2011_Nature_Role of Middle Gap in Current

8/2/2019 2011_Nature_Role of Middle Gap in Current

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nATuRE CommunICATIons | 2:486 | DoI: 10.1038/c1492 | www.atre.c/atrecicati

2011Macmillan Publishers Limited. All rights reserved.

Received 1 Apr 2011 | Accepted 25 Ag 2011 | Pblihed 27 sep 2011 DOI: 10.1038/ncomms1492

Cllidal eicdctr acrytal have attracted igicat iteret r applicati

i lti-prceable device ch a light-eittig dide ad lar cell. Hwever, a

pr dertadig charge traprt i acrytal aeblie, pecically the relati

betwee electrical cdctace i dark ad der light illiati, hider their techlgical

applicability. Here we iltaely addre the ie dark traprt ad pht-

cdctivity i l Pbs acrytal, by icrpratig the it ptical eld-eect

traitr i which the chael cdctace i ctrlled by bth gate vltage ad icidet

radiati. spectrally relved phtrepe thee device reveal a weakly cdctive id-

gap bad that i repible r charge traprt i dark. The echai r cdctace,

hwever, chage der illiati whe it bece diated by bad-edge qatized

tate. I thi cae, the id-gap bad till ha a iprtat rle a it ccpacy (ted by the

gate vltage) ctrl the dyaic bad-edge charge.

1 Center for Advanced Solar Photophysics, C-PCS, Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Correspondence and requests for materials should be addressed to V.I.K. (email: [email protected]).

Rle id-gap tate i charge traprt ad

phtcdctivity i eicdctr acrytal

l

Prahat nagpal1 & Victr I. Kliv1


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nATuRE CommunICATIons | DoI: 10.1038/c1492



Semiconductor nanocrystals (NCs) abricated by chemical1and physical2 methods have been considered promising mate-rials or applications in solution-processable devices includ-

ing light-emitting diodes35, eld-eect transistors (FEs)611 ,photodetectors12, and solar cells1318. In addition to processabilityrom solutions, NCs are attractive because o a variety o novelphysical properties that can be controlled by NC dimensions,shapes, and internal structure19. Several recent examples have alsodemonstrated a large promise o NCs or the realization o genera-

tion-III photovoltaics by employing concepts such as multiexcitongeneration through carrier multiplication2024, and hot-electronextraction25,26.

A signicant problem in realizing practical NC-based devicesis poor understanding o charge transport in NC lms. raditionalassumption is that electrical conductance in NC-based structuresis mediated by a network o overlapping band-edge quantizedstates20,27. However, recent demonstrations o a dramatic eect osurace treatments on dark conductivity (0) o NC lms

9, com-bined with observations o relatively weak sensitivity o0 to NCsize polydispersity10, suggest the involvement o intra-gap states(probably o surace origin) in charge transport. Furthermore, pre-vious FE studies have indicated that changes in the occupancy osurace traps might be responsible or observed changes in apparent

levels o doping o NC lms11

.Whereas it is typically dicult to assess the nature o states

involved in dark charge transport, a photoresponse shouldinvolve quantized states, as these states get populated as a resulto light absorption. Te relative contribution o quantized statesto photoconductivity compared with the states that dominatedark charge transport is unclear. For example, the studies o NCphotovoltaics indicate that although the open circuit voltage (Voc)does scale with NC band-gap energy (Eg), it is always appreciablylower than the ideal Voc calculated or a given Eg (res 14,15,17,27)(see Supplementary Inormation or discussion on semiconduc-tor bandgap and open-circuit voltage). Tis might be consideredas an indication o a mixed character o photoconductivity, whichcould involve both quantized and surace-related states. One hur-

dle in elucidating the nature o electronic states responsible orconduction in dark and under illumination arises rom the actthat the data on dark transport and photoconductivity are nor-mally obtained using dierent types o devices that are, respec-tively, three-terminal FEs, and two-terminal photodetectors orphotovoltaic cells.

Here we investigate the roles o quantized band-edge andintra-gap states in NC-lm conductance by using three-terminalPbSNC-based optical FEs (OFEs). We simultaneously addressthe problems o dark transport and photoconductance, and elu-cidate the roles o equilibrium charges injected by applying gatevoltage versus non-equilibrium carriers generated by photoex-citation. Spectrally resolved studies o a gate-voltage-dependentphotocurrent reveal the existence o mid-gap states in NC lms

that orm a weakly conducting band (mid-gap band or MGB),which serves as a charge conduit in dark. We also observe thatthe nature o charge transport changes under illumination when itbecomes dominated by carrier migration through the network oband-edge quantized states, which is characterized by much highermobility than the MGB. Te MGB still has an important role inthe photoresponse as its occupancy controls the photoconductionby controlling recombination dynamics o band-edge charges.Te analysis o the gate-voltage dependence o photoresponsesindicates that lietimes o band-edge electrons are much shorterthan those o holes indicating a much greater probability oelectron capture at MGB states compared with holes. Tis sug-gest that photoconductivity in our lms is dominated by photo-generated holes.

ResultsDark charge transport in NC flms. Te layout o the OFEdevices used in the present study is shown schematically inFigure 1a (abrication details in Methods). Its channel is abricatedrom PbS NCs with a mean diameter o 3.3 nm (Fig. 1b inset). Te

corresponding band-gap energy Eg = 1.3 eV. First, we characterizethese structures in dark (black curve in Fig. 1c) by monitoring thesourcedrain current (Isd) as a unction o gate bias (Vg). When Vg = 0(at-band condition in our devices in dark), the OFE channelis only weakly conductive. However, Isd quickly increases undernegative gate bias, which corresponds to injection o holes into theNC lm. At Vg = 25 V, Isd becomes ca. three orders o magnitudehigher than at Vg = 0. From gate-source capacitance measurements(Fig. 1d), we estimate that that the average number o holes injectedper NC (n0) at Vg = 25 V is n00.1 (Methods).

