photoconductance and spectral absorption of … bound... · du coefficient d'absorption. ......

R 457 Philips Res. Repts 17, 363-381, 1962

PHOTOCONDUCTANCE AND SPECTRALABSORPTION OF ANTHRACENE *)

by J. W. STEKETEE and J. de JONGE

537.312.5: 535.34: 547.672.1

SummaryThe photoconductivity of anthracene crystals is measured in a sandwichtype of cell, the crystals being illuminated through the positive electro-lytic electrode with plane-polarized light. Photocurrent and spectralabsorption of anthracene crystals are measured with the same opticalsystem. A plot of the photocurrent per quantum of incident light againstwavelength shows a close correspondence to the absorption spectrum,the current being a function of the extinction coefficient. The wavelengthdependence observed confirms the theory that absorbed energy is trans-ferred as excitons to the positive surface of the crystal where chargeseparation can take place. The electron is captured by the electrode whilethe positive hole moves through the crystal to the opposite negativeelectrode. The diffusion length of the exciton is about 1200A. The verysmall photocurrent found when the negative electrode is illuminatedappears also to be due to the light absorbed in a region close to thepositive electrode. .

RésuméLa photoconductivité de l'anthracène est étudiée, Le cristal, monté entredeux électrodes électrolytiq ues, est irradié à travers l'électrode positiveavec de la lumière polarisée et monochromatique. En utilisant Ie mêmeappareil optique, on mesure Ie spectre d'absorption de I'anthracènecristallin. On trouve que la photoconductivité varie avec .la longueurd'onde comme I'absorption optique et que le courant est une fonctiondu coefficient d'absorption. L'effet de la longueur d'onde confirmel'hypothèse qu'un quantum d'énergie, absorbé dans Ie cristal d'anthra-cène, est transféré par diffusion vers la surface positive (sous forme d'unexciton) oü une séparation des charges est effectuée. L'électron est prispar l'électrode tandis que la charge positive se déplace à travers Ie cristal .vers l'électrode négative. Une valeur de 1200 A a été calculée pour ladistance de diffusion d'un exciton. La faible photoconductivité observée,si I'on irradie à travers l'électrode négative, est due à I'absorption de lalurnière dans une couche mince du cristal auprès de l'électrode positive.

ZusammenfassungDie lichtelektrische Leitung von Anthrazen wird gemessen. Hierzu wirdein Kristallplättchen zwischen zwei Elektroden (wässerigen Lösungen)montiert. Polarisiertes monochromatisches Licht wird durch diepositive Elektrode eingestrahlt. Der EinfiuB der Wellenlänge auf denPhotostrom und die spektrale Absorption der KristalIe wird mit ein undderselben optischen Anordnung bestimmt. Es zeigt sich, daB der Photo-strom sich mit der Wellenlänge in derselben Weise ändert wie dieoptische Absorption; der Strom ist eine Funktion des Absorptions-koeffizienten. Die gefundene Wellenlängenabhängigkeit ist im Einklangmit der Theorie, daB die im Kristall absorbierte Lichtenergie zur positi-ven Kristalloberftäche wandern kann (Exzitonen), wo dann eine Ladungs-trennung ausgelöst wird. Die Elektronen werden von der Elektrode auf-genommen, und diepositiven Ladungsträger (Defektelektronen) bewegen

*) Presented at the Conference on Organic Semiconductors, Chicago, April 18 and 19, 1961.

364 J. W. STEKETEE and J. de JONGE

sich durch den Kristal! zur gegenüberliegenden negativen Elektrode.Die Länge des Diffusionsweges des Exzitons konnte errnittelt werdenund beträgt 1200Á. Wird die negative Elektrode belichtet, so wird nurein sehr kleiner Photostrom gemessen; dieser läBt sich aus der Licht-absorption in einer dünnen Randschicht der Kristalle an der posi-tiven Elektrode erklären.

1. Introduetion

Much attention has been paid to the photoconductivity of anthracene inrecent years. Several authors have studied the effect ofwavelength and intensityofthe incident light, ofthe strength and direction ofthe applied external electricfield and of the temperature on the photocurrent. Reviews on the subject havebeen given by Garret and by Kommandeur 1). The greater part of the investi-gations has been carried out with single crystals, the photoconductivity ofwhichcan be measured in two types of cells:(1) in a surface eel!, a single crystal with both electrodes on one face and thearea between them illuminated;(2) in a sandwich or bulk cell, a single crystal with the electrodes on two op-posite faces with illumination through one of the (transparent) electrodes.With anthracene in surface cells it has been found that a plot of the photo-

current with varying wavelength is very similar to the absorption spectrum ofanthracene 2) 3) 4). A theory explaining this observation has been given byLyons 4). The main assumption in this theory is that charge carriers are formedonly at the surface of the crystal.The effect of wavelength on the photoconductivity of anthracene in sand-

wich cells has also been investigated 3) 5) 6); in this case no similarity of thespectral sensitivity of the photocell to the absorption spectrum was detected.This had led to theories in which it has to be assumed that light absorbed inanthracene produces charge carriers in the interior of the crystal.This state of affairs led us to carry out a re-investigation into the relationship

between photocurrent and absorption spectrum in sandwich cellsof anthracene.

