Coductivity i ulk ad ilm-type Zic Oxide Je Hua Koo* ad Jisug Coi # ad Gook Hee Ha $ Departmet of Electrical ad iological Pysics, Kwagwoo Uiversity, Seoul 39-7, Korea Abstract Te coductivity of ZO is calculated ad is compared wit experimets. Te coductivity of ZO is domiated by double quatum wells were te larger potetial barrier at eds is from te badgap ad te oter iside te large quatum well is from te impurity door. Te coductivity sowig a delta fuctio results from te trasport iside quatum wells. Te trasport witout a peak origiates from te oppig above wells. * E-mail: koo@kw.ac.kr # E-mail: eoled@kw.ac.kr $: Correspodig autor, E-mail: g98@ate.com, Tel:+8-()-94-533, ax:+8-()-943-38 Keywords: Quatum Well; Zic Oxide; adgap; Coductivity; Ladau Level PACS umbers: 77.55.f, 73.63.Hs
Pure zic oxides are well kow as semicoductor wit direct bad gap, 3.37 ev [,]. Oe of caracteristic properties for ZO is te sesitive temperature depedece of bad gap but tis is explaied by empirical teories. [] Accordig to materials doped ito ZO, te doped ZO is used from magetic to optical applicatios. Recetly pure ZO is widely applied as electrodes i solar cells ad a specific doped ZO is a ligt-emittig diode uder ivestigatio. [] Covetioal teories tat are applied to calculate bad gaps use a model wit stadig wave-like wave fuctios, by applyig ragg diffractio ad aoter sceme tat makes use of periodic loc wave equatios [3,4]. Altoug ZO is a semicoductor wit simple structures, te coductivities for bulk oe ad ZO film are mysterious ad ot well explaied by covetioal teories [5,6]. I tis paper, we explai te coductivities of bulk ad film ZO i fit wit experimets respectively. We ca te calculate te curret desity of bulk ZO i te presece of applied voltage V to be ev Eg J ev eev J ' J ta( ) J ' () kt were is te total umber desity of electros ad oles, e is te electro umber desity, is te ole umber desity, ad te average velocity of a electro is assumed to be same as tat of a ole, e ev Eg exp( ) kt, ( ev Eg ) exp( ) kt, k is te oltzma costat, V is te applied voltage, T is te temperature, E g is te bad gap, J is a ormalizatio costat, is te curret from oter mecaism. As sow i ig., te curret desity of bulk ZO is rewritte by ( ) ev ev E g Ed J [{ta[ ] kt Eg Ed ev Ed Ed ta[ ]} {ta[ ] ta[ ]}] k T k T k T were oppig E oppig V L v is te ermi velocity, te system, ad te effective voltage is caged ito E d is te door level. oppig is te coductivity, E is te electric field, L is te size of ( ev kt ) / e, as sow i ig. ad Te average umber desity of a electro i te absece of te magetic field, is give by E () J '
d d f( ) d eel exp exp k T k T eff ( eel ) kt l[ exp ] kteff l[ exp ] k T k T eff were f ( ) is te ermi-dirac distributio, ( ) parameters, mageto ad by N te desity of states, i are positive costat is te ermi eergy, is te exteral agular frequecy, is te or kteff kt EeEL is te Plack costat divided by. Here te effective temperature is give. (4) (3) Te coductivity from oppig above quatum wells for bulk ZO is give by ev k ( ) T Eg Ed e vl E oppig ( LJ ) [{ ta [ ]} V 4k T k T ev k T E d E { ta [ ]}] kt were te coductivity from oppig above quatum wells for bulk ZO sample is sow i ig.. I te double quatum wells of te ZO film were te large potetial well at eds is from te eergy gap ad te small potetial well iside te large potetial well comes from te impurity door, we ca obtai te Hall coductivity of ZO film from Drude relatio ad Loretz force as follows [3]: e e mv ev, v x L l l, xy l (6) mv (7) mv S (8) ( ) were deotes te de roglie wavelegt of electro wic is smeared out to be o-iteger quatum Hall effect i ZO film ad is te Plack s costat. We assume ere te uit surface of S, l L defies te size of te quatum well wit l represetig a iteger ad, umber desity of ermi electros. Te diagoal coductivity is give by e xx ( x L) (9) m L/ v () (5) 3
wic ca be reduced to rom te ucertaity priciples xx e l ( x L). p x () e m diagoal coductivity ca be sow to become xx l ( b ), were b l e, E mv, ad were m is te mass of a electro ad E is te Ladau level. me Te coductivity is give by e m xx l ( b ) ( kt kt) l e kt (). were te effective magetic field is caged ito te above relatio ad T is te specific temperature. Accordig to Ladau levels i quatum wells, it is give by e *e xx kt kt kt k T ( ) ( ) *3e * e kt k T kt k T ( ) ( ) 3 oly if p E E ( ) geometric c 8mL e c m p, : itegers were (3) E geometric is te eergy of geometric quatizatio i te quatum well. Te total coductivity of oe from oppig above quatum wells ad te oter iside quatum wells to be applied to ZO films is give by 4
oppig g d e vl E [{ ta [ ]} xx ev k T ( E E ) 4k T k T ev kt Ed E { ta [ ]}] kt ( k T k T ). (4) I coclusio, te coductivity of ZO film from Eq. () is calculated as sow i ig.3 i good correspodece wit experimetal data. Te coductivity of ZO film is domiated by double quatum wells were te larger potetial barrier at eds is from te badgap ad te oter iside te large quatum well is from te impurity door. Te coductivity sowig a delta fuctio results from te trasport iside quatum wells. Te trasport witout a peak i bulk ZO origiates from te oppig above wells. Refereces [] C. Jagadis, S. Pearto, Zic Oxide ulk, Ti ilms ad Naostructures, Elsevier, New York, 6. [] N.H. Nickel, E. Terukov, Zic Oxide-A Material for Micro- ad Optoelectroic Applicatios, Spriger, New York, 5. [3] C. Kittel, Itroductio to Solid State Pysics, Wiley & Sos, Sigapore,. [4] N.W. Ascroft, N.D. Mermi, Solid State Pysics, Holt, New York, 976. [5] K. Ellmer, A. Klei,. Rec, Trasparet Coductive Zic Oxide, p. 37, Spriger-Verlag, erli, 8. [6] N. rilis, D. Tsamakis, H. Ali, S. Krisamoorty, A.A. Iliadis, Ti Solid ilms, 56 (8) 46. 5
igure Captios ig. Te bad gap, E g ad te door level, E d are plotted were C.. (V..) meas te coductio bad (valece bad). ig. Te coductivity from oppig above quatum wells is plotted usig te data of bulk ZO [5]. ig.3 Te coductivity is plotted from experimetal data for ZO films [6] ( x x ) ( xx ) 3. were te delta fuctio is approximated as 6
ig. Te bad gap, E g ad te door level, E d are plotted were C.. (V..) meas te coductio bad (valece bad). 7
coductivity[s/cm] 5 4 3 Teory Data 3 4 5 Temperature [K] ig. Te coductivity from oppig above quatum wells is plotted usig te data of bulk ZO [5]. 8
l[][coductivity] 6.6 6.55 6.5 6.45 Teory Data 6.4 6.35 6.3 6.5 6. 3 4 Temperature [K] ig.3 Te coductivity is plotted from experimetal data for ZO films [6] ( x x ) ( xx ) 3. were te delta fuctio is approximated as 9