a report on

Modeling of Organic Semiconductors

June 4, 2010

Submitted By:

Jayant P. Thatte1

Mentor:

Prof. K. S. Narayan2

Jawaharlal Nehru Centre for Advanced Scientic Research, Jakkur

Bengaluru 560 064, India

Abstract

The report starts with the basics of how charge diusion takes placethrough organic solids, giving a brief overview about behavior of interca-lating ions in a thin lm, trap states and its equivalent RC circuits. Withthis background, the next sections talk about two applications of organicsemiconductors. The major application beingsolar cells. Sections 4 and5 deal with solar cells, conventional model, need for a dierent modelfor organic solar cells and describes the new models which can be usedto simulate organic solar cells in DC and AC simulations respectively.Extraction of physical parameters of a solar cell from its I-V curve bytwo dierent methods is discussed in sections 6 along with the discussionsabout accuracy of the two methods. Section 7 and 8 deal with basic theoryof Electrolyte Polymer Interface (EPI) and its equivalent circuit. Basedon this knowledge, the last section deals with modelling of human nerveswith an equivalent circuit and nding equivalent circuit in particular forthe retinal neurons involved in retinal electrography.

1Department of Electrical Engineering, Indian Institute Of Technology Madras, Chennai.Phone : 09962266524; email : meetjayant@gmail.com

2Head of Molecular Electronics Laboratory, Jawaharlal Nehru Centre for Advanced Scien-tic Research, Bengaluru. email : narayan@jncasr.ac.in

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1 Introduction

Silicon has been celebrated for years as the most popular element in the semi-conductor industry. All semiconductor devices are made of a semiconductormaterial, a conductor and an insulator. Semiconductor is amorphous silicon,conductor is doped silicon and insulator in silicon oxide. Thus, silicon is proba-bly the only element to display all three properties under dierent forms. More-over, interconversion between silicon and its oxide is very easy industrially. Thisis one of the main reasons for the widespread use of silicon in the semiconductorindustry.Silicon, however, has a drawback. If the dimensions of the component are large(e. g. solar panels, television screens etc. ) then manufacturing a single waferof pure silicon becomes very dicult and costly. This is where organic semicon-ductors (OS) come into picture. Fabrication of OS is extremely simple. The OSmaterial is converted to ink and then any required circuit can be simply printedout. Solar energy tapping is one of the most essential tasks before mankind inthe view of energy crisis. Bulk Heterojunction Polymer Solar Cells are promis-ing candidates for economic solution for renewable energy source with relativelylow manufacturing complexity. The OS are thus gaining an increasing impor-tance.The physics behind OS and their working is not understood as completely asthat for inorganic semiconductors. It is therefore necesssary to understand thephysics behind semiconductors in order to be able to build a model for OS. Thenext section deals with the basics of OS and how charge transfer takes place inOS.

2 General OS Theory : Trapped States and IonDiusion in Organic Semiconducting Material

2.1 Introduction

It is well established that ion motion in a solid environment occurs by hoppingbetween localized sites. Ions reside for most of the time at minimum energysites, but eventually they jump from one site to another overcoming the intersitebarrier by a thermally activated process. Such sites are calles intercalation sites.There are dierent types of intercalation sites: a set of connected shallow siteswhich allow fast diusion of the intercalating ions throughout the material, andslower types of sites which trap the intercalating ions.

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Semiconductors have both extended states (e. g. conduction band levels)and localised levels. The Fermi level approximately separates the occupied andthe empty levels. Each trap state in a semiconductor is equivalent to an RCcircuit. The equivalent circuits for two specic levels are shown in the abovediagram. For each level, the resistance corresponds to the thermal release of theions to the extended states. Thus, the resistance of the equivalent RC circuitdepends upon the energy or potential dierence between the trap level and theextended states and also the occupancy of the trap state. This resistance iscalled extraction resistance. The capacitance refers to the energy stored in thetrapped state and hence depends upon both the energy of the trap state abovethe localised levels and the occupancy of the trap state. This capacitance is anew type of capacitance called Chemical Capacitance [1-2] also known as Accu-mulation Capacitance [3]. The extended levels also posses chemical capacitancealthough it is not shown in the diagram.

