Quantum Dots: A Primer - unizg.hr · 2014-03-20 · 18A Volume 56, Number 1, 2002 focalpoint FIG.3....

16A Volume 56 Number 1 2002

focal pointBY CATHERINE J MURPHY

DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY

UNIVERSITY OF SOUTH CAROLINA

COLUMBIA SOUTH CAROLINA 29208

AND

JEFFERY L COFFER

DEPARTMENT OF CHEMISTRY

TEXAS CHRISTIAN UNIVERSITY

FORT WORTH TEXAS 76129

QuantumDots APrimerINTRODUCTION

C rystalline inorganic so lidscan be divided electronicallyinto three well-known clas-

ses metals semiconductors and in-sulators In these extended solidsatomic orbitals overlap to give near-ly continuous electronic energy lev-els known as bands1 Metals are elec-tronically characterized by having apartially lled band semiconductorshave a lled band (the valence band)separated from the (mostly) emptyconduction band by a bandgap Egcorresponding to the familiar HOMO-LUMO energy gap for small mole-cules Insulators are conceptually thesame as semiconductors in theirelectronic structure except that thebandgap is larger in insulators (Fig1) In terms of Egs metals have Eg

less than 01 eV semiconductorshave Egs from 05 to 35 eV andinsulators have Eg 4 eV (1 eV5 1602 3 10219 J 5 80655 cm21)

There are some key differenceshowever between the electronicstructure of molecules and solid-statematerials such as semiconductors

Author to whom correspondence should besent

The description of an electron mov-ing through a solid lattice is gener-ally derived as a modi cation of afree electron wave upon encounter-ing point charges that represent theatoms In the free-electron modelthe electronrsquos momentum is propor-tional to k the lsquolsquowave vectorrsquorsquo whichis related to its wavelength l1

k 5 2pl (1)

In solving the Schrodinger equationfor an electron in terms of its wave-length (and hence k) one nds thatthe energy levels in the one-dimen-sional case are

E 5 h2 k 2 (8p2m) (2)

where E is the energy of the electronm is its mass and k is its wave vec-tor1

The simpli ed band structure di-agram of Fig 1 can be redrawn interms of k (Fig 2) Note that fromEq 2 the shape of the energy bandsis parabolic with respect to k Semi-conductors in which the lowest-en-ergy transition does not involve achange in k are called lsquolsquodirect band-gaprsquorsquo materials conversely semi-conductors in which the lowest-en-ergy transition does involve a changein k are lsquolsquoindirect bandgaprsquorsquo materi-

als Electronic transitions for whichDk plusmn 0 are formally forbidden al-though defects in the lattice and oth-er reductions in symmetry may makethe transitions more allowed19

Silicon and germanium in GroupIV are the only two elements that aresemiconductors Si and Ge are bothindirect bandgap materials Com-pound semiconductors lsquolsquoaveragersquorsquoout to these electron con gurationsin general thus GaN GaP GaAsInP and InAs are IIIndashV semiconduc-tors while ZnO ZnS CdS CdSeand CdTe are IIndashVI semiconductorsSeveral other oxides also exhibitsemiconductive behavior (TiO 2 WO3) Periodic trends in semicon-ductive behavior are observable forexample Eg decreases as one movesdown a column in the periodic tableThe more ionic semiconductors tendto be direct bandgap materials andthus are more suitable for light-emit-ting applications

If the particle size of a bulk inor-ganic crystalline solid is on the orderof nanometers it is now well-knownthat interesting optical and electroniceffects may result Semiconductorswith all three dimensions in the 1ndash10 nm size range are referred to aslsquolsquoquantum dotsrsquorsquo in this size range

APPLIED SPECTROSCOPY 17A

FIG 1 A simplied energy level diagram for metals semiconductors and insulatorsThe shaded boxes represent the lled valence bands the empty boxes represent theempty (at 0 K) conduction bands The arrows represent the bandgap energy Eg

FIG 2 Electronic band structure of direct (left) and indirect (right) semiconductors Thearrows show the lowest-energy transition between the valence band (bottom curves)and conduction band (top curves) a change in k is necessary for the indirect semicon-ductor

electrons exhibit quantum mechani-cal effects2ndash10 In the literature semi-conductor quantum dots are alsoknown as semiconductor nanocrys-tals or nanoparticles

Consider what happens when asemiconductor is irradiated withlight of energy hn Eg (For semi-conductors this corresponds to lightin the near IR through the visibleand extending into the ultraviolet re-gion) An electron will be promotedfrom the valence band to the con-duction band leaving a positivelycharged lsquolsquoholersquorsquo behind This holecan be thought of as the absence ofan electron and acts as a particlewith its own effective mass and

charge in the solid One can calcu-late the spatial separation of the elec-tron and its hole (an lsquolsquoexcitonrsquorsquo) us-ing a modi ed Bohr model

r 5 eh 2 pm re 2 (3)

where r is the radius of the spherede ned by the three-dimensionalseparation of the electron-hole paire is the dielectric constant of thesemiconductor m r is the reducedmass of the electronndashhole pair h isPlanckrsquos constant and e is the chargeon the electron For many semicon-ductors the masses of the electronand hole have been determined byion cyclotron resonance19 and aregenerally in the range of 01 me to 3

me For typical semiconductor di-electric constants the calcu lationsuggests that the electronndashhole pairspatial separation is 1ndash10 nm formost semiconductors9 In this sizerange when the exciton is createdthe physical dimensions of the par-ticle con ne the exciton in a mannersimilar to the particle-in-a-box prob-lem of physical chemistry There-fore the quantum effects such asquantization of energy levels can beobserved in principle Alternativelyone can think of the nanoparticle ashaving an electronic structure inter-mediate between bands and bonds(Fig 3) One consequence of this in-termediate character is that Eg is cor-related with size as the dimensionsof the particle decrease Eg increases

Brus has developed a popular ef-fective mass model that relates par-ticle size (neglecting spatial correla-tion effects) to the bandgap energyof a semiconductor quantum dot12