2. General outline of the investigation

The absorption spectrum of very thin anthracene crystals was determinedwith light polarized parallel to the a-axis or the b-axis of the crystal. Usingexactly the same optical apparatus (the same slit width and so on), we deter-mined the photocurrent of anthracene crystals mounted in a sandwich cell asa function of wavelength.

3. Materials and experimental methods

3.1. Purification of anthracene

Technical anthracene was distilled together with ethylene glycolin an atmos-phere of nitrogen and received under water 7) 8).. The anthracene was filtered

PHOTOCONDUCTANCE' AND SPECTRAL ABSORPTION OF ANTHRACENE 365

off, washed with ethylalcohol and dried in vacuo. It was further purified bypassing a solution in hexane over a column of activated alumina in an atmos-phere of argon or nitrogen. The latter purification was carried out in the dark 9).

3.2. Preparation of the crystals

The crystals used for the determination of the absorption spectrum wereprepared 10) by heating pure anthracene together with a piece of solid C02 ina beaker covered with a top-down paper cone and a watchglass. After cooling,the paper cone, covered with thin anthracene crystals, was taken out and suitablecrystals could then be selected (thickness 0·1 to 0·4 (.L, surface area about 4 mmê).The crystals used for the determination of the photocurrent were prepared 11)

by dissolving pure anthracene in dichloroethane by heating. After cooling toabout 40°C a I-cm thick layer ofhexane was brought to the top ofthis solution.The crystals tend to grow at the interface between solution and hexane layer.Good crystals can be obtained, these being 20 to 80 (.L thick and having a sur-face area of more than -t cm2•

The two faces of both sorts of crystals (thin plates) were always parallel tothe a-b plane.

3.3. Absorption spectrum of anthracene

The absorption spectrum was measured in the usual way with the aid of adouble monochromator. The light source was a ISO-watt high-pressure xenonlamp with a stabilized a.c. supply. The outgoing beam was polarized by a"Nicol" prism in a fixed position, leaving the apparatus through a carefullycentred hole of 1 mm diameter in a rotatable metal disc. The hole in the discwas covered by a small plane-parallel ground piece of silica glass, supportingthe anthracene crystal. The thin anthracene crystal adhered to the silica glassby itself. The transmitted light was directed on a photomultiplier tube, fed byan 800-volt d.c. source. The current was passed through a resistance (variablebetween 1 kQ and 1.25.109 Q) shunted over an E.I.G. Vibron electrometer(10 to 1000 mV full scale) connected to a recording instrument.Wavelength variation was accomplished by having a synchronous motor

drive the wavelength drum of the monochromater at such speed as resultedin the region between 3600 A and 4100 A being passed in about 15 minutes.The bandwidth of the monochromatic beam was 30 A for 3600 A and 40 Afor 4100 A.

Fluorescence and stray-light corrections in the extinction measurements havebeen made with the aid of suitable filter combinations.

3.4. Measurements of the thickness of the crystal

The thickness of a crystal was determined from the optical retardation


(sodium light) measured with a Berek compensator. The values for the refractiveindices used in the calculations have been taken from Obreimov 12).

3.5. Photocurrents

The cell used for most measurements of the photocurrent (fig. 1) was amodification of that described by Kallmann and Pope 13). It consisted of ahollow cylinder, made of polytetrafluoroethylene. The cell was filled with avery dilute solution of boric acid in water and after that a crystal was :fixedover the hole with the aid of vacuum grease, Itwas placed in a brass housing

~~S;,8rass housing8490

Fig. 1. Diagram of the cell with one liquid and one silver electrode.

having two plugs connected to the electrodes of the cell. The cell could berotated in the housing around the cylinder axis. The cell was then broughtinto a position such that the beam of the monochromater mentioned abovewas directed through the silica window perpendicularly to the plane of thecrystal. The correct position of the cell could be obtained by using light with"awavelength longer than 4100 A for the adjustment and observing the beamthrough the crystal from the rear side. After that, an electrode of silver dag(colloidal silver in toluene with a resinous binder) is painted on the rear faceof the crystal, just covering the hole in the cell. The silver electrode is connectedwith one of the plugs in the housing in such a way that the cell can be rotated"freely.