Although Isd also appears to increase considerably on apply-ing the positive gate-source voltage, this growth is an arteact oour measurements, in which we switch the sign oVg without chang-ing the sign o the sourcedrain voltage. As a result, the gate-drain

Light

VSD

Vg

4060nm

G

Si++

5

4

3

2

1

100

0.0

350

300

250

200

150

100Capacitance(nFcm2)

0.11.0

5.020

100300

>400

10

0.125

20

30 20

Q

10

Vg(V)

0 1015

10Vg(V)

5 05 10

0.001Lightintensity

0.010.1

1.0

1Current(nA)

01.0 1.5 2.0

Photon energy (eV)

Dark

2.5 3.0 3.5 4.0

DS

Absorbance(a.u.)

Figure 1 | Dark conductance and photoconductance in PbS NC OFETs.

(a) A cheatic PbsnC oFET. s, D ad G dete rce, drai ad

gate electrde, repectively. Illiati PbsnC l relt i

phtidced crret betwee the rce ad the drai electrde, which

i itred a a cti light iteity ad eergy icidet pht,

while iltaely varyig the gate vltage. (b) Abrpti pectr

Pbs nC i lti. The bad-edge 1s peak i at 1.3 eV. The iet hw

a repreetative traii electr icrgraph the nC (cale bar

repreet 10 ). The ea nC diaeter i 3.3 0.6 . (c) The Id ver

Vg characteritic i dark (black crve) ad der 2.25 eV illiati a a

cti light iteity (relative it; 1 crrepd t 30W c 2) i

a three-dieial repreetati. Light illiati relt i icreaed

carrier ccetrati ad a reltat rder--agitde icreae i

phtcrret at the fat-bad gate vltage (Vg = Vgi; crrepd t

the phtcrret ii) de t the phtcdctive eect. uder

illiati, a extra pitive vltage, which cpeate r the

phtvltage de t charge acclati der the rce/drai electrde,

i reqired t achieve the fat-bad cditi (traced by the black lie i

the ctr plt at the btt). (d) Capacitace eareet r the nC

l i dark idicate acclati hle i the chael der egative

gate bia. The agitde the acclated charge ca be ierred r

the itegral Q C V V Vg= 0 ( )d .


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voltage or Vg > 0 is considerably higher (varies rom + 25 Vto + 35 V) than in the case oVg < 0 (varies rom + 25 V to 0), whichmight lead to a signicant gate leakage current or positive gatevoltages. Tis eect is likely responsible or the increase oIsd whenVg > 0, but not electron injection. Te reason or perorming themeasurements without changing the sign oVsd is that the exposureo OFEs to light leads to changes in the at-band voltage. Becauseo this eect, an extra positive gate voltage is required to achieve theat-band condition on illumination.

From the data in Figure 1c, however, it is still possible to evalu-ate the relative eciencies o electron and hole injection into theNC channel. Specically, because o symmetry between the gate andsource electrodes (both are abricated rom gold), the conditions or

hole injection at Vg = 25 V are equivalent to conditions or electroninjection at Vg = 0 V. A signicantly smaller dark current measuredin the latter case indicates that electron injection in our devices ismuch less ecient (likely negligible) than hole injection. Te capac-itance measurements (Fig. 1d) also do not show any detectable elec-tron injection in our structures in the range oVg > 0.

Spectrally resolved photoresponses o OFETs. Illumination othese devices with monochromatic light leads to a dramatic increase

in Isd even at low light intensities, as illustrated by the three-dimen-sional plot in Figure 1c, or incident uxes rom 120 nW cm 2 to30W cm 2 (2.25 eV il lumination). Te respective densities ophotogenerated charges can be estimated rom the product o thegeneration rate (G) and the carrier lietime (), which yields ca10 4 to 10 6 per NC or the maximum photon ux (Methods). Tisdensity is orders o magnitude lower than the number o chargesinjected into the lm by applying a gate voltage (or example,n00.1 or Vg = 25 V). Tereore, the act that exposure to lightleads to a dramatic increase in conductivity implies that photogen-erated charges are characterized by much higher mobilities thanequilibrium background charges. Tis strongly suggests that thenatures o electronic states involved in charge transport in dark andunder illumination are dierent.

Light illumination also results in the apparent, intensity-dependent shif o the at-band voltage traced by the black linein the contour plot at the bottom oFigure 1c. Tis is a reectiono the photovoltaic eect due to accumulation o photogeneratedcarriers under the source/drain electrode, which changes the totalgate bias and hence the sourcedrain current (light acts as theourth terminal in our OFEs). As a result, under illumination anextra positive voltage is required to achieve the at-band conditionand the magnitude o this excess bias can serve as a measure o thephotovoltaic eect.