E (quantum dot)g

5 E (bulk)g

2 21 (h 8R )(1m 1 1m )e h

22 18e 4pe eR0 (4)

where Eg is the bandgap energy ofthe quantum dot or bulk solid R isthe quantum dot radius m e is the ef-fective mass of the electron in thesolid mh is the effective mass of thehole in the solid and e is the dielec-tric constant of the solid The middleterm on the right-hand side of theequation is a particle-in-a-box-liketerm for the exciton while the thirdterm on the right-hand side of theequation represents the electronndashholepair Coulombic attraction mediatedby the solid Implicit in this equationis that the quantum dots are sphericaland that the effective masses ofcharge carriers and the dielectricconstant of the solid are constant asa function of size The Brus modelmaps Eg and size well for largerquantum dots but its predictions donot match experiment well for verysmall part icle sizes Many othermore complex approximations havebeen derived theoretically that bettermatch experimentally determined


focal point

FIG 3 Energy level diagram comparing a bulk semiconductor to its molecular analog(eg bulk Si compared to Si clusters of a few atoms) and a quantum dot The semi-conductorrsquos electrons are in bands the moleculersquos electrons are in molecular orbitals(bonds) The vertical arrow denotes the bandgap Eg for the bulk semiconductor andthe highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy gap in the molecule On the nanometer scale the electronic structure ofa semiconductor quantum dot is in the intermediate regime between bands andbonds

bandgap energies and quantum dotsizes5ndash9 Many excellent reviews ofthe electronic and optical propertiesof quantum dots are available2ndash10 Inparticular some workers refer toquantum dots as lsquolsquoarti cial atomsrsquorsquobecause their quantized electronicstates bear many analogies to atomicelectronic states

SYNTHESIS

As quantum dots are not (yet)commercially available the spectros-copist must either make these na-nomaterials in the lab or collaboratewith a synthetic chemist Thus asubstantial portion of this article ex-amines the current methods of mak-ing these materials

There are two general approachesto synthesizing quantum dots Oneof these is the lsquolsquobottom-uprsquorsquo ap-proach more familiar to chemistsmolecular or ionic precursors to thequantum dots are allowed to react to-gether in solution to produce thequantum dot materials as colloidsThe other approach more familiar toengineers is the lsquolsquotop-downrsquorsquo ap-proach feature sizes on the 1ndash10 nm

scale are carved out lithographicallyor electrochemically from a semi-conductor substrate Hybrid ap-proaches are also possible for ex-ample chemists make molecularprecursors for the quantum dotswhich then react in the gas phase andare deposited as thin lms on sub-strates

Synthesis From the Bottom UpIIndashVI Materials CdS and CdSehave been the most well-studied ofthese materials due to the availabil-ity of precursors and ease of crystal-lization and also due to their band-gap energies In the bulk at roomtemperature the Eg of CdS is 24 eV(520 nm) Eg for CdSe is 17 eV(720 nm) Thus quantum dotsmade of these materials will haveEgs in the visible and just into theultraviolet range the correspondingonset of absorption can be readilymonitored with standard spectropho-tometers (see below)

Arrested Precipitation From theKsp of CdS it is clear that simplymixing Cd 21 and S 22 solutions inwater (at nanomolar concentrationsor higher) would lead to the precip-

itation of CdS One method of ar-resting this precipitation is to mixaqueous solutions of Cd 21 rst witha water-soluble polymer that has ba-sic coordinating groups such as po-lyphosphate1 2 or amines1 3 14 Thesubsequent addition of sul de resultsin the formation of CdS quantumdots whose size depends on the rel-ative concentration of reagents pHtemperature etc The function of thepolymer in this case is to competewith sul de for metal ion bindingsites and presumably to stericallyhinder small nanoparticles from ag-gregating together and growing intolarger ones

Organometallic Precursors Themost highly cited method for makingCdE (E 5 S Se Te) quantum dotsis that of Murray Norris and Baw-endi15 In this synthesis Cd(CH3)2 ismixed with a chalcogenide reagentin a coordinating solvent (trioctyl-phosphine oxide this also acts as asurfactant) at relatively high temper-ature (200ndash350 8C) in an inert at-mosphere Careful control of mono-mer injection rates temperatureconcentration etc leads to crystal-line nanoparticles coated with sur-factant that are highly monodispersecompared to other methods (5standard deviation in diameter fromthe average) A recent report sug-gests that CdO far less toxic thandimethylcadmium can be used asthe Cd precursor to CdE quantumdots with the chalcogenides as ele-ments in a phosphonic acid solventsurfactant16 Well-de ned moleculescontaining both the Group II elementand the Group VI element as a sin-gle-source precursor can be decom-posed to produce IIndashVI quantumdots1718

Particle Growth Terminationwith a Capping Agent Thiols underbasic solution conditions can be de-protonated to thiolates RSndash thatcompete very well with sul de li-gand(s) in making CdS or ZnS quan-tum dots Again nal particle size isdictated by solution conditions mostimportantly the ratio of sul de tothiolate19ndash23 The nal CdS or ZnSnanoparticles then are capped withthiolates


FIG 4 Band offsets (eV) and lattice mismatch () in coreshell nanocrystals based onan InAs core and various shell structures (adapted from Ref 39)

Synthesis Inside a NanoscaleCavity If the reaction between di-valent cadmium or zinc with sul deor selenide is performed in a restrict-ed environment on the nanometerscale then IIndashVI quantum dots willbe formed Examples of nanoscalecavities include porous glasses andxerogels24 reverse micelles25 zeo-lites 2 6 membranes 2 7 LangmuirndashBlodgett lms28 and hollow pro-teins29

Biosynthesis Yeast and tomatoesand likely other organisms produceCdS quantum dots as a detoxi cationresponse to an overload of cadmi-um3031 the CdS thus produced iscoated with particu lar peptideswhich in turn can be used as the sta-bilizing thiol to make CdS quantumdots as described above32

Synthesis From the Bottom UpIIIndashV Materials The direct gapcharacter for many IIIndashV compoundsemiconductors coupled with theirassociated luminescence behavior inreal devices33 makes the construc-tion of three-dimensionally con nednanocrystals of this family of semi-conductors an important goal At thesame time challenges associatedwith achieving crystallinity in IIIndashVmaterials of nanophase dimensionadd an extreme level of syntheticcomplexity to such studies

CoreShell Nanocrystals Synthet-ically the pioneering use of dehal-osilylation reactions by Wells andco-workers has proven to be a usefulroute for the formation of a wide va-riety of nanocrystalline IIIndashV mate-rials 3 4 the early paradigm beingGaAs3536 While the size-dependentspectroscopic behavior of a numberof IIIndashV species (such as InP37) havebeen thoroughly investigated themetastab ili ty of surface-cappingmoieties for many IIIndashV nanocrys-

tals interferes with the radiative re-combination of electronndashhole pairsby the introduction of detrimental in-terfacial defects Hence very recentindependent approaches by Nozik etal38 and Banin and co-workers39 in-volving the formation of hybrid coreshell nanocrystal systems are of val-ue in this regard As pointed out bythese groups in the design of suchcoreshell structures it is importantfor the core and shell interfaces tobe lattice-matched (Fig 4) If this isnot the case strain develops duringgrowth relieved only by the forma-tion of large numbers of interfacialdefects on the core surface incom-plete cap growth is also likely Cap-ping a quantum dot core with a larg-er-bandgap semiconductor shell hasalso been used to stabilize the corein IIndashVI materials

The approach of Banin and co-workers has entailed the synthesis ofa number of shell structures (InPGaAs CdSe ZnSe and ZnS) onInAs cores in a two-step process39

