Dielectric Dependent Absorption Characteristics in CNFET Infrared Phototransistor

. In future infrared photodetectors, single-walled carbon nanotubes (SWCNTs) are considered as potential candidates due to their band gap, high absorption coefficient (10 4 - 10 5 cm − 1 ), high charge carrier mobility and ease of processability. The SWCNT based Field Effect Transistors (CNFETs) are being seriously considered for applications in optoelectronics. In the proposed work optically controlled back gated CNFET is modeled in Sentaurus TCAD to observe the impact of high dielectric oxides on its photo absorption. The model is based on analytical approximations and parameters extracted from quantum mechanical simulations of the device and depending on the nanotube diameter and the different gate oxide materials. Small deviation in SWCNT chirality shows significant change (more than 50 %) in channel current. Transfer characteristics of the device are analyzed under dark and illuminated conditions. CNFET integrated with HfO 2 dielectrics exhibits superior performance with a significant rise in photocurrent current. Precise two dimensional TCAD simulation results and visual figures affirm that the ON state performance of CNFET has significant dependency on the dielectric strength as well as width of the gate oxide and its application in enhancing the performance of carbon nanotube based infrared photo detectors.


Introduction
Infrared photodetectors can be used for a variety of applications in the military, security, medical, industrial, and telecommunication areas. Photo devices' flexibility and broadening the photosensitive spectral range with low cost are foreseen to be the fundamental areas in promoting the relevancy of IR photodetectors [1]. Amongst the various preferred detector materials for infrared light, SWCNTs are being seriously considered as one of the potential candidates due to its outstanding electrical, optical, thermal, and mechanical properties. Researchers have demonstrated that SWCNTs show strong absorption in the IR (≈10 5 cm −1 ), [2, and 3] due to high charge carrier mobility, 1D structure, and high aspect ratio of SWCNT. In particular, SWCNT based planar photoconductors devices are one of the important research areas in recent years due to their customizable electronics properties and 2D architecture. Also the same existing CMOS structure can be reused in SWCNT based phototransistors due to their compatibility with conventional MOSFETs, potentially enabling their on-chip integration, and multifunctional optoelectronics. SWCNT acts as the channel in CNFET and is responsible for transport mechanisms. Still the performance of infra-red SWCNT phototransistors has thus far been inferior compared to other IR photodetectors regardless of their potential [2,4]. One of the main reasons for CNFET's low performance can be attributed to relatively low dielectric and larger thickness of SiO2 gate oxide. Steep switching between ON and OFF states for CNFET can be attained by the incorporation of thin high dielectrics gate oxide. High dielectric gate oxides and SWCNT channel interface develops with reduced dangling bonds and hence do not degrade the carrier mobility in the SWCNT channel. [5] In this proposed work, the possible impact of high-κ gate dielectric HfO2 on CNFET phototransistor is studied through TCAD simulation. The distinctive features of the CNFET device with high dielectric HfO2 gate oxide are observed and measured with those of a CNFET with low dielectric SiO2 gate oxide in terms of output characteristics and responsivity. In this simulation approach; the 2D CNFET model is implemented including the principles of calculation of SWCNT charge, which is responsible for the current transportation. This charge developed on the SWCNT surface is due to the potential across SWCNT which is responsible for channel band alterations [6]. The CNFET model considers SWCNTs with different diameter and channel length. This model is valid as long as the active channel SWCNT in CNFET phototransistor is behaving as semiconducting.

A. Optical Properties of SWCNT
SWCNTs are tiny, hollow cylinders constructed by rolling up a 2D graphene sheet. Ch around rollup vector in the graphene sheet and describes how the sheet is rolled up to form SWCNTs with varying diameter and different electronics properties. Depending on the chirality of the graphene cylinder, SWCNT diameter can be varied and SWCNTs results in semiconducting and metallic tubes shown in figure 1(a). Chirality vector, Ch with (n, m) defines diameter, bandgap, and the threshold voltage of SWCNT. Figure 1(b) indicates the presence of more than a few sub-bands with all energy bands having their maxima or minima at the same K points, indicates that nanotubes are unique material with direct bandgap. Such direct bandgap semiconducting SWCNTs due to their strong light absorption and fast light response over a broadband can be used in wide optoelectronics applications. However, with reduced dimensionality in SWCNTs many-body effects dominate the light absorption. The most significant body effects amongst various optical properties are excitons, which are electronhole pairs easily formed with much larger Columbic interaction energies. As seen in figure 1(b), photoexcited electrons in SWCNT can be directly excited from valence bands to conduction bands for energies larger than its bandgap. But in the presence of excitons in semiconducting SWCNTs the optical absorption spectrum is completely altered; each band to band transition gives a series of sharp excitonic peaks. Free electrons and holes may be produced in lower subbands via excitations of excitons to higher energy subbands, followed by decaying to lower energy subbands to become free electrons and holes. In the first sub-band, excitons have large exciton binding energy, hence it is usually difficult for them to decay to become free carriers. As in photodetectors, external electric field or band bending due to doping are usually utilized to separate the photo carriers. In the excitonic picture, a larger electric field needs to be applied to disassociate the excitons into a free electron and hole [2].