2.2 Fast state capacitance

The intercalating ions ll the fast states uniformly. This charging and discharg-ing of the fast sites with ions according to the externally applied voltage can bediscribed in terms of a capacitance called Fast State Capacitance and is denotedby C0.

2.3 Ion Trapping Process

The slower types of sites are dicult to access and do not get lled immediatelylike the fast sites. These sites can get lled provided we wait for sucient time.

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.

The fast states network consists of a region connected by relatively low bar-riers, and the hopping of these, i.e. the transitions A→A in Fig. 1, determinesa diusion coecient for the fast charging mode. The system contains in ad-dition single sites B or domains isolated by larger energy barriers, requiring amuch longer time for its overcoming A→B. Hence, a fraction of the intercalatedions have been immobilized at certain sites, and do not participate in diu-sion. Hence, for the equilibrium (low frequency) intercalation capacitance beinglarger than the diusion capacitance. Trapping arises from the fact that mobileions occupy dierent types of sites in the lattice. Sites separated by the largerenergy barriers involve larger hopping times, and sites deep in energy involvelarge release times. In this sense trapping depends upon the time of residenceof ions in a particular site.

2.4 Trapped Charge Capacitance

The total charge passed to the host solid increases as the time passes. This isbecause the connected sites AAA... (see above gure) get lled fast and thesites surrounded by large energy barriers go on lling slowly as the time passes.Hence the net capacitance due to the charging host is not limited to the faststate capacitance C0but also has contribution from each of the trap states.

Ctotal = C0 + Ctrap (1)

2.5 Model for Charging of Thin Film

A charging thin lm can be modeled as shown below.

Figure (a) shows the single trap model while gure (b) shows multiplt trapmodel.

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3 Applications

After knowing the basic theory about OS, one can move on to its applications.OS material is used widely for

• Photovoltaic Cells : These cells are used for tapping solar energy and alsoas detectors.

• OS Electrolyte Interface (Electrolyte Polymer Interface): This is usedmostly in chemical batteries, solar cells etc.

Let us consider these two major applications in detail. Sections 4 to 7 deal withOrganic Solar Cells and Electrolye Polymer Interface (EPI).

4 Model for Organic Solar Cells (OSC)

4.1 Dierence Between OSC and Silicon-Based Solar Cells

Currently, OSC have a much lower eciency as compared to that of the con-ventional thin lm amorphous silicon solar cells (SSC) which is ∼ 10%. Thisdierence arises due to dierent fundamental mechanism of current generation inthe two types of cells. In SSC, onfalling light causes the generation of electron-hole pairs (EHP) which recombine through the external circuit giving rise tocurrent. In most organic solar cells, however, the incident light only causesexcitations and not EHP because the electron binding energy is high. A sim-ple OSC consists of donor and acceptor layers of OS. The excitations producedin the donor diuse to the donor-acceptor (D/A) interface and dissociate toform polaron pairs. These polarons can either recombine or dissociate into freecharge carriers3. These dissociations are mainly driven by the strong electriceld present in the space charge region of the D/A interface. (More details insection 7).

The reason for low eciency is that the minimum thickness of the donor layerneeded for ecient light absorption is considerably more than the maximumthickness upto which the photoexcitations can diuse. This means that only afraction of the excitations is actually converted to current. Again, dependingupon the mobility of the electrons and holes, some of the EHP recombine withinthe OS layer iteslf and only the remaining are obtained as current output. Thisleads to quite low eciency for OSC of ∼ 2− 3%.

To overcome this problem, bulk heterojunctions consisting of an interpen-etrating network of donor and acceptor materials have been used to ensurethat all photo-generated excitons nd a D/A interface within a diusion length.

