(August 17, 2010) — Rohit Pathak, Acropolis Institute of Technology & Research, Indore, M. P., India and Satyadhar Joshi, Shri Vaishnav Institute of Technology & Science, Indore, M. P., India, have analyzed the effect of innovations in nanotechnology on wireless sensor networks (WSN) and have modeled carbon nanotube- (CNT) based sensor nodes from a device prospective. A WSN model has been programmed in Simulink-MATLAB and a library developed. Integration of CNT in WSN for various modules such as sensors, microprocessors, batteries etc has been shown. Also, average energy consumption for the system has been formulated and its reliability has been shown holistically. A proposition has been put forward on the changes needed in existing sensor node structure to improve its efficiency and to facilitate as well as enhance the assimilation of CNT based devices in a WSN. Finally we have commented on the challenges that exist in this technology and described the important factors that need to be considered for calculating reliability. This research will help in practical implementation of CNT based devices and analysis of their key effects on the WSN environment. The work has been executed on Simulink and Distributive Computing toolbox of MATLAB.

The proposal has been compared to the recent developments and past experimental results reported in this field. This attempt to derive the energy consumption and reliability implications will help in development of real devices using CNT, which is a major hurdle in bringing the success from lab to commercial market. Recent research in CNT has been used to model an energy efficient model which will also lead to the development CAD tools. Library for Reliability and Energy consumption includes analysis of various parts of a WSN system which is being constructed from CNT. Nano routing in a CNT system is also implemented with its dependencies.

Finally the computations were executed on a HPC setup and the model showed remarkable speedup.

The combination of recent technological advances in electronics, nanotechnology, wireless communications, computing, and networking has hastened the development of Wireless Sensor Networks (WSNs) technology. Since CNT remains the main technology that threatens the CMOS technology due to its immense interesting properties our work has been to realize where the technology stands and the results of energy and reliability modeling. Wireless Sensor and Actor Networks (WSANs) constitute an emerging and pervasive technology that is attracting increased interest for a wide range of applications. WSN see application in various areas like space research, biomedical engineering, military applications such as battlefield surveillance and the quest for making low power, reliable and cheap sensor nodes has been a prime focus in recent years.

Nanotechnology has enabled realization of low power devices such as MEMS devices and CNT based FETs [11-12]. CNT based sensors have shown many benefits over their past counterparts and are suitable candidates in this Nanotechnology driven age [24]. Nanotechnology uses the smallest unit of matter to engineer new materials and devices atom by atom, aiming at achieving superior properties and performance through atomic scale architecture. An improvement in techniques of Nanocharacterization and Nano-fabrication has helped us to pave the way to develop many novel materials that can be applied to various spheres of technology. For example the impact of Nanotechnology on Wireless Communications has been shown by Er. Ping Li in [14]. An Architecture of Quantum-Based Nano-sensor Node for Future Wireless Sensor Networks has been proposed in [10]. WSN with Biomedical Applications has been shown by Zachary Walker describing the importance of Middleware [22]. Miniature Acoustic Communication Subsystem Architecture for Underwater Wireless Sensor Networks has been proposed by Saunvit Pandya [33]. WSN architecture for the Wireless Health Mobile Bio-diagnostic System for physiological studies has been proposed [34]. In our previous work, we have shown Nano based WSN where the importance of CNT and MEMS technology in WSN has been shown [32]. WSN plays a very important role in the overall development of a developing nation, which is being felt in the recent years [4]. Also planetary sensing applications have been proposed in recent years [6]. In this paper we have proposed energy and reliability models for a CNT based WSN. The models were developed using Simulink and Distributive Computing Toolbox, which were tested on a HPC setup.