o gain urther insights into the origin o charge-transportingstates, we investigate the Vg-dependence o photocurrent spectrathat are derived rom the Isd-versus-Vg characteristics measured ordierent excitation wavelengths (Figs 2a and b). Under zero gate

bias, the photocurrent spectrum (blue curve in Fig. 2c) reproducesa general behaviour o a linear absorption spectrum (Fig. 1b) andspecically exhibits a similar spectral onset at ~1.3 eV. Applica-tion o negative Vg leads to an overall increase in the photocurrentacross the entire spectrum. Te most striking eect o gate voltage,however, is the development o new spectral eatures at ~0.9 eV(M1S) and ~1.5 eV (MX). Te act that the M1S-band is located inthe region o nominal transparency o the NC lms (~0.4 eV belowthe 1S band-edge peak) points towards the involvement o MGB

107

108Dark

Cur

rent(A)

109

107

108 Dark

0.89 eV1.13 eV

1.55 eV

1.77 eV

2.07 eV

2.48 eV

3.10 eV

4.13 eV

109Current(A)

1010

301.5

6 V

3 V

0 V

3 V

6 V

9 V

18 V

1.01.2 eV

1Se1Sh

XeXh0.5A(arb.units)

0.0

1.0 1.5

Photon energy (eV)

2.0 2.5 3.0

25

20

Numberofphotoelectrons

perincidentphoton(%)

15 M1s

MX0.6 eV

10

5

00.9 1.2 1.5 1.8

Photon energy (eV)

2.1 2.4 2.7 3.0 3.3 3.6 3.9 4.2

30 25 20 15 10 5 0

Vgmin

Vg (v)

5 10

101025

2015 10 5

Vg(V)

0 5 10

0.62

1

2

Pho

tonen

ergy

(eV)

34

0.0

3 1010

9 1010

2 109

5 109

2 108

5 108

1 107

>2 107

Figure 2 | Spectrally resolved responses o OFET indicate presence

o mid-gap states orming weakly conductive band. (a) Id-ver-Vg

characteritic btaied i dark (black lie) ad der illiati a a

cti pht eergy tartig r 0.62 eV (white lie i the ctr

plt at the btt). Clred llig belw the white lie i iterplati

betwee the eareet i dark ad der 0.62 eV illiati. Black

lie i the ctr plt at the btt trace chage i the fat-bad

ptetial. (b) Cr-ecti btaied r the three-dieial plt

i pael a hw the variati the rcedrai crret a a cti

gate vltage der illiati at dieret pht eergie (hw i the

leged). (c) Phtcrret a a cti icidet pht eergy hw i

ter the ber phtelectr per 100 icidet pht (derived

r data i pael a). The pacig betwee the tw priet eatre

(M1s ad MX), that develp der egative bia, i hal the pacig

betwee the 1s ad X eatre i the ecd-derivative the abrpti

(A) pectr (iet). Thi gget that the m1s ad the mX peak are

likely de t traiti betwee the ccpied 1s ad X valece bad tate

ad the ccpied mGB tate, repectively.


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states. Further, as MGB states only maniest under negative bias,

this suggests that at Vg0 they are ully occupied with electrons.However, some o these states become depopulated under negativeVg, when the Fermi level shifs below the MGB edge. Te introduc-tion o holes into the mid-gap states unblocks optical transitionsrom the valence-band to the MGB levels (solid arrows in Fig. 3a).Te M1S eature is likely associated with the transition involv-ing the 1Sh valence-band state, whereas the MX peak is probablydue to some lower-lying level (labelled Xh in Fig. 3a). Because omirror symmetry between the valence and the conduction bandsin PbS28,29, the band-to-band XhXe optical transition is expectedto be located ~1.2 eV to the blue rom the 1S peak, which is twicetheM1SMX separation (~0.6 eV). Indeed, the second derivative othe absorption spectrum o the solution sample (inset oFig. 2b)shows a pronounced eature at ~2.5 eV, which is ~1.2 eV higher thanthe band-edge peak. More examples that illustrate the development

o extra MGB-related spectral eatures in the photocurrent undernegative Vg are given in Supplementary Figure S1.

In the case o a ully or partially occupied MGB, one mightalso expect to see the transitions that promote the MGB electronsinto the unoccupied conduction-band states (red-dashed arrowsin Fig. 3a). Although such transitions may indeed exist, their rela-tive contribution to the photocurrent is much smaller than that dueto the M1S and MX eatures because, as discussed in detail below,the electron lietimes in these structures are much shorter than the

hole lietimes due to a higher probability o electron capture at theMGB states.

Te observed spectral eatures due to the MGB are wider(~0.5 eV) than the 1S absorption peak (~0.2 eV). Tis dierenceis likely due to the act that in addition to NC size-polydispersity,random NC-to-NC dierences in the positions o the mid-gaplevels and a systematic variation in the local Fermi level in the NCchannel along the sourcedrain direction also contribute to thelinewidths o the M1S and MX bands.

An interesting eature o the photocurrent spectra recordedunder negative gate bias is the large amplitude o the MGB-relatedbands, which is comparable to that o the eatures due to intrinsicband-edge transitions. Tis is somewhat surprising given that theoscillator strength o the intrinsic NC transitions is expected to be

stronger than or transitions involving surace-related MGB statesthat have a reduced spatial overlap with the wave unctions o thequantized levels. However, in addition to the oscillator strength, thecontribution o a given optical transition to photocurrent dependson the relative raction o photogenerated electron-hole pairs thatexperience spatial separation (characteristic time sep) beore recom-bination compared with the raction o charges that recombinesgeminately at or near the photogeneration site (characteristic timeeh). Tis contribution can be characterized in quantitative termsby the ratio =eh/sep, assuming that it is smaller than unity. It isnatural to expect that the electron-hole pairs generated in intrinsicNC states have a shorter geminate recombination time and a longercharge-separation time compared with the electron-hole pairs pro-duced through the MGB-related transitions, because the latter are

characterized by a certain degree o spatial separation immediatelyollowing photogeneration. As a result, the transitions involving theMGB, although, perhaps, not as pronounced in optical absorptionspectra, can still provide a signicant contribution to photocurrentdue to the enhanced value ocompared with transitions involvingthe quantized states.

