ECR study of electron photoemission from gas solids

Physica B 428 (2013) 53–64

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ECR study of electron photoemission from gas solids Yu.A. Dmitriev n A.F. Ioffe Physico-Technical Institute, 26 Politekhnicheskaya Street, St. Petersburg 194021, Russia

art ic l e i nf o

a b s t r a c t

Article history: Received 18 April 2013 Received in revised form 29 June 2013 Accepted 9 July 2013 Available online 17 July 2013

Electron photoemission from rare gas solids (RGS) was obtained using VUV open discharge sources. Temperature dependencies of the photoyield were measured by recording the ECR absorption of free electrons emitted from the RGS surfaces. Two types of photoemission were observed for solid Ne: intrinsic and extrinsic. The first one was attributed to the escape of the electrons photoexcited into the conduction band (CB), while the second one was an exciton assisted emission. In both cases, the electron yield is governed by the surface processes. In heavier rare gases, Ar and Kr, the intrinsic photoemission was found to be sensitive to the trapping of CB-electrons in the bulk. For the solid Ne, doping experiments (He, CH4, D2, CO, O2) revealed that dopant molecules and atoms which have negative or small positive affinities suppress the photoyield by “deteriorating” surface sites active for the electron emission, while impurities with large positive affinities quench the photoemission by scavenging CB electrons in the bulk as well as on the flat surface. Evidence is presented of the transient mobility of CH4 molecules adsorbed on the solid Ne at liquid helium temperatures. & 2013 Elsevier B.V. All rights reserved.

Keywords: Rare gas solids Electron cyclotron resonance Photoelectron emission

1. Introduction. In the electron photoemission or photoelectric effect, electrons are emitted from a substance illuminated by photons above a threshold frequency. To produce an electron, the photon energy should be greater than ϕ+EB, where ϕ, the material work function, is measure of the potential barrier at the surface that prevents the valence electrons from escaping, and EB is the binding energy. Both quantities depend on the substance studied. The process of electron escape is considered as consisting of three steps: the excitation of the electron in the bulk solid, scattering of the excited electron on its path to the surface by the atoms constituting the solid, and transmission through the surface potential barrier. This barrier exists for substances with positive electron affinity when the conduction band minimum is under the vacuum level. However, some substances possess negative electron affinity, so that electrons present at the conduction band can be freely emitted from the surface into vacuum without having to overcome a barrier. It should be noted that electron emission may be caused by low-energy photons in case the substance has been preirradiated with some kind of ionizing radiation. Thus, the electron emission stimulated by 510 nm photons was found from solid Ne preirradiated with an electron beam [1]. The article presents recent findings in the field of cryogenic solids physics focusing on the electron emission from these solids

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subjected to “soft radiation” – vacuum ultraviolet (VUV) photons. Cryogenic condensates of noble gases, Ne, Ar, Kr, Xe, and simple volatile molecular gases, H2, N2, O2, CO, CH4, etc., make up a particular group of cryogenic solids. All their constituent atoms or molecules are stacked in simple crystal lattices bound by extremely weak intermolecular forces. This feature makes them especially attractive for condensed matter theory and there has been a tremendous growth in research of the field with advances in low temperature technique, see [2] and references therein. The above mentioned solid gases are of special astrophysical interest. Theoretical and observational arguments indicate the cycling of dust between dense interstellar clouds where star and planet formation takes place, and the diffuse clouds in the interstellar medium. Small silicate particles that are blown out of cool evolved stars are believed to serve as condensate nuclei for volatile gases at temperatures 10–20 K representative for the dust in the interstellar medium (ISM) [3]. Dust grains produced inside the galaxies and transported into the ISM are composed of either silicate or graphite. Any gas atom/molecule periodically hits a dust grain and may stick with a probability which exponentially depends on the temperature and the physisorption energy. All species, except H2 and He, thus eventually stick on the coldest grains of dense molecular cores [4]. Grains therefore accrete mantles of low volatile compounds. If photoelectric heating is the dominant mechanism, the resulting gas and dust grain temperatures will be higher or lower for the grains covered with mantles as referred to the bare ISM dust grains. Adsorption of noble gases by dust grains is also possible, thus explaining some of the characteristic features of noble gases in meteorites [5].