CNT sensors and nano processors

Research on carbon nanotubes is yielding many results in labs and many theories are being proposed, but many parallel work on areas like reliability, packaging and energy constrains in CNT devices are still not being explained. Realization of CNT based sensors devices can make them a suitable candidate for WSN sensor nodes. Functional CNT can lead to novel device application giving advantages of their unique properties [25]. We know that conductance of CNT depends on the rolling of the graphene sheet which in turn depends upon the chiral vector C_h as given by the equation

C_h =na¹ + ma² (1)

Here n and m are integers and a1, a2 are unit vectors in the bi-dimensional hexagonal lattice of the graphene sheet. The radius of the nanotube being

R = a₀(n² + m² + nm)^1/2 /2π (2)

This is most basics idea of CNT that is known to all. Mathematics of CNT and their latest paper in this regard has been discussed in later part of the work. Hence we can model a sensor dependent on the above parameters as follows:
1. Define m, n and calculate the radius required for the particular sensor as electronic structure
(energy band gap structure) depends on the integers m and n.
2. Take note of the impact of working temperature and environmental factors on the reactivity of
CNT like hydrogenation, oxygenation, NO₂, NH₃, CO, O₃ as studied in [24, 25].
3. Effect of elasticity, mechanical motions and effect of other adsorbent on CNT surface.
4. Predicting the reliability of the sensor.

Fig. 1. Interaction of CNT and other molecules.

We know that variations in current conductance properties of CNT make it a useful for detecting gas and chemicals. We can illustrate the variation of current vs. time in a CNT based sensor from the graphs in [24]. The special semiconducting properties of CNTs have been exposited that makes them a suitable candidate for the future development of Nano-processors and Nano-scale circuitry [28, 30-31]. Atashbar et al. [37] has asserted that SWNT (Single Wall Nanotube) based efficient gas sensor using SWNT functionalized with Sodium Dodecyl Sulfate improved the solubility of SWNT in DI water significantly. He proposes that this functionalization reduces the short range attraction forces by introducing repulsive forces of equal strength and this result in the alteration of structural, electronic, and mechanical properties of the nanotubes. We are aware that there is a change in conductance of CNT on absorption of CO, NH₃, CO, O₃ NO₂ and O₂ and other gases [24]. Jing Li [18] has proposed a unique and marketable way to develop Nano-scale chemical sensors with polymer-coated CNTs for selective chemical sensing in gas phase. But we need more exploration in coating and doping techniques for broad application coverage. Carbon Nanotube also sees its very important application in biosensors [9, 13]. The main challenge for any engineering application of CNT is its reliability and interconnects. The effect of various gases has on CNT is shown in Fig. 1.

Modeling of low-bias electronic transport in ballistic conductor. There are various models developed for calculating the conductance of CNT. In this section the most applicable model is stated from the literature which is then implemented to calculate the energy consumption and reliability analysis. We know that Electronic transport in ballistic conductors can be assumed as the sum of I_L and I_R the currents flowing right and left; this forms the basic model of calculating current in CNT based devices where it is capable of carrying high currents [1] 

(3)

(4)

Here D(E) is the density of states in units of (states/eV/nm), ν(E) is the electron velocity and f (E) is the Fermi function with Fermi levels E^FR in the right lead and E^LF in the left lead. These equations are simply expressing the fact that the current at energy E is the product of the number of charges ε D (E) f (E – E_F) and their velocity ν(E). This is the current through metallic CNTs which forms the basis of the WSN network based on CNT. The total sum of right and left current in a ballistic system is thus

(5)

The difference of the Fermi functions implies that most of the current will flow between the two Fermi levels. There are two generalizations of the above derivation that need to be considered when describing transport through real systems. The first is that in general there may be several modes that contribute to the current, and each mode will contribute one quantum of conductance. The second point is that, because of scattering processes in the conductor, the electron transmission probability may be less than unity. Putting this together gives the final expressions for the current

(6)

And the total conductance (including spin) is given as

(7)

Thus this part of the system is the observation for conducting CNTs now in our work we have worked on the reliability and energy consumption as shown classically in [1].

CNT sensors. Sensors are the most important applications of CNTs. The sensing mechanism and the charge transfer needs to be modeled for the sensor part of the wireless sensor network. Using the expression for the capacitance per unit length of a CNT we can obtain an expression for the maximum relative change in conductance [27].