3Organic solar cells convert excitations into separated electrons and holes primarily at theD/A interfaces because the organic semiconductors on which the cells are based are excitonicin nature. The excitonic nature causes electron and hole pairs that form by absorption oflight to be bound together by several tenths of an electron volt, a binding energy that is muchgreater than ambient thermal energy. At the D/A interfaces, the driving force to separate thecharge carriers is great enough to overcome this binding energy.

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Bulk heterojunctions have increased the eciency of organic photovoltaic cellsto 3-4% [4].

4.2 Existing Model for Solar Cells

All existing models of solar cells assume that the current by the cell is constantfor a given light intensity. The conventional model of solar cell is shown in thefollowing two gures.

The rst gure shows model with parasitic resistances RSandRSh. Thesecond one is the ideal version without these resistances. Let ILbe the generatedcurrent. Let the I-V characteristics of the cell be denoted as I = f(V ). Thismaximum current is called ISC . The open circuit voltage of the cell is calledVOC . Then the measued current of the cell can be expressed as:

I = IL − f(V ) (2)

As one can observe,f(VOC) = IL (3)

4.3 New Model for OSC and its Need

All the existing models for SSC assume that the current generated is constantfor a given light intensity. Although this assumption holds good for inorganicsolar cells, it does not hold for their organic counterparts. How eectively theexcitations diuse to the D/A interface also depends upon the electric eldpresent inside the cell, which in turn depends on the voltage applied acrossits terminals. The current provided by the cell reduces when voltage appliedacross its terminals increases. Thus the current is maximum when the outputterminals of cell are shorted.

A more appropriate assumption for OSC is that the generation rate of po-laron pairs is constant for a given light intensity. Some of these may recombineinternally. Thus the following change can be made in the conventional modelto get an appropriate model for the OSC.

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In the above model, IP represents the total polaron pair generation rate. Thediode Drecrepresents the loss in output current due to internal recombinationof the polaron pairs, diode Dextrepresents the extraction of the dissociated freecarriers and diode Ddarkrepresents the I-V chracteristics of the cell under darkconditions. Note that while taking I-V characteristics in dark, Dextbecomesreverse biased and therefore only Ddarkcontributes to the I-V characteristics.Drecand Dexthave an eect only under light conditions. We can write

I = IP − Irec − f(V ) (4)

Irec = frec(Vint) (5)

where frecrepresents the I-V characteristic of Drec. ISC is given by the followingtwo expressions

ISC = IP − frec(Vint) (6)

ISC = fext(Vint) (7)

One can notice that as the applied voltage is in reversed bias with respect toDext, the current owing across it, under light conditions, will reduce untilnally when the applied voltage is sucient to make the current zero. This isVOC .

A parameter ξis used to express the departure of the OSC from conventionalinorganic cells.

ξ = f(VOC)/ISC (8)

For inorganic cells, current remains constant, and hence for an ideal inorganiccell, ξ = 1. Whereas in the other extreme case f(VOC) = 0and hence ξ = 0.Thus for a cell under consideration, if ξis close to unity, then the conventionalmodel for solar cells can be used. However, if the departure of ξ from unity issignicant, then this new model would prove to be more accurate.

4.4 Changes in Model for AC simulations

The model given above is used onlt to obtain the DC characteristics of solarcells. For AC characteristcs, the model will have to be modied. Firstly, sincethe cell is made up of OS, instead of having only a shunt resistance Rsh, we will

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now also have the fast state capacitance and the trap capacitance in series withextraction resistance (Refer section 2). Also, the diodes are used only in the DCModel. Hence, the solar cell model that should be used for AC is shown below.

Note that all the above resistance and capacitance values depend upon thesurface area of the solar cell and hence are usually expressed as Ωcm2 andF/cm2. Current is also expressed as mA/cm2.