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Study of electron photoemission from noble gas solids is not only of fundamental scientific interest, but also has the potential to generate knowledge and technologies that can lead to development of new types of measuring instruments. One of the possible applications is a photosensitive material for radiation hard and chemically inert VUV photon solar blind and soft x-ray detectors. In late forties, Davidson and Larsh [6] as well as Hutchinson [7] observed electron conductivity in liquid and solid Ar initiated by nuclear radiation and suggested condensed noble gases as a possible active matter for ionizing radiation detectors. Later, Gullikson [8] measured long escape depth of hot electrons in noble gas solids and put forward a possibility of using these solids as extremely sensitive photocathodes for x-ray detection. These model insulators are the widest band gap materials in nature and their electronic excitation energy ranges up to about several tens eV: 20.3, 13.9, 11.9 and 9.7, for solid Ne, Ar, Kr and Xe, respectively. The wide band gaps as well as large photoelectron yields are of much significance for studies of the sun′s ionizing radiation at wavelengths under 125 nm (9.9 eV). It is well known that the solar spectrum has its maximum radiation intensity in the visible region [9,10]. For the quiet sun, the intensity of the radiation fluxes (measured in quant cm
2 s
1) in the soft x-ray and extreme-UV regions is approximately 7 orders of magnitude smaller than in the visible region. Therefore, in order to investigate variations of solar activity in the shorter-wavelength region, the monitoring should be done by means of detectors with the largest degree of solar blindness [11]. Using of ordinary silicon detectors (or even diamond and cubic boron nitride) implies application of rather large number of film-filters of, e.g., In, Ge, Ti, Al, Be, Sc, C, B. The presence of various kinds of microcracks and microholes is virtually unavoidable in available filters with thicknesses of about 100–1500 nm, and this substantially degrades the optical and mechanical characteristics of the filters [11], or the filters degrade with time under the hard irradiation [12]. Detectors based on the solid noble gases would also be applicable in controlling radiation of VUV coherent sources. In such sources the radiation power of UV pumping lasers is orders of magnitude greater than the effective coherent output power. The detectors on solid noble gases could provide cutting off the phone radiation. Very recently, there is growing interest [13–15] in using solid noble gases as materials for the detection of new weakly interacting massive particles (WIMPs) within the scope of search for Dark Matter, neutrinoless double-beta decay, coherent neutrino scattering. Of the advantages of using solid noble gases as targets for WIMPs is that these targets allow read out 3 signals at a time: phonon, ionization and scintillation. Also they provide more scintillation light, faster drifting electrons, higher ionization yield, no background contamination through circulation loop (no convection mix), possible container-free design, no outgassing issue, less sensitivity to mechanical vibrations [15,16]. Xenon and neon have no long life radioisotopes and thus contain no intrinsic background source of radiation. Among others, electron emission detectors are considered as the most promising detector technology to be employed in the search for exotic particles and rare events in experiments having fundamental significance [17]. Two-phase emission detectors employ condensed (liquid or solid) phases nonpolar dielectrics (in particularly, noble gases) as massive and dense active media interacting with detected radiation. Ionization electrons extracted from the condensed phase are relatively easy to detect within the gas or vacuum as a particular case of gas of low density. Despite the fact that the high electron yield from solid noble gases makes them very attractive in various fields of research and applications, their usage is hindered by insufficient knowledge concerning electron trapping in the bulk of these solids [17] and emission through the surface. In our earlier studies [18,19], an effect has been found that a small gas flow of He provided onto the cold substrate where the gaseous Ne

