The basic measurement of the primary state of ionization related to the formation of a non-rectifying contact by the electrolysis of insulating solids under homogeneous and heterogeneous contacts has been carried out. The activation energy involved in the first stage has been found to correlate with the band scheme of energy of contact which is necessary for creating the defect centres towards space charge limited injection.Načinili smo osnovna mjerenja početnog stanja ionizacije pri uspostavljanju neispravljačkog spoja nastalog elektrolizom na dodiru istorodnih ili neistorodnih izolatora. Našli smo da je prvotna aktivacijska energija vezana sa shemom pojaseva energijskih vrpci spoja koji su potrebni za stvaranje defektnih središta blizu ograničene injekcije prostornog naboja

Bandyopadhyay, Swarupa

Goswami, Kushalendu

Kar, Satyajit

Maiti, Ajay Kumar

Ray, Kamal Kanti

English

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ISSN1330–0008CODENFIZAE4ELECTROLYSIS THROUGH HOMOGENEOUS AND HETEROGENEOUSCONTACTS IN INSULATING SOLIDSSATYAJIT KAR, AJAY KUMAR MAITI, SWARUPA BANDYOPADHYAY, KAMALKANTI RAY and KUSHALENDU GOSWAMI1Department of Physics, Jadavpur University, Kolkata 700 032, IndiaReceived 15 September 2001; revised manuscript received 27 July 2002Accepted 16 September 2002 Online 7 February 2003The basic measurement of the primary state of ionization related to the formation ofa non-rectifying contact by the electrolysis of insulating solids under homogeneousand heterogeneous contacts has been carried out. The activation energy involved inthe first stage has been found to correlate with the band scheme of energy of con-tact which is necessary for creating the defect centres towards space charge limitedinjection.PACS numbers: 72.20.Jv, 72.90.+y, 73.40.Cg UDC 537.311.4Keywords: electrolysis, ionic solid, Galvani voltage, contact potential1. IntroductionThe energy diagram for the injection [1] of electrons into a crystalline insulatingsolid is understood through the system of heterogeneous metal-insulator contactgeometry [2]. The high amount of electrons generated from the metal into theconduction band [1] or to intermediate metastable band into the insulator needsthe contact of the type as mentioned. The essential requirement in the first stageof electrolysis [3] is to form an ohmic contact [2,4], i.e., a non-rectifying contact.To activate the process of injection, it is necessary that the ionization [5] be setto form the appropriate contacts. The present paper deals with the mechanism ofprimary ionization stage with the geometries of homogeneous and heterogeneousmetal insulator-metal contacts [2,6,7] and with the comparison of the results, withthe aim to evaluate some physical parameters relevant for obtaining the appropriatesignature before electrons are injected into the insulating solid.1Corresponding author: E-mail address: kushal@juphys.ernet.inFIZIKA A 11 (2002) 3, 113–120 113kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .2. ExperimentalPure NaCl (E-mark powder 99.99%) and impurity doped NaCl : Ba2+ (0.006M% ), NaCl : Mg2+ (0.001 M%), NaCl : Al3+ (0.001 M%) and NaCl : Cd2+ (0.001M%) single crystals were grown in the laboratory by the Czochralski-Kyropolousmethod, using a microprocessor-controlled furnace and servo-controlled rotationpulling arrangement. Crystals were cleaved along the <100> direction and surfacepolished. A specimen so prepared was placed between two flat electrodes, onemade of brass and the other of platinum. The system was housed in an electricalfurnace. The injection experiment was carried out at different temperatures underconstant fields of 415 V cm−1 or 600 V cm−1. In a separate experiment, the injectionprocess was