5 Simulations of solar cell

5.1 I-V Characteristics and Fill Factor

Using the above model, the solar cell was simulated and the dependence of theoutput current on various circuit elements in the model is observed. For all thesimulations, the following typical values are assumed: Rsh = Rext = 1kΩcm2;Ctrap = 2nF/cm2; Cfast = 20nF/cm2. The value of Rs depends upon the setupof the cell and the quality of electrical contact. Value of series resistance canvary in a very wide range from less than 1Ωcm2to a few kΩcm2. For simulationsthe value Rs = 100Ωcm2 has been chosen. The value of source Ip is set suchthat VOC lies in its typical range of 550mV to 750mV . The value of Ipused inthis case is 4mA/cm2.

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As was stated earlier and can be seen in the I-V curve above, current outputgoes on decreasing as the voltage is increased. Hence there is a particular valueof voltage Vp, at which the cell delivers maximum power output. This point iscalled as peak power point (PPP). Fill factor is dened as the ratio of powerdelivered by the cell at PPP to the total area under the I-V curve in the IVquadrant. In the gure shown below, Vp = 450mV and ll factor is roughlyequal to 0.66.

The images show the I-V characteristics of the solar cell in light and dark.In the light conditions, VOC ≈ 630mV and ISC ≈ 3mA/cm2.

The following four graphs show how the I-V characteristics of the cell forRsequal to 125, 100, 75 and 50 Ohm-sqcm. respectively keeping all other param-eters constant.

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From the graph, we can conclude that for the same value of VOC , ISC islarger for smaller value of Rs. Thus, a solar cell with smaller Rsis preferable.

Similarly, the I-V characteristics are compared for Rsh values 0.5, 1, 3,5kΩcm2 respectively.

From the graphs one can observe that the ll factor of the I-V curve improvesis Rsh increases. In the above case, ll factor increased from 0.56 to 0.62 forRsh equal to 0.5 and 5Ωcm2 respectively. This is because, smaller the value ofRsh, larger are the internal losses in the cell, Ip being constant. Hence, cellswith larger value of Rsh are prefered.

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5.2 AC Sweep

The DC sweep or the I-V plot only gives us information about the resistanceparameters in the cell. However, to get information about the knee frequency(KF) and how it varies with dierent parameters, AC sweep is mandatory. ACsweep is used for impedance measerement of the solar cell. For AC sweep, Ip isan AC source and its frequency is sweeped from 10Hz to 100kHz and amplitudeof the output current is plotted versus frequency. In the following simulations,an eort has been made to show how the frequency characteristics change withchanges in dierent paramerters. Note that in most of the graphs, frequency isplotted in logarithmic scale.

Knee Frequency (KF): KF is the frequency above which the current am-plitude shows a sudden drop. Thus, knee frequency is the maximum frequencyupto which the cell is responsive. The time corresponding to KF is called theResponse Time (RT) of the cell. RT gives the time resolution of the cell. Forexample, if amplitude of the light incident on the cell varies faster than the RTof the cell, then the cell will not be able to see the variations. Thus, when thecell is being used as a photodetector, larger KF is prefered.Following plots show the frequency characteristics for Rsh equal to 10, 5, 1 and0.3 kΩcm2 respectively.

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Observations There is a knee at around 15kHz. The overall amplitude goeson falling with decrease in Rsh.Following graphs show variation of frequency characteristics when Rs varies as1000, 500, 100, 10 Ωcm2.

As Rs decreases, the knee frequency and the overall amplitude of the currentincreases.Following frequency characteristics are ploted for Cfast equal to 200, 100, 50, 1nF/cm2.

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Knee frequency increases rapidly with drcrease in value of Cfast.Following function characteristics are for Ctrap equal to 20, 10, 1, 0.1

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Following frequency characteristics are plotted for Cs equal to 10, 50, 100,200 nF/cm2.*

The common feature seen in all of these graphs is a knee frequency at around10kHz and then a steep fall in current. Before the knee frequency, current out-put is quite high and nearly constant. However, experimentally obtained fre-quency sweep curves show a dierent feature. Experimentally obtained curvesshow a nearly constant current and then a sharp maximum at roughly 5-10kHzand then a steep fall. This dierence can be attributed to the polaron gen-eration current itself to be frequency dependent. This is because the polarongeneration involves many internal processes. The basic prevailing microscopic

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kinetic processes of carrier generation, recombination and charge carrier trap-ping along with associated rate constants form the microscopic Ip(ω) as shownin the gure.

