56 Applicationsof SurfaceScience14(1982—83)56—72North-HollandPublishingCompany

SECONDARY ELECTRON EMISSION AND CONDUCTIVITYMECHANISMS OF EPITAXIAL MgO FILMS

J.W. GIBSONand R.E. THOMASNaval ResearchLaboratory, Washington,DC 20375, USA

Received4 May 1982; acceptedfor publication 29 July 1982

Secondaryelectron emission andelectronbombardmentinducedconductivity measurementshave beenmadeon epitaxial MgO films (50—200A thick) depositedon a (l00)Mo substrate.Thefilms were depositedand measurementsmade under UHV conditions.Changesin the samplesurfacepotential (Vs) were determinedfrom changesin the thresholdenergyof the secondaryemissionenergydistribution,thus allowing current(I) versus curvesto bemade. It wasfoundthat the conductivity data could be fitted best by a Poole—Frenkelconductivity mechanism.Mechanismsfor electroninjection from the substrateinto the film were not consistentwith thedata, implying that holesarethe dominantchargecarriers.This is in contrastto most resultsonpolycrystallineMgO films which conclude that electrontunneling is probablydominant in suchfilms. The possiblewaysthat thesedifferencesin conductionmechanismscanaffect processesthatdegradethesecondaryemissionpropertiesof thesefilms arediscussed.

1. Introduction

Secondaryelectronemissionfrom MgO has beenthe subjectof numerousinvestigations.Lye [1] andWhettonand Laponsky[2] havereportedmaximumvalues of secondaryemission(

6max) of 20 to 25 on singlecrystals of MgOcleavedin ultra high vacuum. In addition, Whetton and Laponsky [3] as wellas Haxby [4] haveobtainedvaluesof ~max comparableto thebulk singlecrystalin thin crystalline films 100 to 500 A thick. Other workers have investigatedMgO films on various substrates[5—8],and it is generally found that thesecondaryemissionpropertiesare dependenton the substratesusedand themethodsof film preparation.From previous measurementson MgO films(generally thicker film or bulk material) several effects of interest havebeenreported.Theseincludea dependenceof ~ on internal field [3], persistenceofemissionafter turningoff the primary beam(time dependenteffects)[9], andelectronbombardmentdegradationof S [10]. Theseeffects are important inany practical secondaryemission application,and are all related to chargetransportmechanismsin MgO.

Information on the chargetransportmechanismis usually obtainedviaconductivity measurements.Conventionalconductivity measurementon bulk

0378-5963/82/0000—0000/$02.75© 1982 North-Holland

J.W. Gibson,R.E. Thomas/ Epitaxial MgOfilms 57

singlecrystal MgO havedeterminedthat both ionic andelectronicconductionmechanismsare present.The type of conductivity that dominatesdependsonsuch factors as temperature,oxygen partial pressure,and the purity of thesamples[11—13].Most conductivity measurementsare made by applying apotential acrossthe sample,and do not necessarilycreateconditionsin thesamplerepresentativeof thoseexistingunderelectronbombardment.However,Dresner [9] has measuredconductivity effectsunderelectronbombardmentconditions in films somewhat thicker than used here. For his samplesheattributes the chargetransportmechanismsprimarily to electron tunnelingthroughthe substrate—MgOinterfaceSchottkybarrier.

In the studiesreportedhere, thin epitaxial films of MgO, from 50 to 200 Athick, are producedon a (lOO)Mo substrateat ambient temperature.Theelectronbombardmentinducedsurfacepotential,V~,is measuredas a functionof primary beamenergy,E~,the net current,‘N’ andsampletemperature.Theresultsof thesemeasurementscombinedwith previouslyreportedvalues[14]ofboth work function, ~, and electronaffinity, x~leadsus to concludethat, forthese films, the chargetransportunderelectronbombardmentconditionsisprimarily via hole conduction.Theimplications of this conductionmechanismto the performanceof devicesusingMgO as a secondaryemissionsurfacearediscussedbelow.

2. Experimentaltechmques

The MgO films wereevaporatedfrom a heatedMgO sourceonto a polishedandetchedsurfaceof a singlecrystal(100)Mo substratewhich wasin the formof a cylindricaldisc0.04 inch thick and0.140inch in diameter.The sourcewasMgO cataphoreticallycoatedon a Jr ribbon from a slurry of MgO powderinmethyl alcohol. Iridium was usedbecauseit doesnot reduceor significantlyreactwith MgO. The thicknessof the films wasgenerallydeterminedfrom thesimultaneousevaporationof the film ontoa quartzcrystal thicknessmonitor.All films wereevaporatedin the sameUHV chamberin which the experimen-tal measurementswere made. Pressuresin the chamberwere from 2 to8 X l0 ~ Torr during measurements.

