Polymers and molecular solids: New frontiers in surface science

Surface Science 70 (1978) 674-691 0 North-Holland Publishing Company

POLYMERS AND MOLECULAR

SOLIDS: NEW FRONTIERS IN SURFACE

SCIENCE

C.B. DUKE Xerox Corporation, Xerox Square-l 14, Rochester, New York 14644, USA Received 14 April 1977

A brief review is given of the present state of knowledge of the surface properties of polymers and molecular solids. These materials are shown to exhibit surface phenomena which are dramatically different from those characteristic of metals and covalent solids. The origin of these differences resides in the combined occurrence both of large electronic and atomic polarizabilities and of small probabilities for the transfer of an electronic excitation from one molecular site to another. The interplay of these two quantities leads to a diversity in the character of the resulting electronic excitations, ranging from localized molecular ion states in aromatic pendant-group polymers to quasi-one-dimensional metallic behavior in certain charge transfer salts and polymers. The primary role of the surface in such materials is the introduction of large, inhomogeneous fluctuations in the relaxation energies associated with the polarization of the solid by an excitation. These fluctuations produce a number of novel phenomena including localized surface states in the absence of dangling bonds, inhomogeneous broadening of photoemission spectra, and alterations of the charge state of surface molecules. A simple, unified theoretical framework is developed for the interpretation of these phenomena.

1. Introduction

In this paper we examine briefly the nature and origin of a variety of novel surface phenomena characteristic of the molecular solid state. By “molecular” solids we mean those for which the entities comprising the solids are molecules in the sense that interatomic distances within these entities are smaller (i.e., driven by covalent bonding) than those between them (typically sums of Van der Waals radii). Several distinct types of such solids occur, depending on the detailed characteristics of their bonding. Typical condensed gases (e.g., COa, benzene) exhibit Van der Waals (vdW) bonding in three dimensions. Polymeric solids often are characterized by vdW bonding in the two dimensions normal to the (covalently bonded) polymer backbone. Layered crystals (e.g., graphite) consist of two-dimensional covalent networks bound by vdW forces in the third dimension. Herein we focus our attention on three specific classes of molecular solids: vdW solids comprised of close-packed arrays of molecules [ 11, polymers [2,3], and quasi-one-dimensional charge transfer salts consisting of parallel, segregated stacks of molecules exhibiting weak n-elec674

C.B. Duke / Polymers and molecular solids

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tron overlap within the stacks and a combination of ionic and vdW bonding between them [3,4]. Since it might seem odd to discuss this topic in a volume commemorating the inventor of the field emission and field ion microscopes, perhaps a few words of motivation may be useful. Major advances in man’s knowledge often follow the invention of a new analytical technique, the synthesis of a novel class of materials, or the creation of a new level of theoretical insight. It can be argued [S ] that the modern renaissance in surface science is caused by a fortunate combination of a11 three, with emphasis on the former to which Professor Miiller has contributed so profoundly. The continuing development of this field will require increasing emphasis on the latter two, however, as was the case for solid-state physics during the period 1930-1970 [S]. Moreover, recent advances in the art of preparing molecular and polymeric solids for their electronic properties have been substantial, as have been those in the development of a panoply of theoretical ideas for the description of these properties [3,4]. The theme of this article is that the extension of the advances in Surface Science technique to characterize the novel materials and to test the new ideas emanating from studies of molecular solids is a timely and rewarding enterprise. Consequently, it is appropriate to dedicate the article to Professor Miiller, in the hope that we in the profession who follow him in time can maintain the impressive pace of accomplishment which his life and work have set for the field of Surface Science. Our presentation is divided into two major parts. In section 2 we consider the composition and structure of molecular solids. Central points of emphasis include the occurrence of large unit cells (i.e., comphcated structures), multiple phases and polymorphs, large and complex thermally excited molecular motions, and the susceptibility of these materials to damage by both electrons and photons. Indeed this last aspect of their behavior is often regarded as a great asset (hence their use as resists in electron(e)-beam and photolithography), although we shall be concerned primarily with e-beam and photophysics rather than chemistry. Our main interest, however, lies in their electronic properties which are examined in section 3. Here a new world emerges before our eyes. Surface states without dangling bonds, molecular ions at polymer surfaces, the electrical and chemical inertness of chain-folding surfaces, and insulating surface layers on organic metals are only some of the ingredients of the array of fascinating electronic phenomena associated with the surfaces of molecular solids. Following a brief indication of the nature and origins of these phenomena, we conclude with a synopsis.

