The Relationship between Exciton Absorption and the Photoelectric

RELATIONSHIP BETWEEN EXCITON ABSORPTIOKA N D PHOTOELECTRIC EFFECT

74.5

The Relationship between Exciton Absorption and the Photoelectric Effect'

by S. Nikitine, A. Coret, J. P. Zielinger, C. Jeanclaude, C. Boehm, and M. kouaghi

Downloaded by CENTRAL MICHIGAN UNIV on September 10, 2015 | http://pubs.acs.org Publication Date: March 1, 1965 | doi: 10.1021/j100887a006

Laboratoire de Spectroscopie et d'0ptique de Corps Solide, Institut de Physique, Cnicersitt de Strasbourg, France (ReceiTed October 6 , 1964)

The photoconductivity spectra of Hg12, Pb12, GaSe, and CuzO crystals, a t low teniperatures, show an important edge which is shifted toward the longer wave lengths in comparison with the absorption edge and a number of maxima and minima which correspond with the absorption lines attributed to excitons. Different mechanisms can explain these phenomena, and for each crystal a model is proposed. The photoelectroniagnetic effect is also studied for CuzO crystals.

Introduction The absorption spectra of many semiconductors consist of a number of absorption lines on the low energy side of an edge of continuous absorption. The lines are interpreted as transitions to exciton states and the continuous absorption is interpreted as band-to-band transit i o m 2 It is obvious that the latter type of transition corresponds to the formation of a free hole in the valence band and a free electron in the conduction band. Both can carry a current. Hence, the absorption of light in the continuum is expected to correspond to photoconductivity, Le., the internal photoelectric effect. As will be seen later, it is not obvious whether a photoeffect is to be observed on irradiation of the photoconductor by light within the exciton lines. This relation between the exciton part of the absorption spectrum and the photoconductivity has been studied recently in different laboratories. Though the interpretation is still rather complicated, an attempt is made in this communication to summarize and discuss the results obtained by the Strasbourg group for sonie substances; crystals of HgL, PbL, GaSe, and C u 2 0have been studied in sonie detail. Theoretical Background. Frerikel and Peierls have suggested that electrons and holes could be created in a bound state in which a rather small Coulomb interaction exists between them. This bound pair corresponds to an excited state of the crystal and is called an exciton. The excitons can diffuse through the crystal; however, no current is carried by excitons as they consist of a bound pair of charges of both signs. In an exciton, the binding energy is quantized as

in a hydrogen atom, and therefore, a series of energy states of the exciton is possible. Transitions to these states correspond to a series of sharp absorption lines converging to a limit. The theory of exciton spectra has been developed by Elliott.3a H a k e ~ iand , ~ ~Dresselhaus4 and is well kiiow~i now ; therefore, we intend to omit these developments here. A very simple model, however. shows that the interaction between the electron and the hole is an electrostatic Coulomb interaction in a dielectric medium of dielectric constant e. The problem is then similar to a hydrogen-like atom, and the exciton states are quantized. The binding energy of the exciton is then giver1 by

Eb is the binding energy, E , the energy of the lowest state of the conduction band, pLe= mhine/(mh m r ) , e is the charge of the electron, fi is Planck's constant divided by 2a,and n is a quantum number. It has to be emphasized that, in an exciton transition, the ground state is an unperturbed crystal, and the excited state consists of an exciton in an otherwise un-

+

(1) Presented to the International Conference on Photosensitization in Solids, Chicago, Ill., June 22-24, 1964. (2) S. Nikitine, Progr. Semicond.. 6 , 235 (1962). (3)(a) R. J. Elliott, P h y s . Rec., 108, 1402 (1957); R. J. Elliott and 11 Loudon, J . P h y s . Chem. Solids, 8 , 382 (1959); (b) H. Haken, Fortschr. P h y s i k , 38, 271 (1958); "Halbleiterprobleme." Vol. 11, W. Schottky. Ed., Vieweg, Berlin, 1955; J . P h y s . Chem. Solids, 8 , 166 (1959): Z . P h y s i k , 155, 223 (1959). (4) G. Dresselhaus, J . P h y s . Chem. S o l i d s , 1, 14 (1955).