A standardfour-grid retarding voltage LEED system(PHI-model 15—180)wasusedto makeall the measurements.TheLEED patternsobtainedfrom theMgO films verified theepitaxialnatureof thefilms. Augerspectrafor thefilmswereobtainedby usinga primarybeamenergyof 2500 eV and5 V peak-to-peakmodulationon the retardinggrids. TheAugerspectrashowedMg and0 peakstypical of MgO with no observablecontaminantsor impurities. Thelow energysecondaryelectronemission energy distribution, N(E), was measuredusing0.5V pead-to-peakmodulation on the retarding grid. As will be discussedbelow,theselow energydistribution curveswereusedto determinethe surface

58 J. W. Gibson, RE. Thomas/ Epitaxial MgO films

potential.The samplewas biasedto + 300 VDC to measurethe primary beamcurrent,J~,,andwith —6 ~DC on the sampleand +22.5 VD(. on grid 1, the netelectron current to the sample,‘N’ was determined.Thereby the secondaryelectronemissioncoefficient,

6 = ‘~/‘~= (i~— 1N)/Ip’

could be calculated.Eachfilm was characterizedby the thickness,the LEEDpattern, Auger spectra, and secondaryelectron emission coefficient as afunction of primary beamenergy.

Electronbombardmentdensitiesfrom the LEED systemelectrongun usedduring the measurementof energydistribution curves were typically 1 ~sAwhich for our beam size correspondsto about 1 mA/cm2. During Augeranalysisthe sample was bombardedby electroncurrentsof up to 60

1.tA at2500 eV which is about 0.1 A/cm

2 or 0.25 kW/cm2. Even with this highbombardmentdensity for periods of an hour or more no effect of anydegradationof 6 for the MgO films wasobserved.

3. Secondaryelectronemissionmeasurements

6-Values for several different film thicknessesversus the primary beamenergy are shown in fig. 1. The maximum6 for the thickest film (— 200 A) is19.4. The range of the first crossovervoltage is from 14 eV for the thicker

22

20 200A

~4:~/hhIhhhhhh111I~0 200 400 600 800 1000 1200 1400 1600

PRIMARY BEAM ENERGY, Ep(eV)

Fig. I. Secondaryemissionratio (~)as a function of primary beamenergy(Er) for differentthicknessMgO films on Mo.

J. W. Gibson, R.E. Thomas / Epitaxial MgO films 59

films, to about 20 eV for the thinnestfilms. The valuesof 6 obtainedarecomparableto the highervaluesof 6 usuallyobtainedfrom singlecrystalMgO[1—4].Thereweresomeinconsistenciesin the valueof 6 measuredfor films ofnearlythe samethickness.This is not fully understoodat this time, but it isbelievedto be due to variationsin the temperatureof the sourcefrom whichthe MgO was evaporatedonto the substrate.As the source of MgO wasdepleted, higher temperatureswere required to evaporateMgO onto thesubstrate.This may have causedsome reduction of the MgO resulting inchangesin stoichiometryof the depositedfilms.

4. Surfacepotentialmeasurements

Whena beamof electronsis incident on the surfaceof an insulatingfilm ofMgO, a voltagedrop developsacrossthe film, the polarity of which dependson 6. In the case where 6> 1, more electronsare leaving the surfaceassecondariesthanare incident on it. Thus, in steadystate the surfacepotentialbecomespositiveandchargemustbe transferredthroughthe film from the Mosubstratein order to compensatefor those electronsleaving the surface. Bymeasurementof this surfacepotential changeas a function of E~and ‘N’

insight canbeobtainedinto the mechanismsof chargetransportin thesefilms.In order to interpret these datain terms of conductionmechanisms,it is

essentialthat any changesin ‘N be proportional to current densitychanges,i.e., the beamdiametermustnot changesignificantly as the beamcurrentorbeamenergychanges.The currentdensityprofile of the beamwas measuredusing a Faradaycage with a 0.013 cm hole. It was found that under thefocusingconditionsusedhere,the beamprofile wasessentiallyGaussianwith ahalf-width of ~0.038 cm. Over a currentrange from 5 X iO~to 105A thehalf-width remainedeffectively constant(within ‘~ 5%). When was variedfrom 50 to 300 eV the meanbeamareadecreasedabout 20%.The efffect ofthis will be discussedin section6.