2. Composition and structure 2. I. Molecular crystals and glasses An identifying feature of molecular solids is the persistence of the molecular structure of their constituents within the solid state [ 11. For crystals bound by vdW

forces in all three dimensions the solid-state structures are analogous to those of close-packed arrangements of molecules whose size and shape are determined by the volume which is the union of the Van der Waafs spheres of their constituent atoms. The resulting low~symmet~, com~lieated crystal structures are consequences of the unusual shapes of the molecular species and, occasionally, of orientations adopted to take advantage of hydrogen bonding. Since the vdW forces are weak and the molecules are large, several structures often have the same energy within several hundred degrees Kelvin per molecule. This situation causes the existence of palymorphs and quite complex phase diagrams X1,6]. Indeed the vdW forces are SO weak that small molecules are liquids or gases at room temperature. Only large molecular masses or the occurrence of charge-transfer (ionic) contributions to the crystal bonding lead to solids at standard temperature and pressure. Two elements which occur as molecular solids under these conditions are sulfur and selenium, for which structures of molecular solid-state allotropes are indicated in fig. ‘ta and fig. 2b for o~orhomb~~ sulfur (o-S) and ~-nlon~c~~n~~ selenium (m-Se), respectively. Both sulfur and selenium aIso exhibit polymeric solid state allotropes (e.g., fibrous sulfur [7,g] and trigonal selenium (t-Se) 19,103) as well as numerous other molecular allotropes [7-IO]. Most molecular solids, however, are formed from organic species [6,10]. It is evident from figs. 1 and 2, as well as the many diagrams in refs, [8-IO], that mofecufar crystals admit numerous cleavage faces, If exhibiting complicated structure. A ~arti~ulariy attractive feature of these materials, however, is the fact that observed p~~otoemission spectra are almost independent of molecular packing fl1,12] and/or cleavage face [ 13]. Consequently, the unknown surface structures do not constitute a major obstacle to the interpretation of the electronic structure of molecular solids, Indeed, as shown in figs. lb and 2c, molecular-orbital calculalations [I 1,12,14] for the molecular species constituting the solid provide an entirely satisfactory description of measured photoemission spectra of o-S [ 12,14-163 and m-Se [12]: a general result which has emerged from all studies of single-molecule vdW sohds to date [l l-14,17,18]. A final important feature of molecufar solids is their generahy large vibrational motions. Typical Debye temperatures characteristic of acoustical vibrations of the molecules are BD 2 5 meV (60 K) f19--211. moreover, because of the presence of multiple molecules per unit cell, most af these materials exhibit between three and twelve additional rotational-librational normal modes in the energy range 5 S fro 4 20 meV. Since room temperature corresponds to 25 meV, it is evident that under standard temperature and pressure ~ond~t~ol~sthe constituents of a molecular solid are in a state of considerable vibrational movement, which in turn generates appreable dynamic disorder in a crystalline lattice. From the perspective of surface-stmture analysis, we would expect this extensive vibrational motion to reduce substantially the intensities of low energy electrons diffracted from surface species [22]. This fact is e~caura~llg in that it suggests that structure analyses by lowenergy electron diffraction may be performed using economical single-scattering metals:nearly

C.B. Duke /Polymers

and molecular solids

UPS-VAPOR

617

Ss

(BOSCHI AND SCHMDT )

Se : AMORPHOUS (NIELSEN) S,: CNDO-S I

8

I

IO IONIZATION

I

I

12

14

POTEMIAL

t eV

t

16

1

(b)

Fig. 1. Diagram of the structure of orthorhombic sulfur [ref. [8], Panel (a)] and a comparison in Panel (b) of gas phase UPS data [ 151, solid-state UPS data [ 161, and the calculated valence electron density of states of Sg [ 12,141. #designates the shift (to lower binding energy) of the solid-state relative to the gas phase UPS data. (“kinematical”) methods [22,23]. Evidently, however, such studies may have to be carried out at low (i.e., liquid helium or nitrogen) temperatures. Turning to a brief consideration of “quasi-one-dimensional” organic stack conductors [3,4,24], we note that they typically are two component donor-acceptor (e.g., D’A-) ch ar ge t ransfer salts in which, however, a given molecular species may

TRIGONAL

8 * MONOCtINIC

f TCPVIEW~

t SIDE VlEWl

(a)

(b)

