Modeling Nano enabled elements of solar and fuel cell

Abstract- We have proposed a unified approach to the modeling and study of developments in the field of Nanotechnology and its application in futuristic Nano-enabled Cells. The necessity of a nonporous membrane has been eminent in recent fuel cells. The need for MEMS based models for porous silicon based membranes based on nano imprints technology has been met by modeling it in SUGAR in MATLAB environment. We have identified and categorized the domains of Nano enabled solar cells and have put forth a proposition for multi scale modeling of Solar cells. Multi scale modeling on HPC (High performance computing) of a Nano enabled solar cell is shown under MCCS (Microsoft compute cluster environment) environment using extreme optimization numerical library is implemented. Distribution and performance analysis of four levels of computation in a multi scale model is implemented with the distribution being carried out from classical semi-conductor to quantum levels as to accurately predict the behavior and properties of the solar cell as per the needs of the engineering of devices.

I. INTRODUCTION

rowing concerns of climate change concomitant with the escalation in oil prices, peak oil and increasing support in the Government and private

sector are driving increasing alternative and renewable energy legislations, mounting up of incentives and commercialization of this technology. Solar cell and fuel cell technology provide us with the ideal alternative in this energy-driven age. Fuel cell technology has seen a rapid growth in recent years. Due to the developments in Nanotechnology and their application in fuel cell technology and solar cells, newer methodologies are being developed. The penetration of the market dominated by today’s bulky batteries is only possible with the paradigm of nanotechnology. The ultimate aim is to minimize and shrink down the size of fuel cells using nanotechnology and MEMS. Application of MEMS in a MEMS based Fuel cell has been shown in Fig. 1. Solar cells are the most promising technology for green and clean energy. Futuristic models of solar cells will use advanced nanomaterials for increasing efficiency and reliability of solar cells [13]. Quantum dots based solar

harvesting architecture has been discussed [1]. Photo voltaic effects of a PbSe nanocrystal quantum dots based photo diode has been studied [5]. Quantum Well Multi junction solar cells have been discussed that describe the growth and testing of thin layers of AlGaAs-GaAs [3]. Thus the quantum mechanical behavior of the solar cell needs to be taken into consideration while modeling it. Hence the application of such solar cells depends upon its various quantum physical behaviors. Solar cell integration with autonomous sensor networks and their powering has been discussed [2].

Fig. 1. MEMS based fuel Cell.

II. MODELING MEMS BASED FUEL CELLS

DMFC (Direct Methanol Fuel Cell) has benefited maximum from progression in MEMS technologies in bringing about advances in its existing framework. MEMS based fuel cell system has been proposed where the power density was stated to be 220 mW/cm2 when the potential was 0.65 V thereby showing the advantages of integration of MEMS based devices in fuel cell technology [6].

Fuel cells have been the favorite candidates for portable electronics where indirect hydrogen, direct methanol and Nanotechnology based fuel cells have been of prime focus [8]. The relationship between energy content and respective fuel volume used is shown in Fig. 2. Higher density, lower form factor and minimization of cost have remained the prime focus for fuel cells. Key requirements of micro fuel cell system for portable electronics incorporating MEMS technologies have been conferred and are being developed at MotorolaTM [9]. Development of hydrogen fuel cell cycle has been discussed from a thermo dynamical perspective and the challenges that exist for transformation from a fossil-fuel based economy to a hydrogen based economy have been stated. Also historical aspects in fuel-cell technology have been conversed [10]. Various methods for generation of energy for portable devices including fuel cell technology as a practical solution and hybrid of various technologies including like piezoelectric, photo voltaic are

Modeling Nano Enabled Elements of Solar and Fuel Cell Rohit Pathak, Satyadhar Joshi, Pawan Kotak, Salman Ahmed, and Virendra Verma

G

Manuscript received April 15, 2009. Rohit Pathak is with the Computer Science Department, Acropolis

Institute of Technology & Research, Indore, M.P., India (e-mail: [email protected])