The microscopic processes span over multiple time scales (ps ms). Theassociated parameters are: primary excitons generation rate (gL), exciton dif-fusion lifetime (τ1 ∼ ns), charge-carrier (nfree) life time τ2, secondary excitongeneration process and trapping kinetics. All of these processes depend on fre-quency causing polaron generation current to depend on frequency. To accountfor this the model should not only include the circuit of resistors and capaci-tances as given in section 4.4, but also that the resistors and capacitors shouldthemselves be functions of frequency.

6 Extracting Physical Parameters from Given I-V Curve*

6.1 Extracting Rs and Rsh using slopes

From the circuit model, one can easily see that the eect ofRs becomes negligibleat voltages close to Voc. Hence the slope of the I-V curve at V = Voc, is equalto 1/Rsh. Also, under short circuit conditions, Rs and Rsh are in parallel.Therefore slope of the I-V curve at V = 0 is equal to R−1

s + R−1sh . However,

since Rs Rsh, the 1/Rsh term may be neglected. Thus, slope of I-V curve atV = 0 is approximately equal to 1/Rs. However, this method has a disadvantagethat it may be very dicult to measure the slopes of the I-V curve accuratelyat the short circuit and open circuit ends [7-9].

6.2 Extracting Parameters Using the Four Point Method

The ve cell parameters are

• Dark Current Density (Jo) at Voc

• Photogenerated Current Density (Jph)

• Rs

• Rsh

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• Diode Ideality Factor (η)

This method is a simple explicit power-law JV model that is applicableto a wide variety of solar cells. This method allows an easy prediction of theentire JV curve, peak power point, and ll factor (assuming single diode modelof solar cell shown above) from four simple measurements of the bias pointscorresponding to Voc, 0.6 Voc, Jsc, and 0.6 Jsc, where Voc is the open-circuitvoltage and Jsc is the short-circuit current density. Four points are neededon the I-V curve. Note that the measurement points should not be close toeither the short- or open-circuit point because small measured values are proneto large percentage errors. On the other hand, a point on the sharply turningcurve corner also gives erroneous results because the neglect of the term vm inthe derivation of γ is invalid for this condition. This is the reason for choice of0.6 [7].The I-V curve of a solar cell by nature of an implicit form and hence isdicult to deal with.In this method, the I-V curve is tted with an explicit power law model whichworks for a wide range of cells. For this purpose we denote J/Jsc by j andV/Voc by v. Then the I-V curve can be expressed as [8]

j = 1− (1− γ)v − γvm (9)

When v is small, the linear term dominates tting the slow fall in current nearthe short circuit end while the power law term models the steep fall near Voc.Let the current density and voltage at the peak power point be denoted by vpand jp respectively. Then we have the relation

δ(jv)

δv|v=vp= 0 (10)

Solving this we get

1− 2(1− γ)vp − γ(m+ 1)vmp = 0 (11)

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and for γ = 1, it turns into vp = (1 + m)−1/m. Then the above equation isempirically adjusted [7] as

vp ≈ (m+ 1)− 1/m− 0.05(1− γ) (12)

Thus, vp is obtained and hence jp and FF can be found out.Now we nd out m and γ in terms of current density and voltage at the fourpoints of measurement. m usually ranges from 7 to 15 while γ lies between 0.9and 1.0.