(8)

At the other end of the spectrum, one can consider the impact of a single analyte on the nanotube conductance. Under the assumption that the transferred charge is delocalized over the entire channel length, we can estimate the relative change in conductance to be

(9)

The appearance of the channel length is made explicit in this expression. This equation relates the conductance with channel length so it is an important part of parameter. For detection of analytes of concentration c in a gas or liquid phase, it is useful to relate the surface coverage θ to the analyte concentration. This can be accomplished by considering equilibrium surface coverage with analyte binding energy E_b and analyte chemical potential in the gas or liquid μ. The partition function is then given by

(10)

Here zvib is the vibration contribution. The expression for the concentration dependence on the coverage can be combined with that for the threshold voltage shift, to obtain

(11)

Contacts and interconnect. The most important issue that is being talked about is contacts and interconnects in a CNT-based system. This research is also very useful for developing CNT based NOC which is an area of research for the near future. The presence of charge near the interface will change the electrostatic potential and hence the electrostatic potential in the semiconductor (z > 0) is calculated as [2]

(12)

The first term in this equation is the potential due to the image charge in the metal while the second and third terms arise from the charge in the semiconductor. This is the part which needs to be studied in light of reliability and energy consumption. Thus the electrostatic potential hence derived is

(13)

Thus we can see that V_bulk (z) is given above it where the potential attains a constant value at z>>q^-1 which is

(14)

Diode of CNT systems. Diode as we see is one of the main things that are used in the circuitry which is being shown in this part. Assuming that the band edge simple tracks the Fermi levels in the leas (i.e. far away from the junction), the diode physics of CNT is shown as [3]

(15)

(16)

Here E∞ _c is the energy of the conduction band edge on the n-type side far from the junction. As shown above it is the celebrated ideal diode equation describing rectifying behavior, except that here it was derived under the assumption of ballistic transport. This is important for considering the current in the diode part. I here is the celebrated ideal diode equation describing rectifying behavior, except that here it was derived under the assumption of ballistic transport.

Ohmic contacts and transistor. Temperature has been a major issue that needs to be taken in account. The temperature dependence of the ON state conductance also provides further evidence for the presence of ohmic contacts. Assuming perfect transmission through the contacts and the nanotube, the obtained temperature-dependent ON state conductance as [5]

(17)

Here Δ = EV − EF represents the position of the Fermi level in the valence band. The conductance G monotonically decreases with increasing temperature in agreement with the work done earlier. Thus, even in carbon nanotube field effect transistors without electron–phonon scattering it is expected that the conductance will decrease with increasing temperature, and can be reduced by as much as a factor of two at room temperature compared to its low- temperature value. Expression for conductance in a Schottky barrier nanotube transistors is [2, 7]

(18)

Here

(19)

Here t_ox is the gate oxide thickness. The much different physics behind the operation of Schottky barrier nanotube transistors has important implications on the scaling of various performances parameters with device dimensions. As discussed above, it was predicted that reducing the thickness of the gate insulator improves the sub threshold swing because it allows the gate to more effectively modulate the band-bending at the contact. Such a behavior has been verified experimentally by fabricating nanotube transistors with gate oxide thickness between 2 and 20nm. Thus this is the study of the CNT based transistor.

CNT electromechanical systems. Once the transmission probability is known for the relevant range of energies, the conductance is calculated from [3]

(20)

Here T_ij is transmission probability between bands i and j. This equation signifies the relations of bending vs change in conductance. Impact of bending causes change in bond length which causes change in conductance which is shown. For the metallic nanotubes, a band-gap opens around the Fermi level, and the conductance at the Fermi level follows the relation [26]

(21)

Model for power consumed in a CNT-based WSN

Contemporary work in computation of WSN reliability is pretty generalized and Nano-scale devices based WSN has not been the sole focus of the research done in this area. In our previous work we have shown that MEMS reliability can be calculated using HPC thus making their practical applications possible [38, 37]. Effects of the failure of sensor nodes are studied and no compromise data acquisition methods have been proposed in [21]. Requirement for sustained, reliable and fault-tolerant operations have been conferred and a solution has been proposed by Kaminska in [15]. In this regard, the reliability calculations by probabilistic graph models and algorithm have been demonstrated by Hosam M. F. Abo El Fotoh [17]. Reliability studies in respect to Common Cause Failures have been examined [20]. Modeling and evaluating the reliability of Wireless Sensor Networks as subject to common cause failure has been described in [18]. Data transport and the reliability of data transport protocols have been discussed in [19]. Thus if we can predict the cause of failure then we can modify the protocols in our system accordingly. In Nano domains the failure can be caused due to large number of problems and errors which needs to be modeled and predicted in advance. Ad hoc wireless architecture has been introduced by Kamiska in [15] for the sustainability of self-configuring Wireless Sensor Networks and the routing scheme forwards sensor data along fuzzy and intentionally redundant paths to provide for reliability and fault-tolerance has been proposed. In [23] Zhand Dingxing discusses coverage algorithm based on probability to evaluate point coverage. Reliability in Wireless Sensor Networks using Soft Sensing and Artificial Neural Network methodology has been demonstrated by Rubina Sultan [21]. Optimizing availability and reliability in Wireless Sensor Networks applications by the use of middle wares has been shown in [16]. Thus we need to develop middleware in accordance with the challenges that exist. The CNT memory developed is not considered in our model [29, 35].