supplied through a gas discharge tube was condensed suppressed the electron photoemission from the solid Ne. The electron emission occurred from a solidified Ne layer subjected to irradiation from an electrodeless open discharge running in the gaseous Ne. The electron photoemission yield was measured using cyclotron resonance of free electrons (ECR) emitted from the solid Ne. In observing the resonance, we utilized a conventional X-band EPR spectrometer with the cylindrical microwave cavity. The arrangement of DC magnetic field and RF electric field was shown [2,20] to be favorable for ECR line detection with the use of this cavity. The experimental results [18,19] revealed an important role a surface plays in the process of photoelectron emission from noble gas solids. Also we were able to show that the bulk He impurities have negligible effect on the electron emission compared to the surface ones. To gain a better insight into the roles of bulk and surface impurities in the photoemission of free electrons, we tested this process using an impurity with lower ionization potential and readily adsorbed by a sample at liquid He temperatures. The molecular CH4 was utilized as such a probe [21]. The net effect of doping by the CH4 impurity on the photoelectron yield from the solid Ne was that the free electron emission decreased with increasing methane flow rate onto the Ne surface. Though the bulk CH4 impurities were believed to take some part in quenching emission, their influence was not elucidated. The major role was played by the surface CH4 molecules. The atomic He, however, is a particle with very small positive affinity, 0.0054 Ry [22] which is equal 0.073 eV, and the CH4 molecule has large negative electron affinity, Ea ¼–5 eV [23,24]. Thus, despite the affinities of different magnitudes and signs, both He and CH4 impurities turn out to be effective traps in solid Ne, not allowing the electrons to escape into the vacuum. Tentative explanation [25] was that the observed effect could be related to the processes of electron trapping in insulator materials [24,26]. Another explanation [25] for the quenching mechanism of the electron emission by impurities was that the electron affinity of the impurity does not account for the effect, i.e., a surface impurity of any kind may prevent bulk electrons from appearing at the surface. To check this assumption, we carried out experiments with molecular D2 [25]. It is generally agreed that the electron affinity of the H2 molecule is negative, though the exact magnitude is under question. With respect to the electron affinity, the molecular hydrogen is between He and CH4 impurities [25]. The effect of the D2 doping on the electron photoemission from solid Ne was studied at the sample temperatures from 1.5 K to 4.2 K. The results turned out to be unexpected. As opposed to the experiments with He and CH4 impurities the deuterium one yields nonmonotonic dependence of the emission on the impurity concentration. What is more surprising is that the emission shows increase with increase in the dopant concentration. A tentative explanation of the observed effect was presented based on the exceptional properties which the neon–hydrogen solid mixture is believed to have. Thus, with the dopants we have studied so far, the effect of the surface electron trapping takes over the electron scavenging in the bulk. One may suppose that this is due to negative or near zero positive electron affinities of the impurities used. In the present study, we tested oxygen, O2, molecules as the traps in order to elucidate whether the bulk lost of electrons may be the major process governing the yield of photoelectrons. The O2 molecule has a moderate positive electron affinity of 0.43 eV [27,28]. Previously, temperature dependence was found of the ECR signal obtained with solid Ne subjected to the VUV irradiation from open He gas discharge source [29]. The electron yield decreased with decreasing the sample temperature from 4.2 K down to 2.2 K. In the present study, we clear up whether the yield decreasing is due to the peculiarities of the photoelectron formation and loss in the bulk or this effect may be accounted to the efficient adsorption of He atoms on the solid Ne surface at low temperatures [18,19].

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We found earlier that results for the CH4–Ne system [21] and those reported for He–Ne system [18,19] differ significantly in the temperature behavior of the photoemission. Indeed, the Ne–He pair showed faster drop in the photoelectron yield for the 1.6 K samples as compared to the 4.2 K ones, while an inverse situation was observed for the Ne–CH4 pair. As opposed to He atoms, the methane molecules are readily adsorbed on the Ne surface at any liquid helium temperature. That is why we supposed [21] that the observed temperature effect in Ne doped with CH4 could tentatively be explained by changing sample quality at different deposition temperatures, i.e. growing Ne sample with more defects and steps on the surface upon decreasing the substrate temperature. On the other hand, no temperature effect of the kind was observed in Ne doped with D2 [25]. In the present study, check experiments are carried out to elucidate an origin of the temperature effect found previously in CH4–Ne system [21].

2. Experimental The setup and experimental procedure have been presented elsewhere [20,30]. Briefly, they were as follows. The bottom of a quartz finger filled with liquid helium served as a low temperature substrate for the gases being condensed. The bottom was located at the left of the microwave cavity of an X-band EPR spectrometer. The cavity was evacuated and cooled externally with liquid nitrogen vapor providing a cavity temperature from 77 to 300 K. An electrodeless high-frequency (15 MHz) discharge operating in pulsed regime was excited in the gaseous Ne which was passed through a glass tube with an outlet of approximately 0.6 mm diameter. The products of the discharge entered the cavity and condensed on the finger bottom, forming Ne solid. The solid was subjected to the action of the irradiation from the outlet, which, thus, operated as an open discharge source. The electrons emitted from the solid with kinetic energy of approximate 20 meV [20] were captured by magnetic field lines close to the sample surface and eventually returned to the solid. Consequently, in the experiment, we found no degradation of the ECR signal during prolonged runs which verifies that the sample was in neutral state. The additional gas flow (O2, Ne, CO) was supplied to the substrate by a quartz tube inserted into the cavity. The tube was placed outside the discharge zone. The end of the quartz tube was located close (3 mm) to the substrate. Thus two separate channels supplied gases under study to the substrate: the discharge channel and the matrix channel. Both gaseous flows were cooled with liquid nitrogen vapor prior to deposition. The substrate temperature was lowered down by pumping-out the liquid He bath. The temperature of the liquid helium was obtained by measuring the He gas pressure in the bath. The base pressure in the experimental chamber was 2  10–6 Torr. Pure gases were used with the following impurity contents: 0.004% Ne, 0.02% CO (molecular hydrogen and nitrogen being the major impurities), and 0.001% O2. The working pressure of the microwave discharge was assessed as being of some 100 Pa whereas the pressure in the cavity was in the tens of mPa range. The pressure difference was maintained by either small diameter of the outlet or differential pumping provided by both the cold surface of the quartz finger and the set-up pumping facilities.