The method used in this work to determinethe surfacepotential is tomeasurethe shifts in the thresholdenergy for secondaryemission obtainedfrom the secondaryelectron energy distribution curves, N(E). The energydistributioncurvesrepresentthe numberof secondaryelectronsbetweenE andE+ dE emittedas a function of their energyE. A typical pair of N(E) curvesfor different values of ‘N is shown in fig. 2. The energy at which the initialslopeof this curve extrapolatesto zero is a measureof the surfacepotential.Ashift in this extrapolatedvalueis equal to the changein surfacepotential.Thefigure showsa shift in the surfacepotential resultingfrom a changeof the netcurrentthrough the sample.As will be seen,a similar shift would occur for achangein temperatureor a changein primary beamenergy.

By plotting the threshold voltage, E’~,from a seriesof N(E) curves for

60 J. W. Gibson,R. E. Thomas/ EpitaxialMgO films

1N108 ~

NORMALIZED

NI E)

~ws__1 ~ E(eV) 20

Fig. 2. Distribution in energy(N(E)) of the secondarycurrentas a function of energy E fordifferentvaluesof netcurrent(‘N) in thesample.The curvesarenormalizedto give thesamepeakvalueof N(E). This illustratestheshift in surfacepotential(~Vs).

differentvaluesof ‘N andfixed E~,oneobtains‘N versusthesurfacepotential.Typical plots of this type are shown in fig. 3. In order to determinethe filmconductivity it is necessaryto know the voltage ~ J7~— V~developedacrossthe film. J’~wasdeterminedby extrapolatingthe ‘N versusV~curvestozero ‘N’ as shownby the dotted lines in fig. 3. Thevalueof V

0~determinedinthis mannerchangesoverperiodsof 24 hours due to adsorptionof ambientgaseson the surface.The determinationof Vc~was probably the greatestuncertaintyin the conductivity measurements.However, extrapolationsmadeon cleanfilms wereconsistentbetweenfilms.

Since, as describedabove, the current density profile is approximatelyGaussian,andnot uniform, the surfacepotentialwill vary over the beamarea.Thequestionthen arisesas to how valuesof ~ measuredin the abovemannerare to be interpreted.The variation in V~as a function of current densitydependsupon the conductionlaw. Theconductionlaw that best fits the data(seeeq. (9) below) results in a 20% variation in 1’~overthe centralpartof thebeam,which contains3/4 of the total current.Moreimportantly, this variationis essentiallyindependentof total beamcurrent,so that the averagingprocessfor 1”~is independentof total beamcurrent.The measuredvalues of V~areobtained by fitting the slope of the N(E) curves at approximatelyN(E)= ~N(E)ma,(. Becauseslopesare taken this high up on the N(E) curves, thevaluesof V~areweightedtowardthe areasunderthebeamreceivingmaximumbeamcurrent. Although an exact calculation has not been made, a semi-quantitativeestimateis that the measuredvaluesof V~are within 10% of thevalueof J’~thatwould be obtainedif the currentdensitywasconstantover the

J. W. Gibson,R.E. Thomas/ EpitaxialMgOfilms 61

9-

8- /- FILM THICKNESS /

90A

6-

E~=150eV

-~ E~=50eV4-

3

2

48 4.’6 4.4V

05 VSIeV)

Fig. 3. Net current(‘u) as a functionof surfacepotential (F’5) for two different primary beamenergies(E1,).The zerocurrentvalueof surfacepotential(F’~)is obtainedby extrapolation.

beamandequalto J0/ira2 (where2ais the half-width of thebeam).Hencethe

Gaussianprofile of the beam does not introducea significant difficulty ininterpretingV~.

S. Model of potential distribution

In order to interpret the ‘N versusLW5 curves a model of the potential

distribution and its relation to the band structurewithin the films is needed.Fig. 4a shows the proposedband diagram for the film when thereis no netchargeor current flow. A flat band condition is assumed,but it will be seenlater that anyreasonablebandbendingdue to interfaceor surfacestateswouldnot affect the conclusionsdrawn. From previously publishedmeasurements[14], it was found that the work function 4 of thesefilms is 3.5 eV, and theelectronaffinity x 0.85 eV. For the flat bandcondition this requiresa value

62 J.W. Gibson,R. E. Thomas/ Epitaxial MgOfilms

(a) NO e-BOMBARDMENT

= 0.85eV

Mo SUBSTRATE ~‘=3.5eV~b=2.]eV

~

MgO FILM VACUUM_____ t

(b) UNDER e-BOMBARDMENT

~—9 e—~sECoNDARIEs

R TRAPPED

~

Fig. 4. Energydiagramto illustrate bandstructureof MgO films usingvaluesof ~ andxobtainedfrom [14]; (a) illustratesthe flat bandno bombardmentcondition, and (b) shows the proposedbandbendingunderelectron-bombardment.

