Goswami, Kushalendu

Maiti, Ajay Kumar

Sengupta, Manjusri

IACS Institutional Repository

Indian J. Phys. 71A(2), 143-151 (1997)IJP A—  an international journalKinetics of trapped electrons in alkalihalide crystals under electron injectionManjusri Sengupta, Ajay Kumar Maiti and Kushalendu Goswami Department o f Physics, Jadavpur University, Calcutta-700 032, IndiaR e c e iv e d  1 1  J u n e  1 9 9 6 . a c c e p te d  2 8  N o v e m b e r  1 9 9 6Abstract : An injection expenment is performed in single crystals of KCI and KI under space charge limited condition. The kinetics o f electron traps like nature o f traps, shallow or deep and drift mobility of carriers are determined. Variation of the drift mobility o f carriers with colouration is also studied to have a comparative idea o f the density o f states in conduction bend for these two types o f crystals.Keywords : Electron injection, colour center, density of states PACS Nos. : 7 1.20.Fi, 6 1,72.Ji. 72.20.Ju1. IntroductionThe electrical performances of the contact between an insulating solid like ionic crystal and liietal is a difficult problem till date. The first stringent condition to be fulfilled is that the ionic processes in the crystal create conditions at the cathode crystal interface which are the pre-requisite for the onset of the injection of electrons from the cathode into the crystal [1], The ionic transport paves the path for the formation of a new secondary cathode of alkali metal. Essentially, this process allows the electron injection during the second and third zone [2]. The secondary contact is termed as Ohmic and with such contact, the current voltage relationship is nonlinear and depends upon number of factors [3]. The term ‘Ohmic’ is inappropiate so far as the current voltage relationship is concerned and the linear conduction is achieved only at low fields. The conduction becomes nonlinear when the carrier injection from the electrode or the space-charge effect predominates. In other words, an Ohmic contact can also be realised as one which creates [4] an accumulation of charges extended from the interface of the metal-insulator to the interior of the solid. When a suitable contact is obtained, SCL current dominates the conduction in an ionic crystal containing large number of trapping sites [5].© 1997 IACSThe present paper deals with the determination of some kinetics of trapped electrons like mobility and thereby obtain a comparative picture of the density of states of the conduction level of the crystals.2. ExperimentalCrystal flakes of KC1 and KI cleaved along <100> directions of dimensions 0.86 cm x0.73 cm x 0.61 cm and 1.00 cm x 0.60 cm x 0.40 cm respectively, were obtained from the single crystal blocks grown in the laboratory, adopting Kyropoulos method [5], a crystal flake was mounted between a pointed brass cathode and a flat platinum anode. An electron injection experiment [6] was performed using these crystals at a constant temperature of 723 K under the application of different electrical fields between 925 and 1100 V cm-' for KCI <100> ; 100 and 175 V c n r ' for KI <100> separately. The injection current and colouration growth have been recorded simultaneously as a function of time by Bausch and Lomb series 5000 double pen recorder with pen speed 2.5 cm min-1 for KCI and 5 cm min ' for KI at each injection field. The optical measurement of the colouration growth have been carried out by shinning maximum F  absorption light for KCI and KI on a small portion of the specimen very near to the pointed cathode with the ^ielp of an Oriel grating monochromator. The injection operation was stopped well before ifie advent ol the third zone [7], From the accumulated data, graphs of current and optical densityagainst time were plotted for each electrical fields for KCI and KI crystal as shown in Figure 1.] 