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B. Phototransistor Structure Figure 2. Back Gated CNFET structure with High Dielectric HfO2 gate insulation Schematic for the proposed back gated CNFET structure is shown in figure 2. The CNFET structure is of the standard back gated MOSFET with n doped SWCNT as an active channel. Chiral numbers (n, m) which describe the different SWCNTs is responsible for its electronic properties.
(1) a1 and a2 are the unit vectors along the unit cell in 2D graphene sheet. Chiral vector Ch is the linear combination of lattice vectors a1 and a2 with m and n as integer indices [8]. In SWCNT, its diameter and bandgap are dependent on chiral indices and hence calculated with the help of (n, m) [9]. SWCNT diameter is derived by a is the distance between neighboring carbon atoms and its value is 0.142 nm [9]. Bandgap in SWCNT is dependent on its diameter [10] and is calculated as: Vppπ is the carbon π-π bond energy with value 3.033 eV [11].
The transport mechanism in SWCNT which is dependent on the intrinsic charge carrier concentration can be calculated as [11]: D(E) , f(E) represents the density of states, Fermi-Dirac distribution in SWCNT respectively. D(E) and f(E) values are calculated using equations (5) and (6): EC is the conduction band energy. The density of state value is calculated for the first sub-band only since in SWCNTs the contributions of next level sub-bands is negligible.
T is the operating temperature, K is the Boltzmann constant, and EF is the first sub-band Fermi level value in SWCNT. Substituting (5) and (6) in (4) Channel current calculation is done using an expression in equation 9 [12].
In intrinsic SWCNT Fermi levels are zero on the source and drain side. By introducing n-type doping in SWCNT, the nature of CNFET is affected, and hence current along the channel also changes accordingly. Shift in Fermi level, EF due to doping is given as [11]: N represents the amount of doping concentration. VS, VD be the source, drain bias respectively then the channel current IDS is calculated using the Launder Equation as [15]: h is Planck's constant and q is the electronic charge. Ψ (0) and 0 is the surface potential on the top and bottom of SWCNT.

III. Sentaurus TCAD Modeling and Simulation
Technology computer-aided design (TCAD) is a well-established discipline and optimization technique used in electronic device simulation in the market [14].

A. CNFET Model
All the required set dimensions of the device are listed in the table I.

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Following it, to develop the simulation model, an ordered description of the statements loaded in sde_dve.cmd file and region-wise doping styles and doping concentration are defined and listed in Table II.   The electrical properties of CNFET are based on the simultaneous solution of various partial differential equations. During the device simulation calculation of these equations is done at the locations of intersection points in the mesh defined across various regions of CNFET shown in figure 4. As seen in figure 4, an active layer is defined with more dense mesh to obtain optimized simulation results considering the speed and accuracy of TCAD software. The complete 2D CNFET structure established in SDE tool is shown in figure 5, without any physical model applied to it. Therefore to carry out the CNFET simulation further, the SDEVICE tool is used for initializing appropriate physical and mathematical models across different regions in CNFET.

B. CNFET Simulation
2D numerical simulation of CNFET is carried out in TCAD to calculate electrical parameters. Simulator makes use of the Poisson's and drift-diffusion formulation discretized over a multidimensional numerical mesh [14]. The Coupled and Quasistationary commands are used to solve a set of equations and to ramp a solution from one boundary condition to another respectively. The Coupled command activates a Newton-like solver over a set of equations includes the Poisson equation, continuity, and the different thermal and energy equations [14]. The simulator solved these basic equations using the drift-diffusion model evaluating for the potential, hole, and electron concentration with appropriate assumptions and calculated the drain current at a specified gate bias. With our very small dimensions of CNFET; some quantum modification items are added to the simulation for results to be closer to the real condition [15,16]. Optical generation is computed using the transfer matrix method (TMM) which is based on the propagation of plane waves through layered media in CNFET. Shockley-Read-Hall (SRH) and Auger recombination with doping dependence is used to calculate recombination during the simulation.