Satyadhar Joshi is with the Electronics & Electrical Dept., Shri Vaishnav Institute of Technology & Science, Indore, M.P., India (e-mail: [email protected])

Pawan Kotak is with the Electronics & Communication Department, Acropolis Institute of Technology & Research, Indore, M.P., India (e-mail: [email protected])

Salman Ahmed is with the Electronics & Electrical Dept., Shri Vaishnav Institute of Technology & Science, Indore, M.P., India (e-mail: [email protected])

Virendra Verma is with the Electronics & Communication Dept., Shri Venkateshwar Institute of Technology, Indore, M.P., India (e-mail: [email protected])

2009 Conference on Innovative Technologies in Intelligent Systems and Industrial Applications (CITISIA 2009) Monash University, Sunway campus, Malaysia, 25th & 26th July 2009.

978-1-4244-2887-8/09/$25.00 ©2009 IEEE 281

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studied [11]. Hence a comprehensive approach in the modeling of fuel cells is necessitated. MEMS based electrodes, PEM, pumps [7] reactors have been proposed that make MEMS based fuel cell a possible candidate for future devices. The fabrication technology used here is same as one used in MEMS manufacturing.

Fig. 2.Comparison of fuel volume vs energy for fuel cells and current

lithium-ion cells [8].

MEMS based fuel cells needs to be modeled for the current application. As discussed in [15-18] the application of MEMS based technologies are imminent. We have put a model as per the requirements of the current MEMS enabled fuel cells which are discussed in [15-18] where there is a need of porous membrane of MEMS model as shown by the output of our modeling in Fig. 5. We have used SUGAR library for simulation [19]. SUGAR is basically a node based MEMS simulation package that runs within MATLAB and much like SPICE it provides us a tool for specifying devices in a netlist type format and using different simulation and mathematical techniques it allows us to perform their analysis. MEMS based membrane has been modeled that can also be analyzed for use in enhancing the reactivity of methanol in a Direct Methanol fuel cell (DMFC). MEMS pumps, MEMS based Membrane can be further modeled using SUGAR. MEMS based Membrane for DMFC model has been programmed as shown below:

CODE 1 DEMO CODE FOR MODELING MEMBRANE

use("mumps.net") use("stdlib.net") gridDim=100u fringeDim=40u beamw = gridDim-fringeDim beaml = gridDim --array junction junction = { node{} } for n=1,16 do --loop for rows for m=1,16 do --loop for cols --nodes junction[n] = node{n*beaml, m*beaml, 0} junction[n+1] = node{}

junction[n+2] = node{} junction[n+3] = node{} --beams beam3d { junction[n], junction[n+1] ; material=p1, l=beaml, w=beamw } beam3d { junction[n+1], junction[n+2] ; material=p1, l=beaml, w=beamw, oz=90 } beam3d { junction[n+2], junction[n+3] ; material=p1, l=beaml, w=beamw, oz=180 } beam3d { junction[n+3], junction[n] ; material=p1, l=beaml, w=beamw, oz=270 } end --cols end –rows

Fig. 3.Out put of the Code.

For modeling of Solid Oxide Fuel Cells (SOFC), three types of models have been suggested, subject to the length scale involved in the contemporary literature available. These are (i) macroscopic continuum electrode theories, (ii) Monte Carlo (many-particle) methods and (iii) local current density distribution models within individual particles [26, 27]. Till now the modeling studies of SOFC modules have been concentrated on the electrodes (cathodes or anodes) but it appears that much less work has been done on the modeling of specifically the membrane region of the SOFCs [30]. Example of multi-scale modeling in SOFC: -

A. Macroscopic Continuum Electrode Theories A composite cathode of height h made from an electrode/electrolyte mixture, with high electronic conductivity, fast gas diffusion in pores and effective ionic conductivity ionσ . On the macroscopic continuum level, oxygen level is reduced at any place on the cathode and current density of oxide ions is formulated [27] as

2

2 2ion O

O

di

e dyσ −

−

Φ= − (1)

where e represents electric charge of an electron and the electrochemical potential of the oxide ions is denoted by 2O −Φ . The electrochemical reaction rate is given by [27]


282

( )2

2 2,2O vol

O eq O

di Ydy e

−

− −= Φ − Φ (2)

where volY is a rate constant for the volumetric reaction

and 2 ,O eq−Φ denotes the electrochemical potential of

2O − at zero current density.