By monitoring coreshell growthwith absorption and photolumines-cence spectroscopy it is found that

the bandgap of the core shifts to thered upon growth of InP or CdSeshells while for the larger bandgapshells ZnSe and ZnS the band gapenergy of the core is maintained Itis important to note that the photo-luminescence quantum yield isquenched in InAsInP coreshellsbut increases up to 20 for InAsCdSe and InAsZnSe coreshell nan-ocrystals For InAsZnS coreshellmaterials the enhancement of thephotoluminescence quantum yield isapparently smaller (8)

The work of Nozik and co-work-ers has focused on the use of Zn-CdSe2 capping layers on InP nano-crystals known to provide strain-free interfaces in the bulk38 The lat-tice matching permits epitaxialgrowth of the ZnCdSe2 shell on col-loidal InP nanocrystals shell thick-nesses up to 50 AEcirc were grown on theInP nanocrystal core The ZnCdSe2

shell causes a shift of the electronicstates of the corendashshell nanocrystalsto lower energy compared to pureInP quantum dots For small coresizes the electron is apparently de-localized over the whole nanocrys-


focal point

tal while the hole is mainly local-ized within the core region Theoret-ical calculations have been employedto determine the electron probabilitydensity of the quantum dots andcompared with the experimental re-sults

Group III Nitrides One class ofIIIndashV nanocrystalline materials re-ceiving extensive recent interest isthe nitrides especially GaN Suchmaterials are of interest given thepossibility of blue emitting laserslight-emitting diodes (LEDs) androbust photodetectors based on thissemiconductor4041 Routes to nano-crystalline gallium nitride have beenreported that permit some controlover the particle size and a degreeof crystalline phase-inhomogeneityof the materials One viable precur-sor is polymeric gallium imideGa(NH)32n which can be convert-ed to nanocrystalline cubichexago-nal GaN42 Another method involvesroutes to gallazane [H 2GaNH 2] x from the combination of LiGaH4 andNH 4X (X 5 Cl Br) in Et2O43

Synthesis From the Bottom UpGroup IV Materials Much but notall of the interest concerning thepreparation of nanocrystalline ele-mental semiconductors from thisGroup has focused on the paradigmof solid-state microelectronics sili-con Common bottom-up routes forthe preparation of homogeneous Sinanocrystals include the gas-phasepyrolysis of silane or disilane44ndash47 aswell as the Zintl phase route of Kau-zlarich and co-workers using NaSi ina glyme-type solvent under inertconditions48

Advances in Group IV nanocrys-tal synthesis have not been limitedexclusively to silicon The Zintlphase route noted above has alsobeen successfully extended to ger-manium49ndash51 and tin52 For the case ofGe these nanocrystals can be pre-pared via the reaction of NaGe (orKGe or MgGe) with excess GeCl4 inglyme-type solvents at re ux tem-peratures Depending on solvent andsurface termination crystalline Genanocrystals ranging in size from 45to 10 nm can be obtained with a rel-atively broad size distribution While

inhomogeneously broadened thereis clearly a size-dependent shift inthe emission maxima of these sam-ples Ge nanocrystals with a meandiameter of 35 nm emit clearly inthe blue 62-nm particles in the yel-low-green and 8ndash10-nm crystallitesin the red For Sn the nano-sizedparticles are prepared by the reactionof SnCl4 with Mg2Sn in glyme In-terestingly Sn core structures withSi shells can also be constructed bysubstituting SiCl4 for the tin halidespecies in the above reaction Highresolution transmission electron mi-croscopy (HRTEM) analyses con- rm that crystalline Sn in a tetrago-nal structure is obtained solid stateNMR spectra and X-ray powder dif-fraction con rm the b-tin environ-ment52 Typical nanoparticle diame-ters for these materials range from 7to 15 nm

Capping Si quantum dots withSiO2 is dif cult to avoid but is ben-e cial in that it protects the under-lying Si from further oxidation Oneof the intrinsic dif culties associatedwith oxide-capped Si nanocrystals isthe dif culty in achieving monodis-perse size distributions notably ac-centuated by the aggregation tenden-cy of the SiO2 capping layer Henceviable surface modi cation routesare an important part of advances inthis area ideally to ease both puri- cation and processing in other re-quirements This is also a strength ofthe Zin tl approach noted abovewhereby the as-prepared nanoparti-cle surfaces are reactive (given theirchlorine termination) with alkyl lith-ium reagents such as methyl or butyllithium or Grignard reactants such asoctylmagnesium bromide53 Suchtransformations perm it alkyl-func-tionalized surfaces with ample sol-ubility in organic solvents For thecase of erbium-doped silicon nano-crystals the Coffer group has alsoencountered success with the use ofsurface derivatization reactions em-ploying functional groups w ithslightly different polarit ies ie ndashSiMe 3 ndashSi(CH 2)3CN and ndashSi-(CH2)3NH2 such surface modi ca-tion occurs most effectively whenthe capping agent is present as the

nanoparticles are collected in thebubbler immediately after their for-mation in the py rolysis oven 54

While the derivatized doped nano-crystals retain the desired lumines-cence at 1540 nm associated withthe erbium centers for the ndashSiMe3

and ndashSi(CH2)3CN-capped nanocrys-tals there is a clear improvement oftheir solubility in solvents such asbutylphenyl ether In contrast pro-pylamine-mod ed surfaces becomeless soluble in the solvents testedpresumably as a consequence of ex-tensive hydrogen bonding inducedaggregation In general the ability towork with these nanocrystals in awider variety of solvents may notonly improve size-selective quantumdot isolation but also their use in oth-er applications

Synthesis From the Top DownLithographically patterned quantumdots painstakingly fabricated from aseries of plasma or wet chemicaletched processes and anchored to asubstrate remain the method ofchoice for much of the solid-statephysics and engineering communi-ties33 However the focus of this partof the review is an examination ofrelatively facile methods almost allelectrochemical in nature for pro-ducing quantum dots of a given typeby self-limiting reactions Based onties to industrially relevant wet etchprocesses such reactions have typi-cally focused on semiconductorsfrom the Group IV family

The paradigm of this type of ma-terial is porous silicon porous layersof nanocrystalline Si wires and dotstypically prepared by a constant cur-rent anodization of bulk crystallineSi in ethanolic HF While its exis-tence has been known since 195655

interest in porous Si experiencedsomething of a renaissance in the1990s as a consequence of Canhamrsquosdiscovery of visible light emissionfrom porous Si in 199056 A numberof developments have been de-scribed by Buriak in a recent re-view57

As with quantum dots preparedfrom bottom-up approaches thesetop-down electrochemical routes arenot restricted simply to silicon A


very recent account by Buriak andChoi has described a novel biopolaretch process for the fabrication ofporous germanium58 Using HCl asan etchant a brief (5 min) anodicetch at relatively high current den-sities (350 mAcm 2) produces asurface chloride andor hydroxidelayer that subsequently dissolves aswitch to cathodic bias of the samemagnitude for one minute is believedto be a crucial step for the formationof a hydride-terminated porous Gesurface A four electron reduction ofa given Ge center in an acidic envi-ronment is proposed

