the current density in a nonlinear array of semiconductor carbon nanotubes with a spatial modulation of the refractive index are constructed. The dependences of the maximum value of the current density on the modulation parameters of the refractive index of the medium are established.

Influence of Laser Intensity and Location of the Fermi Level on Tunneling Processes for High-Harmonic Generation in Arrayed Semiconducting Carbon Nanotubes

Influence of Laser Intensity and Location of the Fermi Level on Tunneling Processes for High-Harmonic Generation in Arrayed Semiconducting Carbon Nanotubes

Monodispersed semiconducting SWNTs significantly enhanced the thermoelectric performance of regioregular poly(3-dodecylthiophene) films

The improved thermoelectric (TE) properties of conducting polymers are generally achieved through the use of single-walled carbon nanotubes (SWNTs) as additives. However, their aggregation and aggregation-induced over-loading of SWNTs generally result in high thermal and low electrical conductivity. Herein, sc-SWNTs were selectively captured by regioregular poly(3-dodecylthiophene)(rr-P3DDT) in a toluene solution containing a semiconducting and metallic carbon nanotubes mixture (mix-SWNTs) to achieve rr-P3DDT films with monodispersed semiconducting SWNTs (rr-P3DDT/sc-SWNT). The single sc-SWNTs were tightly wrapped by a rr-P3DDT layer with a thickness of several nanometers, which was orderly aligned at the micrometer scale. The large number of rr-P3DDT/sc-SWNT nanointerfaces present in composite films contributed to increasing carrier mobility through π–π conjugation while reducing the thermal conductivity via phonon scattering. Thus, the rr-P3DDT/sc-SWNT films had significantly higher electrical conductivity and lower thermal than the rr-P3DDT/mix-SWNT composite films. Both the electrical conductivity and Seebeck coefficient of the rr-P3DDT/sc-SWNT composite films were much greater than the calculated values using the parallel connected mixture model. The maximum ZT value of the rr-P3DDT/sc-SWNT composite film was 0.1, approximately 18 times greater compared to the rr-P3DDT/mix-SWNT films and among the highest for the polymer/carbon nanotube composites. This work provides a convenient but efficient method to maximize the TE properties of conducting polymers.

Optimization of the Spray-Deposited Carbon Nanotube Semiconducting Channel for Electrolyte-Gated Field-Effect Transistor-Based Biosensing Applications

Electrochemical biosensors are widely investigated as they represent attractive analytical tools for detection of a broad range of bio-molecules, thanks to their simplicity, high sensitivity and short response time. Especially, biosensors employing an electrolyte-gated field-effect transistors (EG-FETs) as electrochemical transduction element have gained increasing interest, due to the signal amplification and the intrinsic low voltage range of operation. In this work we report the fabrication of flexible EG-FETs using spray-deposited semiconducting carbon nanotubes (CNTs), with a specific focus on the optimization of the CNT channel to optimize the performance of the resulting CNT-based EG-FET (EG-CNTFET). The transfer and the output characteristic of different devices with varying spraying parameters were tested, finding out that only devices with source-drain resistance of about ≤10 kΩ showed proper EG-CNTFET operation: for these devices we recorded a typical p-type behavior with an on–off ratio of 214 A/A up to 469 A/A (depending on number of the spray-deposited CNT layers). The fabricated EG-CNTFETs were functionalized with anti-spermidine antibodies to detect polyamine spermidine - a well-known chemical indicator of food quality. To ensure controlled immobilization and at the same time to preserve the electrical properties of the nanotubes, the spray-deposited films were modified with a bifunctional molecule, which attaches to the CNT via non-covalent π - π interactions and leaves a free NHS-ester group for amide coupling of the antibodies. The fabricated EG-CNTFET-based immunosensors showed a linear detection range for spermidine from 10-3 to 102 nM, with the sensitivities ranging from -1.03 to -2.45 μA/decade.