Organic Electronic Devices

Transcription

1 Orgai letroi Devies Week 3: Charge rasport Leture 3.3: Multiple rap ad Release MR Model Brya W. Boudouris Chemial gieerig Purdue Uiversity

2 Leture Overview ad Learig Objetives Coepts to be Covered i this Leture Segmet Itrodutio to rap States withi the Badgap o Semiodutig Materials xplaatio o the Physial Ratioale Behid the Multiple rap ad hermal Release MR Model Quatiiatio o the Mobility o a Semiodutor usig the MR Model ad Materials ad Devie Properties Learig Objetives By the Colusio o this Presetatio, You Should be Able to:. xplai how the trap eergy levels ad the desity o traps aet the trasport o a harge aordig to the MR model. 2. Deie the terms eetive mobility, eetive desity o states or traps ad the eetive desity o states at the odutio bad edge. 3. Derive a ressio or the eetive mobility o a semiodutor based o the MR model.

3 Itrodutio to the Multiple rap ad hermal Release MR Model he key dieree betwee bad trasport i traditioal solid state physis ad orgai eletroi devies is the LARG AMOU O DISORDR i most orgai eletroi systems relative to iorgai semiodutors. I some orgai materials, trasport is limited by loalized states idued by deets ad uwated impurities. hese deets ad impurities are reerred to by the athall term o traps. Imagie a rasport Bad with Impurity States C ergy,,2,3 Loalized states with trap eergies at 3 distit eergy levels here is a iite probability that the arrier will be trapped i ad that the arrier will be released rom oe o the lower eergy trap states available due to the deets ad impurities.

4 Assumptios ad Deiitios o the MR Model. he trap states are highly loalized ad arriers trapped i these states aot move easily rom these loatios i the eergy badgap. 2. Charge arriers arrivig at the trap site are aptured istataeously ad with a probability o lose to. 3. he release o the trapped arriers is otrolled by a thermally-ativated proess. 4. We will talk about two types o traps. a Shallow traps are withi 2-3 k o the bad edge ad arriers stuk withi these traps have a harateristi time o release. b Deep traps are > 2-3 k rom the bad edge ad arriers loalized i these traps have a very diiult time beig removed without a exteral stimulus. 5. wo key parameters will gover the slowig o the harges as they move through the semiodutor: the eergy levels o the traps ad 2 the umber o traps.

5 Desribig Charge rasport with a etive Mobility A eetive mobility e or the harge arriers a be writte as: α k Bad rasport Mobility or the Mobility i e the Absee o raps ergy Level o the rap α Measure o the rap Desity ote that this is i terms o a sigle trap eergy level, but it a be geeralized to model traps with a variety o eergy levels. How a the α term be quatiied i a more rigorous maer based o ressios we have derived i the past? Deie:. etive Desity o States or the rap Sites 2. C etive Desity o States at the Codutio dge

6 Desribig Charge rasport with a etive Mobility Part II ow, we see that the total arrier oetratio O must either be i the ree or trapped state. So: Reall that we a write the oetratio o ree arriers as the ollowig O + k k I a similar maer, we a write a aalogous equatio or the oetratio o trapped arriers k k

7 Desribig Charge rasport with a etive Mobility Part III he ratio o ree harge arriers θ a the be ressed as ollows Substitutig i the deiitios o the previous slide yields the ollowig O + θ his redues to: + k k k θ + k θ

8 Desribig Charge rasport with a etive Mobility Part I I the limit that: he the equatio o the previous slide redues to: But, reall the iitial deiitio o the eetive mobility >> k k k θ k e α

9 Desribig Charge rasport with a etive Mobility Part hereore, we a rewrite the eetive mobility as: e θ α his tells us that as the desity o states i the odutio bad grows relative to the desity o states o the trap levels, the mobility should irease. I real systems, the trap desity will be distributed with respet to eergy. A simple model assumes a oetial distributio with a harateristi temperature. D ad see that ; where : > k k I we assume a step-utio or the ermi-dira distributio, the the itegratio to determie the umber o trapped harges beomes: k

10 Deiig the hreshold oltage I order to overome this oetratio o trap states, oe a apply a voltage as the exteral stimuli. his applied voltage a be related to the threshold voltage, whih is a measure o the umber o trapped harges i the semiodutor, aordig to the ollowig equatio. C q C q Capaitae o the ide separatig the metal otat rom the orgai semiodutor udametal Charge he, we a say that: k C q Solvig or the ermi eergy yields: C l k q

11 Deiig the hreshold oltage Part II Isertig this ito the deiitio o the ree harge arriers gives the ollowig Ivokig the deiitio o the eetive mobility used earlier yields: + q C d k D 2 θ + + e e q C q C q C ypial values ~45 K, ~ 2 2 m -3

12 Summary ad Preview o the ext Leture ergy e + C q C q he multiple trap ad release MR model is a useul desriptio or the trasport o harges i a somewhat disordered semiodutor. hat is, whe there are deet sites or impurities that have eergy levels that are withi the badgap o the semiodutig material, oe a aout or these i the orgai material still has a somewhat well deied bad struture. Geerally, the parameters or this model a be haraterized by perormig temperature-depedet trasport erimets. + C By usig a ombiatio o ew theory related to the MR model ad the stadard theory assoiated with bad trasport, we were able to derive a equatio or the ressio o the eetive mobility relative to the bad trasport mobility. ext ime: rasport i Highly Disordered Orgai Semiodutors q 2