carried out under similar conditions as in the first arrangement witha specimen mounted between a pointed brass cathode and a flat platinum anode.The process was stopped before the onset of the second zone electron injection [8,9].The measurements were repeated for all specimens. The current was measured witha Bausch and Lomb series 5000 strip-chart recorder.3. Results and discussionThe current growth curves (Figs. 1 and 2) for single and doped crystals indicatethe effect of temperature for particular fields of 415 V cm−1 and 600 V cm−1.600 700 800 90001234(a) NaCl : Cd2+ NaCl NaCl : Al3+ NaCl : Ba2+ NaCl : Mg2+Current Density in µA cm-2Temp in K600 700 800 900-0,50,00,51,01,5(b) NaCl : Ba2+ NaCl : Cd2+ NaCl : Mg2+ NaCl : Al3+ NaClCurrent Density in µ A cm-2Temp in KFig. 1. Current density against temperature for pure NaCl, NaCl : Ba2+,NaCl : Mg2+, NaCl : Cd2+ and NaCl : Al3+ at a constant field of a) 415 Vcm−1,b) 600 Vcm−1 for homogeneous contacts.114 FIZIKA A 11 (2002) 3, 113–120kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .600 700 800 900 1000-0,50,00,51,01,5(a) NaCl NaCl :Ba2+ NaCl :Al3+ NaCl :Mg2+ NaCl :Cd2+Current Density in µA cm-2Temp in K500 600 700 800 900-0,50,00,51,01,52,0(b) NaCl : Ba2+ NaCl : Cd2+ NaCl : Mg2+ NaCl : Al3+ NaClCurrent Density in µ A cm-2Temp in KFig. 2. Current density against temperature for pure NaCl, NaCl : Ba2+,NaCl : Mg2+, NaCl : Cd2+ and NaCl : Al3+ at a constant field of a) 415 Vcm−1,b) 600 Vcm−1 for heterogeneous contacts.From the theoretical approach [6,10,11], the ionic current density does not de-pend on the shape of electrodes and is given byJ = (eµEnc) exp(−W0/kT ) , (1)where E is the electric field, µ the mobility, nc the effective density of states ofelectrons in the conduction band, W0 the activation energy for ionization, k theBoltzmann constant and T the temperature.Activation energy [11,12] for ionization has been calculated from lnJ vs. 1/kTplot (not shown) for both fields of 415 V cm−1 and 600 V cm−1. The results forthe investigated specimens are shown in Table 1. It is clear from the table thatvalues of W0 for heterogeneous electrodes are less than those for homogeneouselectrodes. These expected results indicate the non-uniformity of fields in the caseof the pointed cathode.So far as the band scheme is concerned, thermodynamical equilibrium demandsthe Fermi energy to have the same value everywhere in a homogeneous system.If the two systems of particles are brought into contact at a temperature T , theequilibrium will be established and thereby the free energy of the whole systemattains a minimum value. The contact geometry can be basically explained on theprinciple of obtaining Galvani voltage [5] in the case of a metal – insulator andinsulator – metal contact.FIZIKA A 11 (2002) 3, 113–120 115kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .TABLE 1. Ionic-conductivity activation energies of pure NaCl, NaCl : Ba2+,NaCl : Mg2+, NaCl : Al3+ and NaCl : Cd2+ at constant fields of a) 415 Vcm−1 b)600 Vcm−1, for homogeneous and heterogeneous contacts.Activation energy (eV)Sample Homogeneous electrodes Heterogeneous electrodesField Field Field Field415 Vcm−1 600 Vcm−1 415 Vcm−1 600 Vcm−1Pure NaCl 0.963 0.648 0.928 0.594NaCl : Ba2+ 0.966 0.775 0.952 0.630NaCl : Mg2+ 0.768 0.772 0.730 0.692NaCl : Al3+ 0.774 0.624 0.702 0.535NaCl : Cd2+ 0.942 1.033 0.677 0.640The contact or Volta potential [5] will obviously be equal to the difference ofthe work functions of the contacting materials as given by|Vc| = 1e|W1 − W2| . (2)To make it clear, consider in the first step a metal – metal contact. Later thiscan be modified to the case of a metal – insulator or insulator – metal contactsituation by neglecting the