In a number of experiments a symmetrical cell has been used in which theanthracene crystal is mounted between two such polytetrafluoroethylene cylin-ders. In this case both electrodes were electrolytic.The applied voltage was taken from a stabilized d.? source variable between

PHOTOCONDUCTANCE AND SPECTRAL ABSORPTION OF ANTHRACENE 367

o and 600 volts, which means a fieldstrength in the crystal up to 12.104 V/cm.Measurement of the photocurrent with varying wavelength was carried out'

in a way similar to that followed in the determination of the transmitted lightfor the absorption spectrum, the cell replacing 'now the photomultiplier. Wealso used the same speed of wavelength variation, this being low enough withrespect to the response time of the anthracene crystal to wavelength variation.The shunt resistance was 1.25.109 n. '

The photocurrents were not affected by painting a guard ring of silver dagaround the silver electrode already present on the non-illuminated face of thecrystal. The measured currents were therefore real bulk currents.In order to be able to calculate the photocurrent per quantum of incident

light, the (relative) intensities of the polarized monochromatic beam weremeasured in the used region of the spectrum before and directly after the photo- ,current was measured.

4. Results of the measurements

4.1. Absorption spectrum of anthracene betw~en 3600 A and 4050 A

The extinction coefficient is defined in the usual way by B = (l/d) log (10/1)where d = thickness of the crystal, 10 and I being the intensities of the incidentand the transmitted beams respectively. The symbols Ba and Bb are used whenthe plane of polarization is parallel to the a-axis or b-axis of the crystal 'res-pectively.

TABLE I

light pol./ la-axis light pol./ tb-axisL1y

Bb/Baauthorft. (in A) B (in cm-I) ft. (in A) B (in cm-I) (in

cm-I)

1 st max. this paper 3923 0,44.105 3941 1,23.105 117 2·8C. and H. 3922 3931 58B. and L. 0.49.105 1.49.105 3·0L. and L. 3927 336

1st min. this paper 3809 0,077.105 3820 0.33.105 4·3C. and H. 0.37.105B. and L. 0.10.105 3·7

2ndmax. this paper 3716 0,37.105 3732 1.04.105 116 2·9C. and H. 3716 3725 65B. and L. 0~41.105 1.15.105 200 2·8L. and L. 200


Table I gives the wavelengths of the maxima and minima together with theextinction values. Included are data of Craig and Hobbins 14) together withdata of Bree and Lyons 15). Values of the Davydov splitting as given by Laceyand Lyons 16) are also included. The agreement between the various data maybe considered to be satisfactory.

In table Il, our values of ea and eb are given for a set of wavelengths. Thesedata have been used for drawing the absorption spectrum given in fig. 5.

TABLE II

~ ea eb l/ea I/eb(A) (105 cm-I) (105 cm-I) (100 A) (lOO A)

3573 0·10 0·33 100 313600 0·08 0·27 126 373627 0·10 0·30 99 343654 0·57 0·44 58 233682 0·26 0·63 38 163710 0·37 0·92 27 113716 0·37 - 27 -3732 - 1·04 - 103738 0·32 1·03 32 103767 0·16 0·68 64 153697 0·09 0·41 118 243809 0·08 - 119 -3820 - 0·33 - 313826 0·08 0·34 119 293855 0·15 0·48 66 213886 0·266 0·70 39 143917 0·44 1·08 22 93923 0·44 - 22 -

3941 - 1·23 - 83949 0·26 1·18 38 93981 0·08 0·80 134 124016 0·014 0·29 72 344052 - 0·06 - 175

As can be seen in table I, we found a larger distance (.dy) between the positions of twocorresponding maxima of Ba and Bb than given by Craig and Hobbins, but a smaller one thangiven by Lacey and Lyons. The latter authors point out that incomplete polarization causesa shift of the maximum of eb towards the maximum of Ba, a shift increasing with the thickness


of the crystal. Our values were obtained with crystals about 0'2 I-' thick. The data of Laceyand Lyons are considered the most accurate.The ratio between the maximum and minimum values of Ea were found the same for all

crystals. Such fixed ratios were not found, however, for the maxima and minima of /lb ofvarious crystals, the thicker crystals giving lower values of /lb at the maxima than the thinnerones. The reason may be incomplete polarization of the incident light. As unpolarized lightgives an extinction coefficient lower than e», incompletely polarized light must also lower thevalue of /lb. This effect is larger with thicker crystals, particularly in the maxima of Bb. A smalldeviation of the direction of the b-axis of the crystal from the plane of polarization of theilluminating beam will have a similar effect, which is again larger with a thicker crystal. Bycalculation, these two effects could be shown to be possibly responsible for the behaviour ofthe b-absorpt~on spectrum with thicker crystals. For this reason, the highest values calculatedfrom our measurements were considered to be the best ones. Such values were always obtainedwith the thinnest crystals.