Te lms abricated rom as-prepared NCs do not show anygating eect. Tis implies that the mid-gap states are likely intro-duced by ligand-exchange procedures, which urther suggests thatthese states are possibly o surace origin. Te MGB has a role ocharge conduit under dark and its conductivity is controlled bygate bias. Te MGB can be either insulating (i it is completely lledor empty) or conductive (i lled partially). In the latter case,transport through MGB can be explained in terms o either electron

or hole conductivity depending on whether the Fermi level is near thebottom or the top o the MGB, respectively. Tis might explain thepossibility o acile switching the conductivity o NC lms betweenn- and p-type through relatively simple chemical or heat treat-ments711,30. In our lms, under the at-band condition, the Fermilevel is located near the top o the MGB, and thereore, at Vg = 0this band is essentially nonconductive. Application o negative gatebias shifs Fermi level deeper inside the MGB, which generates anincreasing amount o MGB holes and results in a sharp increase odark conductivity observed in Figure 1c.

While in dark, MGB serves as a charge conduit, its role is di-erent in the case o photoconduction. Specically, our observationo a dramatic enhancement o Isd under illumination suggests thattransport o photogenerated charges is mediated by intrinsic quan-tum-conned NC states that orm a more conductive network,

MX

M1S

MGB

Slow

Xe

100

10 26.0 W cm2

10.4 W cm2

3.3 W cm2

1.0 W cm2Photocurrent(nA)

1

25

100

VgminVg=3v m=0.48

m=0.76

m=0.61

Photogeneration rate (104 s1)

Vg=9v

1

1

10

10 100 1,000

Photocurrent(nA)

102

103

104

105 Electrons

Holes

enNC(G/)1/2

enNC(G/)1/2

/ = 0.002

1060.0 0.2 0.4

x=no/N0

0.6 0.8 1.0

Photoconductivity

20 15 10 5 0 5 10

Vg(V)

1Se

EF

1Sh

Xh

1Se1Sh

M1S

MX

XeXhEg

Fast

Figure 3 | Eect o MGB occupancy on photoconduction. (a) The eergy

level diagra illtratig ptical traiti betwee the nC-qatized

ad mGB tate (red arrw) a well a relaxati pathway (wavy blackarrw) r phtgeerated bad-edge carrier. The ble arrw ark the

piti the Feri level (EF). (b) Phtcrret eared at dieret

gate vltage (ybl) r light iteitie r 1.04 t 26.1W c 2

(idicated i the gre leged) ig 2.25 eV illiati. Lie are

calclati ig eqati (4) ad (5). I the dellig, the excitati

iteity wa characterized by the dieile qatity g = G/(N02).

o the bai the phtcrret eared at large egative Vg r

26.1W c 2 (lid black qare), g wa deteried t be 1.310 3.

Fr ther trace, g wa btaied by calig thi vale accrdig t light

iteity ed i the eareet. ad V0 were adjtable paraeter

deteried r the t. The btaied vale yteatically varied r

0.016 t 0.007 (0.001) r ad r 2 t 6 V (0.15 V) r V0 with

icreaig light iteity. (c) Calclated phtcdctivity de t electr

(dahed-ad-dted red lie) ad hle (dahed black lie) ig eqati(3) ad aig thatx i withi the iterval r 0.05 t 0.95. slid ble

lie i the hle phtcdctivity btaied ig eqati (4). The arrw

ark the hle-ly (let) ad electr-ly (right) phtcdctivitie

i the liit x = 0 adx = 1, repectively. (d) The depedece Id

phtgeerati rate r dieret gate vltage (3.1 eV pht eergy).

A expected r a traiti r bileclar t liear recbiati, the

lglg lpe thi depedece i ~0.5 r the large egative gate bia

(mGB i cpletely epty) ad apprache ity a the gate bia get

re pitive (mGB bece pplated).


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because o a greater extent o overlapping electronic wave unctionscompared with surace-related MGB states. Te act that, even in thiscase, channel conductance is sensitive to changes in gate voltage canbe explained by the eect o MGB occupancy on recombination dyna-mics o band-edge carriers, as elaborated in the Discussion section.

DiscussionAccording to our earlier estimations, the densities o photogeneratedcharges (n and p or electrons and holes, respectively) are much

smaller than 1 per NC, while the density o mid-gap states ( N0) isat least on the order o 1 because they orm a percolated conductivenetwork. Becausep, nN0, the relaxation o photogenerated carri-ers is dominated not by band-to-band recombination but trapping atthe mid-gap levels. From charge neutrality, the density o non-equi-librium electrons in the MGB under photoexcitation is nm =p n.Alternatively, the eect o photoexcitation on occupancy o MGBstates can be characterized in terms o photogenerated holes withdensitypm = n p. Under steady state, the trapping rates are equal tothe photogeneration rate:

G n N n n= a ( ),0 0 m

G p n n= +b ( ),0 m

where and are electron- and hole-capture coecients, respec-tively.