3. Results and discussion Fig. 1, shows ECR signal intensity, A, open circles, and gas pressure in the microwave cavity pcav, open triangles, for the 4.2 K sample versus pressure p measured at the warm end of the tube

Fig. 1. ECR signal intensity A (open circles), and gas pressure in the microwave cavity, pcav, (open triangles), for the 4.2 K sample versus pressure p measured at the warm end of the tube supplying the gaseous O2 to the substrate. The pressure, p, is proportional to the rate of the O2 impurity gas flow. Fitting curves: red dashed curve suggests a major role of the surface O2 impurities; green solid curve is calculated on the assumption that bulk O2 impurities play a major role in photoemission quenching. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

supplying the gaseous O2 to the substrate. The pressure is proportional to the rate of the O2 impurity gas flow. This warm end was attached to a needle valve which governed p and, hence the He flow. The flow might also be assessed by the gas amount consumed from the storage container. The rate of an impurity gas flow q depends linearly on p [19]. Intensity data are obtained based on the amplitude and width of the ECR resonance. No line broadening was observed in the present study, thus implying that the intensity is proportional to the signal amplitude. Fig. 1 suggests the monotonic decrease in the ECR signal intensity with increasing the impurity gas flow. The effect of the O2 dopant on the photoelectron yield matches that of the previously studied He and CH4 dopants [18,19,21], i.e. quenching electron emission from the sample. Let us test a model which applies well to photoemission from solid Ne quenched by impurity helium and methane [19,21]. We found that most of the A(p) dependence is described by a term as follows: AðpÞ ¼

b1 1 þ c1 pd1

ð1Þ

Eq. (1) was obtained under the assumption that the surface impurity particles play the major role in quenching photoemission. The fitting procedure gave a best value of d1 close to 2. An analysis of the value of d1 led to the conclusion that the electrons escape the sample from special regions on the surface near the lines where two Ne planes cross, and these regions are, possibly, atomic step sites (step edges) on the Ne surface which are responsible for the sample growth. We now apply Eq.1 with d1 ¼2 to fit the experimental data for photoemission from solid Ne quenched by O2 impurities. Red dashed curve in Fig. 1 presents a result of the fitting procedure which suggests that we arrive at no reasonable agreement between theory and experiment. Next we test the bulk effect. If q is the rate of free electron production in the bulk, k is a rate constant which pertains to trapping these electrons by O2 impurities, and k1 is a rate constant for the electron loss through emission from the surface, then, in the steady-state condition q
knN
k1 N ¼ 0

ð2Þ

Here N is the free electron concentration in the bulk, and n is the O2 concentration.

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Hence, the A(p) dependence can be written in the form AðpÞ ¼

a2 1 þ b2 p

ð3Þ

with constants a2 and b2 to be obtained in the fitting procedure. The above dependence plotted in Fig. 1, green solid curve, fairly well matches the experimental data. Another model deals with surface O2 impurities, suggesting that the electron emission into the vacuum proceeds from the Ne surface free of adsorbed O2 molecules. Let Sfree and Soccup be the surface areas which are free of adsorbed O2 molecules or occupied by these molecules, respectively. It is reasonable to assume that Sfree/Soccup is proportional to pNe =pO2 , where pNe is the gaseous Ne pressure in the cavity and pO2 is the oxygen pressure: Sfree p ¼ γ Ne Soccup pO 2