temperature dependence of the Fermi energy, with thesimplifying assumption that the metals (1 and 2) be at the same temperature Tand also that W1 < W2. When such two metals are brought from infinity to a smallmutual distance, an exchange of electrons will set in simply because the thermoionicemission exists at T > 0 K. Since W1 < W2, more electrons will initially cross frommetal-1 to metal-2, resulting in an excess of negative carriers on metal-2. As aresult, an electric field builts up, causing the formation of a potential differencebetween the two metals. The potential difference is established at such a valuethat the net current between the two metals vanishes. It reaches the value Vc of thecontact potential in thermodynamic equilibrium. If ξ1 and ξ2 are the Fermi energiesof metal-1 and metal-2 while in contact and ξ′1 and ξ′2 those before contact, we canwrite(ξ′1 − ξ1) + (ξ2 − ξ′2) = eVc , (3)because of the equipotential behaviour in a metal and because the energies ofelectrons in metal-1 and metal-2 are reduced by (ξ′1−ξ1) and increased by (ξ2−ξ′2),respectively. Zero of the energy scale before contact lies below the vacuum potentialby an amount of(ξ′1 − W1) = (ξ′2 − W2) or (ξ′1 − ξ′2) = W2 − W1 . (4)116 FIZIKA A 11 (2002) 3, 113–120kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .The free energy of the total system is given byF = F1 + F2 .The condition of minimum free energy, (δF )T,V,N = 0 now readsδF =δF1δN1∣∣∣∣T,V1dN1 +δF2δN2∣∣∣∣T,V2dN2 = 0 , (5)where volumes V1 and V2 contain N1 and N2 particles before contact at temperatureT .With the additional conditionN1 + N2 = N(constant) , (6)Eq. (5) reduces toδF1δN1∣∣∣∣T,V1=δF2δN2∣∣∣∣T,V2=δFδN∣∣∣∣T,VSo,ξ1 = ξ2 = ξ . (7)Equations (3), (4) and (7) yieldW2 − W1 = eVc . (8)It may be inferred that the band diagrams of the initially separated metals aremutually displaced by eVc when the contact has been formed. It is a commonpractice to assume the band scheme of one of the contact materials to be the fixedone (ξ′1 = ξ1), so that scheme for the other material is shifted by the full amountof the contact potential i.e. ξ2 − ξ′2 = eVc.From these equations, and with a good approximation for the electron concen-tration Eq. (5), we haveξ′1 − E′c1 = ξ1 − Ec1 , (9)ξ′2 − E′c2 = ξ2 − Ec2 , (10)where (E′c1, E′c2) and (Ec1, Ec2) are the bottom-energies of the conduction bandsof the two metals before and after the contact, respectively. Taking ξ1 = ξ2 = . . . =const. and subtracting Eq. (9) from Eq. (10), we obtain,Ec2 − Ec1 = (ξ′1 − E′c1) − (ξ′1 − E′c1) = (ξ′1 − ξ′2) − (E′c1 − E′c2) , (11)eVG = Ec2 − Ec1 = eVc − (E′c1 − E′c2) . (12)FIZIKA A 11 (2002) 3, 113–120 117kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .The quantity VG is known as the Galvani voltage which corresponds to the energydifference between the bottoms of the conduction bands of the conducting materi-als. By adopting E′c1 = E′c2, Galvani voltage is identical to the contact potentialdifference under the effect of identical electron affinity of the two metals.In ionic solids, like alkali halides, the electric current under electrolysis begins toflow by the motion of ions and the ion mobilities are enhanced thermally. Due to theprocess of electrolysis, the anions reach the cathode and the cations the anode. Theions pile up under the influence of the metal field, and the metal surface potentialis raised to such an extent that leads electrons on the negative ions to the Fermilevel of the metal anode, or to lower the holes on the positive ions to the Fermi levelof the metal cathode so that the charges of both types of ions can be transferredto the metal electrodes.The activation energy connected to the formation of the contact has a correlationwith the Galvani