When MGB is completely empty (n0 = 0), equations (1) and (2)yield nG/(N0) and p

2G(1 + 1p/N0); these expressions areobtained assuming thatp, nN0. As we show below, in our struc-tures , thereore, p (G/)1/2, and consequently, n can beexpressed as np(p/N0)(/). Te latter relationship suggeststhat np, and thereore, nmp. In this case, photoconduction isdominated by holes and the photoconductivity can be expressed asph,h = ehnNCp = ehnNC(G/)

1/2, where h is hole mobility and nNC isthe density o NCs in the lm. As MGB gets lled, the contributionrom holes to photoconduction decreases whereas the contribu-

tion rom electrons increases until the latter reaches the value oph,e =eenNCn = eenNC(G/)1/2 (e is electron mobility) when the

MGB is completely ull (n0 = N0). Te above two limits describe thesituations o, respectively, large negative and at-band gate biases,when the Fermi level is either below or above the MGB (Fig. 3a).

Because o symmetry between the conduction and valence bandsin PbS28,29, e and h in our lms are likely similar (he =).Tereore, i the electron- and hole-capture probabilities were thesame, the lling o the MGB would not lead to changes in totalphotoconductivity, ph =ph,e +ph,h, as the decrease in ph,h wouldbe compensated by the increase in ph,e. However, our experimentaldata (Figs 1c and 3b) indicate a decrease in the photoconductivityby a actor () o ca 20 to 50 as Vg changes rom large negative val-ues to the at-band voltage. Tis implies that the electrons provide

a smaller contribution to photoconduction than holes and, urther,suggests that is much greater than . Specically, in the limits oempty and ull MGB, the total photoconductivity can be expressedas ph(empty)ph,h =enNC(G/)

1/2 and ph(ull) = enNC(G/)1/2

+ph,h(ull), respectively, which yields the ratio = enNC(G/)1/2/

[enNC(G/)1/2 +ph,h(ull)]. From this expression, we obtain

(/)1/2 =[1 +ph,h(ull) (enNC) 1(/G) 1/2], which suggests that

(/)1/2 >. On the basis o the measured ratio o the photocurrents(Fig. 3b), we can conclude that is at least 400 times greater than .Tis result indicates that band-edge electrons in our lms are muchshorter lived than holes () and thereore provide a smallercontribution to the photocurrent. Tis is probably because o closeproximity o the MGB to the conduction band (~0.4 eV versus~0.9 eV separation rom the valence band), which makes trappingthrough multiphonon emission easier or electrons than or holes31.

(1)(1)

(2)(2)

o quantiy the relative contributions o band-edge electrons andholes to photoconduction, we solve equations (1) and (2) or the situ-ation when the density o MGB equilibrium charges is much greaterthan the density o photogenerated carriers (n0nm and N0n0nm),and hence, the dynamics o both electrons and holes are controlledby the equilibrium occupancy o the MGB. In this case, ph is

sm

b

phNC=

+

e n G

N

u

x x0 1

1

( )

,

where u =/1 and x =n0/N0. Equation (3) indicates a lineardependence oph on G and it approximates the behaviour ophbetween the limits o almost complete lling and almost completedepletion o the MGB. Te rst and the second terms in the right-hand side o equation (3) correspond, respectively, to electron andhole contributions. In Figure 3c, we compare them or /= 0.002(black dashed and red dashed-and-dotted lines or holes and electrons,respectively). Interestingly, up to near-unity values ox, the photocon-ductivity is dominated by valence-band holes and even or x= 0.95,the hole contribution to ph is more than 20 times greater than that oelectrons. Tis is a direct result o a high capture probability or elec-trons that quickly relax rom the band-edge states into the low-mobility

MGB. Te short electron lietime also explains why optical transi-tions, where MGB electrons are promoted to the conduction band(M1S and MX transitions in Fig. 3a; red dashed arrows), are not prom-inent in the photocurrent. Te dominant role o hole photoconduc-tion in our devices helps also to rationalize the overall Vg-dependenttrends observed in the photocurrent spectra (Fig. 2c), namely theincrease in Isd when Vg changes rom positive to progressively morenegative values. Tis behaviour reects the change in the lietime ophotogenerated holes, which becomes progressively longer as MGBgets more depleted o electrons under increasing negative gate bias.

Assuming hole-dominated photoconductance, rom equations(1) and (2), we can obtain the ollowing expression or ph, whichin addition to the regime described by equation (3) also allows us totreat the transition to a completely depleted MGB, that is, the range

ox rom 1 to 0 (is a small quantity dened by the conditionN0n0nm or nm/N0):

s s mb

ph ph,h NC = +

e n

n G

n

0

022

14

1 .

We urther use this expression (the corresponding dependenceis shown by the blue solid line in Fig. 3c) to model the measuredVg-dependence o photocurrent or dierent excitation intensities(lines in Fig. 3b). In our modelling, we relate n0 to N0 and Vg by

n N E k N V V k T F g0 0 0 0= = exp[ / ] exp[ ( )/ ],B B g

where kB is the Boltzmann constant, T is the temperature, andEF = (Vg V0) is the Fermi energy (is the dimensionless constantand V0 is the at-band voltage). Equation (5) correctly predicts thatunder the at-band condition (Vg =V0), n0 =N0, which correspondsto a ully occupied MGB, and n0 exponentially decreases or pro-gressively more negative gate voltages. Using equations (4) and (5),we can accurately describe both the gate-voltage and the illumina-tion-intensity dependence o the measured photocurrent (Fig. 3b;compare calculations shown by lines with measurements shown bysymbols). Tis conrms the validity o our model and provides anextra piece o evidence that photoconduction in our structures isdominated by valence-band holes.