ð4Þ

Here γ is the proportionality coefficient. Taking into account that Sfree+Soccup ¼const, one concludes
 pO2
1 Sfree  1 þ ð5Þ γpNe Based on the suggestion that A and pO2 are proportional to Sfree and p, respectively, we again come to the above A(p) dependence, Eq. (3). Therefore both bulk O2 impurities and those on the flat surface are responsible for quenching electron photoemission. Possibly, the O2 molecules located at the atomic step sites are also responsible for the quenching of the electron photoemission, though, their contribution (if only) is too small to be discriminated by the above analysis. Previously [21] we found a faster drop in the photoelectron yield for the 4.2 K CH4 doped Ne samples as compared to the 1.6 K ones. The observed temperature effect of the photoelectron emission was tentatively explained by changing sample quality at different deposition temperatures. We suggested that low deposition temperature led to larger number of steps on the Ne surface and that more CH4 flow was necessary to block emission occurring, as we supposed, from these steps. Interestingly, in a paper by Khizhniy et al. [31], the temperature stimulated luminescence (TSL) and temperature stimulated exoelectron emission (TSEE) from solid Xe pre-irradiated by low-energy electrons were also found to be sensitive to the sample deposition temperature. The authors pointed out that the effect is explained with growing number of lattice defects on lowering deposition temperature. It was also found that TSL and TSEE from solid Ne pre-irradiated with an electron beam are sensitive to the sample structure which depends on the sample deposition temperature and prehistory [32]. In the present study, we undertook experiments with the discharge running in gaseous Ne while additional Ne gas flow was supplied to the substrate avoiding the discharge zone. We measured ECR signal intensity versus the rate of the additional Ne flow, while the flow through the discharge tube was set constant. It is believed that the condensate structure is sensitive to the value of gas flow condensing on the low temperature substrate [33,34]. The greater the quantity of gas is provided onto the low temperature substrate, the smaller is the size of crystallites [33] and larger number of steps appear on the condensate surface. Fig. 2 shows ECR signal intensity, A, open circles, and gas pressure in the microwave cavity pcav, open triangles, for the 4.2 K sample versus pressure p measured at the warm end of the tube supplying the additional gaseous Ne to the substrate. The pressure is proportional to the rate of the additional Ne gas flow. At low and moderate rates, the ECR intensity remains unaltered. The figure, therefore, suggests that the density of steps at the Ne surface is not a factor which governs the photoelectron yield. At large rates, an increase in the signal intensity follows an

Fig. 2. ECR signal intensity A (open circles), and gas pressure in the microwave cavity, pcav, (open triangles), for the 4.2 K sample versus pressure p measured at the warm end of the tube supplying the additional gaseous Ne to the substrate. The pressure is proportional to the rate of the additional Ne gas flow.

abrupt increase in the gas pressure in the cavity, Fig. 2. The same effect was observed in Ne doped with D2 [25]. It is reasonable to suggest that the extra emission comes as a thermally activated process triggered by the heat of condensation at large gas flows [25]. Previously, we considered [25] a maximum temperature gradient through the sample thickness which happens because of the heat of condensation loaded on the sample surface at maximum deuterium flows. The heat resistance of the quartz finger bottom was shown to be much larger than the resistance of the condensate. We estimated the temperature gradient for the 1 mm thick D2 solid film to be ΔT≈0:4 mK, while the gradient through the bottom thickness amounted to 0.2 K. Because of similar physical properties of D2 and Ne solids, the above estimates hold true for the latter one also. With so moderate an averaged surface heating at hand, we believe that the thermally activated electron emission comes from some surface regions with high enough temperatures which happen to exist because of the nonuniform temperature distribution across the sample [25]. One could suppose that the overheating of these surface regions is due to the lattice relaxation of the quench condensed gaseous Ne. Our previous findings [20,29] may also be considered as an additional support to the suggestion that growing number of the surface steps has no effect on the photoelectron yield from CH4 doped Ne at the lower temperatures. Fig. 3 shows ECR signal intensity versus substrate temperature. The discharge was running in the gaseous Ne while no gas was supplied through the tube avoiding the gas discharge zone. The figure suggests no reliable ECR signal growth with decrease in the sample temperature below 5 K. As a result, we come to the conclusion that the possible fine crystallinity of the sample could not explain the temperature effect found in CH4 doped Ne [21]. In order for a methane molecule to be trapped at a step edge site, the molecule should have nonnegligible diffusion path length at the terrace site of the surface where condensation occurs. One may suppose that the temperature effect under study has something to do with a temperature dependence of the molecule diffusion path length upon adsorption at low temperatures. 4 Let us estimate the binding energy, ECH , of the interaction b between the CH4 molecule and flat neon substrate. A reasonable assumption is that the binding energy is proportional to the Ne–CH4 pair interaction potential. Let ε be the depth of the potential well. The well-known empirical mixing rule by the Lorentz–Berthelot, see, for example, Layer et al. [35], gives the depth of the potential well, εAB, for two different interacting