Current consumed in all elements can be distributed as follows:
I_p = current in processor
I_s = current in sensor
I_d = current in diode
I _em =current in Electro mechanical CNT
I_dp = CNT diplay device if attached
I_con = Contact of metal and CNT
I_trs= current in transporting
Energy consumed in V₁² G₁ + V₂²G₂ + V₃² G₃ + V₄²G₄ + V₅²G₅

(also we need to take into account the Capacitance of the inter connects for the energy consumption:
G₁ is conductance in processor of FET based on CNT, here it’s a function of L (Length of nanotube) and energy consumed in capacitance:
G₂ is the conductance in sensor is also depended in L
G₃ diode does not depend on Length
G₄ current depends on deformation and bond length not L
G₅ It depends on L
G₆ does not depend on length; here capacitive effects may come into picture.
Thus total energy consumption is a function of L length of the tube, length of the sensor tube, length of the display tube
E = f (I, L₁, L₂, L₃, Number of contacts,)
(Assumed for diameter to be constant)

This can be done using MATLAB Distributive Computing Toolbox to calculate energy consumption at various temperatures so that we can model the circuit in the desired way. Using HPC needs to done in an optimum way by correct distribution of the jobs in the work load. Thus to calculate E we need the power of HPC to distribute the various parameters on an HPC setup because the system is complex. Capacitive effects on joining points or inter connects needs to be also taken in account which is ½ CV2. In most the cases it is can be considered in Diode and Contacts. If all of the system is just made of CNT then all the energy consumed in each part will be a function of CNTs parameter such. Our model results are done on HPC but an abstraction level function for overall consumption of the energy can be stated as

P= K₁e^-k 1 ^V (Energy used in circuit) + K₂1/2 CV² (Energy lost at interconnect) (22)

Fig. 2. Y axis X axis, P vs. V(applied) for a derieved CNT WSN system.

Fig. 3. Graph between Power Consumed vs. Voltage applied vs. Capacitance of the system.

First term is of energy used in circuitry and 2nd term is for the interconnects. The variations can be seen in the figure plotted with the help of derived equation in Fig. 2 and taking all 3 parameters with number of inter connects, current, power the variations are shown in Fig. 3. It can therefore be used in an abstraction way as the formulae above but for accurate calculations we need high computation power, which can be done. Thus using this equation we can calculate the energy consumed in a CNT based Wireless Sensor network. But reliability and performance of the Node in a CNT based Sensor Node depends on the Sensor, Nano-processor, Nano-battery sources. Thus we need to make appropriate changes in the middle ware and Operating System. The energy for such a system can be derived from a MEMS better-less system where energy is induced in transponders, recent proposals shows real prospectus of such a technology maturing [8].

Unified reliability model developed for nano WSN

Probability function density of the failure for the device can be calculated as follows:
f(t) is depended on frequency CNT device operate, electrostatic forces and electromagnetic forces it is subjected to, material which defines the strength of the device in various forms.
υ= frequency of operation, also the frequency of CNT antenna will have a part in the function
κ = stress it is subjected to, this is reaction RA and damping force as described earlier in case of a CNT mechanical sensors
η = viscosity of the medium (which is most cases air) for a CNT mechanical sensor
Є_C = electro static and effect, like capacitance based which for example shows at the interconnect of Carbon Nanotube metal junction
Є_M=electromagnetic forces, like for inductive CNT antenna and transponders there is no mechanical motions but force due to inductance and induced voltages
M _{(ρ, С, r)} = material properties of the device, which also is the parameter of the density, head capacity, resistivity, strength and dielectric capabilities
Ī=current flowing in the device for example which can be derived of various part of CNT based circuitry
T_o=in some cases temperature may also be a cause of discrepancies which needs to be taken in account
f(t) is a function of υ, κ, η, Є_C, Є_M, M _{(ρ, С, r)}, Ī, T_o

We have discussed the physics of these devices which is where we have given the current through various parts of the system.