44 Manjusri Sengupta, A jay Kumar Maiti and Kushalendu GoswamiFigure 1(a). Growth o f injection current and optical density against time at 723 K under an iqection field o f  925 V cm - 1  for KCI single crystal.CUHRENT IN ±jAKinetics o f trapped electrons in alkalihalide crystals etc 145zm5Z>-tnzLlIo<u&Figure 1(b). Growth ol injection current and optical density against time at 723 K under an injection field of 1050 V cm"* for KCI single crystalskc i 0 o d >FIELD 1100 V cm'1• CURRENT O OPTICAL DENSITYFigure 1(c). Growth of injection current and optical density against time at 723 K under an injection field of 1100 V cm- 1  for KCI single crystals.146 Manjusri Sen gup ta, Ajay Kumar Maiti and Kushalendu Goswami3. Results and discussionsFigures 1(a), 1(b) and 1(c) show the growth o f  current and optical density (colouration) for KC1 crystal in which the ionic /o n e  is shown to be in existence for a brief period o f  time when the necessary conditions lor contact are satisfied  to ensure the flow  o f  the space charge limited (SC L) current through the crystal w ell within the second zone. The time scale in recording current and optical density (colouration) is arbitrarily truncated in each injection process. Sim ilarly, the growth o f  current and colouration  for KI crystal is exhibited in Figures 1(d), 1(e) and 1(0- Comparing the current o f  growth o f  KCI and KI, iiFigure J(d). Giowih ol injection current and optical density against time at 723 K  undei an lnicctilin field of 100 V cm- * for K I single crystalsis observed that KI needs a much low er electrical field  than KCI, w h ile  the SCL current Now is many times more in KI. The Hal nature o f  the current growth curve in KCI lot all the liclds, suggests that the growth rate is sluggish  w hich may be due to the deep lying traps in KCI |8 ]. H ow ever, in KI crystal, the current grow s very rapidly under quite low  electrical fields, suggesting that the traps may be shallow er in nature. Thus, the current and colouration growth o f KCI and KI are quite distinguishable from each other.The effective  drift m obility (/i) o f  the electrons undergoing trapping-defrapping under thermal equilibrium, is determined using the equation o f  the formKinetics o f  trapped electrons in alkalihalide crystals etc 147where E is the applied field, e is the electronic charge and n is the number of electrons per unit volume of the specimen, n is given by1 t u ?jn  =  r id t  j ( 2 )eLa  Jowhere a  is the cross section of the specimen, v is the drift velocity of the carrier in this napping-detrapping zone and i the current through the specimen.Figure 1(c). Growth o f injection current and optical density against time at 723 K under an injection field of 150 V cm* 1 for KI single crystafs.From the nature of the experimental data, the best fit equation for current appears to he u nonlinear function of limei = a t h. (3)Alter some algebraic manipulations and using eqs. ( 1 ) and (2), the mobility is obtained as,/ r  ~\'lh• (4)r  e  L/(*>+!)_The value of a and b have been deduced by the method of averages from the available data using eq. (4). Mobility of the electrons at the experimental temperature of 723 K have been evaluated and variations of mobility values with trapped centre (in terms of optical density) have been plotted for different fields as shown in Figure 2.148 Manjusri Sengupta, Ajay Kumar Maiti and Kushalendu GoswamiFigure 1(f). Growth of injection current and optical density against time at 723 K under an injection field of 175 V  c n r J for K l single crystalsIt is clear from Figures 2(a) and 2(b) that the mobility value decreases in a mannci more or less like a rectangular hyperbola, as the optical density (colour centers) increases. Let us try to understand the situation from the physical point of view At the very beginning of the growth of colouration (also the current growth), there is an ample scope for trapping and detrapping of the carriers injected from the secondary contact. Practically at first, the trapping occurs along the least path which is from the pointed cathode to the anode in a straight line and then in all possible directions randomly. Consequently, the velocity ol the electrons is more sensitive on how many and in what fashion the electrons are being trapped. With time, the electrons on their way through the bulk solid are trapped with increasing number when they become less mobile, thereby decreasing in mobility value. As most of the vacant traps are persistently filled up, randomness in trapping appears to be restricted, which attributes the mobility to attain a constant value, while during the trapping process, the number of electrons to reach the anode