An interesting prediction o equation (4) is that in addition to themagnitude o photoconductivity, the type o light-intensity-dependence

(3)(3)

(4)(4)

(5)(5)


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o photoconduction can also be controlled byn0, and, hence, gate voltage.

For example, in the regime o a depleted MGB, when n02(G/)1/2

,which realized in our devices or large negative Vg, the band-edgeelectrons quickly relax into the mid-gap states and hole dynamics aredominated by bimolecular recombination with these non-equilibriumMGB electrons. Tis results in a square-root dependence oph on G:ph,h =ehnNC(G/)

1/2. However, as MGB becomes occupied with evena moderate number o electrons (n02(G/)

1/2), the hole dynamicsare dominated by recombination with pre-existing MGB electrons,which leads to a linear dependence oph on G: ph,h =ehnNCG/(n0).

Our data indeed indicate an approximately square-root scalingo the photocurrent with G or large negative Vg (Fig. 3d; open redcircles). We also observe that the ph versus G dependence becomesprogressively steeper as Vg gets less negative, and the number o MGBelectrons increases (compare data shown by solid black squares and

open green triangles in Figure 3d; see also Supplementary Fig. S2 or adierent device, which shows a similar change in the scaling o photo-current with light intensity). Tis behaviour is consistent with thepredicted transition to the linear scaling described by equation (4).

Te demonstrated control o recombination dynamics by gatevoltage is useul in photodetection, where it can be employed orcontrolling both device sensitivity and its dynamic range. A sig-nicant increase in device sensitivity can be obtained by combin-ing contributions rom photoconductive and photovoltaic eects.Tis is illustrated in Figure 4 (inset) where we compare a purelyphotoconductive response measured at Vg = Vgmin (the photocur-rent minimum) with one obtained or Vg = 0; the latter signalexhibits a much aster growth with G due to a photovoltaic con-tribution. Te enhancement in sensitivity arising rom the pho-tovoltaic eect is also pronounced in the spectral dependence o

a photoresponse (main panel oFig. 4; compare traces shown bysolid and dashed lines).

Te observed dierence in hole and electron relaxation timesresults in a peculiar, mixed character o photoconduction, whenholes are transported through quantized states whereas electrons

through the MGB. One implication o this transport mechanism isthat the photovoltage, which can be derived rom such a structure,is determined by the energy dierence between the valence-bandedge and the MGB. As a result, while displaying correlation withthe band-gap energy it should be always lower than the ideal Voccalculated or a given Eg. Tis trend has indeed been observed in NCsolar cells1315,17,27,32,33 (Supplementary Fig. S3).

o summarize, we have investigated OFEs abricated rom PbSNCs. Spectrally resolved studies o Vg-dependent photocurrentreveal the existence o mid-gap states in NCs lms that orm a weaklyconducting MGB. Tis band serves as a charge conduit in dark, how-ever, the mechanism o charge transport changes under illumina-tion when it becomes dominated by a more conductive network oquantized band-edge states. In this case, the MGB still has an impor-

tant role as its occupancy controls photoconduction by controllingrecombination dynamics o band-edge charges. Te mechanisms ordark and light transport are schematically illustrated in Figure 5.Te results o our studies together with the developed model shouldhelp one to predictably engineer both charge transport properties oNC lms in dark as well as under illumination. Interesting opportu-nities could also be opened by engineered placement o MGB stateswithin the NC energy gap. Tis could allow, or example, switchingbetween electron- and hole-dominated photoconductivity and, per-haps, help in practical realization o advanced photovoltaic conceptssuch as intermediate-band solar cells34.

MethodsOFET abrication. PbS NCs with a mean diameter o ca 3.3 nm, were synthesizedaccording to re. 35 (see transmission electron micrograph in the inset oFig. 1b).

3.0

400

300

200

m=0.76

G (104 s1)

100

200 400 600 80000

2.5

Sensitivity(A/W) 2.0

Vgmin

Vgmin

Vg= 0 V

Vg= 0 V

m=0.9

IsdGm

Isd

(nA)

1.5

1.0

0.5

0.01.2 1.5 1.8 2.1 2.4 2.7 3.0

Photon energy (eV)

Figure 4 | Eect o gate bias on OFET sensitivity. seitivity (deed

a phtcrret per ity icidet light iteity) a a cti pht

eergy at the fat-bad vltage (lid black crve; prely phtcdctive

repe) ad Vg = 0 (dahed red crve); 3.1 eV pht eergy. The higher

eitivity i the latter cae i a relt a cbied ctribti r the

phtcdctive ad the phtvltaic eect. The ctribti r the

phtvltaic eect al icreae the teepe the depedece the

phtcrret phtgeerati rate (cpare data hw by red lid

circle ad black pe qare i the iet).

Conduction in dark

Conduction under illumination

Fermi

level

Eg

VOC

CB

MGB

VB

CB

MGB

VB

Figure 5 | Conduction mechanisms in NC flms in dark and under

illumination. (a) Dark charge traprt ccr thrgh a aild

weakly cdctive mGB tate. I r l, the mGB i cpletely ll, ad

hece, ilatig der the fat-bad cditi. Applicati a egative

gate bia lead t ijecti hle it the mGB, which lwer the Feri

level ad pe a cdctig pathway thrgh the mGB tate. (b) The

echai r charge traprt chage der illiati. I thi cae,

the phtgeerated electr get rapidly trapped r the cdcti-

bad (CB) level it the id-gap tate ad are traprted thrgh the

mGB. o the ther had, phtgeerated hle, that are ch lger lived,

are traprted via re-verlappig, highly cdctive valece-bad

(VB) tate. Hle traprt via the VB level diate phtcdcti.