XPS MONOCLINIC SELENIUM CNDO -S Se8 MOLECULE

J a

, I5

i IO

g 5

I

EF BiNDING ENERGY RELATlVE TO &,feVf ICI

Rg. 2, Diagrams of the structure of (‘polymeric”) trigonal selenium [ref. [IO), Pane8 (a)], (“molecular”) p-monoclinic selenium [ref. [lo], Panel (b)] , and a comparison in Panel (c) of measured [ 121 XPS data of these two allotropes of selenium with the calculated ( 121 valence electron density of states of Set+ The energy scale is measured relative to the Fermi energy of the gold substrate on which the selenium was grown, and that of the calculated valence density of states was shifted to lime up the lowest~b~d~g~nerg~ calculated peak with the observed peak.

exhibit mixed valence states (e.g., A’ and A-). The materials which exemplify the properties of this class of solids are charge transfer salts of 7,7,8,8-tetracyano-pquinod~methane (TCNQ) with donors [e.g., alkali metals, quino~in~um, N-methyl-

p~~n~inin~ (~~P)~ tetrathiofulva~~~~ (TTF)]. tn the cases of interest to us, the TCNQ and donor molecules form separate parallel stacks in the solid state, with a donor stack being surrounded by acceptor stacks 1241. For molecular charge transfer salts [i.e., those in which both donors and acceptors are organic molecufes, e.g,, (TTF~)(TCNQ-)~ ~M~i)(TCNQ-)], the observed structures are roughly consistent with the molecular close packing arguement [ 1,241 given above for single-component vdW solids, although both metallic [24] and ionic 1251 contr~but~ous to the cohesive energy seem to be substantial. The novel feature of these stmctures relative to vdW crystals is the significantly larger overlap of n-electron wave functions between adjacent molecules in the same stack. Thus, they exhibit hi tropic eIectronic properties, and may become weakly metallic or semiconducting along the stack direction. Nevertheless, from the perspective of composition and structure they are an~ogous to sin~ecQmponent vdW solids in that their cfeavage faces exhibit comphcated structures; 3, +.,5 meV; and many vibrations normal modes are excited at room temperature. One new complication arises, however, in that the surface composition and degree of donor-acceptor charge-transfer may differ from that in the bulk [26]: an important topic to which we shall return in section 3.

~o~yrne~~csoiids are composed of macromolecules of molecular we~~t greater than about i04 atomic mass units. The macromolecules themselves are composed of covalently bonded molecular subunits: most commonly hydrocarbons or their compounds with oxygen, nitrogen and halogens [2]. While rather few substances exist as polymers in their elemental form, sulfur [7,8] and selenium [9,10] exhibit polymeric allotropes. The solid-state crystalline polymeric fomr of selenium is trigonaf selenium (tSe) which consists of infinite chains in helical conformations packed in a hexagonal array [ 101, Each helix has threefold symmet~ in which the repeating triplet of Se atoms is almost identical to the corresponding triplet in Sea. A top view, Le., t-Se(~~l), of these chains is shown in fig. 2a. Such macros moIecuIes arc of interest to us here because they ihustrate the final stage of the realization of the concept of quasi-one-dimensional sohds. In contrast to the iinearstack charge transfer salts, the macr~molecu~ar chains exhibit covalent bonding along the chain backbone. They also can exhibit metallic conduct~~ty along the chain as in the case of (SN), [3]. The bonding between the backbone chains is env~aged to be due to vdW forces in simple cases f1,2], although weak metallic and ionic bo~d~g also can occur for chains on which the ind~vidu~ molecular species exhibit mixed+alence states. Three levels of structural information must be specified for polymeric solids, The molecular configuration is the sequence and composition of the molecular repeat units along the individual macromolecular chains. Nomopolymers consist of macromolecules built out of a single repeating unit, as, for example, fibrous S, t-Se,