B. Monte Carlo (Many-Particle) Methods In the Monte Carlo models the electrode is treated as a random mixture of particles of three phases- (a) electrode, (2) electrolyte, and (3) gas [27]. The electrochemical and electrical properties are analyzed using multifarious types of resistors each for a different characteristic that needs to be measured. The current between two solid particles of phase k is controlled by a resistor kr . It is related to the phase conductivity kσ and

a geometric factor geof mathematically as [27]

/k geo kr f σ= (3)

where geof justifies the particle shape and the contact necks between the adjacent particles.

C. Local Current Density Distribution Models The studies that have been performed on the modeling of local current density distributions on the individual particle length scale have been implemented by finite element method, finite difference method or resistor network simulations carried out with many resistors in a single particle [28, 29].

2

2i i

ic cDt x

∂ ∂=∂ ∂

(4)

where ic , t and iD , are concentration, time and mass diffusion coefficient of specie i . On application of high over-potential to an electrode, there is a quick progression of reaction, and thus the concentration of reactants in the chemical reaction is rendered nearly zero at surface of electrode. The rate of reaction is computed from the bulk concentration oc by process of diffusion to the electrode, i.e. limiting current flow is present. In presence of such conditions, the reactant concentration to x and t is formulated as:

( ),2

o xc x t c erftD

⎛ ⎞= ⎜ ⎟⎝ ⎠

(5)

as given in [31]. Thus these parameters are fed into the multi scale library and computations are performed. Reliability of MEMS devices can be calculated using an HPC setup as shown by Rohit et. al[25].

III. MULTI SCALE MODELING OF SOLAR CELLS USING HPC

There are challenges that exist in the current proposals in this realm of harvesting energy from solar cells that can be predicted with the help of multi scale modeling. Some solutions for skin effect resistance and low voltage per antenna that can prove to be useful for harvesting of solar energy have been discussed [4]. Multiscale modeling plays a very important role in engineering today in predicting properties that remain inexplicable under current modeling scenarios [12].

Multiscale modeling of Nano materials based solar cells can be done as shown in Fig. 4. considering the distribution of various domains from classical semi conductor behavior of solar cell to quantum dots. We have used C# MPI [20, 21] on a MCCS environment [22]. MPI is essentially a message-passing application programming interface (API) interface offering us a language-independent communication protocol used for point-to-point and mutual communication for performing parallel computation [24].

Fig. 4.Multi-scale modeling of Nanotech enabled solar cells.

CODE 2 MPI CODING FOR CONNECTING NODES

using System; using System.Collections.Generic; using System.Linq; using System.Text; /*Including the namespace of the MPI.NET library*/ using MPI; namespace hydroCode1{ class Program { static void Main(string[] args) { using (new MPI.Environment(ref args)) { Communicator comm = Communicator.world; Console.WriteLine("Check from process " + comm.Rank); switch (comm.Rank) { case 0: /*PROCESS ONE CODE*/ /*Fundamental Semiconductor Property*/ /*Level 1 Computation Code goes down*/ Console.WriteLine("Process " + comm.Rank + ": Fundamental Semiconductor Property"); /*End of PROCESS ONE CODE*/ break; case 1:


283

/*PROCESS TWO CODE*/ /*Device Specific Optical and Electrical Property*/ /*Level 2 Computation Code goes down*/ Console.WriteLine("Process " + comm.Rank + ": Device Specific Optical and Electrical Property"); /*End of PROCESS TWO CODE*/ break; case 2: /*PROCESS THREE CODE*/ /*Nano-Crystalline/PN-Junction Basic Properties*/ /*Level 3 Computation Code goes down*/ Console.WriteLine("Process " + comm.Rank + ": Nano-Crystalline/PN-Junction Basic Properties"); /*End of PROCESS THREEs CODE*/ break; case 3: /*PROCESS FOUR CODE*/ /*Quantum Dot/Thin Film/Dye Sensitized Quantum Level Property*/ /*Level 4 Computation Code goes down*/ Console.WriteLine("Process " + comm.Rank + ": Quantum Dot/Thin Film/Dye Sensitized Quantum Level Property"); /*End of PROCESS FOUR CODE*/ break; default: /*Any other process*/ /*Code to be executed by rest of the processes*/ Console.WriteLine("Process " + comm.Rank + ": Idle"); /*End of code*/ break; }/*End switch*/ /*All processes join here*/ comm.Barrier(); /*All processes completed*/ if (comm.Rank == 0) { Console.WriteLine("All processes finished"); } } } }}

The requirement here is to calculate various parameters of different solar cells at various levels from Macro to Nano as well as hybrid models of solar cells arranged in any array. As stated in [14] the Fermi level of an intrinsic semiconductor is calculated to be

2 2C V V

C

E E kT NF ln NE +

= + (6) Here EF is Fermi energy, k the bolltzmann constant, T is absolute temperature, N is the effective density of holes in the valence band and Nc is the effective density of states of electrons in the conduction band.

The basic principles of solar cell using nano crystalline materials have been discussed in [14] and an analytical approximation for the lowest excited 1s state is given by the expression

2 2

2

1 1 1.8* ( )8

g

e h

h qE Er m m r

≈ + + − (7)

where r is the crystal radius, me an effective mass of electrons and mh is the effective mass of holes for the crystalline.

Fig. 5.Output of the computations.

As given [14] the electrical property of a dye sensitized solar cell

( )[1 exp ]ocSC

B

q V VJ JnK T

−= − (8)

where J is the output current density, Jsc the short-circuit current density, q the elementary charge, V the external applied voltage, kB the Boltzmann constant, and T the absolute temperature. Here, n is called “ideality factor”. It is an extension for the diode based model.

Fullerenes based photo voltaic material [14] follow the expression for current as

( )exp 1S So p

Sh

q V IR V IRI I InKT R

⎡ + ⎤ +⎛ ⎞= − + −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (9)

where Ip is the photocurrent, Io and n respectively denote the reverse saturation current and diode quality factor of the p-n junction, Rs and Rsh are lumped series and shunt resistances of the cell, respectively [14]. Thus the distribution of modeling in four different domains has been achieved to form multi scale modeling of a nanotechnology enabled solar cell. The output has been shown in Fig. 6.

Extreme Optimization Numerical Demo Code for computation on four node cluster setup:

CODE 3 SUDO CODE TO DISTRIBUTE COMPUTATIONS

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace hydroExtreme1{


284

using MPI; // The DoubleComplex structure resides in the Extreme namespace. using Extreme; // The delegate classes reside in the Extreme.Mathematics // namespace. using Extreme.Mathematics; // We also use the Extreme.Mathematics.SpecialFunctions namespace. using Extreme.Mathematics.SpecialFunctions; // calculas part using Extreme.Mathematics.Calculus; class Program { static void Main(string[] args) { using (new MPI.Environment(ref args)) { Communicator comm = Communicator.world; Console.WriteLine("Check from process " + comm.Rank); if (comm.Rank == 0) { double Ec = 1, Ev = 1, T = 1, Nv = 1, Nc = 1; Console.WriteLine("Process " + comm.Rank + " status: calculating Ef"); Console.WriteLine("Process " + comm.Rank + " status: " + "Ef as calculated is: " + Ef(Ec, Ev, T, Nv, Nc)); } else if (comm.Rank==1){ double Eg = 1, me = 1, mn = 1, r = 1; Console.WriteLine("Process " + comm.Rank + " status: calculating Excited Energy"); Console.WriteLine("Process " + comm.Rank + " status:" + "Excited Energy as calculated is: " + energyExcited(Eg, me, mn, r)); } else if (comm.Rank == 2) { double Jsc = 1, T = 1, V = 1, Voc = 1, n = 1; Console.WriteLine("Process " + comm.Rank + " status: calculating J"); Console.WriteLine("Process " + comm.Rank + " status: " + "J as calculated is: " + J(Jsc, T, V, Voc, n)); } else if (comm.Rank == 3) { double Io = 1, V = 1, I1 = 1, Rs = 1, Rsh = 1, Ip = 1, n = 1, T = 1; Console.WriteLine("Process " + comm.Rank + " status: calculating I"); Console.WriteLine("Process " + comm.Rank + " status: " + "I as calculated is: " + I(Io, V, I1, Rs, Rsh, Ip, n, T)); } else { Console.WriteLine("Process " + comm.Rank + " status: Idle"); } /*All processes join here*/ comm.Barrier(); /*All processes completed*/ if (comm.Rank == 0) { Console.WriteLine("All processes finished"); } }/* End of MPI Environment namespace */ } /*Mathematical functions listed below*/ static double Ef(double Ec, double Ev, double T, double Nv, double Nc) { double Ef, t1, t2, t3, K; K = 1.3806503e-23; t1 = (Ec+Ev)/2; t2 = (K*T)/2;