In contrast to porous Si only ex-tremely weak red emission is detect-ed at 77 K by the unaided eye fromthese bipolar-etched porous Gestructures (with 365-nm excitation)a luminescence that is apparently tooweak to be observed with charge-coupled device (CCD) detection58

The anodically etched layers on theother hand produce yellow-whitephotoluminescence upon excitationwith 254-nm light at 77 K The latteremission is believed to be oxide re-lated given the absence of GendashH x

species in these lms and the factthat their brief exposure to a 25aqueous HF solution eliminates thistype of luminescence Thus it is pro-posed that the weak emission ema-nating from the bipolar-etched hy-dride-terminated material originatesfrom Ge nanoparticles while that ofthe anodically etched oxide struc-tures is a consequence of oxide58

OPTICAL ELECTRONIC ANDSTRUCTURALCHARACTERIZATION

For colloidal solutions of quantumdots electronic absorption spectros-copy is a simple and easy way to es-timate the bandgap energy Figure 5illustrates the UV-vis spectra for CdS

nanoparticles with diameters of 2ndash10 nm as the nanoparticle decreasesin size the band edge blue-shiftsFor a semiconductor that has a bulkbandgap in the near-IR its visiblecolor can be tuned from black (bulk)to red to yellow to white depend-ing on nanoparticle size4

Photoluminescence in quantumdots arises from the radiative recom-bination of electronndashhole pairs (Fig6) The fate of the photogeneratedelectronndashhole pair in the solid is crit-ically tied to applications of thesematerials Slight defects in the solidsuch as vacancies impurities or ad-

sorbates at the surface cause the for-mation of lsquolsquotraprsquorsquo states into whichthe photo-excited electron can fallor the photo-excited hole canlsquolsquo oatrsquorsquo

The resulting photoluminescencecan thus be quite Stokes-shifted fromthe absorbance depending on therelative energies of these trap statescompared to the valence and con-duction band edges The photo-ex-cited electron or hole can interactwith adsorbates in a donorndashacceptorcharge-transfer manner familiar toinorganic chemists59 to yield changesin emission lifetime or quantumyield forming the basis for somesensor applications If the electronndashhole pair does not recombine in thesolid it may reduce or oxidize mol-ecules at the surface (eg TiO2 pho-tocatalysis) One way to eliminatetrap states is to coat the quantum dotwith a shell of a higher-bandgap ma-terial this leads to light emissionthat is quite close to the absorptionenergy and that can have quantumyields approaching 05060ndash62 Thusemission spectra are also often ob-tained for quantum dot materials asa means to characterize them

Due to the sensitivity of photolu-minescence of quantum dots to de-

fects and adsorbates the opticalproperties of the materials may de-pend heavily on the synthetic pro-cedure used to make them For ex-ample in the pyrolysis of organo-metallic precursors to make GaNquantum dots generally intrinsicbandgap photoluminescence (emit-ting in the blue region with a maxi-mum near 410 nm) andor broad de-fect photoluminescence (known toemit in the yellow region) can be ob-served63 In general the observedemission spectra are strongly depen-dent on pyrolysis temperature andchoice of precursor GaN derivedfrom pyrolysis of a solid gallium im-ide precursor typically exhibits yel-low defect photoluminescence withthe reaction temperature in uencingthe intensity of the emission Pyrol-ysis of this same precursor in a rel-atively high boiling amine solventyields blue photoluminescence withan emission maximum near 420 nmGaN derived from pyrolysis of a po-lymerized gallazane precursor incontrast yields blue light emissionwhose quantum yield can be im-proved by a brief HF etch presum-ably through the reduction of non-radiative pathways The core-shellsynthetic approaches outlined abovecan be bene cial in reducing defectemission and promoting band-edgeelectronndashhole recombination

Emission spectra for quantum dotscan be extremely narrow5ndash1062 (Fig7) Quantum yields as high as 05have been reported60 62 Time-re-solved photoluminescence data arecomplex and depend a great deal onsample quality time scales fromfemtoseconds to microseconds havebeen observed and correlated withelectron trapping times (femtosec-onds to picoseconds) band-edgeelectronndashhole pair recombination(picoseconds to nanoseconds) andelectronndashhole pair recombinationfrom trap states (nanoseconds to mi-croseconds) in addition microsec-ond lifetimes are observed due to re-combination from lsquolsquodarkrsquorsquo excitonicstates at low temperature5ndash106264

Doping bulk semiconductors withpart-per-million levels of impuritiesis a well-recognized means of con-


focal point

FIG 5 Ultraviolet-visible absorption spectra of CdS quantum dots of different diame-ters in aqueous solution 20 AEcirc (solid line) 40 AEcirc (dashed line) and 125 AEcirc (dotted line)

FIG 6 Photoluminescence from a semiconductor quantum dot Upon absorption of aphoton or electrical excitation (solid up arrow) an electron from the valence band ispromoted to the conduction band leaving a hole behind If trap states are present inthe bandgap (due to impurities defects etc) the electron and hole can be trapped(dashed arrows) Photoluminescence (solid down arrow) results when the electron andhole recombine to emit a photon of light For defect-free and impurity-free semicon-ductors the luminescence is from radiative band-edge recombination Not shown arenonradiative decay pathways for electronndashhole recombination

trolling electronic and optical prop-erties111 Quantum dots can be dopedwith metal ions that have energystates within the bandgap and lightemission from these introduced trapstates can be observed64ndash72 For thecase of Si nanocrystals the Coffergroup at Texas Christian Universityhas recently succeeded in the prep-aration and characterization (bothstructural and photophysical) of dis-crete Si nanoparticles doped withEr31 ions7172 Erbium is of particularinterest in this regard because of itsknown emission at 1540 nm thetransmission maximum of SiO 2 Such nanoparticles are prepared viaa gas-phase pyrolysis of disilane inthe presence of an erbium chemicalvapor deposition (CVD) precursorand harvested as a colloidal solutionin the reactor Unlike other knownhomogeneous Si nanocrystals (andporous silicon) these Er31 doped Sinanocrystals solely yield the desirednear IR photoluminescence associ-ated with the erbium centers as a re-sult of carrier-mediated excitationfrom the Si exciton

Electronic effects in quantum dotshave been intensely explored by thecondensed-matter physics communi-

ty7374 Only one quantum effect willbe described here the lsquolsquoCoulombblockadersquorsquo7576 [7576] Because ofthe small size and quantized natureof the electronic states within aquantum dot adding a single elec-tron to a quantum dot costs a great

deal of energy with additional elec-trons costing even more thus elec-tron ow through a quantum dot canonly proceed one electron at a timecreating the lsquolsquoblockadersquorsquo75 76 Thisblockade effect could in principle beused to construct nanoscale gatesand cavities that could form the basisfor new optical and electronic devic-es