4.2. The photocurrents in anthracene with illumination through the positive elec-trode

The effect of a number of variables on the photoconduction of anthracenewas studied. Experiments were carried out with various voltages across thecrystals illuminated with polarized light of variable wavelengths and intensities.

In a large number of experiments it was established that the photocurrent isdirectly proportional to the light intensity. This holds for a wide range of inten-sities, both with polarized and unpolarized light. This linearity was observedat various voltages (10-600 V) across the crystals. Figure 2 illustrates thelinearity for two different wavelengths corresponding to a maximum and a

A

200r----t-----+----,_----+-~--~t012xi""

Î 150r---+---1----f-+---If---+-!

60 80-Ia

100 %IIH1

Fig. 2. The photocurrent is proportional to the light intensity. Curves 1 and 3 are obtainedwith light polarized parallel to the b-axis (wavelengths 3940 and 3820A); curves 2 and 4 referto experiments with the light polarized parallel to the a-axis (wavelengths about 3920 and3800 A). The voltage was 600 V over a 50-(.1.cristal.


minimum in the absorption. In this experiment the intensity variation wasaccomplished with the aid of neutral filters.The linear dependence of the photocurrent on light intensity allows the re-

calculation of the photocurrents to currents that would have been observedat equallight intensities (quanta) for all wavelengths.The photocurrent i, with constant light intensity and wavelength of light,

varies with the applied voltage V. A plot of the current versus voltage givesmainly a sublinear curve; only at Iow voltages is it superlinear. No completesaturation was found with fieldstrengths of up to 15.104 volt/cm. Some ex-perimental results are given in fig. 3.

5

,/1"3960.3.

~

/v-

I".......... 3740 ..4

I ,/" I-:/ -- ~3820 .3.---0

I~ /"

0 .,J,v

A

15012 •

T100

o 200 600 800V8491

Fig. 3. The photocurrent as a function of the applied voltage at various wavelengths of theincident light.

The actual shape of these i-V curves varies somewhat from crystal to crystal.However, for one and the same crystal the voltage effect is independent of theother variables, namely, intensity and wavelength of the incident light. Thisholds if the :voltage is not too low (e.g. 50 V for a 50-fLcrystal). The value ofthis limit varies from crystal to crystal.The three i-V curves of fig. 3, obtained at three different wavelengths and

intensities, thus have the same shape, as can be seen by a linear transformation.of the vertical scale. This fact is also demonstrated by the experiment withanother crystal. At a voltage of 600 V, the currents measured with light of3660 A and 4040 A were equalized experimentally by decreasing the intensityof the 3660-A beam with a neutral filter. It then appeared that the two photo-currents were equal at all voltages (fig.'4).The photocurrents measured a,t various wavelengths were normalized to a

5

.......v--1--- ........ :"'"

l/"1/

J

[7

I o For 3660A with filter• " 4040J. without filter

fI1


common light intensity Cquanta/second). It appeared that the photocurrent perquantum of incident light varies with wavelength in the same way as the ex-tinction coefficient for each of the two directions of polarization of the illumi-

A

20

15

10

849]

oo 100 200 300 400 500 600 700 800V

Fig. 4. The effect of voltage on the photocurrent is independent of the wavelength of theincident light.

nating beam. The corresponding maxima and minima for photocurrent andextinction coefficient occur at the same wavelengths. As an example of whatwas generally found, the behaviour of one crystal is represented in fig. 5. Bothin the photocurrent and the absorption spectrum a Davydov splitting is clearlyobserved.Figure 5 i.tselfindicates that the effect of wavelength in the photocurrent is

mainly a matter of absorption coefficient. In order to illustrate this more clearly,the currents of fig. 5 have been replotted, this time with the value of the cor-responding extinction coefficients as parameter, in fig. 6. The points C.) re-present a number of photocurrents as found with the monochromatic lightpolarized parallel to the b-axis of the anthracene crystal. A well-fitting curvehas been drawn through these points, showing that the photocurrent is a mono-tonie function of the extinction coefficient of anthracene. There is no furthereffect of wavelength on the photocurrent.A similar curve is obtained when the photocurrents of the same crystal with

the incident light polarized parallel to the a-axis (0) are plotted against theextinction coefficient Sa.

The photocurrents of several anthracene crystals were measured in this way.It appeared that the curves relating photocurrent and extinction coefficient hadthe same shape for all crystals. This indicates that the bulk photocurrent ofanthracene is a unique function of the extinction coefficient.