of 4h for the barrierat the Mo/MgO interfaceof 4ib 2.7 eV.Under electron bombardmentelectron—holepairs are createdup to some

depthR within the film, as indicatedin fig. 4b. R increaseswith the primarybeamenergy.All measurementsshownhereare for 6> 1. Thus,the net flow ofelectronsis in the vacuumdirection.Sinceholes in materialssuchasMgO tendto quickly becometrapped[15], whereasthe electronsare moving with highervelocity so that some escapethe film, it would be expectedthat the trappedholesprovide the main contributionto the spacechargenearthe surface.Fig.4b illustratesthe resultingpotential distribution through.the film underelec-tron bombardment.At this point it shouldbe noted that for all the measure-mentspresentedherethe voltagedrop,~ acrossthefilm was less than 1 eV.Therefore,since 4 — x = 2.7 eV, the conduction band edge at the vacuuminterfaceis higherthan the Fermi level in the Mo substratefor the conductivityconditionsof the presentmeasurements.This implies that electron tunneling

J. W. Gibson,R.E. Thomas/ EpitaxialMgOfilms 63

throughthe interfacebarrier(suchas foundin ref. [9]) is eliminatedasa meansof chargeinjection into thesefilms. This conclusionis valid for any reasonablezero current potential distribution, and is not dependenton the flat bandconditionassumedin fig. 4a.As well be seen,tunnelingis also not consistentwith the behaviorof the ‘N versus curves.

6. Analysisof ‘N versus curves

In general,the voltagedrop acrossthe film will be dueto spacechargeaswell as the current flow. The current mustbe self-consistentwith the electricfield ~. Weassumethatelectron—holepairsare createdup to a depthR withinthe film. The net chargeproduced in the film must be positive for 6> 1becauseof the lossof secondaryelectrons.In the regionof the film where noelectron—holepairsare createdit can easilybe shown from Poison’sequationthat, for the currentsusedhere,the spacechargep producedby the net currentflow is negligible (p ‘-‘ lots electrons/cm3,whereasp

10t9 electrons/cm3is

requiredfor a I eV drop across100A). Hence, the only spacechargein thisregionwould be dueto trappedelectronsandholes,andit would be expectedthat much less of these would be present in this region than where thegenerationoccurs.Therefore,the voltage drop acrossthis part of the film isdeterminedby the electric field ~ that is self-consistentwith the net currentflow. ~ then dependson the mechanismlimiting current flow. The obviouspossibilitiesfor this mechanismare [16]: (1) emissionof electronsor holesovera Schottky barrier at the MgO—Mo interface,(2) electron tunneling throughthe interfacebarrier, (3) Frenkel—Pooletransportof charge(field enhancedionization of trappedchargemaking it mobile), (4) ohmic conduction,or (5)spacecharge.

The curvesof fig. 3 are obviously not ohmic, nor do they behaveasJa V2as in the case of spacechargelimited currents.Thereforethesewill not beconsideredany further.

Forany of the mechanismslisted it is necessaryto know the relationshipofthe surfacepotential ~ to ~. Consistentwith the previous argumentsweassumethat the potentialvariation throughoutthe regionwhereelectron—holepairs are generatedis dominatedby the spacecharge. Thus, from Poisson’sequation,the electric field at x = R is givenby

dV l1R ~~iR

dxR~JOc (I)

wherep is the chargedensity,and is the dielectricconstantof MgO. ~ is theaveragevalueof p. Sincefor R <x ~ t thereis no spacecharge,the field ~=

is constantfor this region. For the conduction mechanismsdescribedit isexpectedthat the field in this region will determinethe net current flow. Itshould also be noted that ~ must be consistentwith ~ The contributionto

64 J. W Gibson, R.E. Thomas/ Epitaxial MgOfilms

L~J’~from this regionwill be

(2)

The voltage drop ~ across the space charge region is obtained byintegrating Poisson’sequationby partsto give

RcR icR~ —J p(x)dx —J xp(x)dx. (3)�0

Letting p = ~5+ ~p, andusingeq. (1) to define ~R’ eq.(3) gives

~v=~_!fRx~pdx (4)

where L~pis the deviation from the averagechargedensity, ~, throughoutthespacechargereigon. Thus, from eqs.(2) and(4) the total voltagedrop acrossthe films is given by

LW1 + ~ ~t — R/2) 11R ~p dx. (5)

Neglectingthe integral term in eq. (5) the internal field in the film can beexpressedin termsof the surfacepotentialas

(6)

An extremecasefor the error in eq. (6), due to the neglectof the integralterm,would be if p varied linearly from 2~at the surfaceto p = 0 at x = R. Inthiscasethe integral term is equalto ~R/6, which would makeeq.(6) in errorby about 30% for R = t. Thus, to a reasonableapproximationeq. (6) shoulddescribethe internal field in termsof the surfacepotentialof the sample.