t3 = ElementaryFunctions.Log1PlusX((Nv - Nc) / Nc); Ef = t1 + (t2*t3); return Ef; } static double energyExcited(double Eg, double me, double mn, double r) { double Ex, h, Epsilon, q, t1, t2, t3; h = 6.62606896e-23; Epsilon = 8.8541878176e-12; q = -1.602176487e-19; t1 = ElementaryFunctions.Pow(h, 2) / (8 * ElementaryFunctions.Pow(r, 2)); t2 = (1/me)+(1/mn); t3 = (1.8 * ElementaryFunctions.Pow(q, 2))/(Epsilon*r); Ex = Eg + (t1*t2) - t3; return Ex; } static double J(double Jsc, double T, double V, double Voc, double n) { double J, K, t1, t2, t3, q; K = 1.3806503e-23; q = -1.602176487e-19; t1 = q*(V-Voc); t2 = t1 / (n * K * T); t3 = ElementaryFunctions.ExpMinus1(t2); J = -1 * Jsc * (t3); return J; } static double I(double Io, double V, double I1, double Rs, double Rsh, double Ip, double n, double T) { double K, t1, t2, t3, t4, q, I; K = 1.3806503e-23; q = -1.602176487e-19; t1 = q * (V + (I1 * Rs)); t2 = n * K * T; t3 = ElementaryFunctions.ExpMinus1(t1/t2); t4 = (V + (I1 * Rs)) / Rsh; I = (Io * t3) + t4 - Ip; return I; } }}

Figure 6.Output of computations.

CONCLUSION AND FUTURE CHALLENGES

Thus we have shown the modeling of MEMS based fuel cell in MATLAB using SUGAR and multi scale modeling of solar cell in an HPC setup using extreme optimization


285

library under MCCS environment. Simplified parametric values have been assumed in the computations to generate the output. SUGAR modeling of a DMFC is programmed in code 1. The output is a MEMS based membrane as illustrated in Fig. 3. MPI program code has been executed in code 2 and the respective output is shown in Fig. 2. And finally programming code for an extreme optimization numerical demo on a four node cluster setup has been achieved, as exemplified by Fig. 3. We have carried out and executed the distribution process of the jobs in an HPC setup has been and the modeling of certain aspects of solar cells which has been shown in Fig. 6. A MEMS based membrane that can help in modeling of MEMS based cells of [15-18] and provide acceleration to research in this field. Nanotechnology and MEMS enabled solar and fuel cells will have optimum characteristics. This was done as part of Project [23]. Future commercialization of such solar and fuel cell will see greater use in diversified areas. Portable fuel cells will see the replacement of contemporary bulky battery technology. The cost of solar cells will decrease and their efficiency will increase significantly in the future via the use of these techniques.

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Modeling Nano enabled elements of solar and fuel cell

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