It is assumed that the function will be exponential with some modification since it’s a standard reliability function used. It is obvious that f(t) will increase with υ, κ, η, Є_C, Є_M, M _{(ρ, С, r)}, Ī, T_o

As these parameters are linked to the failure rate therefore to insert their equivalent they are calculated by operator f’ where increase in any of them will increase the failure of the device, this operator converts the respective value to a function that needs to be inserted in the main failure probability distribution equation.
Also it is obvious that the variation will have an exponential distribution for the failure rate distribution which can be derived from the basic principle of exponential distribution of reliability theory.
So,

(23)

(24)

We have assumed we are given all parameters and they remain constant throughout the cycle of the CNT device then (f(υ) + f(κ) + f(η) + f(Є_C) + f(Є_M ) + f(M _{(ρ, С, r)}) + f(Ī) + f(T_o)) = λ is assumed constant for computation that is being done on MATLAB. This formulation developed need to be modified as the exact dependencies of a case specific CNT device for example CNT based RFID or CNT based WSN. For example we need to derive for RFID which has CNT based antenna and transponders.

(25)

where I is the current through the system, n is the number of interconnects, and L is the approximate length of CNT used in the system. The failure probability distribution can be visualized as given in Fig. 4. And assuming only current and no interconnect effects the system behaves as shown in Fig. 5.

Fig. 4. Failure probability distribution f(t) vs I (current) and n (number of inter connects), which is the function derived.

Fig. 5. Failure rate function vs. I (current in the device) with no capacitive effects.

f(t)=( I + n+ L) e ^{-(I + n+ L)} (26)

The other model can be assumed in case the system is behaving in alternative way which is not satisfied by the first one can be seen in Fig. 6.

f(t)=( I n L) e ^{-(I+ n L)} (27)

Fig. 6. Failure probability distribution f(t) vs. I (current) and n (number of inter connects).

Thus for many CNT based devices in a WSN that are arranged in serious the probability of combined functioning can be calculated by the formulae below

(28)

A series system’s reliability decreases (increases) if the reliability of any unit decreases (increases). A series system’s reliability decreases (increases) if the number of units increases (decreases). A series system’s reliability is worse than the reliability of any of its units. Switching technology has been used very effectively and since at MEMS devices we have MEMS switches to shift to the redundant part of the system we need to analyze the reliability of the system with switch added. In a CNT system we can also use them. P_syst(t)=P_SD(t)P_m(t) where P_m(t) is the probability of failure free operation of redundant group, P_SD(t) of switching device and P_syst(t) of the system as a whole. A specific reliability function of switching device can be calculated in this way. Other miscellaneous issues that might come into factor are discussed below:
Reliability of CNT depends on miscellaneous factors such as:
1. Functional group(s) attached, length and chirality of the CNT molecule
2. Packaging model used
3. Integration with other devices and interconnects
4. Other factors such as temperature and environmental parameters

Developed model for nano routing. Now we need to find a path in which the distance, the load at node (which is defined in terms of n which is also the number of connection is made) and the energy conservations to makes least energy dissipation for routine in a CNT based sensor network. Now this energy loss will be calculated by each node and then it will decide the path of propagation. Nanotechnology has enabled modeling of Nano antennas and MEMS technology enable transducers thus we can see that energy consumption can be greatly minimized. Propagation of waves is an independent area for a WSN and routine methodology formation can be worked as shown below:
Here we have calculated the energy loss as a function of distance, load on the device, and the Voltage at which the CNT device is working. We know that Energy at a distance r is E_r= k/r² (this is the relation of the energy received at a distance r and k is assumed constant) by classical propagation theories. Now the energy loss is a function E_L=f(l_t,n_l, N_f)

E_L = k/l²_t + n_l + (K₁e^-k₁^V + K₂1/2 CV²), (29)

l_t = length at which the transmission is to be made;
N_f = Nano-factor for a CNT which is dependent on the energy conservation formulae derived in the earlier part, which is assumed as the energy conserved in the CNT as a function of Voltage which may be induced by MEMS transducers in this case;
n_l = load due to n devices at a node, which can also be said as the load complexity and also weighted value can be taken, in some cases it is the interference or the number of nodes surrounding the node that is a part of transmission or the interference nodes. It can also be stated as number of nodes in the path into average number of surrounding nodes (n_path*n_avg). Also the relation can be studied graphically as E_L vs. l_t vs. V as shown below.