At v = 0.6, vm 1 and hence can be ignored. Therefore, at v = 0.6, eqn 9gives us

(1− γ)× 0.6 = 1− j |v=0.6 (13)

Thus

γ =j |v=0.6 −0.4

0.6(14)

Knowing γ, m can be found out easily as

m = log

(0.4− (1− γ)v |j=0.6

γ

)/logv |j=0.6 (15)

The single exponential current density-voltage equation of an illuminated solarcell is given by [8-9]

J = Jph − Jo(eV+JRsηVt − 1)− V + JRs

Rsh(16)

where, Vt is the thermal voltage of diode4. From the model, we can get thefollowing equations

Is(eVocnVt − e

IscRsnVt )− Isc(1 +

RsRsh

) +VocRsh

= 0 (17)

(Rso −Rs)(1

Rsh+

IsnVt

eVocnVt )− 1 = 0 (18)

4Thermal Voltage at any temperature T is given as Vt = kT/q, where k is the Boltzmannconstant and q is the electronic charge.

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1

Rsh− 1

Rsho −Rs+

IsnVt

eIscRsnVt = 0 (19)

IseVocnVt +

Voc − VpRsh

− (1 +RsRsh

)Ip − IseVp+RsIpnVt = 0 (20)

where, Ip and Vp are current and voltage at peak power point, Rso and Rshoare reciprocals of slopes of the I-V curve at open circuit and short circuit pointsrespectively, and n is the diode ideality factor. The above four equations canbe simplied taking into account typical values of various parameters leading tofour equations below

IseVocnVt − Isc +

VocRsh

(21)

(Rso −Rs)IsnVt

eVocnVt − 1 = 0 (22)

Rsh = Rsho (23)

IseVocnVt +

Voc − VpRsh

− Ip − IseVp+RsIpnVt = 0 (24)

Solving these equations expressions for Rs, Is, Iph and n can be obtained.

n =Vp +RsoIp − Voc

VT

(ln(Isc − Vp

Rsho− Ip)− ln(Isc − Voc

Rsh) +

IpIsc−(Voc/Rsho)

) (25)

Is = (Isc −VocRsh

)e−VocnVt (26)

Rs = Rso −nVtIs

e−VocnVt (27)

Iph = Isc(1 +RsRsh

) + Is(eIscRsnVt − 1) (28)

Starting with the above equations, we express Rsho and Rso as

Rso =VocJsc× 1

γ(m− 1) + 1(29)

Rsho =VocJsc× 1

(1− γ)(30)

Hence n after some very simple algebraic manupulations can be written as

n =Voc(vp +

jpγ(m−1)+1 − 1)

VT

(mlnvp + jp/γ

) (31)

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Thus, n can be computed since we already know Voc, vp, jp, m and γ. Similarlysubstituting for Rso and Is , we can express Rs as

Rs =VocJscγ

×

(1

(m− 1) + 1/γ− nVtVoc

)(32)

Rs, Rsh and n have been extracted. Now we proceed towards extraction of Joand Jph. Equation (16) when evaluated at open and short circuit points lead tothe following two equations.

0 = Jph − Jo(eVocηVt − 1)− Voc

Rsh(33)

Jsc = Jph − Jo(eJscRsηVt − 1)− JscRs

Rsh(34)

Solving them simultaneously, Jo and Jph can be found.

Jsc = Jo(eVocηVt − e

JscRsηVt )− Voc − JscRs

Rsh(35)

Assuming that JscRs Voc, the equation can be further simplied as

Jo = γJsce−VocηVt (36)

Similarly, using above three equations, Jph is extracted.The parameter ξ introduced in section 4 can also be found out using Jo.

ξ = γe−VocηVt (37)

7 Electrolyte Polymer Interface(EPI)

7.1 Basic Theory

Let us consider the interface betwen electrolyte solution and a semicinductorelectrode. For the two phases are in equilibrium, they should have the samechemical potential. The potential of the electrolyte solution is determined bythe redox potential of the solution. The chemical potential of the emiconductorelectrode is determined by the Fermi Level (FL)5. For an n type semiconductor,FL is usually higher than the redox potential and hence electrons ow from thesemiconductor to the electrolyte to balance the charges. Thus, the semiconduc-tor gets a net positive charge which does not remain conned to the boundary(like it would if we had metal instead of semiconductor) but diuses into thebody of the semiconductor. The magnitude of charge in the semiconductor

5Fermi Level (FL) is dened as the energy level at which the probability of occupation ofthe level by an electron is exactly half. For a pure intrinsic semiconductor without doping,FL lies at the midpoint of the Band Gap. For a p-tye semiconductor, FL lies just above thevalence band whereas for an n-type semiconductor, it lies just below the conduction band.