746

perturbed crystal. The oscillator strengths of exciton lines have been calculated by Haken,3b ElliottJaaand Dresselhau~.~I t can be shown that different exciton spectra can be observed. The transition +matrix element can be expanded as a function of k , the wave vector, the value of which has to be very close to zero ( k ‘v 0). T h e First Class of Spectra. A spectrum of the first class corresponds to the case when the first term of the expansion differs from zero. It can be shown that, in this case, the second term is usually aero, and excitons in spectroscopic S states are formed. The intensity of the lines decreases as l / n 3 ,and in the visible region, the absorption coefficient is expected to be about 2 to 4 X lo5cni.-‘. Second Class of Transation. In some transitions the first term of the expansion of the matrix element for the transition moment may be zero. I n this case, the second term of the expansion may differ from zero, and excitons in spectroscopic I’ states are formed. The oscillator strength can be written f a = [ ( n z - 1)/ n5e5]C2,where Cz is a constant. The absorption in this kind of transitions is expected to be roughly l o 3 times weaker than that in transitions of the first class. Photoconductivity in the Exciton Lanes.5 The theory of photoconductivity in connection with excitons has not been worked out. It is clear that the excitation of an electron into the conduction band by absorption of a suitable photon fiw > E, should correspond to the creation of a free electron and a free hole, both of which can carry a current. When excitons are created by optical absorption, an electron and a hole are created in a bound state, and excitons cannot carry a current. However, different cases have to be examined regarding the fate of the excitons. (a) Once created, the exciton can be annihilated by a radiation or a radiationless process, and therefore, no free carriers will be created. (b) The exciton can, however, dissociate on an impurity or defect, and the majority carrier can be trapped. The minority carrier is likely to recombine rapidly with a majority carrier. (c) The exciton may dissociate with the liberation of a majority and a minority carrier which do not recombine immediately. (d) The exciton may dissociate, and the minority carrier may be trapped. In both cases a and b, no photoeffect is expected when light is absorbed i n an exciton line. In case c and particularly in case d, a photocurrent is expected when the crystal is irradiated in the line.6 Usually the exciton lines are superposed on a background ahsorption, the origin of which is not clear but is certainly connected with defects, impurities, etc.,

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SIKITINE, CORET,ZIELINGER,JEANCLAUDE, BOEHM, A N D ZOUAGHI

The Journal of Physical Chemistry

though part of this absorption may also be due to a tail of the band-to-band transitions. The threshold frequency of this edge is usually not well defined, and the absorption ends gradually. This continuous background usually gives B contribution to the photocurrent. Furthermore, active impurities or defects can give a strong photocurrent even beyond the intrinsic absorption. These effects may be complicated, but usually, in cases a and b the exciton absorption line is observed as a minimum in the photoconduction response curve. I n cases c and d, the exciton line is observed as a maximum on the photoconduction response curve. Some other complications in the interpretation of photoconduction curves will be discussed later. It is interesting to note that Frenkel suggested the existence of excitons in order to explain an absorption which does not give use to photoconductivity. He had obviously in mind one of the cases a or b considered above. But in some cases (c and d ) , the exciton line corresponds to a maximum of the photocurrent, in contradiction with Frenkel’s expectation.

Experimental Results Mercuric Iodide Crystals (Red Variety). The crystals were prepared by Professor Sieskind in this laboratory by evaporation of a solution of HgIz in acetone. HgL has a tetragonal structure and a t 20 and 4°K. is dichroic. When the electric vector of the light vibrates parallel to the axis (El and when the vibration is perpendicular to the axis ( E l c ) , the absorption spectrum is not the same. In the first case, the spectrum is called the extraordinary spectrum; in the second, the ordinary. So far, we have investigated the photoconductivity spectrum of the crystals a t 77”K., and the “ordinary photoconductivity spectrum” is the same as the “extraordinary photoconductivity spectrum.” Gross and Xovikov’ have found, however, different photoconductivity spectra for the two orientations of E . In Figure 1, we have represented the photoconductivity spectrum. We observe, after the rise of the photoconductivity on the low energy side of the absorption edge, an $portant drop and two minima a t X = 5330 and 4900 A. The absorption spectrum shows two lines for these two wave lengths which are due to exciton transitions of the first class. Furthermore, for crystals a few millimeters thick, a strong photoeffect is observed on the low energy side of

IC)

( 5 ) A. Coret and S. Nikitine, J . Phys. R a d i u m , 24, 587 (1963). (6) We are thankful t o Professor Stookmann of Karlsruhe for stimulating discussions on this subject.