From the aboveresults,it is seenthat if ~ (or p) dependsonly on ‘N’ thedepthR to which electron—holepairs are createdby the primary electroncanbe estimatedfrom the variation in surfacepotential occurring when E1, isvaried(for constantIN)• It shouldalso be notedfrom eq. (6) that in the limitsas R —~0 andR —~

______ — LWs(E~-.oc) — 1 7

LW5(R~o) - Av~(E~~o) 2

Fig. 5 showsplots of L1V~versusE~for a 90 A film at differentvaluesof ‘N•

It is seen that in general ~ decreaseswith E~.similar to what would beexpectedbasedon eq. (6). For ‘N = 0.01 jiA, R ~ t for E~~ 150 eV. However,the highercurrent curvesdo not show the samedistinct saturationof ~J7~asthe 0.01 p.A curve.For thesecurvesthe energyat which full penetrationof thefilm occurs is not as well definedas for the lower currentcurve. This is notsurprisingsincethe effect of the integral term in eq.(5) is to increasethevalueof 1/5, andthis term shouldincreasewith ‘N~ However,the chargedistribution

J. W. Gibson,RE. Thomas/ Epitaxial MgO fl/ms 65

Vo,iVo

;~‘:~~ —0.4 :~

:‘~)/80AMgO FILM

50 100 150 200 250 300 350 400PRIMARY BEAM ENERGY (eV)

Fig. 5. Surfacepotentialchangeasa functionof primary beamenergyfor a 90 A MgO film. Curvesareshownfor different valuesof ‘N~

shouldbecomemore uniform as E~increasesso that eventually the ~p termbecomesnegligible again.This is consistentwith the fact that indeedthe valueof L1r’~(E~—~ ~)/~V~(E~ —~0) is close to 1/2 for all thesecurves,as predictedby eq. (6). It shouldbe pointed out that, asdescribedin section2, the currentdensitycould changeas much as 20% asE~varies from 50 to 300 eV. Thisshould introduceanerror greaterthan is indicatedby the experimentalratiosof ~V~(c)/~V~(0) from fig. 5. However,this ratio is also sensitiveto the valuechosenfor V~.Thus an offsettingsystematicerror could be partly responsiblefor the good agreementwith theory. Nonetheless,to a reasonableapproxima-tion the simpletheoryseemsto predictthe dependenceof internal field on thesurfacepotential, andgives a rough estimateof the effectivedepthat whichsecondariesare generatedat a givenvalueof E~.

7. Datacomparisonwith conduction laws

Using eq. (6) to express~ in termsof L~1’~in the various conductionlaws,onecanfit the datafor ‘N versusL~l’~to determinewhich law providesthebestfit. To test for tunnelingthrough the metal/MgOSchottkybarriera Fowler—Nordheimplot (log ‘N versus~V~)wasmadeof the data.Thisgaveby far theworst fit. Also, as will be discussedbelow, the valuesof ~ found for thesefilms

66 J. W. Gibson,R.E. Thomas/ Epitaxial MgO films

are in most cases too low to provide field emission. Both Schottky emission(logI~versus~/~/)andPoole—Frenkel(log(I~/AV~)versusv~~s)lawscouldbe madeto fit the datareasonablywell. However,the Poole—Frenkellaw is inbetteragreementwith all aspectsof the data, as is discussedbelow.

Fig.6 shows plots of log(J~/~V~)versus \/~i/ for a 90A film at twodifferent valuesof E~.ThePoole—Frenkeltheory[16]gives

‘N eE e3’2~~2log—~- A + ~+B, (8)ç 2.3kT 2.3kTVIT�

whereEA is theactivationenergyfor chargehopping,e is theelectroniccharge,k is Boltzmann’s constant,T is the temperaturein K, and B is a constant.Substitutingfrom eq. (6) for ~ it is seenthat the slope(S) of theplots in fig. 6shouldbe given by

e3~2 1S . (9)

2.3kT~tr�t — R/2

For Schottkybarrieremissionthe theoreticalslopeof a plot of log ‘N versus

106 - 90A MgO FILM

E~=150eVSLOPE=6.13/ IR=88A ~ /

z / 7— / / Ep5OeV

/ / SLOPE=5.05

ia—7 R=48A

i08 I U I0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fig. 6. Plots of log(I~/iM’S) versus for primary beamenergiesof 50 and ISO eV.