fpS), and poly(methy~ methacrylate) EMMA). Copolymers contain macromolecular chains constructed from two independent repeat units, e.g., styrene and methyl methacrylate. They occur in two common varieties; alternating in which the repeat units alternate and block in which large segments of the chains are either one component or the other. The richness in structure at the molecular ~ou~gurat~on level is web illustrated by the occurrence ofisomerism. PS, for example, exhibits positional isomerism because the mdecutar repeat units can be placed head-to-head or head-to-tail on the macromoIecular chain [2]. Other polymers, e.g., poIy(butadiene), exemplify structural isomerism because they can exist in either linear or branched form [2], It is evident from these simple examples that even at this lowest molecufar ~on~gurat~o~ level of information, the specification of the structure of polymeric solids [2] may be qu~~ta$ively mare complicated than that of molecufar solids, which in turn is qua~~tat~v~~~~ more complicated than that of most metals and covalent solids (e.g., Si, Ge, GaAs). The second tevei of polymer structural ~nfomtation is the spe~i~~ation of the configuration of the macromolecular chains. While changes in molecular configuration require breaking the covalent bonds which hold the chains together, the chains can assume many shapes (of nearly equal free energy) merely by altering the rotation of the various molecular groups about a bond. Moreover, the shapes that individual macromolecules assume in the solid state are clearly related both to their molecular ~on~gurat~~~s (because of steric and packing energy considerations) and packing (i.e., neighbor) in the solid. Typical solid-state ~on~gura~ons for poiymers without balky molecular side groups are hetices, of which we see an exampfe in the t-Se structure shown in fig. 2a. Such polymers often form crystalline solids [2]. Poiymers with irregularly spaced or oriented side groups usually do not crystallize but rather form what are called (rather imprecisely) amorphous polymers [2]. The final level of polymer structural information is the specification of a sample’s morphology, i.e., its macroscopic form and shape, especially insofar as these data may be used to infer the rna~~~~~~~o~~ti~tt of individual rna~rornole~u~a~ chains. Fo~ymeri~ solids are classified as either aInorphous or crystalline, and within the latter classification folded-chain Inacro~onfo~nations are distinguished from extended-chain macroconformations. More complex structures also occur, as described in a thorough review of this subject by Wunderlic~ [ZJ. Recent attention has focused on conducting polymers [3’Jand the fo~ation of novel polymer single crystals by solid-state poIyme~2ation [27]. ow present interest in these materials centers around the s~e~i~ea~~~n of their surface &omposit~on and structure, Unfy in rare cases are these properties expected to be uniform in the vicinity of a surface. It is widely betieved that even In near& ideal cases (e.g., highly perfect lameilar crystals), organic polymer crystals are at least partly covered with “amorphous” materials [2]. Moreover, the surface cornposition may be quite unrepresentative of the bulk, especially in the case of COPO~Ymet-s or polymers with hydrophilic or hydrophobic side groups. The chemical cornposition of polymer surfaces conventionalty is determined by X-ray photoelectron pobfstyrene)

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681

spectroscopy [28], which provides information about the uppermost few atomic layers. This depth is small relative to that in which structural and chemical inhomogenities are thought to occur [2], so improvements in technique would be welcome. The structure of polymer surfaces is most often examined by decoration or electron microscopic techniques in order to determine the nature of surface defects [2]. An interesting and important surface-structure issue, however, is the structure of the fold surfaces of folded-chain polymer crystals [2]. An example is provided by t-Se(OOO1) as illustrated in fig. 2a. Both Se and Te crystallize in the trigonal form. In the case of Te, however, the crystal bonding is largely covalent, so that one might expect [29] the (0001) face to exhibit a structure in which all the bonds are saturated. In fact, there is fragmentary evidence from low-energy electron diffraction (LEED) that a bond-saturating reconstruction does occur [30]. Stated in terms of polymer structure, this reconstruction provides evidence for adjacent re-entry of Te chains whereas the (1010) face, which contains only extended chains, appears to exhibit the same structure as anticipated for bulk Te [30]. Similar results are expected for Se, with the chain-folding re-entry surface reconstructions expected to lead to chemically inert t-Se(OOO1) surfaces whereas an unreconstructure surface would be chemically active due to the “dangling bonds” from the Se atoms at the ends of the macromolecular chains. Thus, we see that conventional Surface Science techniques, in particular LEED and photoemission spectroscopy, can be applied to achieve a new level of insight into the structure and properties of polymer surfaces, although this field presently is almost totally unexplored.

3. Electronic

structure

A consideration of the electronic structure of polymers and molecular solids could focus on either of two aspects of the topic: ground-state properties or electronic excitations. We already have noted that these materials exhibit weak bonding in at least one direction: vdW crystals in all three, polymers in the two normal to the chain axis, and organic linear-stack conductors along the chain axis. The challenge for calculations of the ground-state energy in these cases in the prediction of their geometrical structure. While the ingredients of such computations are wellknown [ 1,24,25,3 11, successful predictions are not yet commonplace. Our emphasis herein is placed on the electronic excitation spectra directly accessible via spectroscopic measurements (e.g., ultraviolet absorption (WA), ultraviolet photoemission (UPS) and X-ray photoemission (XPS) spectroscopy). Electronic excitations in polymers and molecular solids range from localized molecular-ion states (e.g., in aromatic pendant-group polymers [32-341) to more-or-less conventional delocalized band states (e.g., in (NMP’)(TCNQ-) [35] or (SN), [36]). Therefore the properties of these materials reflect an enormous variety of physical phenomena quite different from those typically characteristic of metals and covalent semiconductors. Specific surface phenomena of unusual interest