(7) E. F. Gross and B. V. Novikov, J . Phys. Chem. Solids, 22, 87 (1961).

RELATIONSHIP BETWEEN EXCITON ABSORPTION AND PHOTOELECTRIC EFFECT

Nitsches by a method of chemical transport. They are thin slices about 200 p thick; their illuminated surfaces are perpendicular to the optical axis. The photoconductivity spectrum a t 77°K. (Figure 3) shows a maximum a t X = 5900 A. which corresponds to the absorption doublet observed in this laboratoryg and a minimum a t 5790 8. which corresponds to a weak band observed by Gross.'O

4

1

.3 C _


L

4 -

747

b

4600 ' 52'00

56'bOA

Figure 1. Photoconductivity spectrum of HgI, a t 77°K.

4949A

1

optical absorption

Figure 3. Photoconductivity spectrum of GaSe a t 77°K.

I

4000

4400

1

4800

c

'

5200 A inA

Figure 2. Photoconductivity spectrum of PbIz a t 20°K.

the absorption lines. This effect, due probably to impurities, can cower the band-to-band transitions. Lead Iodide Crystals. The crystals were prepared by Mrs, Schmitt-Burckel in this laboratory by evaporation of an aqueous solution of PbIz which crystallizes in the hexagonal structure. All of the crystals studied have been perpendicular to the axis. The photoconductivity spectrum a t 20°K. shows a maximum a t X = 4949 1.which corresponds to the first absorption line (Figuroe 2 ) . However, the second maximum a t X = 4908 A. does not correspond to the second exciton absorption line a t 4898 8. Gallium Selen,ide Crystals. The crystals were prepared a t the RCA Laboratory of Zurich by Professor

Figure 4.

Optical absorption spectrum of CuzO a t 4.2"K

(8) R. Nitsche, J. P h y s . Chem. Solids, 17, 163 (1960). (9) S. Nikitine, R. Nitsche, M . Sieskind, and J. Vogt, J . chim. p h y s . , 60,667 (1963). (10) E. F. Gross, B. S. Rasbirin, and G. Suslina, O p t . i Spectroskopiya, 6,569 (1959).

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NIKITINE, CORET, ZIELINGER,JEANCLAUDE, BOEHM, A N D ZOUAGHI

CUPTOUS Oxide. The photoconductivity of cuprous oxide samples has been studied inore in detail than that of other crystals for several reasons. In the first place, the absorption spectrum shows many absorption edges and many exciton series (Figure 4) which are now well known." (1) Two edges in the red correspond to indirect transitions to an exciton state with emission or absorption of a phonon. (2) There is a first series of lines in the yellow preceding ai1 edge. Figure 5 shows the band scheme of CuzO given by Elliott12; there are two valence bands and two conduction bands (owing to the spin-orbit splitting). Transition 1 is the yellow edge. ( 3 ) A second series of lines and a second edge are in the green (transition 2). (4) There is a maxiinuni of (transition 3). (5) There is also absorption a t 4800 a maximum of absorption a t 4585 A. (transition 4). The calculated oscillator strength of the lines and the values of the absorption coefficient show that the yellow and the green series are due to the second class of exciton spectra. The two maxima in the blue are due to the first class of exciton spectra. A second reason is that thick samples can be used. They are prepared in this laboratory by Dr. Grosinann from plates of copper which are oxidized a t 1000" in oxygen a t low pressure. Aquadag is applied to the two broad faces of the electrodes. However, the study of the spectrum has shown that the photoconductivity properties of CupO depend greatly on the state of the optical surface. Indeed, two kinds of spectra are observed, as we have already mentioned in a preceding paper.5 (a) For a natural surface or for a surface etched with dilute nitric acid, the response of the photoeffect is rapid and corresponds to an increase of the conductivity of the sample. The absorption lines appear either as maxima or as niininia in the photoeffect. The sec. relaxation time is T < For a sainple which has been left a few days in (b) the open air the photoeffect is quite different). The response is inuch slower (about a few m i y t e s ) , and in a limited domain of wave lengths (6200 A. < X < 5000 k ) ,a negative photoeffect has been observed; that is to say, the conductivity decreases under illumination. This last effect depends also on the applied potential (the greater the potential, the greater the effect) and on the dimensions of the domains. We shall study only the first case in detail. Figure 6 shows the photoconductivity spectrum of the Cup0 sample at 4°K. We can coinpare it with the absorption spectrum at the same temperature (Figure 4). The dispersion of the nionochroniator used does not allow the observation of the lines of high quantuni nuinber. However. we can see the lines n = 2 of the TIir .Joitrnal o.f Physical Chcmistry