voltage. The Galvani voltage type barrier must be overcome tohave an adequate ionization current. Thus the activation energy (W0) under ionicprocess is at most equal to eVc.The non-uniformity of fields in the case of a pointed cathode is very impor-tant for the formation of the ohmic contact. A large supply of carriers from thepointed cathode will be active immediately when the contact is formed. Otherwise,less space charge [6,11] is tantamount to more carriers flowing through the anodethereby attenuating the contact formation energy.The cessation of this thermodynamical process is consequent upon the formationof an ideal contact and under inhomogeneous geometry of the contact, copiousamount of electrons start the process of space charge current necessary for trappingthe carriers (general feature of alkali-halide crystals towards the formation of colourcentres).From the results for the activation energy, it is clear that the heterogeneousgeometry is effective in deriving the electrons in stage 2 under the influence of thespace charge limited (SCL) current and also the basic demand for the continuationof injection. Instead, many point contacts (homogeneous) disturb the geometry onthe atomic scale, resulting in the absence of SCL current.This persistence of ionic current and the absence of the second stage currentcause noticeable deviation from the pointed contact geometry along with the exhi-bition of increase in the value of the activation energy, and are important for theformation of the ohmic contact by yielding disorder in the crystal matrix.4. ConclusionThe ideal condition of contact is confirmed with a heterogeneous cathode-anodecontacting system which is a prerequisite for the electronic current to flow beyondthe ionic zone, while under homogeneous contact, there is no evidence for suchspace-charge limited current injection to follow.118 FIZIKA A 11 (2002) 3, 113–120kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .References[1] N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals, 2nd ed., Dover,New York (1964), Ch. 4.[2] K. C. Kao and W. Huang, Electrical Transport in Solids, vol. 14, Pergamon (1981) p.73.[3] J. H. Schulman and W. D. Compton, Color Centres in Solids, Pergamon, Oxford (1962)Ch. 1, 3.[4] M. T. Montojo, F. Jaque and C. Sanchez, J. Phys. Chem. Solids, 38 (1977) 657.[5] G. Busch and H. Schade, Lectures on Solid State Physics, 1st ed., Pergamon, Oxford(1976) Ch. C & H.[6] A. K. Maiti, K. Goswami and A.K. Lahiri, Fizika (Zagreb) 22 (4) (1990) 589.[7] A. K. Maiti, K. Goswami, A. Manna, S. Choudhury and A. Choudhury, Fizika (Zagreb)14 (1) (1982) 7.[8] M. A. Lampart and P. Mark, Current Injection in Solids, Academic Press, New York(1970) Ch. 5-9.[9] G. A. Andereev, G. B. Semuskin and A. N. Tsikin, Sov. Phys. Solid State 9 (1968)2564.[10] A. K. Lahiri, A. K. Maiti and K. Goswami, Solid State Comm. 59 (1986) 457.[11] S. Kar, A. K. Maiti, M. Sengupta and K. Goswami, Fizika A (Zagreb) 9 (4) (2000)159.[12] M. Sengupta, A. K. Maiti and K. Goswami, Fizika A (Zagreb) 2 (1993) 3.FIZIKA A 11 (2002) 3, 113–120 119kar et al.: electrolysis through homogeneous and heterogeneous contacts in . . .ELEKTROLIZA KROZ HOMOGENE I NEHOMOGENE SPOJEVEIZOLATORANačinili smo osnovna mjerenja početnog stanja ionizacije pri uspostavljanju neis-pravljačkog spoja nastalog elektrolizom na dodiru istorodnih ili neistorodnih izo-latora. Našli smo da je prvotna aktivacijska energija vezana sa shemom poja-seva energijskih vrpci spoja koji su potrebni za stvaranje defektnih sredǐsta blizuograničene injekcije prostornog naboja.120 FIZIKA A 11 (2002) 3, 113–120

Elektroliza kroz homogene i nehomogene spojeve izolatora

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