from the pointed source of infinite resorvoir of carriers are increased causing the increase in current. This situation may also be realised from a theoretical standpoint. I f  the free electron concentration ;s disturbed from its thermal equlibrium value (JV0 ) by injecting to a new value {N ), then on a time-scale long compared to the microscopic trapping and detrapping times, the population (N ,)  of the electron traps will be in quasithermal equilibrium with N [9]. Then the entire body of the injected electrons will predominantly be the trapped electrons, and the presence ofKinetics o f trapped electrons in alkalihalide crystals etc 149Figure 2(a). Mobility o f injected carriers against optical density under different injection fields at 723 K for KC1 single crystalsthermally generated free electrons will be insignificant in number in contrast to Nt. The drift mobility (/J) will follow an equation of the type [10]= ^ 0[ | + K / A/c)exp(M'(/ ^ 7’) r *  (5)where Nt is the density of states in conduction band, W, is the activation energy for the formation of F center, and is of the order of 1 eV for KI and KCI, K and T are respectively Boltzmann's constant and temperature of the experiment. For the crystalline materials in question, at the working temperature of 723 K, (N J N c) exp(W JK T)  )) 1, as (Nf//V( ) 10 '1 -  10-3 and the eq. (5) takes the simple formv  = n {n c/ N' ) cM ~ w ' I k t )- (6)From eq. (6), it is clear that at a particular temperature and for a specific specimen as Nt being the intrinsic property of the material, all the terms other than Nt in the right hand side of the equation arc constant and fl bears an inverse relationship with /Vp which is justified150 Manjusri Sengupta. Ajay Kumar Maiti and Kushalendu GoswamiFigure 2(b). Mobility of injected earners against optical density uhder different injection Helds at 723 K for K1 single crystals.experimentally by Figure 2. From the plot of fj vs 1 INf in the curved portion of Figure 2, an approximate straight line is obtained as shown in Figure 3. The slope of the straight lineFigure 3(a). Mobility of injected carriers against inverse of colour center per c.c. for KC1 single crystals.will,provide the value of PqNc exp (-  Wf / K T )  for the specimens. If we assume that the carrier mobility (/Iq) of the ideal crystal be of the same order for both KCI and KI, then N, for KI turns out to be approximately ten times higher which is an indication of higherKinetics o f  trapped electrons in alkalihalide crystals etc 151conduction power of KI in constrast to KC1. We have seen experimentally that KC1 requires much higher field approximately ten times compared to the field required for KI to producecolour center. This result may be the consequence of higher density of states in conduction band of KI as compared to KC1. Thus, this can oe a very interesting field of study and can provide us with significant information about the Space Charge Limited conduction in alkalihalide crystals.AcknowledgmentManjusri Sengupta extends her gratitude to the Council of Scientific and Industrial Research, Government of India, for funding.References[1] M T Moniojo, F Jaque and C Sanchez /  P h ys. C hem . S o lid s  3* 6S7 (1977)[2] G A Andreev, G B Semushkin and A N Tsikin Sov. P h ys. Sol. S la te  9 2564 (1968)[3] K C Kao and W Whang E le c tr ic a l T ra n sp o rt in  S o lid s  14 77 (1981)[4] A Rose and M A Lampcit P h ys. R ev . 113 1227 (1959a)[5] A K Maiti, A K Lahiri and K Goswami P h y s ic s  T ea ch er  { S p e c ia l issu e  o f  In d ian  P h y s ic a l S o c ie ty ) 29 38(1987)16] Manjusri Sengupta. Ajay Kumar Maiti and Kushalendu Goswami FIZ1KA A2 3 145 (1993)[7] M T Montojo and C Sanchez/ Phys. Chem. S o lid s  35 1437 (1986)[8] Ajay Kumar Main, Kushalendu Goswami and Anjan Kumar Lahiri FIZIKA  3 15 247 (1983)[9] M A Lampcit and P Marie C u rren t In jection  in S o lid s  (New York : Academic) ( 1970)[10] V B Sandomirsky and N M Mushakhanova S o lid  S ta te  C om m on. 4 0  607 (1981)

Kinetics of Trapped Electrons in Alkalihalide Crystals Under Electron Injection

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Kinetics of Trapped Electrons in Alkalihalide Crystals Under Electron Injection

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