J.W. Gibson,R. E. Thomas/ Epitaxial MgOfilms 67

~ shouldbe S/2 [16]. Forthe = 150 eV curve in fig. 6 it is expectedthatR t (see fig. 5). Usinga valueof dielectric constant� = 8.7X l0 ‘~ [17], andequatingeq. (9) to the slope of the 150 eV curve gives t=88A, in goodagreementwith the measuredvalue of 90A. The only way that the slopederived from Schottky emissiontheory could be made consistentwith thisthicknesswasto adjustthe extrapolatedzero current surfacepotential l’~(seefig. 3) to an unrealisticvalue.In addition, for Schottkyemissionthe valueof ‘N

extrapolatedto zero field shouldshouldbe given approximatelyby

1N(0) =A x l20T2 exp(—eq~/RT), (10)

whereA is the areaof the electronbeam(A 1 X l0~ cm2) and 4h is theinterfaceSchottkybarrierheight.Theconstantof 120 assumesa chargecarrierwith a free electron mass and neglects any reflection coefficient at theinterface.It is expectedthat this would be accurateto within two ordersofmagnitude.From eq.(10)and usingthe extrapolatedvaluesof IN(~VS-.0)/A,a Schottky barrier height of 4ib = 0.85 eV is required. However, from theprevious measurementsof the work function and electron affinity [14] (seefig. 4), 4b 2.7 eV for electrons.Thiswould give valuesof ‘N many ordersofmagnitude less than are found in this experiment. Although it might bespeculatedthat therecould be a smaller barrier for hole injection from theMgO to the Mo, the slope of the curves is still in betteragreementwith aPoole—Frenkelmechanism,and,as will be seenbelow,measuredvaluesof theactivationenergyare toolow to be consistentwith Schottkybarriercontrol ofthe current.

Using the Poole—Frenkeltheory, the curvesof fig. 5 give penetrationdepthsof R = 48 and88A for E~= 50 and 150 eV, respectively.Thus, at E~= 150 eVelectron—holepairproductionis taking placethroughoutnearlytheentirefilm.This is consistentwith the shapeof the ~1/~versusE~curvesof fig. 5. A powerlaw for the energyloss of primariesis often assumed[18] which resultsin thepenetrationdepthbeing given by

RccE~. (11)

In the energyrangefrom E= 0.3 to 7 keY, Young [19]hasfoundn 1.35 givesthe best fit to mostdataon secondaryemission.However,to fit our data,mostof which are takenat E~~ 300 eV, a valueof n = 0.5 is required.This canbeunderstoodby realizing that R is proportionalto the meanfree path (A) forpair production[18], andit is well known that A usuallyhas a minimumin thelow energy range 25 to 150 eV [20]. Therefore,it is not surprising that theeffectivevalue of n in this energyrangemay be considerablysmallerthan forhigherenergies.

As seenfrom the abovecomparisonsof the datawith the various conduc-tion theories,the Poole—Frenkellaw is in bestagreementwith all aspectsof theexperimentaldata, and that electron injection through or over the interface

68 J. W. Gibson,R.E. Thomas/ Epitaxial MgOfilms

Schottky barrier is not in agreementwith the value of ~h or extrapolatedcurrentvalues.

8. Temperaturedependenceof emission

Sincethe Poole—Frenkelmechanisminvolveschargehoppingfrom onetrapto another,it is expectedthat an activationenergyEA is involved. This canbedeterminedby measuring the temperaturedependenceof the conductivity.Sincethe slopeS (eq. (9)) canbe obtainedfrom plots of log(I~/~V~)versus/T~~ from eq. (8) it is seenthat EA can be obtained from a plot of log ‘N

versusl/kT(holding ~ constant),or from theslopeof a plot of (S~i~+ logversus1/kT (holding ‘N contant).Valuesof EA wereobtainedusingboth

techniquesfrom a seriesof curvesof ‘N versus~V5overa range of tempera-tures from 50 to 671°C.Both techniquesgave the samevalue, of EA withinexperimentalerror. Fig. 7 illustrates the later plot for a 103 A film with aconstantvalueof ‘N ~X l0~A. S has beenevaluatedas0.1l8/kT from theslope of plots as shown in fig. 6. A valueof EA = 0.49 eY is obtained.If theSchottky equation is used EA 0.55 eY results. A Schottky barrier of thisheight would haveto apply to holes,as discussedin section9. However, thisbarrier height would allow approximately4 orders of magnitude larger cur-rents(extrapolatedto ~ = 0) thanare observedin thesefilms.