682

C.3. Duke f Polymers and molecular solids

include surface-exciton resonances in th optical reflectance spectra of anthracene [37], polarization induced shifts of gas-phase UPS spectra [l I-131, broadening of solid-state UPS spectra by surface-induced relaxation energy fluctuations 1331, and surface-induced changes in the charge state of molecules in donor-acceptor charge-transfer salts [26,38-401. Our objective in this section is the development of a unified conceptual framework within which to interpret this wide range of observations. Two concepts are central to the interpretation of these phenomena: large (and fluctuating) relaxation energies [32] and weak intermolecular electronic overlap [33]. Suppose an added charge or electron-hole excitation (“exciton”) is placed on a molecular entity in a pdymeric or molecular solid. The resulting alteration in charge density relative to a neutral molecule does two things. First, it polarizes the electronic charge density of both the molecular entity itself (intramolecular electronic polarization) and the surrounding solid (intermolecular electronic polarization). Second, it causes atomic relaxations both within the molecular entity (intramolecular atomic polarization) and in neighboring species (intermolecular atomic polarization). Labeling the contribution to the relaxation energy associated with electronic polarization fluctuations by En, and that caused by atomic polarizations by En,, we can estimate the magnitude of the contribution to these quentities by intermolecular [i.e., En(inter)J and intramolecular [i.e., En(intra)] processes. The intermolecular relaxation energy may be calculated by treating an added excitation as embedded in a lattice of dipoles [41]. Typical values for the electronic and atomic (i.e., vibrational) contributions for an added charge are f32] : En&inter) - l-3 E&inter)

eV ,

- E&inter)/10

04 * 0.1 eV .

(lb)

The intramolecular contributions may be assessed either by comparison of spectral data on neutral ground-state and excited (or charged) molecular species or by molecular orbital calculations. Both methods give as representative values for a molecular ion [32] E,,(intra)

-+ 1-2 eV ,

En,(intra)

* 0.1-0.3

UC)

eV ,

04

leading to the total relaxation lattice : E, = E&inter)

t En,(intra)

energy for a charge (i.e., electron or hole) added to a

+ E&inter)

+ E,,(intra)

- 2-5 eV ,

Oe)

The values of E, associated with exciton states (e.g., singlet states excited in UV absorption) are smaller by a factor of about 10, depending upon the oscillator strength of the associated transition [37,43,44]. Of equal importance to the large magnitude of the polarization-induced relaxa-

C.B. Duke /Polymers and molecular solids

683

tion energies are their spatial and temporal fluctuations [33]. Three sources of these fluctuations can be significant in polymers and molecular solids: surfaces, defects and molecular vibrations. To illustrate the origin of the spatial fluctuations, consider the relaxation energy of a point ion embedded in a medium of dielectric constant K. A schematic expression for this energy is [45]

E,

=J;(1- +3.

(2)

The integral in eq. (2) runs over the volume of the dielectric. The apparent divergence at large r does not occur in actual calculations because the integral is performed in momentum space utilizing an accounting for the momentum dependence of K and handling the divergence at large momentum by introducing a cut off at a measure of the ion’s size. Although it is not useful for computational purposes, eq. (2) reveals clearly the conceptual point that for an ion at a surface, the integration volume is halved, thereby causing a corresponding reduction in the relaxation energy. Proper treatments of the electrostatics yield this result [37], revealing that the intermolecular electronic relaxation energy of a molecular ion or exciton in a surface layer of a molecular solid is roughly 60% of that of the corresponding bulk excitation. These considerations indicate that intermolecular contributions to the polarization energy are expected to be reduced in the vicinity of defects in molecular crystals and to fluctuate in pendant-group polymers because of large variations in the local surroundings of a particular pendant group [2]. Moreover, we noted in section 2 the large molecular vibrational motions in molecular and polymeric solids. These induce temporal fluctuations in the intermolecular polarization energy of magnitude [42] :

MqJ2)l

1’2- E&inter)/10

(3)

We see, therefore, that fluctuations in the intermolecular contributions to the relaxation energy of added charges (e.g., electrons) can amount to several tenths of an eV in molecular crystals and hence are quite comparable to the widths (W - 0.1 eV) of the one-electron energy bands expected for vdW solids [46]. While the absolute magnitude of these fluctuations are smaller for excitons, they still are comparable to (singlet) exciton band widths (IV,, - 0.05 eV) [37,43,44]. We now come to the central question in our discussion: are the electronic excitations localized or extended (e.g., Bloch energy band states [46]) in character? Our estimates of the relaxation energies were made for excitations localized on a single site. Thus, we must inquire into how successfully the one-electron hopping integrals (V- W/6) which are off-diagonal in the site index compete with the fluctuations in the polarization energy. Fortunately, the mathematical formulation of such questions is well developed in the literature [47,48]. Consider the one-electron (or one-exciton in the case of