Fig. 7. Simulink Model of CNT based nano-WSN.

Model of the system in light of recent developments. We have shown that since CNTs which are used in many parts of the sensor nodes, Nano-processors [20], therefore, it is necessary to study the reliability and effect of various parameters on CNT based devices is the motivation behind the work. We have shown the importance of functional CNT and its realistic applications in chemical sensors and other Nano-electronic devices [36]. HPC can be useful for optimization of complex computations which has been shown in [39, 40]. The sensor software has to be modified for CNT specific computations and in case of detection of erroneous readings by the node in CNT based calculations; corrective measures are needed to be incorporated into the software to counter these readings. An algorithm 1 is the algorithm for the functioning of the sensor node:

Modifications needed in current Operating System for CNT based WSN:
1. Minimizing the inconsistency in the readings of CNT sensor nodes due to functional CNTs.
2. Inclusion of correction for the CNT based Nano battery source.

Modeling of CNT based devices in a WSN environment such as CNT Sensors, CNT electronics, CNT-based power sources can be done in this way. Since CNT is the main ingredient of devices, its reliability is of paramount importance. We have corroborated that the reliability of CNT-based sensor node depends upon functionalization of the CNT molecule, application, interconnects and packaging.

VHDL-AMS (VHSIC hardware description language Analog and Mixed-Signal extensions) modeling can be done as substantiated in [26]. The Simulink model shown in Fig. 7. is derived from the various parts of a WSN CNT that has been shown in part II. The programs given in Code 1 and Code 2 are the conversion of the complex mathematical equations into MLATAB format.

Fig. 8. Configuration and status of the HPC setup.

The detailed implementation can be seen in [38]. The configuration of the status of the HPC setup is shown in Fig. 8. Due to symmetry of computation and distributions of various computations on the HPC setup, we got various results. When we fed the reliability computations we got maximum speedup (Fig. 9.), followed by I (current) in various (Fig. 10.), and the least in energy consumptions. Shown below are the speed-up results for various (Fig. 11) calculations that are performed on the HPC set-up in figure 9, 10 and 11. The explanation of the graphs can be predicted from the fact that symmetry of computation and limits used has the most effect on the speed-up. Virtual reality can also be used for taking the analysis in Virtual reality domain with the help of HPC setup.

Fig 9. Speed up which was obtained in reliability computations.

Fig. 10. Speedup in current (I) computations in various parts of the CNT based WSN.

Fig. 11. Minimum speed up obtained in energy consumptions in various parts of a CNT based WSN.

Conclusion

We have shown how novel nanotechnology-enabled devices can be used in a WSN environment. We have addressed the challenges that need to be confronted in CNT based WSN. We have substantiated integration of CNT based devices in WSN including sensors, micro processors, etc. We corroborated the challenges that exist on modeling of CNT based devices for a WSN sensor node and build a reliability model to accurately predict reliability. The modeling of CNT based nodes can be done in packages like Simulink in MATLAB which has been used in this work. We have derived a formulation for energy consumption of CNT based WSN system because energy is the main issue of concern secondly we have derived the reliability equation for the system. Developing a reliability, nano routing and reliability is helpful accelerating time to market for CNT based WSN. Routing plays an important role in CNT based devices where interconnects are very inefficient. Implementation has been done on an HPC setup and comparisons between various calculations have been reported. Control engineering can also play an important role in expanding the work, which is an area of future work. The transmission line equivalent needs to be modified as the new nano scale physics that is currently being developed which is introduced in this paper. To model such systems we have to use complex modeling aspects for which HPC is an eminent need.

Fig. 12. Energy consumption in Nano routing of a CNT based WSN.

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Rohit Pathak, Acropolis Institute of Technology & Research, can be reached at [email protected].

Satyadhar Joshi, Shri Vaishnav Institute of Technology & Science, can be contacted at [email protected]

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