The defectstructurethat gives rise to trappingcentersfor holes in MgO is

/10

671°C 1IkT[eV]~ 127°C

Fig. 7. Plot of (0.118 ~/~T~/kT+log ~V5) versus l/kT for a 103 A MgO film. The activation

energy(EA) of the transport processis obtainedfrom theslope.

J. W. Gibson,R.E. Thomas/ Epitaxial MgOfilms 69

very complex. Severaltypes of intrinsic as well as extrinsic mechanismsarediscussedin the literature[15,21,22].Sincethesefilms are vapordepositedit isbelieved that impurity related traps are not as likely as defects due tonon-stoichiometrysuchas Mg2+ vacancies.Thesecauseholesto be trappedonadjacentoxygen ions. Although the activation energy found here cannotbeprecisely identified with a particular type of trap, it is within the rangeofvalues(0.13 to 1 eV) usuallyattributed to thesevarioushole trappingmecha-nisms.In any casethevalueof activationenergyis moreconsistentwith a holehoppingmechanismthanSchottky barriercontrol of the current.

9. Summary and discussion

The results presentedhere show that the values of secondaryemissioncoefficientof theseepitaxial films are consistentwith valuesobtainedby otherworkerson both bulk singlecrystalsaswell aspolycrystalline films.

It hasbeenshownthat the changein surfacepotentialfor thesefilms underelectronbombardmentcanbe determinedby monitoring the thresholdenergyof the secondaryelectronenergydistribution.This techniqueallows one to plotthe ‘N versus curves for different primary electronenergies.When thesedataare interpretedin termsof a simplemodel for the potentialdistribution inthe film, theyleadto a field dependenceof the net current in the samplewhichis in good agreementwith chargehopping (Poole—Frenkel)mechanismasbeing thecurrentlimiting process.Schottkybarrierprocessesarenot consistentwith the prevouslymeasuredvaluesof 4 — x 2.7 eV [14], which could limitcurrent densities to values several orders of magnitude smaller than areobservedhere.Also themeasuredactivationenergy(EA -=0.55 eY) is againnotconsistentwith the zero field values of ‘N’ The Schottky barrier height forelectronscould,of course,be smallerthan 4 — x if interfacestatespinned theFermi level at the Mo—MgO interface, such that conduction band edge(E~) — EFermi at the interfaceis less than~ — x. However,if this were thecasethe limiting barrier height would probably be independentof ~V

5 (over therange of ~ measuredhere) and a different conduction law would beexpected.

It is clear, then, that conduction in thesefilms is most consistentwith amechanismof activatedhopping of holes to the Mo—MgO interface. Frommeasurementsof the temperaturedependenceof the ‘N versus~V5curves,theactivation energy of this processis found to be 0.5 eY, which is consistentwith varioushole trappingmechanismsthat arediscussedin the literature.

The differencein the conduction mechanismfor theseepitaxial films ascomparedto the moreconventionallyproducedthin MgO films (e.g., producedby oxidationof Al—Mg or Ag—Mg alloys[9,10,23])is illustratedby comparisonwith the dataof Dresner[9]. Dresner’sdataindicatedconductionvia tunneling

70 J. W. Gibson,R.E. Thomas/ Epitaxial MgOfilms

of electronsthrough the interfacebarrier as the currentlimiting process.Forhis films a much higher internal field (~V~/t5 X 10~V/cm) is requiredtoget the J-= l0~A/cm2 than for our films (LW~/t—’6.7X l0~V/cm). Thefield differencesare thusconsistentwith the different conductionmechanisms.

We can only speculateas to the reason for the different conductionmechanism.Sinceour films are epitaxial,no grain boundarybarriersexist. Foran activatedconductionmechanismlike hole conduction,it might be expectedthat grain boundarieswould provide a long lifetime trap and/orannihilationcenters for holes. Thus for polycrystalline films hole conduction may beinsignificant (Dresner[9] indeedindicatedthat the holeswerebelieved to berelatively immobile in his films). Whereasfor single crystal films the holeconductivity could essentiallyshort circuit otherconductionmechanismsat thefields requiredto give the currentdensitiesobservedhere.