C.B. Duke /Polymers and molecular solids

684

optical properties H=

[43]) Hamiltonian:

c ~,&)&a,,, + c

l’$a,t~a~an, ,

n#n’

n,oL

in which n is a site index; (Y designates the molecular orbital; I$$ designate the intermolecular hopping integrals; and anor is the annihilation operator for an electron occupying the orbital (Yat the site n. The molecular eigenvalues at each site, i.e., the (e,(o)}, differ from each other because of the fluctuations in the polarization-induced relaxation energies [e.g., eq. (l)]. These fluctuations always cause localized states at the edges of the energy bands characteristic of a perfectly periodic crystal. If they are large enough, specifically if for three-dimensional motion 2 50( Vnlnn’)*” )

((en - En)?l$

(5)

then localized states fill the whole band. The symbol 0~” designates the average over both thermal fluctuations and variations from one site’to another in a rigid solid. The criteria for localization are even less severe for one and two-dimensional motion [47]. Moreover, fluctuations in V,,! also can cause localized states, especially at surfaces [49]. Thus, in a particular case, the character of the electronic excitations are determined [47-491 by the relative values of A = ((en - Q2$$

v= Wnn’)*”

(64

,

(6b)

)

AY= ((V,,f - I’),‘,$$, The orders of magnitudes indicated in table 1.

(6~) of these quantities

for the systems of interest

to us are

Table 1 Orders of magnitude of one-electron parameters describing one-electron excitations in NYmerit, molecular, and covalent solids; their definitions are given by eqs. (4) and (6) in the text A (eV) -__ 0.1-l

V (eV)

AV

10-4-10-3

10-3

Van der Waals crystal

10-2-10-’

10-3-10-2

10-3

Bulk covalent crystal

1o-3-1o-2

Material Aromatic pendantgroup polymer

Dangling bond surface or disordered covalent solid

0.1

1 1

1

(ev)

C.B. Duke /Polymers

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685

The origin of the diversity of electronic phenomena in polymers and molecular solids is immediately evident from table 1 and some form of localization criteria, e.g., that given by eq. (5). For example, it is informative to compare the mechanism of surface state formation in molecular solids with that characteristic of covalent semiconductors (e.g., Si, Ge). Bulk crystalline covalent solids exhibit extended (Bloch) one electron eigenstates because A & V. Fluctuations (Av) in V may occur in amorphous covalent semiconductors, causing localized states to creep up into the -allowed energy bands. Suface states occur on covalent semiconductors because of the large AV- V at the surfaces (a fact which is the formalization in these terms of the concept of a “dangling bond”). In vdW crystals, however, it is A (rather than Av) which can become quite large relative to I’. For bulk crystals this fact indicates that localized states extend well into the allowed energy bands, leading at room temperature to a temperature insensitive drift mobility [50] reminiscent of impurity-band conduction in heavily doped semiconductors [5 11. Moreover, these materials exhibit characteristic localized molecular excitons associated with vibration-assisted singlet absorption [44] as well as resonances in their reflection spectra associated with surface excitons [37]: both phenomena caused by values of A which are large enough to produce localized states. Thus, we see that surface states in molecular solids are caused by surface-induced relaxationenergy fluctuations (i.e., values of A comparable to v) rather than by dangling bonds (i.e., values AVcomparable to V). In addition to revealing a novel mechanism of surface state formation in polymers and molecular solids, table 1 sheds considerable light on the other electronic properties of these materials. Considering vdW solids first, we see that for these materials at room temperature A -En, > V. Consequently, we expect the electronic structure of the molecules to dominate that of the crystal: a result illustrated for S in fig. lb and for a typical organic vdW solid, i.e., TCNQ, in fig. 3a. Indeed, it has been shown [ 1 l] that an accurate molecular orbital model of the electronic structure of the constituents of vdW solids is entirely adequate to describe their room temperature solid-state photoemission spectra. Such calculations for Sa and Sea are compared with observed solid state spectra in figs. lb and 2c, respectively. Table 1 permits us, moreover, to make some important predictions about the transport properties of vdW crystals. The diagonal energy fluctuations, A, emanate from two sources: defects [33] and thermal vibrations [33,42]. For pure, perfect crystals, we envisage a situation in which the contribution to A from defects, Ad, satisfies the inequality Ad < I! At room temperature, however, we anticipate that since 0~ - 60 K the contributions from thermal fluctuations, Ath (300 K), are comparable to V, i.e., A&300 K) - AVth (300 K) 2 V. As the temperature is lowered below BD, these thermal fluctuations are frozen out. Thus, at temperatures T Q BD, the electronic transport in pure, perfect vdW crystals should become bandlike and the drift mobility, p(T), should be considerably larger than that at room temperature. It also should depend more on the microscopic properties of the individual vdW crystals - e.g., their lattice vibration spectra, energy band structures, and scattering centers. This prediction of our model, i.e., sharp, sample-