1

f

1

4500 cm-' I

1

(3)

(4) 17 725cm-'

(1) (2)

Figure 5. Band scheme of CutO. Transitions ( 1 ) and (2), green and yellow series; transitions (3) and (4), blue and violet series.

t

n

\

$1

\ 5 780A

6 060 A

4250

45'00

4750

5dOo

5250

5500

5750

6000

A

Figure 6. Photoconductivity spectrum of Cu20 a t 4.2"K.

yellow and green series as iiiaxinia in the hotoeffect. On the contrary, the lines a t 4800 and 4585 . appear as minima in the photoeffect. A third line appears at 4718 8. and can be attributed to the line n = 2 of the series corresponding to transition 3 in Figure 5 . The photoconductivity is greatest in the green and blue parts of this spectrum. The photoconductivity curve can be used to observe the absorption lines of a crystal without consideration of its thickness. On account of the high value of the absorption coefficient, thin sainples have to be used for the measurement of the absorption coefficient, and it is not easy to obtain samples of a thickness of a fraction of a niicron (we have seen that for the first class spectra, absorption coefficients of lo5 to 106 are frequent). For the high energy part of the spectrum, the photoconductivity spectrum can give information of great importance on the absorption. Recently, we have studied a different experimental method which allows us to investigate the absorptioii of a sample-the photoelectromagnetic effect (I'EM

H

(11) J. B. Grun, Rea. d'Optique (Thhse), 41, 439 (1962).

(12) J. B. Grun, 2 1 , 119 (1961).

M .Sieskind, and S. Nikitine, J . Phys. Chem. Solids,

RELATIONSHIP BETWEEK EXCITON ABSORPTIOK AKD PHOTOELECTRIC EFFECT

749


I

b

\:

0.01

0.1

1

10

100 500

Q)

Kx

Figirre 8. Photoconductivity (normalized to 1.O a t peak) absorption curve.

5 795 A

1 4500 SdOO

5500

6000

Discussion

L A

Figure 7a. Photoconductivity spectrum of CuzO at 77°K.

"4 4!

31

45y 4800 A

--

I I I

I

Figure 7b. Spectrum of the PEL1 effect of CUSO (same sample as in Figure 7a) at 77°K.

effect). Here we detect the potential difference created by the deviation of the diffusion current of photocarriers by a magnetic field. This effect is proportional to the gradient of the concentration of photocarriers and, thus, directly related to the absorption coefficient. I n Figure 7 we can compare the photoelectric effect atid PEN effect, both a t 77"IC The latter is very important in the blue wh$re we can detect potentials of several volts. The 4800-A. line appears as a iiiaxiiiiuni, and the 4585-A. line, as a minimum.