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varies decreases exponentially with distance from EPI. Similarly, a p-type semi-conductor would aquire a net negative charge. This charged region inside thesemiconductor is called Depletion Region since the majority charge carriers aredepleted in this region. This region is also called as Space Charge Region (SCR)and its thickness usually ranges from 10nm to 1µm [10]. This accumulation ofcharge leads to ban bending (Refer gure). (EF , EC and EV stand for energiesof FL, conduction band and valance band respectively.)

When an external potential is applied to the semiconductor, its band shiftin accordance with the applied potential for the interior of the conductor. Thebands at EPI however do not change because there is charges ow from elec-trolyte to semiconductor or vice-versa so that potential of both the phases isequal at EPI. Thus, depletion regions arise at potentials positive of the atbandpotential for an n-type semiconductor and at potentials negative of the atbandpotential for a p-type semiconductor. Under opposite conditions, accumulationregions (i. e. majority charge carriers increase in this region) will arise.The charge transfer abilities of a semiconductor electrode depend on whetherthere is an accumulation layer or a depletion layer. If there is an accumulationlayer, the behavior of a semiconductor electrode is similar to that of a metallicelectrode, since there is an excess of the majority of charge carrier available forcharge transfer. In contrast, if there is a depletion layer, then there are fewcharge carriers available for charge transfer, and electron transfer reactions oc-cur slowly, if at all.EPI is also used in solar cells. When light falls on the semiconductor, electronsare promoted to the conduction band. In the interior of the semiconductor,recombination of promoted electrons and the resulting holes takes place leadingto heating of the cell. However, if the electron promotion occurs in the SCR,the electric eld present in SCR forces the electron and hole to move away fromeachother. This leads to output current. Thus, the thickness of the semicon-ductor electrode should ideally be equal to the thickness of SCR so that all ofthe incident light will be converted to output current. Practically however, theminimum thickness of the photoelectrode necessary for ecient light absorp-tion is considerably more than the thickness of SCR. This is the cause of loweciency of solar cells. (For details about solar cells, refer sections 4 and 5).N-type semiconducting electrode at positive potentials (with respect to FB) and

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p-type electrode at negative potentials (with respect to FB) act as photoanodesand the corresponding electrolyte soltions act as cathodes.

7.2 Model for EPI

On, one side there is semiconductor equivalent circuit and on the other side is theelectrolyte equivalent circuit. The two circuits are connected by a capacitance.The equivalent circuit for EPI is shown below.

The junction capacitance arises due to the Space Charge in the semiconduc-tor and the charge accumulation at the EPI.

8 Study of Electronics of Nerves

8.1 Generation of Nerve Impulse

8.1.1 Resting Neuron

Within the nervous system, signals travel yo and fro from brain to various partsof the body in the form of electrical impulses. When the nerve is not sendingimpulses, it is said to be 'resting'. The potential within the cell membrane duringthe resting period is called Resting Potential (RP), which is usually negative,due to negatively charged proteins inside the cell and a higher concentrationof K+ions outside. Typical value of RP is ∼ −70mV in humans. Also, theconcentration of K+ions is typically more outside the cell than inside whilethat of Na+ions is more inside the cell than outside. This constant gradient ismaintained by Sodium-Potassium Pumps (SPP) which pumps ions in suitabledirections to maintain this gradient.