As wasmentionedearlier, bombardmentfor 1 h at 0.1 A/cm2 and2.5 keVbeamenergydid not showany degradationof 6 in thesefilms such asis oftenobserved[10]during highintensityelectrombombardment.Also, heatingup to650°Chad no observableeffect on 6. For clean MgO it is believedthat themajor causeof degradationin 6 underelectronbombardmentand heatingisdueto incongruentdisassociationof MgO such thatexcessMg remainson thesurface [10,24]. Dresnerand Goldstein[10] haveproposeda mechanismforthermalandelectronbombardmentdecompositionof MgO which dependsonthe densityof thermalizedelectrons,N~,andholes,P~,in the surfaceregion. Itis assumedthat in order to lose oxygen,thermalizedholes mustbe presenttoneutralize O2 in the surfaceregion, and correspondinglyfree electronsarerequired to createneutral Mg. Thermaldecompositiondependson the equi-librium densitiesN,,°andP,,°,andunderelectronbombardmentexcesselectrons

andholes,~ and~ are created.For example,DresnerandGoldstein[10]assumedthat sinceoxygen loss was higher than Mg loss upon heating theirsamples,P~°>N~°.This also left excess Mg on the surface, resulting in adegradationin 6. In our samplesin Fermi level is 2.7 eV below the conductionband.Therefore,with a band gap of 7.8 eV, in our samplesN~°> P,,°,andwewould expect upon heatingevaporationof Mg would be greaterthan that ofoxygen.This would explain the absenceof 6 degradationwith heating.Uponelectronbombardmentelectron—holepairs are created,and since the surfacechargespositive underelectron bombardment(E~> 20 eV), we know thatz~P~>~XN~.However, the absenceof degradationwould then imply that thehole densitycreatedunderelectron bombardmentis still less than the netelectron densityon the surface. While it cannot be demonstratedthat thislatter condition exists in our films, it can be seen that the presenceof asignificant hole currentbleedingholesout of the surfaceregion would lowerthe steadystatehole density.This follows from a simplesteadystatebalance,andby assumingthat the recombinationrateof holes is given by NH/T, whereNH is the numberof holes presentin a layerof depth R, and T is the hole

J. W. Gibson,R.E. Thomas/ EpitaxialMgO films 71

lifetime. A steadystateconditionrequiresthat

NH/TGHAR—(JHA)/e, (12)

whereG H is the hole generationrate perunit volume, ~‘H is the hole currentleaving the layer, e is the electroniccharge,andA is the bombardmentarea.Dividing eq.(12) by AR/T gives the hole densityP~as

P~NH/ARr(GH—JH/eR). (13)

Thus, eq. (13) shows that for a given hole generationrate, materialhaving asignificant hole conductioncurrent will have less hole densityat the surfacethan one in which hole conductionis absent.

A morerecentpaperby Knotek and Feibelman[25] demonstratesthat forionic materials,such as MgO, oxygenin ionic and possiblyneutral form, canbe desorbedfrom the surfacedueto excitationof theoxygen02 in the latticeinto a neutralor 0~statevia an interatomicAuger transition.For MgO thiswould requirethe primary electronsto createa Mg(2p) core hole which coulddecayby filling from the O(2p)valencestates,kicking out anadditionalO(2p)electron,leavingan0 neutralwhichcanbedesorbed.However,the probabilityof desorptionis enhancedif an 0~is createdvia the reaction0 + P—~ O~.Thus,oxygenlossis enhancedin thepresenceof holesevenby this mechanism.Therefore, the reduction of hole densitynear the surfacedue to the holeconductionmechanismis expectedto alsominimizeoxygenlossevenwhenit isvia the Augerexcitationprocess.

Furtherindicationsthat small singlecrystalsmay have less 6 degradationthanpolycrystalsare foundby DionneandFitzgerald[26]. Theymeasured6 asa function of time of electronbombardmentfor Au—MgO cermet films, andfound unusuallygood stability of 6. This emitter materialwas developedbyHenrichand Fan [27] at Lincoln Labs.Thesefilms consistof particlesof Au(—‘ 100A) separatedby particlesof MgO (—‘100 A). Such particlesare ex-pectedto be singlecrystals.Thus,holeconductionmayalsopredominatein theMgO particleson the surface.

The argumentspresentedhere, to the effect that hole conduction is themechanismthat enhancesthe degradationresistanceof MgO, are not conclu-sive, and more experimentsspecifically oriented to demonstratethis areneeded.However, the strong evidencefound here that hole conductionpre-dominatesin thin single crystals of MgO seemsto be the major differencefound betweenthesefilms which haveunusualstability of 6 andpolycrystallinefilms which have less stability. In addition, the above argumentsshow aplausibletheoreticalreasonon currently postulateddecompositionprocessesinMgO.

72 J. W. Gibson,R. E. Thomas/ Epitaxial MgOfilms

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