Yu.A. Dmitriev / Physica B 428 (2013) 53–64

Fig. 3. ECR signal intensity A (open circles) versus the substrate temperature. The discharge was running in the gaseous Ne while no gas was supplied through the tube avoiding the gas discharge zone.

particles, A and B, in the form involving the geometric mean of the depths of the involved pure substances, that is, pffiffiffiffiffiffiffiffiffi ð6Þ εAB ≈ εA εB where εA and εB are the depths for A–A and B–B potentials. Based on εNe ¼ 3:6 meV [36], and literature data on the methane potential depth, εCH4 ¼ 147:94 K¼12.7 meV [37] and εCH4 ¼ 160:3 K¼13.8 meV [38], we obtain εNeCH4 to be 6.8 meV and 7.0 meV, respectively. These results are not far from the binding energy of 0.22 kcal/mol¼9.5 meV calculated by Zhao and Truhlar [39] for the CH4    Ne weak interaction complex. Next, we base our 4 estimate of ECH on the binding energy of 3He on the solid Ne b He surface, Eb ¼ 37 K, see [40] and references therein. As a result we get 4 ECH ≈ b

εNeCH4 He 6:8 37 ¼ 132 K E ¼ 1:9 εNeHe b

where εNeHe ¼ 1:9 meV [36]. For a thermalized molecule, the time for hopping between terrace sites
 E ð7Þ τh ðTÞ ¼ τ0 exp b ; 2T where T is the surface temperature.  132  11 132 Then, ττhh ð1:6Þ ¼ exp 21:6
24:6 ¼ 1:23  10 . This result implies ð4:2Þ drastic difference between the ECR intensities recorded at the two temperatures for the CH4 doped Ne. However, the experimental results suggest [21] that equal attenuations of the ECR signal at different sample temperatures correspond to methane flows which differ only by eight times. One reasonably assumes that the same would be true for the probability of the methane molecule adsorption on the step edge. Thus, we conclude that the experimentally observed effect is attributable to the surface diffusion of the non-thermalized CH4 molecules. The process of adsorption of atoms and molecules on surfaces is typically divided into three parts: (1) collision with the surface, (2) trapping, and (3) sticking [41]. A trapped adsorbate can exist in a mobile weakly bound state prior to accommodating its excess energy to the surface and sticking at a specific adsorption site. If the surface temperature is sufficiently high, thermal diffusion of the adsorbed species will occur. A second type of adsorbate motion is a transient mobility [42]. Transient mobility is adsorbate motion (at temperatures below the thermal barrier to diffusion) due to the energy of adsorption, the incident kinetic energy upon