8.1.2 Action Potential

In addition to the SPP, there also exist voltage gated channels (VGC) for trans-port of sodium and potassium ions. These gates open on close depending upon

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the potential dierence across the membrane. If a neuron is stimulated be-yond the threshhold potential (typically −30mV in humans), the sodium chan-nels open and sodium rushes into the axon, causing a region of positive chargewithin the axon. This process is called Depolarization of the axon. This briefreversal of the axon potential is called Action Potential. Due to accumulationof positive charge inside the axon, the sodium channels quickly close and thepotassium channels open letting potassium ions out to restore the cell potential.All of this happens roughly 2ms. The SPP again pumps ions to restore the iongradient. This process continues like a chain reaction down the axon. Thus thenerve impulse propagates along the axon.

8.2 Neuron Equivalent Circuit

VGC are electrically represented by a DC power supply in series with a variableresistor which varies with voltage across the membrane as well as time. Theequivalent circuit consists of two such VGC - one for sodium and other forpotassium in parallel as shown in the circuit diagram.

Vin respresents the inside potential of the cell. Because the charge concen-tration inside and outside the cell is not equal, a membrane capacitance needsto be added along with two VGC. Also even when the channels are closed, thereexists a small leakage current represented by a DC voltage source and a constantresistance.

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The nerve cell or the axon consists of myelin sheaths generated by dierentcells separated by Nodes of Ranvier. The portion of axon between two suchnodes is called a compartment. So, an axon consists of many compartments.joined together by Nodes of Ranvier. The circuit above represents one com-partment. The equivalent circuit of an entire axon is got by joining togethera number of above circuits each separated by a resistance. The way in whichthese electrical units are joined together dependes upon the shape of the axonand its extent of branching.

The nerves in the human retina show a peculiar response. They give out aburst of spikes superimposed over the main spike as shown in the gure. Thegure below shows the response obtained by simulation of the equivalent circuitfor retinal neurons.

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The equivalent circuit of these nerves can be generated by superimposing aseparately generated spike-train of exponentially decaying amplitude over themain peak using an adder circuit. One of the possible equivalent circuits isshown below.

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The amplitude, rate of amplitude decay etc. can be controlled using the RLCvalues while the shape of the main peak is controlled by the neuron equivalentcircuit as before.

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9 Acknowledgements

My sincere thanks to JNCASR for giving such a wonderful opportunity to stu-dents. I am deeply indebted to Prof. K. S. Narayan for his invaluable supportand guidane. I am equally indebted to Prof. Vidhyadhiraja6 for his time andguidance. I also thank Monojit Bag7 for his help.

References

[1] Juan Bisquert, Physical Review B 77, 235203 (2008).

[2] Juan Bisquert, Electrochimica Acta 47 (2002) 2435/2449.

[3] C.-T. Sah, Fundamentals of Solid State Electronics World Scientic, Sin-gapore, 1991

[4] S. Uchida, J. Xue, B.P. Rand, S.R. Forrest, Appl. Phys. Lett. 84 (2004)4218.

[5] B. Mazhari, Solar Energy Materials & Solar Cells 90 (2006) 10211033.

[6] IV and CV Characterizations of Solar/ Photovoltaic Cells Using theB1500A, Application Note B1500A-14.

[7] Shreepad Karmalkar and Saleem Haneefa, IEEE Electron Device Letters,Vol. 29, No. 5, May 2008.

[8] H. Saleem and Shreepad Karmalkar, IEEE Electron Device Letters, Vol.30, No. 4, April 2009.

[9] D. S. H. Chan, J. R. Phillips and J. C. H. Phang, Solid-State ElectromcsVol. 29, No. 3. pp. 329-337, 1986

[10] Electrochemistry of Semiconductors, Adrian W. Bott, Ph.D. BioanalyticalSystems, Inc. 2701 Kent Avenue West Lafayette, IN 47906-1382.

[11] http://www.biologymad.com/NervousSystem/nerveimpulses.htm

[12] http://www.biology4all.com/resources_library/source/63.swf

[13] http://www.brains-minds-media.org/archive/218

[14] http://en.wikipedia.org/wiki/Node_of_Ranvier

6Theorotical Science Unit, JNCASR7Ph. D. student, Molecular Electronics Lab, JNCASR

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