6

l- • light JOrizJ, b-oL_0 " " I Q- "

t->L.>.'V0 Lf

0 / ./'

I~~j '3x

~310.2 0.6 0.8 1.(} x 10 cm-f_c

BHS

Fig. 5. The absorption spectrum of anthracene for light polarized parallel to the b-axis (uppercurve) and to the a-axis (lower curve). The broken lines give the photocurrent as a functionof wavelength on an arbitrary scale (the current is normalized to equal light quanta of theincident light).

f20

i~ ioo

Î 8

40

oo

Fig. 6. The photocurrent (normalized to equallight quanta of the incident light) as a function! . of the absorption coefficient of anthracene.

The two curves in fig. 6 refer to one crystal in two different orientations. If thecurrents found with the light polarized parallel to the a-axis had been about20 % higher, these two curves (which have the same shape) would have coincided.Two such curves have been found with nearly all anthracene crystals. It isbelieved that the occurrence of two curves instead of one is due to experimentalreasons. It is very difficult to establish exactly the same irradiation conditionsof the crystal in both orientations, that is, before and after rotation through

PHOTOCONDUCTANCE AND SPECTRAL ABSORPTION OF ANTHRACENE . 373

ninety degrees (the same area of the crystal must be illuminated, the incidentlight beam may not be homogeneous and the reflection may be somewhatdifferent in one or the other position). .

4.3. The photocurrents when the illuminated electrode is negative

These experiments were carried out with a cell in which the negative electrodewas electrolytic, the other electrode being either a painted silver one or, like the'former, an aqueous solution: In the latter case the cell was completely sym-metric. The results with both types of cells were the same.It appeared that "negative" photocurrents can only be observed with thin

crystals, but even in that case they are always very small. At those wavelengthsfor which the absorption was high, the current amounted to some tenths of oneper cent of the "positive" current. There is still some variation with wavelengthobservable; shallow minima appear at the wavelengths where the absorption ismaximum. Photocurrent and absorption are therefore anti-parallel here. This"negative" photocurrent can best be observed at the long-wave side of the fustabsorption maximum (where the extinction coefficient is very small). A maxi-mum in the current at 4100 to 4200 Q is generally observed, as illustrated infig. 7.

180ipht ISO

I~~ +-__J_ __ ~ ~

-- Pos. electrode illuminal--- Neg.

..

39001496

Fig. 7. The photocurrents of anthracene (normalized to a common intensity in quanta) as afunction of wavelength between 3900 and 4300 A. Full curves: the current with the positiveelectrodes illuminated. Broken curves: the same with the negative electrode illuminated(30 x enlarged). Polarized light. Symmetrical cell with two liquid electrodes.

5. Discussion. 5.1. The experimental results

The bulk photocurrent i in anthracene (positive electrode illuminated) appears


to be determined by three independent variables:

i = 10 .f(V) . ~(e) .

The current is always proportional to the incident light intensity 10. Thevoltage function f(V) varies somewhat in shape from crystal to crystal, butfor one crystal it is independent of light intensity and wavelength at field-

• strengths higher than about 2.104 V/cm. The function ~(e) is the same for allcrystals: with varying wavelength, at constant values of intensity and voltage,the current is a (unique) function of the absorption coefficient 8.

Earlier investigations as reported in the literature did not show these results, 'the close correspondence of the spectral sensitivity of an anthracene photocellto the absorption spectrum, in particular, not being found. The main reason forthe discrepancies may be that in the present work at least one of the electrodeswas an electrolytic solution instead of the formerly used conductive glass sheetor the semitransparent metal electrode. Compared to the latter, aqueous elec-trodes give higher photocurrents and faster response times.

5.2. The theory of the photoconduction of anthracene

The sharp maximum in the photocurrent at the absorption edge of anthraceneas observed by Compton 3) and others prompted these authors to propose atheory in which it was assumed that the adsorption of light resulted in theformation of charge carriers in the bulk of the crystal and that the photocurrentwas recombination limited. A theory profounded by Kommandeur 5) has thesame general idea.The effect of wavelength found in the present investigation cannot readily be

understood on the basis of a theory in which it is assumed that absorption oflight results directly or indirectly in the generation of charge carriers in theinterior of the crystal. On the other hand our results appear to be in agreementwith the idea that charge carriers are only formed at the surface of the crystal,a view originally been put forward by Lyons 4) to explain facts on the surfaceconductivity of anthracene.According to Lyons, the primary process is the absorption of light in the

crystal, this producing a stable excited state (exciton) which can migrate throughthe crystal. Only those excitons which reach the surface of the crystal can beactive in producing charge carriers.The exciton state in anthracene crystals is well known from, amongst other

things, work on induced luminescence; it has to be identified with the lowestvibrational level of the first excited state. Each light quantum absorbed, in-dependently of its energy, degenerates via this exciton state.It will be clear that this picture accounts, at any rate qua:Iitatively, for the

observed parallelism of the magnitude of photocurrent and the extinctioncoefficient for the incident light. Since the absorption of anthracene for the