686

C.E. Duke /Polymers and molecular solids

8

IO 12 14 BINDING ENERGY(eVf

16

(0)

BINDINGENERGY(eV]

f b) Fig. 3. Panel (a): compa~~n of the solid state and gas phase UPS data of 7,7,8,8-tetracy~o-pqu~od~eth~e f 11,181. E designates the shift (to lower binding energy) of the solid-state relative to the gas-phase UPS data. Note the increased broadening of the ionization peaks in the solid-state relative to the gas-phase data. Panel (b): computation of the observed solid-state UPS ionization peak, N(E), of a gas phase line represented by j&IT)which has been shifted in the solid state by an amount AE, = [Eb - (EB - ES) exp(-pn)] for a molecule in the layer a depth nd from the surface, where d is the layer spacing. Contributions from deeper layers are weighted by exp(-an), a = p = 0.5, because of the inelastic collision damping of electrons elastically photoemitted from molecules in these layers [ 331.

dependent increases in ~(7) for decreasing T+4 0 D in ultraperfect crystals, has not yet been verified experimentally [SO]. In the linear-stack charge transfer salts, the values of V increase (relative to vdW crystals) for motion along the stacks. Hence, extended states (i.e., band motion) features more prominently in their room-temperature properties. Nevertheless, the large values of A associated with the vibrational motion of the molecules still have substantial consequences. For example, even for those materials, e.g., UP’)(TCNQ-), for which band motion does seem to occur, strong intramolecular electron-vibration interactions [52,53] create a sharp temperature dependence of the mobility [35]. These interactions also are capable of creating charge density wave instabilities which destroy the one-electron band model: a phenomenon that may occur in (TTF’)(TCNQ-) [54]. Turning to a consideration of the localized-state extreme, we note from table 1 that in pend~t-group polymers, e.g., PS or PMMA, the values of V are quite small for the lowest-energy electron states and hi~est-ener~ hole states because the ?r-electron molecular orbitals characteristic of these states do not communicate efficiently either directly or through the polymer backbone [32,55]. Hence for these materials (A/SOP)> 1 except possibly in highly special cases of single-crystals of isotactic vinyl polymers. Consequently, the electronic excitations are localized on the pendant groups as molecular ions or excitons. The energy spectra of these states can be measured by contact charge exchange spectroscopy 132-341. Typical results for molecular ion states in PMMA and PS [34] are given in fig. 4. They reveal the important facts that such states are responsible for the contactcharge-exchange (i.e., triboelectric) properties of polymers and that these properties depend systematically on the local chemical structure of the pendant groups on the polymer backbone. These results for pendant-group polymers, combined with those for vdW crystals and linear-stack charge transfer salts, demonstrate clearly that eqs. (4)-(6) when applied to describe the behavior of electronic excitations whose characteristic parameters (table 1) were assessed independently [11,26,32,41-43, 46,49,50,52,53], indeed are capable of interpreting the dramatic variations in the electrical behavior exhibited by molecular solids and polymers. We finally arrive, therefore, at the major purpose of this section: the application of our new-found insight to interpret the novel surface electronic properties of molecular materials. The unusual and important feature of these properties is their resulting from surface-induced changes in relaxation energy [i.e., the {en(a)) in eq. (4)f rather than hopping integrals [i.e., the {I$$) in eq. (4)]. In the vicinity of a surface the e, for positive molecular ion states vary with depth from the surface appro~mately as [33,37] ~2) = e$+)(bulk) - D(+) exp(-on)

,

(74

in which D s 0.6En,(inter), p z 0.5, and n is the layer index. Those for negative molecular ion states similarly are given by e$-)=

e$-)(bulk)

+ D(-) exp(-fin)

.