The results described can be discussed, a t least qualitatively, on the basis of the different cases of exciton annihilation or dissociation examined above. However some complications may prevent a unique interpretation. The de Vore Eflect. It has been shown'j that the photoconductivity can vary with the optical density of the sample in a rather complicated way. If only one kind of recombination is considered, the photocurrent should increase with Kx ( K , absorption coefficient; z, thickness of the sample) and reach a saturation for high values of K z when all the light penetrating the sample is absorbed (curve I , Figure 8). However, this is never the case, arid it has been shown that the photocurrent passes through a niaxiniuin for a given value of Kx and then decreases asymptotically to a constant value (curve 2, Figure 8). This effect has been explained by de Vore in assuming that the recombination is not the same in the bulk and on the surface of the crystal. This assumption is quite plausible, and it can be foreseen that the reconibination will probably be faster on the surface, on account of the numerous defects and adsorption layers. I t can be shown that, for plausible values of the ratio of surface to volume recombination, the photocurrent passes through a maximum but tends, for greater values of K z , to an asymptotic value. From this value, by coniparisori with values calculated by de Vore, [ can be deterniined. This theory considers the variation of the photoconductivity with K z . Usually, however, the photoconductivity is studied as a function of the waye length. As the absorption varies also with the wave length, the theory can be applied, a t least in a seniiquarititative way, to the photoconduction response curves. The Wing of the Absorption Edge. I t has betm mentioned that the exciton lines are usually observe3 011 top (13) H. B. de Vore, P h y s . Ret., 102, 86 (1956).

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NIKITINE,CORET,ZIELISGER, JEANCLAUDE, BOEHM,A N D ZOUAGHI

of a background absorption. This absorption can be due to the edge absorption or to some absorption centers active regarding photoconductivity. Indirect transitions from the Brillouiri zone center niay also be possible. It appears that, in some cases, the photoconductivity in this part of the spectrum niay be considerable. It has to be noted that this part of the spectruni is not well understood theoretically. The results obtained will be discussed in the light of these considerations and of the mechanisms of exciton decay iiientioried previously. Hg12 at 77°K. As seen from the curve in Figure 1, the photoconductivity of Hg12 a t 77°K. shows a strong inaxiniuni on the low energy side of the exciton line, and the exciton lines are observed as miniilia on the photoconductivity curve. As this substarice is rather strongly luminescent, it is plausible to interpret the iiiiniiiia in the photoconductivity curve according the process discussed under (a). A confirmation of this interpretation is obtained from a study of an HgIz crystal submitted to a therinal treatment (a few hours at 100”). I n this case the exciton line appears as a niaxiniuni on the photoconductivity curve. It seems plausible to assunie that the treatment has produced defects on which the excitons can now decompose. It is to be noted that, in these cases, the study of the photoconductivity shows a pronounced niaxiniuni 011 the low energy side of the exciton line which is an obvious indication in favor of strongly active centers. One is tempted to admit that these centers emit only carrier whereas the band-to-band transition produces carriers of both signs which recombine rapidly. GaSe at 77OK. and PbIz at 20°K. The mechanism of this photoconductivity corresponds to case c or d. Hall photonieasurements which are now being carried out may decide between the two processes. I t has to be mentioned that the de Vore effect explains the low value of the photoconductivity for the band-to-band transitions. Cu20 ut 77 and 4 3 ° K . The photoeffect in crystals with only a “natural” or an etched surface mill be discussed. ,4 tentative interpretation only is suggested. The negative photoeffect of crystals with a surface modified by exposure to open air or after theriiial treatment has been discussed in a previous paper.5 The photoconductivity spectrum shows a positive effect in the exciton lines of the yellow and green series, as well as in the indirect transition red continuuni. , This gives an indication in favor of the decomposition of excitons giving electrons and holes (the last are the majority carriers). The photoeffect passes through a niaximui;i, as predicted by de Vore’s theory, a t about 4650 A. However, with the sainples used, the absorption of T h c tJoiir?7al of PhVsicnl f’hemistry

light is total for the yellow part of the spectruni. Therefore, the niaxiniuni should be expected at niuch lower energies than observed. This may be explained by the suggestion that excitons partly dissociate on a defect and partly reconibine through a radiationless process by emission of a great number of phonons. I n the continuuni the process may be similar; the electron and hole reconibine rapidly, or one or both (the electron probably) are trapped by defects. This effect is likely to shift the maximum of the photoconductivity curve to higher energies as suggested by the experiment. The blue and violet lines are observed as minima, probably essentially on account of the de Vore effect. A different process is not quite excluded though it might be difficult to interpret on the basis of the energy level diagram of Elliott. From the values of the photoconductivity in the high energy part of the spectrum, it is possible to conclude that the ratio f = 3. This value must be considered, rather, as an order of magnitude. Unfortunately, only qualitative data are known regarairig the lifetime of the photoconductivity. We have been able to show that 7 < sec. Further investigations are necessary.