light used is very high, most excitons are generated ~n the crystal in a thinregion nèar the illuminated electrode. The closer to the surface an excitonoriginates, the better the chance it will have of reaching the surface. Therefore,the higher the absorption coefficient for the incident light (that is, the thinnerthe layer in which most of the light is absorbed), the more charge carriers willbe formed and the higher the photocurrent will be..,' The important role ofthe surfacein charge separationin bulk photoconductionhas recently also been put forward by Kallman and Pope 17) 18) on the basis oftheir experiments concerning the effect of the nature of the electrodes of thedark and photocurrents of anthracene. Equally Keppler 19) considers the surfaceas the main site for carrier production, a view derived from experiments on themobility of electrons and holes in anthracene.A more detailed picture of the exciton theory will be given in what follows.

Complete agreement with our experiments on the spectral dependence can beobtained if it is assumed that the photocurrent in a sandwich cell is due to thegeneration of mobile charge carriers (holes) at or very near to the interface ofthe anthracene crystal and the positive electrode. At the negative electrode sucha process does not seem to occur.The relation between photocurrent and absorption coefficient can be put on

a quantitative basis by calculating the probability of an exciton reaching thesurface. It is assumed that the creation of an exciton takes place at the spotwhere a photon is absorbed, that the migration of an exciton may be describedas a free-diffusion process and that it has a certain mean lifetime (due to theprobability of fluorescence or non-radiative transition into heat).The creation, diffusion and decay of excitons in the interior of the crystal can

be described by the following equation:

bn(x) b2n(x) n(x)-- =D----- + sloe-ex,bt bx2· T

(1)

where n(x) is the number of excitons at a distance x from the illuminated faceof the crystal, D the diffusion coefficient in the x-direction, T the mean lifetimeof an exciton and 10 the photon intensity of the incident light.The same equation (1) has been used by Simpson 20) in a problem relating to induced fl~o-

rescence in aromatic hydrocarbons due to the migration of excitons. Sirnpson's solution cannotbe used here because ~f other boundary conditions.

It is assumed that all excitons reaching the surface decay there; the boundaryconditions are therefore: nCO) = 0 and n(d) = O. The solution of eq. (1) for

bn(x)the stationary state, where -- = 0, is

bi

(2)


The photocurrent is assumed to be directly proportional to the exciton fluxthrough the interface between the positive electrode and the crystal. So onecan write for the photocurrents:

. A bn(O) (p .. I d '11 . d) d1+= -- ositive e ectro e 1 uminate anöx .'

i- = A bn(d) (negative electrode illuminated) where A is a proportionalitybx

factor depending on the applied voltage and the nature of the electrode. If *)d > VDT then ed/Vrh >> e-d/VDT and this leads to

A 10i+=Jj 1

V-+ 18 DT

(3)

and

(4)

5.3. Comparison of eqs (3) and (4) with experiment if the positive electrode isilluminated

For a comparison with experiment eq. (3) can be put into a more suitableform:

1 1 ( 0.434)i+= ico 1+ eVDT (5)

where ico = Alo/D, that is, the limiting value of i+ for 8 = 00.

The factor 0'434 arises from the fact that in eq. (5) the extinction coefficient is defined inthe more usual way by I" = Io10-e" instead of by I" = Ioe-e" as used in eqs (1) to (4).

According to this equation a plot of l/i+ versus 1/8 should give a straight line.This appeared to be in agreement with experiments. Through the points offig. 6,replotted in a I/i versus l/e diagram, well-fitting straight lines can be drawn(fig. 8). Itmay be added that the drawn curves of fig. 6 are calculated from thetwo straight lines of fig. 8. It appears, therefore, that the effect of the extinctioncoefficient in the photocurrent may be very well represented by the eq. (3) or (5).The two curves in each figure refer to one and the same crystal irradiated in

the two main orientations. The main difference is the value of the factor

"') This condition will be fulfilled in practice since the thickness of the crystals d = 20-60 IJ.,whilst Vlfr will appear to be of the order of 0·1 IJ..

PHOTOCONDUCTANCE AND SPECTRAL ABSORPTION OF ANTHRACENE 377 .

ioo = (A/D)!, Since A and D are characteristic of one crystal, the 20 % diffe-rence in the factor A/D may be due to a difference in the effective value of 10in the two orientations. Such a variation can be easily explained from experi-mental circumstances.

5.4. The mean free path of the exciton

The expression vn:;. represents the mean free-diffusion path of an exciton inthe anthracene crystal or the mean distance between the sites where the excitonis generated and where it decays. Experimental values for JI_D"; can be easilyderived from the straight lines offig. 8, representing eq. (5); for that crystal JIl).;-amounts to 1300A (b-axis) and 1000A (a-axis). The difference between thesetwo values is considered to be related not to the direction of the plane ofpolarization but to experimental influences.The values of vn:;., calculated in similar way from experiments with other

crystals, alllay between 700 and 2000A. Since the length of the diffusion path

Fig. 8. The photocurrent (normalized to equallight quanta of incident light) is a linear functionof lJe (s = absorption coefficient).

will depend inter alia on the amount of impurities in the crystal, its value mayindeed be expected to vary from crystal to crystal.