IV. Simulation Results
Optical generation in CNFET is activated by illuminating from the top using a monochromatic light source whose spectral range varied from 600 nm to 1550 nm. The TMM optical solver requires the use of the complex refractive index model, and various excitation variables, all such excitation variables specified in TMM are listed in table 3 A. Gate Voltage Dependence Figure 6 presents the plots for the photocurrent under the different bias conditions for CNFET under dark and illumination. It shows that drain current increases with the increase in illumination. This is because with the illumination a forward biasing potential is developed across the SWCNT active layer

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which increases the channel potential. Also, the photosensitivity of CNFET is highly dependent on the bias voltage, from the plot it can be seen that both photocurrent and dark current is increasing with the increasing bias voltage.

B. Channel thickness Dependence
Channel thickness is dependent on the diameter of SWCNT as shown in equations 1 and 2. For the CNFET simulation different zig-zag SWCNTs are used and tabulated in Table IV.  Transfer characteristics between the input voltage Vgs and the output drain current Ids are derived for constant Vds = 0.01 V. The simulation result for both CNFET's with 100 nm channel length is shown in figure 7. Drain current is increasing with the input voltage Vgs. It is observed from the above plot that SWCNT provides high channel mobility so automatically current increases and linearity are more. But drain current is decreasing with growing tube diameter since in SWCNT the bandgap is inversely proportional to its diameter and responsible for reduced carriers across the active channel.

C. Gate Oxide Dependence
The relatively low dielectric oxide such as SiO2 brings limitations for its use as a gate oxide in scaled CNFETs due to high leakage current. With high dielectric gate oxides small thickness deposition is possible and hence allows efficient charge injection into an active channel reducing leakage current. This has further motivated me to explore the integration of high-κ films (~20-30) as gate oxide. The dielectric materials considered for gate oxide during the simulation are listed in table 5. Gate oxide dielectric material-dependent output characteristics of the CNFET are shown in Figure 8, where the thickness of the gate insulator is kept 10 nm.  The results are obtained for the ramping gate bias Vgs from 0 to 5 V while keeping the drain bias Vds fixed at 0.01 V. Figure 8 shows the Ids-Vgs characteristics in CNFET for SiO2 and HfO2 gate oxide materials. For the relative dielectric constant of 3.9, the drain current in the CNFET is 10 μA at Vgs = 3V. For the high dielectric constant, the drain current increases to 0.388 μA. This rise in the drain current is because of high dielectric HfO2 oxide. Sheikh Ziauddin Ahmed et al found that with a more than 50 % rise in ON current when HfO2 is used as the gate dielectric [7]. This justifies our results obtained by Sentaurus TCAD simulation software. For SiO2 dielectrics, to obtain an electrostatic coupling capacitance approaching the quantum capacitance of an SWCNT, an ultra-thin 1-2 nm SiO2 layer is required since in SWCNT, the electrostatic coupling capacitance logarithmically depends on thickness. But the thin SiO2 dielectric causes significant leakage currents, a major transistor scaling trouble.

D. Current Variation at various wavelengths
Figures 9 and 10 depict the variation of current Ids with voltage Vds for the low and high dielectric gate oxide at various wavelengths showing that both models are wavelength insensitive till 500 nm. A prominent decrease in Ids is observed when frequency increases from 1000 nm to 1550 nm because of minority carrier lifetime.  Table VI shows the comparison for Ids at various wavelengths for the developed model with the reference model [2]. It shows that the optically generated current for the model developed is comparable to the reference model for the same dimensions and optical illumination. Through careful optimization of CNFET structure by the use of compact models in Sentaurus TCAD, the impact of the gate oxide dielectric strength on optical generation in CNFET is examined under varied illumination conditions. It has been observed that high dielectric HfO2 reduces leakage current and significantly improves the output current. CNFET with HfO2 shows an improved performance compared to SiO2 with an incremental increase of 50 % under the same operating conditions. Input as well as output current characteristics of CNFET photodetector show that the drain current is sensitive to SWCNT thickness and biasing. It has been observed that output dark and illuminated drain current decreases for the increasing SWCNT thickness. Results obtained from the TCAD simulation of CNFET photodetector are encouraging. It is predicted that TCAD simulation might have the possibility to use to model the material SWCNT and thus CNFET phototransistors for analysis and consequently saving the actual production time and cost. CNFET phototransistor performance can be further improved by optimizing the trap densities at the heterojunction between channel and oxide layer.