Characterization of ColloidalQuantum Dots Quantum dot size isbest measured by transmission elec-tron microscopy (TEM) High-reso-lution TEM (HRTEM) can visualizelattice fringes leading to crystallo-graphic information about the parti-cle including its phase and crystalaxes

X-ray diffraction of dried-downcolloidal nanoparticles can be usedto infer particle size from the broad-ening of the diffraction peaks En-ergy X-ray absorption ne structure(EXAFS) is also a valuable tech-nique in providing details of coor-dination number and local geometryin semiconductor nanocrystals par-ticularly in very small dots where alarge percentage of the total atomcomposition is present at the surface(with an accompanying amount ofstrain)77 In direct gap systems ab-


FIG 7 Absorption (upper panel) and emission (lower panel) spectra of a series ofCdSe quantum dots surface-stabilized with a shell of ZnS and subsequently silanizedfor improved water solubility The change in optical properties is a function of the sizeof the CdSe core which is varied from 27 to 41 nm The dots are dissolved in anaqueous buffer solution at pH 7 The data are normalized for the convenience of thedisplay From left to right blue green yellow orange and red emitting nanocrystalsare shown For blue emitting quantum dots the absorption spectrum does not showfeatures above 450 nm and is therefore omitted Inset Absorption and emission ofsilanized green-emitting nanocrystals in 10 mM phosphate buffer (solid lines) and ofthe same green CdSeZnS particles in toluene (dashed lines) Reprinted with permis-sion from Ref 99 Copyright 2001 American Chemical Society

sorption spectroscopy is used exten-sively to evaluate Eg which is cor-related with nanoparticle size as well(see above) Standard chemical tech-niques such as nuclear magnetic res-onance (NMR) elemental analysisetc can be used to characterize thecomposition of the material

Characterization of SupportedQuantum Dots In addition to opti-cal spectroscopy scanning electronmicroscopy (SEM) scanning probemicroscopies (SPM) and HRTEMare crit ical means of evaluatingquantum dots made from the lsquolsquotopdownrsquorsquo SEM is a very commonlyemployed method and informationconcerning feature size is easily ob-tained in cross sectional analyses asexempli ed by Fig 8 which con-tains an image of porous Ge

APPLICATIONS OFQUANTUM DOTS FOR THEANALYTICAL CHEMISTRYCOMMUNITY

Applications of quantum dots canbe classi ed as (1) light sources (2)photonics (3) photovoltaics and (4)photoluminescent dyes and sensorsThe light source and photovoltaicapplications require that the quantumdot be supported and electricallyconnected to other electronic ele-ments in a device Quantum yieldsof 02 have been reported for sim-ple solution-phase preparations ofcolloidal CdS13 and quantum yieldsof up to 050 are achievable withmore elaborate preparations60 62

Light-emitting diodes based onquantum dots7879 and quantum cas-cade lasers based on quantum wells(two-dimensional semiconductor na-nostructures) have been reported8081

in theory quantum dot cascade la-sers are achievable82 In the quantumcascade laser unlike semiconductordiode lasers the wavelength outputis dependent upon quantum con ne-ment effects Stimulated emissionand optical gain from CdSe quantumdots have been reported83 In recentexciting work semiconductor nano-rods (cylinders not spheres on thenanometer scale) have been shownto exhibit polarized light emissionand lasing107108

As noted earlier the demonstra-tion of ef cient visible luminescencefrom nanocrystall ine Si remnantspresent in porous Si roughly a de-cade ago56 generated tremendous ex-citement with the prospect of legiti-mate Si based optoelectronics84

However the heterogeneity of thenanostructures in this matrix andlong-term stability issues pose seri-ous hurdles to authentic device de-

velopment85 Thanks to the recentlyreported results of Pavesi and co-workers some of the problematic is-sues concerning light emission fromnanocrystalline silicon have nowbeen resolved in an elegant manner86

These workers have demonstratedoptical gain from Si nanocrystals atroom temperature with net modalgain values on the order of 100 cm21

reported86 A key step in securing


focal point

FIG 8 Cross-sectional scanning electron micrograph of a porous Ge lm The colum-nar structure is clearly present Scale bar 5 10 mm (J Buriak and H Choi PurdueUniversity)

FIG 9 Proposed operational scheme of a Si nanocrystal-based laser Upon the appli-cation of voltage p-type and n-type semiconductor layers donate positively chargedlsquoholesrsquo and negatively charged electrons respectively to the structure Electronndashholerecombination within the active region produces a photon and leads to the emission oflight With adequate efciency of light emission that is located between two highly re-ective mirrors such an emitter can be turned into a miniature laser (Adapted fromRef 89)

this result was the use of ion im-plantation methods in conjunctionwith careful thermal annealing toproduce closely packed arrays of Sinanocrystals (with relatively few de-fects) in a SiO2 matrix Pavesi andco-workers suggest that the ability toachieve gain in these nanocrystals isalso strongly dependent on the qual-ity of the SiSiO2 interface with arelatively high number of emissivestates per Si quantum dot One veryinteresting and perhaps controversialmanifestation of this interfacial qual-ity is the presence of a unique ab-sorption band in the near infrared at-tributed to a Si5O species8788 In anyevent as pointed out by Canham89

demonstration of optical gain is amajor step in the right direction to-ward fabrication of a Si based laserbut the production of coherent lightfrom this type of structure remainsto be shown In this regard howeverkey issues have been identi ed anda plausible scenario for such a devicehas been described (Fig 9)89

While the Coffer group has noteda bottom-up approach to kineticallytrapped erbium ions into discrete Sidots71 72 Fauchet and co-workershave exploited the large surfacearea-to-volume ratio of porous Si forfacile Er31 ion incorporation into thismatrix and subsequently observedthe desired near IR electrolumines-cence90 This is achieved by cathodicelectrochemical migration followedby a relatively high temperature an-neal (950ndash1100 8C) in an oxygen ornitrogen ambient The use of an ex-tremely thin (13 nm) semitranspar-ent Au layer facilitated carrier injec-tion into the active emitting regioneither through forward or reversebias with the resultant electrolumi-nescence at 154 mm associated withthe erb ium centers clearly ob-served90 While the structures exhibitan exponential electroluminescenceintensity dependence for either biasdirection differences in device char-acteristics as a function of tempera-ture suggest that slightly differentexcitation mechanisms are operativeUpon increasing the operating tem-perature from 240 to 300 K the lu-minescence intensity decreased by a