These results are in good agreement with the value (2000 A) given by Ere-menko and Mevedev 21). These authors investigated the effect of wavelengthon the surface photoconductivity of anthracene (with unpolarized light). Theirrelation between photocurrent and extinction coefficient (not derived) is iden-tical with eq. (5) in this paper .

~"L_----~ZOO~----~~~---6=OO~O~--~OOOO-f

._--------------------------~_.. ~

8497


From experiments on the fluorescence quenching of anthracene by impuri-ties values of 400, 500, 1000 and 960 Á have been found for the meanfree path of the exciton 2), 21).

5.5. The photocurrent with the negative electrode illuminated

As mentioned, the photocurrents are generally very small in this case, varyinganti-parallel with the spectral absorption and showing maxima at wavelengthsbetween 4000 and 4200 Á. It can be shown from both the magnitude and thewavelength dependence that this small "negative" current is due to light whichpasses nearly the whole crystal and which is absorbed in a layer near the positiveelectrode, where it gives rise -to charge carriers.

The photocurrent i- to be expected on this basis is given by eg: (4). Experi-mentally, the maxima of L are always found at wavelengths-where the absorp-tion coefficient is of the order of 100 cm+, Since l/Vïh is about 105 cm-i, itfollows that e« l/Vïh and consequently ed«d/Vïh. Hence, eq. (4) can besimplified to

A/oeI/Do 'L = lO-ed = Constant do-ed.

0'434D(8)

This expression for Ï- clearly has a maximum with varying e at

s = 0·434/d. (9)

Hence, for a crystal with thickness d the maximum in the negative photocurrentshould be found at that wavelength where the extinction coefficient of anthracenehas the value 0·434/d. With the aid of the absorption spectrum of anthracenefor long wavelengths (fig. 9), that wavelength for the maxima of i- can beobtained and compared with the wavelength observed. This has been done fora number of crystals in table Ill.

100

b-axis I

/ II /

a-axis.:7300

o4500 4400 4IDO 4100

-).()!) 1<498.

Fig. 9. The absorption spectrum of anthracene between 4000 and 4500 A for Jightlpolarizedparallel to the Q- and the b-axis. .

PHOTOCONDO'CTANCE AND SPECTRAL ABSORPTION OF ANTHRACENE 319

It can be seen that the calculated wavelengths for the maxima are close tothe experimentalones; clearly, the maximum shifts to larger wavelengths withincreasing thickness of the crystal, as predicted by eq. (9).

Another consequence of the supposition made is that, at the wavelengthwhere i- has its maximum, the ratio ofthe "positive" and the "negative" photo-current has a fixed value for all crystals independently oftheir thickness: i-/i+=0·37. This result can be obtained by combining eqs (3), (8) and (9).

Experimental values for L/i+ are given in table Ill. Considering the accuracywith which these very low currents can be measured the agreement is satis-factory.

The relations e = 0'434/d and i-/i+ = 0'37, both valid at the maximum of i_, can be moresimply obtained in the following way (in which, in principle, the same approximations areused as in the foregoing treatment):i+ = Constant· e (valid for low values of e, e.g. e < 104)i: = Constant· e . 1O-,di- is maximum for bi/be = 0 or e = 0'434/d and i-/i+ = 0·37.

TABLE III

light polarized light polarized Le(calc.) Ila-axis [lb-exi» - at max. i.:

thickness dfrom eq. (9) i+

.\(calc.).\ (obs.) .\(calc.) .\(obs.)light pol. light pol.

with fig. 9 with fig. 9(f'-) (cm-I) (A) (A) Ila-axis llb-axis

20 230 - 4060 4160 4145 0·21 0·4121 211 4077 4060 4175 4140 0·33 0·3350 87 4120 4110 4214 4170 0·36 0·2954 80 4125 4075 4225 4170 0·30 0·3358 75 4130 4110 4188 4190 0·35 0·2762 71 4135 4110 4225 4190 0·37 0·4068 64 4150 4100 4230 4210 0·29 0·29

6. Conclusion

The effect of wavelength on the bulk photocurrent in pure anthracene withelectrolytic electrodes, with either the positive or the negative electrode illumi-nated, can completely be understood from the assumption that mobile chargecarriers (holes) are generated if excitons reach (come close to) the positiveelectrode.