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adsorption and/or the energy released in an exothermic surface reaction. Theoretical and experimental studies have differed on the length and time scales over which energy accommodation takes place and thus have led to the controversy over the existence of transient mobility [42]. Ferris et al. have shown [42] that benzene molecules adsorbing onto a Ni{1 1 0} crystal at 4 K do not stick at their initial site if they impinge upon the surface within a critical distance of a step edge. Benzene molecules impinging upon the surface within four nearest-neighbor distances of a step edge ( 10 Å for the Ni{1 1 0} surface) move towards and bind to the step edge. Egelhoff and Jacob [43] reported clear reflection high energy electron diffraction (RHEED) oscillations while monitoring metal epitaxy on metal fcc(0 0 1) surfaces, at temperatures as low as 77 K. Strong oscillations have been found at 77 K for all systems studied by that time, including Cu and Fe on Cu(1 0 0) and Ag, Cu, Fe, and Mn on Ag(1 0 0). The oscillation evidenced layer by layer like growth. This effect was unexpected because at 77 K adatom diffusion is supposed to be totally frozen. A possible explanation was offered by the authors: the condensation energy gained by bringing the impinging atom on the surface was somehow transformed into kinetic energy of the adatom, allowing for fast surface diffusion even when the substrate temperature was way too low to overtake any of the relevant barriers. Weiss and Eigler recorded real-space images of Xe atoms on a 4 K Pt{1 1 1} surface [44]. In the dilute coverage limit, they found nearly all the Xe atoms at step edges. From this observation they deduce a lower limit of hundred of angstroms that Xe atoms scatter across the surface before becoming thermally accommodated. Low-energy atomic impacts on the Ag(1 1 0) surface were investigated by molecular dynamics simulations based on reliable many-body semiempirical potentials [45]. Trajectory deflections (steering) caused by the atom–surface interaction were observed, together with impact-following, transient-mobility effects. All the above discussion refers to the atoms and molecules in the ground electronic state. This type of the surface motion of adsorbed atoms and molecules was also revealed in our previous experiments. Earlier we carried out an EPR study of the process of matrix isolation of nitrogen atoms in solid N2 by condensing N/N2 mixture from the gas phase [46]. We have shown that the surface recombination of the nitrogen atoms is mostly governed by the diffusion of nonthermalized atoms. In an EPR study of matrix isolated species condensed onto the low temperature substrate from the methane gaseous discharge [47], we found out that large part of the surface CH3 radicals recombine due to the surface diffusion prior the thermalization of the molecules. The process occurs even at the methane surface temperature as low as 1.5 K. Previous experiments on the solid Ne subjected to the irradiation of the open discharge running in gaseous He [29] suggest that the photoelectron yield is temperature dependent decreasing with decrease of the sample temperature. Fig. 4 shows the intensity of the ECR signal versus sample temperature (adopted from Ref. [29]), A(T). Figs. 3 and 4 evidence that, for samples below 4.2 K, the temperature behavior of the photoelectron yield from solid Ne depends on the light source used in the sample irradiation. This finding raises a question: could the difference originate from different mechanisms underlaying photoemission from solid Ne, or it owes to adsorption of He atoms at the Ne surface at low temperatures. Indeed, we have found previously [18,19] that a helium gaseous flow supplied to the substrate decreases an electron emission from solid Ne kept at 1.6 K. The emission was excited by the Ne open discharge source. Fig. 5 shows intensity of the ECR signal plotted against a flow rate of the gaseous He supplied to the substrate through the tube avoiding the discharge zone, A(p). Given A(T) and A(p) experimental data, Figs. 4 and 5, we may plot the p(T) dependence. If the helium adsorption is the major

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Fig. 4. ECR signal intensity A (open circles) versus the substrate temperature. The discharge was running in the gaseous He while gaseous Ne was supplied through the tube avoiding the gas discharge zone (adopted from R.A. Zhitnikov, Yu.A. Dmitriev, Excitation energy transfer from the metastable excited He 23S1 atom to the neon cryocrystal. J. Phys.: Condens. Matter, 6, 1994, pp. 2721–2138).

Fig. 5. Decrease of an amplitude of the ECR signal upon increasing He flow to the substrate at 1.6 K. The electron emission from solid Ne is excited by an open discharge running in gaseous neon. The fitting curve accounts for adsorption of He atoms on the solid Ne surface. (From Ref. [19]).

mechanism responsible for the emission quenching, p(T
1) would be fairly well fitted with exponential curve. This is because p is proportional to the surface concentration of He atoms [19], while the concentration itself depends on  the adsorption time of He atoms on the solid Ne, τa ¼ τ0 exp ETb . The result is shown in Fig. 6. The figure suggests that the derived lnðpðTÞ=pð4:2ÞÞdependence is not well enough fitted by linear function. Moreover, Eb ¼12 K obtained in fitting procedure is much less than that of 3He on the solid Ne surface: 37 K [40]. Thus, we conclude that while the decrease of the photoelectron yield with decreasing sample temperature, Fig. 4, may be attributable in part to more efficient adsorption of He atoms at lower temperatures, the effect for the most part comes from the process of photoexcitation of the solid Ne by the helium discharge light source. Low-pressure helium discharge generates very high light intensities in the vacuum UV at certain resonance wavelengths. The HeI (58.43 nm equivalent to 21.22 eV) line was found to be the most intense [48,49]. It falls almost exactly within the band of the n¼4 exciton in solid Ne [50]. Table 1 lists energy positions of excitons in