FIG 10 Time dependence of the uorescence intensity of CdSe quantum dots cappedwith ZnS and silanized as in Fig 7 compared to rhodamine 6G under continuous Ar1

laser irradiation (05 mW spot size 700 mm volume of sample 1 mL absorbance5 0065 at 488 nm) The quantum dots are stable for at least four hours while theorganic dye bleaches after 10 min The colored lines correspond to the emission col-or of the quantum dots the black line is rhodamine 6G Reprinted with permissionfrom Ref 99 Copyright 2001 American Chemical Society

factor of 24 under reverse bias andonly a factor of 26 under forwardconditions Such differences havebeen explained on the basis of a hotelectron impact mechanism in re-verse bias where larger temperaturequenching effects could arise as a re-sult of inef cient transport throughthe Er doped porous Si matrixWhile further studies are ongoing itis encouraging to note that externalquantum ef ciencies on the order of001 have been detected in thesesystems

In a subsequent report Lopez andFauchet have successfully construct-ed one-dimensional photonic band-gap structures from a related yetslightly more complex device archi-tecture91 A photonic bandgap mate-rial is one in which certain frequen-cies of light cannot be propagated incertain directions just as the elec-

tronic bandgap in semiconductorsdoes not permit certain energy lev-els92 In this speci c system highlyre ecting porous silicon Bragg re- ectors (each containing six pairs oflow and high porosity layers) arefabricated which sandwich an activelayer the cavities are doped with er-bium by the cathodic electromigra-tion process (as above) and activatedby a high temperature anneal in ox-ygen and nitrogen Interestingly theposition of the Er31 emission maxi-mum may be tuned in such struc-tures by controlling the oxidationtemperature One assessment of theoptical quality of such structures isthe cavity quality factor Q de nedas the wavelength of the resonancedivided by the full width at half-maximum intensity Q values on theorder of 130 have been reported forthis emission with corresponding

full width at half-maximum intensityas narrow as 12 nm

Photovoltaicsmdashthe conversion ofsunlight to electricitymdash is anotherapplication in which quantum dotsmay provide some advantages Theideal photovoltaic device would beone in which a signi cant portion ofthe solar spectrum would be ab-sorbed ef cient charge separationwould be achieved and transport ofcharge through the device would beef cien t Quantum dotpolymercomposite photovoltaic devices havebeen reported with internal conver-sion ef ciencies of 27 which arerespectable compared to the bestphotovoltaics based on silicon(10)93 as the intricacies of the sys-tem are worked out much higher ef- ciencies may be achievable

Colloidal quantum dots with well-passivated surfaces (so that trapstates are avoided in photolumines-cence) can function as large lsquolsquo uo-rescent dyesrsquorsquo that have narrowemission spectra (Fig 7) and rela-tively high quantum yields94ndash99 CdSein the bulk absorbs light from 720nm into the ultraviolet quantum dotsof CdSe also absorb in the ultravioletbut cut off at different wavelengthsdepending on particle size94ndash99 (Fig7) Covalent attachment of biologicalmolecules to the quantum dot sur-face has been demonstrated andthese bioconjugates of quantum dotshave been used to visualize recep-torndashligand interactions in cells asDNA hybridization probes and forother bio technological applica-tions94ndash99 Compared to organic dyesquantum dots have narrower emis-sion spectra (30 nm FWHM) andmany different uorescence colorscan be excited with a single wave-length of light100 due to the overlap-ping absorptions at the high-energyend of the electronic spectra (Fig 7)The extinction coef cients of quan-tum dots have been reported to be onthe order of 100 000 M21 cm2199

Since the emission lines are relative-ly narrow compared to organic dyesdetection of the quantum dots suffersmuch less from cross-talk that mightresult from the emission of a differ-ent uorophore bleeding into the de-


focal point

tection channel for the uorophoreof interest There is also evidencethat quantum dots suitably surface-derivatized for protection are muchmore stable than organic uorescentdyes (Fig 10) one study reports thatquantum dots are stable in solutionfor a month over a pH range of 6ndash8and that under light irradiation nophotobleaching is observed for atleast four hours (Fig 10)

However the surface chemistry ofquantum dots still needs to be furtherworked out and there have been re-ports of lsquolsquophotobrighteningrsquorsquo (the op-posite of photobleaching) whichare still not understood99

For chemical sensor or biosensorapplications the quantum dot sur-face should not be passivated to thepoint where it is insensitive opticallyto its environment but the surfaceshould be available for interactionswith analytes This application ofquantum dots is a broad frontier thatis gaining increasing interest Theuse of the photoluminescence ofquantum dots for detection of differ-ent DNA sequences based on thedifferential adsorption of DNAs tothe quantum dot surface due to localDNA structural deformation hasbeen reported by the Murphygroup101ndash106 Local structural and dy-namic distortions within DNA arecorrelated with some genetic diseas-es and thus quantum dots uniqueprobes with curvature on the sizescale of the distortion may be well-suited as optical detectors of DNAdeformation and damage109

CONCLUSION

The 1990s saw incredible progressin the synthesis characterizationand the beginnings of applicationsfo r quantum dots D ramatic im-provements in particle dispersity andquantum ef ciency of emission havebrought the notion of authentic de-vices based on these materials closerto fruition However there is still agreat need for better synthetic meth-ods for making these materials on alarge scale with less toxic precur-sors

In the construction of real deviceshybrid materials entertaining mix-

tures of inorganic quantum dots withsemiconducting organic architec-tures will likely play a key role Thebiological applications of quantumdots unexpected in the early 1990sare now a likely area for high impactand commercial potential in the nearfuture

ACKNOWLEDGMENTS

The authors thank their co-workers listed inthe references In addition the authors thankthe National Science Foundation (DMR 98-19178 to JLC CHE 95-02929 to CJM)the National Institutes of Health (CJM) theResearch Corporation (CJM is a CottrellScholar) the Alfred P Sloan Foundation(CJM) the Camille and Henry DreyfusFoundation (CJM) and the Welch Founda-tion (JLC) for nancial support of theirquantum dot work

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3 H Weller Adv Mater (Weinheim Ger)5 88 (1993)

4 H Weller Angew Chem Intl Ed Engl32 41 (1993)

5 A P Alivisatos J Phys Chem 10013226 (1996)

6 A P Alivisatos Science (WashingtonDC) 217 933 (1996)

7 J Z Zhang Acc Chem Res 30 423(1997)

8 H Weller Curr Opin Colloid InterfaceSci 3 194 (1998)

9 S V Gaponenko Optical Properties ofSemiconductor Nanocrystals (Cam-bridge University Press Cam bridge1998)

10 S A Empedocles and M G BawendiAcc Chem Res 32 389 (1999)

11 L E Brus J Chem Phys 80 4403(1984)

12 L Spanhel M Haase H Weller and AHenglein J Am Chem Soc 109 5649(1987)

13 K Sooklal L H Hanus H J Ploehnand C J Murphy Adv Mater 10 1083(1998)

14 J Huang K Sooklal C J Murphy andH J Ploehn Chem Mater 11 3595(1999)

15 C B Murray D J Norris and M GBawendi J Am Chem Soc 115 8706(1993)

16 Z A Peng and X Peng J Am ChemSoc 123 183 (2001)

17 T Trinidade and P OrsquoBrien Adv Mater8 161 (1996)

18 T Trinidade and P OrsquoBrien J MaterChem 6 343 (1996)

19 M L Steigerwald A P Alivisatos JM Gibson T D Harris R Kortan AMuller A M Thayer T M Duncan D

C Douglass and L E Brus J AmChem Soc 110 3046 (1988)