Becae the ixed character phtcdcti, which ivlve bth

the VB ad mGB tate, the phtvltage i deteried t by the itriic

bad-gap eergy, Eg, bt the VBmGB eparati.


7/7

ARTICLE



2011 M ill P bli h Li it d All i ht d

Te NC dispersion was cleaned by repeatedly precipitating and re-dispersing intoluene to remove excess reactants. PbS NCs were then ligand exchanged witholeylamine33, and afer removal o excess oleylamine, were re-dispersed in octane.Te puried NC colloidal suspension in octane was spin-coated onto a dopedsilicon/silicon-oxide substrate (the oxide layer thickness was ca 100 nm), whichserved as a gate electrode. Tis was ollowed by lm treatment with 0.1 M o 1,2-ethanedithiol solution in acetonitrile14, and a new spin coating step with the PbSNC suspension and the treatment with 1,2-ethanedithiol. Te nal thickness o theNC lm was ~40 nm, as evaluated rom atomic orce microscopy measurements.Interdigitated source and drain gold electrodes (50m separation) were depositeddirectly on top o the NC lm using a shadow mask.

OFET measurements. Tree-terminal device measurements were conductedusing a semiconductor device analyser (B1500A, Agilent echnologies). Aconstant bias o 25 V was applied between the source and the drain electrodes,while the gate-source bias was varied rom 10 to 25 V. In the measurements othe Isd versus Vg dependences, we ramped the gate voltage in 1 V increments usingthree dierent integration times: tint = 640s, 16.6 ms, and 267 ms. Te measuredphotocurrent did not vary by more than 510% between dierent values otint. Wealso did not detect any dierence in traces recorded by ramping the gate either upor down.

Te light rom xenon or tungsten lamps, ltered through a monochromator(~10 nm bandwidth) was used to illuminate the OFE rom the top, whereas thephotocurrent was monitored as a unction o either monochromatic light intensityor incident radiation wavelength. Te maximum light intensity incident onto thedevice was 50W cm 2.

Density o charges injected by applying gate voltage. We derive the den-sity o charges injected into the channel o the NCOFE rom dark capacitancemeasurements. Te total charge injected or a given gate voltage was calculated rom

Q C V V V

= 0g

d( ) , which yields Q= 1.82C cm 2 orVg= 25 V. Assuming that, in ourdevices, NCs orm a random close-packed solid, we estimate that the NC surace densityper monolayer is ~1013cm 2, which indicates that the average number o charges injectedper NC or Vg= 25 is ~0.1, assuming that the NC lm is ~10-monolayers thick.

Density o photogenerated charges. Using absorption cross section (abs) o10 15cm 2 (re. 36) and uxes (W) rom 5 to 50W cm 2, we calculate the photogene-ration rate, G= (W/)abs, rom 10

4 to 10 6ms 1 (is photon energy). Te lietimeo carriers in our devices () is 0.011 ms. On the basis o these values, an upper limit othe density o photogenerated charges, n=p=G, is 10 4 per NC.

Reerences1. Murray, C. B., Norris, D. J. & Bawendi, M. G. Synthesis and characterization o

nearly monodisperse CdE (E=S, Se, e) semiconductor nanocrystallites.J. Am.Chem. Soc.115, 87068715 (1993).

2. Mangolini, L., Timsen, E. & Kortshagen, U. High-yield plasma synthesis oluminescent silicon nanocrystals. Nano Lett.5, 655659 (2005).

3. Coe, S., Woo, W. K., Bawendi, M. & Bulovic, V. Electroluminescence romsingle monolayers o nanocrystals in molecular organic devices. Nature420,800803 (2002).

4. Mueller, A. H. et al. Multicolor light-emitting diodes based on semiconductornanocrystals encapsulated in GaN charge injection layers. Nano Lett.5,10391044 (2005).

5. Cho, K. S. et al. High-perormance crosslinked colloidal quantum-dot light-emitting diodes. Nat. Photon.3, 341345 (2009).

6. Holman, Z. C., Liu, C. Y. & Kortshagen, U. R. Germanium and siliconnanocrystal thin-lm eld-eect transistors rom solution. Nano Lett.10,26612666 (2010).

7. Kang, M. S., Lee, J., Norris, D. J. & Frisbie, C. D. High carrier densities achievedat low voltages in ambipolar PbSe nanocrystal thin-lm transistors. Nano Lett.9, 38483852 (2009).

8. Mentzel, . S. et al. Charge transport in PbSe nanocrystal arrays. Phys. Rev. B

77, 075316 (2008).9. alapin, D. V. & Murray, C. B. PbSe nanocrystal solids or n- and p-channel

thin lm eld-eect transistors. Science310, 8689 (2005).10. Liu, Y. et al. Dependence o carrier mobility on nanocrystal size and ligand

length in PbSe nanocrystal solids. Nano Lett.10, 19601969 (2010).11. Luther, J. M. et al. Structural, optical and electrical properties o sel-assembled

lms o PbSe nanocrystals treated with 1,2-ethanedithiol.ACS Nano2,271280 (2008).

12. Konstantatos, G. et al. Ultrasensitive solution-cast quantum dot photodetectors.Nature442, 180183 (2006).

13. Gur, I., Fromer, N. A., Geier, M. L. & Alivisatos, A. P. Air-stable all-inorganicnanocrystal solar cells processed rom solution. Science310, 462465 (2005).