Kallman and Pope 17) have explained the preferred formation of chargecarriers at the surface (crystal-electrode interface) on energy grounds. In the

380 J. w. STEKETEE and J. de JONGE

interior ofthe crystal the energy ofthe excited state (about 3·5 eV) is insufficientfor ionization (the ionization energy of anthracene is estimated to be 5·5 eV).At the electrolytic electrode, however, an electron can be captured by a watermolecule, giving an extra energy of about 3·5 eV. Here the energy balance isfavourable for the extraction of an electron from an excited anthracene mole-cule with the simultaneous formation of a positive hole in the crystal (holeinjection). The hole moves through the crystal under the influence ofthe electricfield to the negative electrode, whe~e it is discharged. The complete processresults in a current in the outer circuit.The absence of charge-carrier formation at the negative electrode could,

according to this view, be understood if it be assumed that the energy, relatedto the transfer of an electron from the electrolyte to the anthracene, is too smallto balance the energy deficit of 2 eV in the charge-separation process.A clear picture of the effect of voltage on the photocurrent cannot be given

yet.It may be remarked that other investigators do not consider the positive

surface as the only site for carrier generation. Keppler 19), with a pulsed photo-conductivity technique, concludes that both electrons and holes can be pro-duced from excitons reaching the surface of the crystal, even withoutthe pres-ence of an electrode; both types of charge carriers can move in the crystalunder the influence of an electric field: Moore and Silver 23) investigated thepersistent internal polarization in sandwich cells of anthracene and concludedthat charge carriers are generated in the bulk of the crystal in addition toelectrons and holes generated at the electrodes. Kallman and Pope also assumethe possibility of electron injection at the negative electrode, although theprocess is considered more difficult from the standpoint of energy than holeinjection at the positive electrode. The purity of the anthracene crystals, thecondition of the crystal surfaces and also the nature of the electrode, may befactors responsible for the somewhat different results and opinions.

Eindhoven, June 1962

REFERENCES1) c. G. B. Garret, Semiconductors, N.B. Hannay (Reinhold Publishing Corporation,

New York, 1959) 634; J. Kommandeur, J. Phys. Chem. Solids 22, 339, 1961.2) D. J. Carswell, J. chem. Phys. 21, 1890, 1953; D. J. Carswell and L. B. Lyons,

J. chem. Soc. 1734, 1955; L. E. Lyons and G. C. Morris, J. chem. Soc. 3648, 1957;5200, 1960.

3) D. M. J. Compton, W. G. Schneider and T. C. Waddington, J. chem. Phys. 27,160, 1957.

4) L. E. Lyons, J. chem. Phys. 23, 220, 1955._ 5) J. Kommandeur and W. G. Schneider, J. chem. Phys. 28, 582, 1950.

6) L. E. Ly.ons and J. C. Machie, J. chem. Soc. 5186, 1960.7) A. Bree, D. J. Carswell and L. E. Lyons, J. chem. Soc. 1734, 1955.8) R. Sizmann, Angew. Chemie 71,243, 1959.

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PHOTOCONDUCfANCE AND SPECfRAL ABSORPTION OF ANTHRACENE 381

9) E. Voyatzakis and others, C. R. Acad. Sei. Paris 18, 1756, 1959.10) See ref. 7).11) H. Kallmann and M. Pope, Rev. sci. Instr. 29, 993, 1958.12) S. V. Obreimov, A. F. Prikhotko and E. Rodnikova, Zhur. eksp. teoret. Fiz. 18.

409, 1948.13) H. Kallmann and M. Pope, Rev. sci. Instr. 30, 44, 1959.14) D. P. Craig and P. C. Hobbins, J. chem. Soc. 2309, 1955.15) A. Bree and L .E. Lyons, J. chem. 'Soc. 2662, 1956.16) A. R. Lacey and L. E. Lyons, Proc. chem. Soc. 414, 1960.17) H. Kallmann and M. Pope, Nature 185, 753, 1960; 186, 31, 1960.18) H. Kallmann and H. Pope, J. chem. Phys. 32, 300, 1960.19) R. G. Kep p ler, Phys. Rev. 119, 226, 1960.20) O. Simpson, Proc. roy. Soc. A 238, 402,1956-57.21) V. V. Eremenko and V. S. Medved ev, Soviet Physics Solid State 2, 1426, 1961.22) J. Y. K utsj erov and A. N. Faj dish, Bull. Acad. Sci. U.R.S.S. (phys.) 22,29,1958;

M. Trlifaj, Czech. J. phys. B 8, 510, 1958; M. D. Borisov and V.N. Vishnevskii,Ukrain. Fiz. Zhur. I, 371, 1957.

23) W. Moore and M. Silver, J. chem. Phys. 33,1671,1960.

photoconductance and spectral absorption of … bound... · du coefficient d'absorption. ......

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