20 N Herron Y Wang and H Eckert JAm Chem Soc 112 1322 (1990)

21 Y Nosaka N Ohta T Fukuyama andN Fujii J Colloid Interface Sci 155 23(1993)

22 R Kho C L Torres-Marinez and R KMehra J Colloid Interfac Sci 227 561(2000)

23 J M Whitling G Spreitzer and D WWright Adv Mater 12 1377 (2000)

24 K M Choi and K J Shea J PhysChem 98 3207 (1994)

25 M P Pileni L Motte and C PetitChem Mater 4 338 (1992)

26 X K Zhao S Baral R Rolandi and JH Fendler J Am Chem Soc 1101012 (1988)

27 R S Urquhart D N Furlong T Gen-genbach N J Geddes and F GrieserLangmuir 11 1127 (1995)

28 N Herron Y Wang M Eddy G DStucky D Cox K Moller and T BeinJ Am Chem Soc 111 350 (1989)

29 K K W Wong and S Mann Adv Ma-ter 8 928 (1996)

30 C T Dameron R N Reese R K Meh-ra A R Kortan P J Carroll M LSteigerwald L E Brus and D RWinge Nature (London) 338 596(1989)

31 R N Reese C A White and D RWinge Plant Physiol 98 225 (1992)

32 C T Dameron and D R Winge InorgChem 29 1343 (1990)

33 R Szweda IIIndashV Review 13 14 (2000)34 R L Wells and W L Gladfelter J Clus-

ter Science 8 217 (1997)35 R L Wells C G Pitt A T McPhail

A P Purdy S Sha eezad and R BHallock Chem Mater 1 4 (1989)

36 R L Wells C G Pitt A T McPhailA P Purdy S Sha eezad and R BHallock Mater Res Soc Symp Proc131 45 (1989)

37 J R Heath J Phys Chem 100 7212(1996)

38 O Micic B Smith and A Nozik JPhys Chem B 104 12149 (2000)

39 Y Cao and U Banin J Am Chem Soc122 9693 (2000)

40 F A Ponce and D P Bour Nature (Lon-don) 386 351 (1997)

41 S Nakamura Solid State Commun 102237 (1997)

42 J F Janik and R L Wells Chem Mater8 2708 (1996)

43 J F Janik and R L Wells Inorg Chem36 4135 (1997)

44 K Littau P Szajowski A Muller AKortan and L Brus J Phys Chem 971224 (1993)

45 L Brus P Szajowski W Wilson THarris S Schupler and P Citrin J AmChem Soc 117 2915 (1995)

46 W L Wilson P F Szajowski and L EBrus Science (Washington DC) 2621242 (1993)

47 T Murthy N Miyamoto M Shibo and


J Nishizawa J Cryst Growth 33 1(1976)

48 R A Bley and S Kauzlarich J AmChem Soc 118 12461 (1996)

49 B R Taylor S M Kauzlarich H W HLee and G R Delgado Chem Mater10 22 (1998)

50 B R Taylor S M Kauzlarich G RDelgado and H W H Lee Chem Ma-ter 11 2493 (1999)

51 C-S Yang S M Kauzlarich and Y CWang Chem Mater 11 3666 (1999)

52 C-S Yang Q Liu S M Kauzlarichand B Phillips Chem Mater 12 983(2000)

53 C-S Yang R A Bley S M Kauzlar-ich H W H Lee and G R DelgadoJ Am Chem Soc 121 5191 (1999)

54 J Ji R Senter and J Coffer unpub-lished results

55 A Uhilir Bell Syst Tech J 35 333(1956)

56 L Canham Appl Phys Lett 57 1046(1990)

57 M P Stewart and J M Buriak AdvMater 12 859 (2000)

58 H-C Choi and J M Buriak ChemCommun 1669 (2000)

59 R Cohen L Kronik A Shanzer DCahen A Liu Y Rosenwaks J K Lo-renz and A B Ellis J Am Chem Soc121 10545 (1999)

60 M A Hines and P Guyot-Sionnest JPhys Chem 100 468 (1996)

61 X Peng M C Schalmp A V Kada-vanich and A P Alivisatos J AmChem Soc 119 7019 (1997)

62 M Nirmal and L Brus Acc Chem Res32 407 (1999)

63 J Coffer M Johnson L Zhang RWells and J Janik Chem Mater 92671 (1997)

64 K Sooklal B Cullum S M Angel andC J Murphy J Phys Chem 96 4551(1996)

65 L Levy N Feltin D Ingert and M PPileni J Phys Chem B 101 9153(1997)

66 T Nutz U zum Felde and M Haase JChem Phys 110 12142 (1999)

67 H Meyssamy K Riwotzki A Kor-nowski S Naused and M Haase AdvMater 11 840 (1999)

68 F V Mikulec M Kuno M Bennati DA Hall R G Grif n and M G Baw-endi J Am Chem Soc 122 2532(2000)

69 K Riwotzki H Meyssamy A Kor-nowski and M Haase J Phys ChemB 104 2824 (2000)

70 P Yang M K Lu D Xu D L Yuanand G J Zhou Chem Phys Lett 33676 (2001)

71 J St John J Coffer Y Chen and RPinizzotto J Am Chem Soc 121 1888(1999)

72 J St John J Coffer Y Chen and RPinizzotto Appl Phys Lett 77 1635(2000)

73 C Weisbuch and B Vinter QuantumSemiconductor Structures Fundamen-tals and Applications (Academic PressSan Diego 1991)

74 P M Petroff A Lorke and A Imamo-glu Phys Today 54 46 (2001)

75 C Livermore C H Crouch R M Wes-tervelt K L Campman and A L Gos-sard Science (Washington DC) 2741332 (1996)

76 D Gammon Nature (London) 405 899(2000)

77 S Schuppler S L Friedman M AMarcus D L Adler Y-H Xie F MRoss T D Harris W L Brown Y JChabal L E Brus and P H CitrinPhys Rev Lett 72 2648 (1994)