14. Luther, J. M. et al. Schottky solar cells based on colloidal nanocrystal lms.Nano Lett.8, 34883492 (2008).

15. Pattantyus-Abraham, A. G. et al. Depleted-heterojunction colloidal quantumdot solar cells.ACS Nano4, 33743380 (2010).

16. Kamat, P. V. Quantum dot solar cells. semiconductor nanocrystals as lightharvesters.J. Phys. Chem. C112, 1873718753 (2008).

17. Sun, B., Findikoglu, A. ., Sykora, M., Werder, D. J. & Klimov, V. I. Hybridphotovoltaics based on semiconductor nanocrystals and amorphous silicon.Nano Lett.9, 12351241 (2009).

18. Sun, B. Q., Marx, E. & Greenham, N. C. Photovoltaic devices using blends o branchedCdSe nanoparticles and conjugated polymers. Nano Lett.3, 961963 (2003).

19. Nanocrystal Quantum Dots 2nd edn (ed. Klimov, V. I.) (CRC Press, aylor &Francis Group, Boca Raton, 2010).

20. Nozik, A. J. Quantum dot solar cells. Physica E14, 115120 (2002).21. Schaller, R. D. & Klimov, V. I. High eciency carrier multiplication in PbSe

nanocrystals: Implications or solar energy conversion. Phys. Rev. Lett.92,186601 (2004).22. Ellingson, R. J. et al. Highly ecient multiple exciton generation in colloidal

PbSe and PbS quantum dots. Nano Lett.5, 865871 (2005).23. Sukhovatkin, V., Hinds, S., Brzozowski, L. & Sargent, E. H. Colloidal quantum-

dot photodetectors exploiting multiexciton generation. Science324, 15421544(2009).

24. Sambur, J. B., Novet, . & Parkinson, B. A. Multiple exciton collection in asensitized photovoltaic system. Science330, 6366 (2010).

25. Ross, R. . & Nozik, A. J. Eciency o hot-carrier solar-energy converters.J. Appl. Phys.53, 38133818 (1982).

26. isdale, W. A. et al. Hot-electron transer rom semiconductor nanocrystals.Science328, 15431547 (2010).

27. alapin, D. V., Lee, J. S., Kovalenko, M. V. & Shevchenko, E. V. Prospects ocolloidal nanocrystals or electronic and optoelectronic applications. Chem.Rev.110, 389458 (2010).

28. Kang, I. & Wise, F. W. Electronic structure and optical properties o PbS and

PbSe quantum dots.J. Opt. Soc. Am. B Opt. Phys.14, 16321646 (1997).29. Bartnik, A. C., Eros, A. L., Koh, W. K., Murray, C. B. & Wise, F. W. Electronicstates and optical properties o PbSe nanorods and nanowires. Phys. Rev. B82,195313 (2010).

30. Law, M. et al. Structural, optical, and electrical properties o PbSe nanocrystal solidstreated thermally or with simple amines.J. Am. Chem. Soc.130,59745985 (2008).

31. Ridley, B. K. Quantum Processes in Semiconductors Second edn, (OxordScience Publications, 1988).

32. Luther, J. M. et al. Stability assessment on a 3% bilayer PbS/ZnO quantum dotheterojunction solar cell.Adv. Mater.22, 37043707 (2010).

33. ang, J. et al. Quantum dot photovoltaics in the extreme quantum connementregime: the surace-chemical origins o exceptional air- and light-stability.ACS Nano4, 869878 (2010).

34. Marti, A. & Luque, A. Next Generation Photovoltaics: High Efciency throughFull Spectrum Utilization (Institute o Physics, 2003).

35. Hines, M. A. & Scholes, G. D. Colloidal PbS nanocrystals with size-tunablenear-inrared emission: Observation o post-synthesis sel-narrowing o theparticle size distribution.Adv. Mater.15, 18441849 (2003).

36. Moreels, I. et al. Size-dependent optical properties o colloidal PbS quantumdots.ACS Nano3, 30233030 (2009).

AcknowledgementsWe thank Don Werder or assistance with transmission electron microscopy, Bhola

Pal or help with transient photocurrent data, and Je Pietryga and Lazaro Padilha or

insightul comments regarding the manuscript. Tis material is based on work within the

Center or Advanced Solar Photophysics, an Energy Frontier Research Center unded by

the U.S. Department o Energy, Oce o Science, Oce o Basic Energy Sciences.

Author contributionsV.I.K. and N.P. conceived the idea o using NC-OFEs or evaluating the nature o dark

transport and photoconductivity in NC lms. P.N. and V.I.K. designed the experiments.

P.N. abricated the devices, conducted the measurements, and analysed the data. V.I.K.

directed the study and developed the model or the analysis o OFE data. V.I.K. and P.N.

wrote the manuscript.

Additional inormationSupplementary Inormation accompanies this paper at http://www.nature.com/

naturecommunications

Competing fnancial interests: Te authors declare no competing nancial interests.

Reprints and permission inormation is available online at http://npg.nature.com/

reprintsandpermissions/

How to cite this article: Nagpal, P. & Klimov, V.I. Role o mid-gap states in charge

transport and photoconductivity in semiconductor nanocrystal lms. Nat. Commun.

2:486 doi: 10.1038/ncomms1492 (2011).

License: Tis work is licensed under a Creative Commons Attribution-NonCommercial-

NoDerivative Works 3.0 Unported License. o view a copy o this license, visit http://

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