Conclusions The data obtained are still not sufficient to support a final interpretation of our photoconductivity nieasurements. However, sollie important , though provisional, conclusions can be attempted. I n HgI, the threshold energy of the photons in the photoconductivity curves is lower than that of the exciton lines. This suggests a strongly active wing of the absorption spectrum on the low energy side, possibly owing to defects. The excitons decay probably essentially by a radiative process which is observed in exciton luniinescence. The de Vore effect is responsible for the small value of the photoconductivity in the high energy part of the spectrum. I n GaSe and PbI, the excitons formed can dissociate to give free carriers which make an important contribution to the photocurrent. In CuzO two processes probably take place. (a) The excitons and carriers in the conduction arid the valence bands recombine in a radiationless process ; (b) excitons decay giving probably majority carriers (holes). The electrons niay be captured, so the efficiency of the photoconductivity is diminished by (a). The de Vore effect explains, at least partly, the behavior of the photocoriductivity in the high energy part of the spectrum. Some parameters of the photoeffect have been roughly evaluated. Further experiments are necessary. but it can be con-

751

LUMINESCENCE OF DOPEDAROMATIC CRYSTALS

cluded that the general lines of the photoconductivity and its relations with the decay of excitons are not far

from being understood. No experimental data are yet available for or against a diffusion of excitons.

Luminescence of Doped Aromatic Crystals’


by A. Schmillen Physikalisches Institut der Unirersitat Giessen, Germany

(Received October 5 , 1964)

The transfer constant, a, for the radiationless transfer of excitation energy from a photoexcited host crystal to foreign molecules in the lattice with a lower excitation level is given hy the equation T ~ / T ( c ) = 1 ac, where T O and T are the fluorescence decay times of the host without and with the impurity, and c is the concentration of the impurity, which has been determined for several systems. A phase fluorometer was used to determine decay times from the phase angles of the directly excited fluorescence of the host and of the impurity in the lattice and of the fluorescence of the impurity excited by transfer. For 2,3-diniethylsee. and a is 1.05 X lo5. naphthalene as host and anthracene as solute, r0 is 69.7 X This value of a is similar to the value 0.87 X lo5 for 2,3-dimethylnaphthalene-perylene, although the lowest excitation levels of perylene are considerably below those of anthracene, suggesting perhaps that overlap of host emission with the foreign ~noleculeabsorption may not be a dominating factor in transfer. For fluorene-anthracene, r0 is 7.3 X sec. and a is 8.5 X lo3,although these values may be subject to some systematic experimental error. I n fluorene-pyrene, two anonialies prevent the determination of a. At low concentrations of pyrene, only the fluorescence of anthracene appeared, although the anthracene concentration was less than I t is suggested that a pyrene-anthracene coniplex, with strong mutual coupling, would account for the observations. Also, at high concentrations of pyrene, the excited dimer or “exciiner” fluorescence appeared.

+

One of the main problem on the luniinescence of molecular crystals is the transfer of excitation energy froni the host lattice to foreign niolecules having a lower-lying excitation level. To the nuiiierous experimental and theoretical investigations treating this problem, this paper adds a further modest contribution. Without restriction to a defined energy transfer model, let us suppose that the radiationless transition of excitation energy from the host lattice to the foreign niolecules is a process competing with the luminescence emission of the host material. Further, we may assuine that the transfer probability is proportional to the concentration of foreign niolecules.

Then the following relation should hold between the decay times T and r0 of the host luminescence (with and without foreign molecules) and the concentration C of foreign molecules

where a is a characteristic constant of the transfer. If we use for the decay time ineasureiiients a phase fluoroineter with a periodically varying excitation intensity, the three nieasurable phase angles & (the (1) Presented to the International Conference on Photosensitization in Solids, Chicago, Ill., June 22-24, 1964.

Volume 69. S u m b e r S

March 1965

The Relationship between Exciton Absorption and the Photoelectric

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