78 V Colvin M C Schlamp and A P Ali-visatos Nature (London) 370 374(1994)

79 D Childs S Malik P Siverns C Rob-erts and R Murray Mater Res SocSymp Proc 571 267 (2000)

80 J Faist F Carpasso D L Sivco C Sir-tori A L Hutchinson and A Y ChoScience (Washington DC) 264 553(1994)

81 A Treducucci C Gmachi F CapassoD L Sivco A L Hutchinson and AY Chao Nature (London) 396 350(1998)

82 N S Wingreen and C A Stafford IEEEJ Quantum Electron 33 1170 (1997)

83 V I Klimov A A Mikhailovsky S XuA Malko J A Hollingsworth C ALeatherdale H-J Eisler and M GBawendi Science (Washington DC)290 314 (2000)

84 L T Canham in Frontiers of Nano-Op-toelectronics L Pavesi and F BuzanevaEds (Kluwer Academic Boston 2000)pp 85ndash87

85 A G Cullis L Canham and P D JCalcott J Appl Phys 82 909 (1997)

86 L Pavesi L Dal Negro C MassoleniG Franzo and F Priolo Nature (Lon-don) 408 440 (2000)

87 Y Kanemitsu and S Okamoto SolidState Commun 103 573 (1997)

88 Y Kanemitsu and S Okamoto PhysRev B 58 9652 (1998)

89 L Canham Nature (London) 408 411(2000)

90 H Lopez and P Fauchet Appl PhysLett 75 3989 (1999)


92 J D Joannopoulos R D Meade and JN Winn Photonic Crystals Moldingthe Flow of Light (Princeton UniversityPress Princeton NJ 1995)

93 W U Huynh X Peng and A P Ali-visatos Adv Mater 11 923 (1999)

94 M Bruchez Jr M Moronne P Gin SWeiss and A P Alivisatos Science(Washington DC) 281 2013 (1998)

95 W C W Chan and S Nie Science(London) 281 2016 (1998)

96 H Mattoussi J M Mauro E R Gold-man G P Anderson V C Sundar F VMikulec and M G Bawendi J AmChem Soc 122 12142 (2000)

97 S Pathak S-K Choi N Arnheim andM E Thompson J Am Chem Soc123 4103 (2001)

98 M Y Han X H Gao J Z Su and SNie Nature Biotechnology 19 631(2001)

99 D Gerion F Pinaud S C Williams WJ Parak D Zanchet S Weiss and A PAlivisatos J Phys Chem B 105 8861(2001)

100 J Lee V C Sundar J R Heine M GBawendi and K F Jensen Adv Mater12 1311 (2000)

101 R Mahtab J P Rogers and C J Mur-phy J Am Chem Soc 117 9099(1995)

102 R Mahtab J P Rogers C P Singletonand C J Murphy J Am Chem Soc118 7028 (1996)

103 R Mahtab H H Harden and C J Mur-phy J Am Chem Soc 122 14 (2000)

104 J R Lakowicz I Grycynski Z Gry-cynski K Nowaczyk and C J MurphyAnal Biochem 280 128 (2000)

105 R Mahtab and C J Murphy ProcSPIE-Int Soc Opt Eng 3924 10(2000)

106 L Gearheart K Caswell and C J Mur-phy J Biomed Optics 6 111 (2001)

107 J T Hu L S Li W D Yang L MannaL W Wang and A P Alivisatos Sci-ence (Washington DC) 292 2060(2001)

108 M H Huang S Mao H Feick H QYan Y Y Wu H Kind E Weber RRusso and P D Yang Science (Wash-ington DC) 292 1897 (2001)

109 C J Murphy Adv Photochem 26 145(2001)


FIG 1 A simplied energy level diagram for metals semiconductors and insulatorsThe shaded boxes represent the lled valence bands the empty boxes represent theempty (at 0 K) conduction bands The arrows represent the bandgap energy Eg

FIG 2 Electronic band structure of direct (left) and indirect (right) semiconductors Thearrows show the lowest-energy transition between the valence band (bottom curves)and conduction band (top curves) a change in k is necessary for the indirect semicon-ductor

electrons exhibit quantum mechani-cal effects2ndash10 In the literature semi-conductor quantum dots are alsoknown as semiconductor nanocrys-tals or nanoparticles

Consider what happens when asemiconductor is irradiated withlight of energy hn Eg (For semi-conductors this corresponds to lightin the near IR through the visibleand extending into the ultraviolet re-gion) An electron will be promotedfrom the valence band to the con-duction band leaving a positivelycharged lsquolsquoholersquorsquo behind This holecan be thought of as the absence ofan electron and acts as a particlewith its own effective mass and

charge in the solid One can calcu-late the spatial separation of the elec-tron and its hole (an lsquolsquoexcitonrsquorsquo) us-ing a modi ed Bohr model

r 5 eh 2 pm re 2 (3)

where r is the radius of the spherede ned by the three-dimensionalseparation of the electron-hole paire is the dielectric constant of thesemiconductor m r is the reducedmass of the electronndashhole pair h isPlanckrsquos constant and e is the chargeon the electron For many semicon-ductors the masses of the electronand hole have been determined byion cyclotron resonance19 and aregenerally in the range of 01 me to 3

me For typical semiconductor di-electric constants the calcu lationsuggests that the electronndashhole pairspatial separation is 1ndash10 nm formost semiconductors9 In this sizerange when the exciton is createdthe physical dimensions of the par-ticle con ne the exciton in a mannersimilar to the particle-in-a-box prob-lem of physical chemistry There-fore the quantum effects such asquantization of energy levels can beobserved in principle Alternativelyone can think of the nanoparticle ashaving an electronic structure inter-mediate between bands and bonds(Fig 3) One consequence of this in-termediate character is that Eg is cor-related with size as the dimensionsof the particle decrease Eg increases

Brus has developed a popular ef-fective mass model that relates par-ticle size (neglecting spatial correla-tion effects) to the bandgap energyof a semiconductor quantum dot12

E (quantum dot)g

5 E (bulk)g

2 21 (h 8R )(1m 1 1m )e h

22 18e 4pe eR0 (4)

where Eg is the bandgap energy ofthe quantum dot or bulk solid R isthe quantum dot radius m e is the ef-fective mass of the electron in thesolid mh is the effective mass of thehole in the solid and e is the dielec-tric constant of the solid The middleterm on the right-hand side of theequation is a particle-in-a-box-liketerm for the exciton while the thirdterm on the right-hand side of theequation represents the electronndashholepair Coulombic attraction mediatedby the solid Implicit in this equationis that the quantum dots are sphericaland that the effective masses ofcharge carriers and the dielectricconstant of the solid are constant asa function of size The Brus modelmaps Eg and size well for largerquantum dots but its predictions donot match experiment well for verysmall part icle sizes Many othermore complex approximations havebeen derived theoretically that bettermatch experimentally determined


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SYNTHESIS






















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CONCLUSION




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CONCLUSION




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Quantum Dots: A Primer - unizg.hr · 2014-03-20 · 18A Volume 56, Number 1, 2002 focalpoint FIG.3....

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