0)

688

C.B.IhA? I ~al~merS nnd ~r~ecul~r solids

BULK STATE DENSITY

( ld9/crn3 /eV)

(0)

-

lo

- i--NOISE I, I 2 4

t, 6

8

I IO

I I2

BULK STATfZ DENSITY

I 14

f 16

tIO”/cm3

f,t 18

20

11 22

E (gallon)

24

kV)

fb) Fi$. 4. ~~~~~~~~~n of iocafized molecular ion states in ~~~y~~e~hy~~~~hacry~a~e~[Panei (a)] and ~~~~s~~~e~ $Panel QI)]. The h~t~~r~s give measu~~ents of these state densities by contact charge exchange whereas the solid curves are Gaussian d~s~r~but~onsfit to the data /33,34]. In both cases the e, are negative numbers (the binding energies of the corresponding bulk molecular ion states). For excitons we obtain a formula like eq. (7b) in which, however, e,{bulk) is a positive quantity, i.e., the bulk maiecular exciton

C.B. Duke /Polymers

and molecular solids

689

energy [37]. These variations in e, in the vicinity of a surface are responsible for the unique surface properties of molecular and polymeric solids. Since no chemical bonds are broken in the formation of the surfaces of such materials, the values of AV are negligible so that the manifestations of dangling bonds, long familiar from covalent solids [29,49], are absent. Perhaps the most obvious manifestation of eqs. (7) is the appearance of surface states when D - V. As noted earlier, this phenomenon has been observed directly for ‘BZu excitons at the (100) surface of anthracene [37]. For one electron states, the observation of such surface states by photoemission will be obscured by the electrons [26,56]. If finite inelastic-collision mean free path, h,,, of photoemitted h,, is much less than the crystal layer spacing, only electrons elastically photoemitted from the uppermost layer are observed, giving rise to an apparent reduction in relaxation energy by D+. This might be called the surface-state limit since only surface states are observed by photoemission. If h,, is much greater than the layer spacing, emission from surface states only adds a small high-binding-energy shoulder to the bulk photoemission spectrum. In practice, however, h,, is typically comparable to or slightly greater than the layer spacing [26,33], leading to a broadening of the photoemission lines by virtue of the occurrence of molecular surface states. Such a result is illustrated in fig. 3b for a model in which the uppermost gas-phase n-electron emission line of TCNQ (fig. 3a) is described by a narrow Gaussian line, &(E), and the inelastic collision damping is taken into consideration by weighting elastic photoemission from the nth layer by exp(-cwz). The construction and numerical manipulation of this model are described elsewhere [33]. In addition, for molecular charge transfer salts the polarization-induced reduction in anion energy plus the smaller Madelung energy [25] at the surface can undo the charge transfer characteristic of the bulk, a phenomena which may lead to excess neutral species at the surface of (TTF+)(TCNQ-) [26,38-401. Finally, the effects of eqs. (7) on the properties of polymer surfaces are not yet well understood [34], due largely to the presently poor state of the characterization of such surfaces. It is evident, however, that the domination of the surface electronic properties of molecular solids by relaxation-energy fluctuations rather than by dangling bonds is a unique and important characteristic of this class of materials.

4. Synopsis Our thesis in this paper has been that the surface properties of polymeric and molecular solids are fascinating and that, consequently, applications of modern Surface Science techniques to characterize molecular materials constitute important new frontiers in Surface Science. The technological importance of the surface properties of such materials is well known [5]. Herein we have focused out attention on a less widely recognized aspect of these materials - the fact that their electronic properties, (including their surface electronic structure) are different in kind

from those of the typical metals and semiconductors toward which surface scientists currently are turning their attention. Specifically, we proposed a conceptual framework [eqs. (4)-(7). table l] for the understanding of the surface and bulk electronic properties of polymeric and molecular solids, and demonstrated that this framework is consistent with the extant data on these materials. Finally, it is the author’s pleasure and privilege to dedicate this modest contribution to Professor Erwin Miiller, whose inventions have changed the face of modern surface science and whose career is an inspiration to his colleagues.

Acknowledgments The author is indebted to L. Kennedy for assistance, to M.M. Shahin for his generous support of this work, to T.J. Fabish, W.R. Salaneck, L.B. Schein, N.O. Lipari, M.J. Rice and A. Paton for their collaboration over the years on the subjects considered in this paper, to J.B. Flannery and J.J. O’Maliey for their enthusiastic encouragement of these studies, and to L.J. Brillson, W.H.H. Gunther, J.S. Miller and J.J. Ritsko for helpful comments on this manuscript.

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C.B. Duke /Polymers and rn#~ec~~rsolids

691

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