Fig. 6. Based on the data presented in Figs. 4 and 5, a dependence p (T) is derived in assumption that the ECR signal quenching, Fig. 4, is attributable to the increase of He adsorption on the Ne surface with lowering sample temperature. Here p is proportional to the concentration of He atoms on the solid Ne surface. Dashed line is an attempt of linear fitting the experimental data.

solid Ne obtained from transmission data. The energy of the photon is between ETh ¼20.3 eV and EG ¼ 21.58 eV, where the former is the threshold for photoelectron emission (vacuum level), while the latter is the band gap. Pudewill et al. reported an experimental study of the photoelectric yield of pure and doped solid Ne in the extreme ultraviolet (ℏω ¼ 8
30 eV) by use of synchrotron radiation [51]. They measured intrinsic photoemission above threshold and found that the energy dependence of the photoelectric yield exhibited a pronounced structure in the energy region E¼20–21.5 eV as well as a sharp rise of the photoemission yield in the energy range above 21.5 eV. It can be obtained from Fig. 3 [51] that one of the maxima in the yield exhibited at 21.2 eV which corresponds to the energy position of the n¼4 exciton, Table 1. Another HeI (53.70 nm equivalent to 23.09 eV) line may markedly contribute to the electron yield because the appropriate photon energy corresponds to the maximum of the yield curve [51]. According to Ref. [49], the 53.70 nm line intensity is two-fifth of the intensity of the 58.43 nm line, while the ratio for these oscillator strengths was reported to be 1: 3.8 [52]. However, Paresce et al. [53] found in their studies of the He continuous discharge that the intensity of the 58.43 nm line is one order in magnitude larger than that of the 53.70 nm one. Vorburger et al. [54] observed that when a microwave discharge source was operated with He gas, the only significant features in the emission spectrum were those due to the HeI 21.22 eV line and the HeII 40.81 eV line. The contributions from other principal lines in He were negligible. The authors informed also that at the HeII maximum the intensity of the emission from the d-band feature for HeII radiation is about 1/16 of that for HeI and about 1/55 of that for HeI at a lamp pressure of 250 Pa (1.88 Torr). In solid rare gases, after the maximum at E≈EG , the photoemission line shape exhibits a minimum at the photon energies of approximately 2EG, in Ar and Kr, and of ≈E1, in Xe. Here E1 is the energy of the n ¼1 exciton. The minimum was assigned to the electron–electron scattering [55]: as the photon energy is increased, the primary electron can excite a valence electron to the bottom of the conduction band at E ¼ 2EG . Interestingly, the minimum occurs for solid Ar matrix with negative electron affinity EA ¼
0.3 [55], as well as for Kr and Xe with positive EA of 0.3 and 0.4, respectively [55]. The solid Ne electron affinity was measured to be negative, EA ¼
1.3 [56]. The threshold energy ESC for electron–electron scattering was experimentally assessed by different methods. The scattering onset is given by ESC ¼EG+E1 when an excited valence electron in the

Yu.A. Dmitriev / Physica B 428 (2013) 53–64

59

Table 1 Energy positions of excitons in solid Ne from transmission data [50]. Here, n is for the principle quantum number and j is for the momentum of the hole. n

1

j Energy position (eV)

3/2 17.36

2 1/2 17.50

3/2 20.25

3 1/2 20.36

3/2 20.94

4 1/2 21.02

3/2 21.19

5 1/2

3/2 21.32

1/2

Table 2 Energies, wavelengths, and relative intensities of the He and Ne discharge photons most contributing to the electron photoemission from solid Ne. The relative intensities are taken from handbook by Sansonetti and Martin [49]. The table compares the line intensities for each element separately. The relative intensities are not basic data, depend upon the light source, excitation conditions and must be taken with caution [49] (see the text for details). Photon energy (eV) Wavelength(nm) Spectrum Relative intensity

20.14 61.56 NeI 170

20.95 59.18 NeI 70

21.02 58.99 NeI 30

21.22 58.43 HeI 1000

conduction band is inelastically scattered to the bottom of the conduction band by exciting another valence electron to the n¼ 1 exciton state [56]. A difference in the threshold could be expected from a process corresponding to a recapture of a primary electron by one of the holes and the subsequent decay into two excitons on photoabsorption experiments. In this case ESC would be smaller, ESC ¼ 2E1. Then, one obtains for solid Ne 2E1 ¼34.72 eV, EG+E1 ¼38.86 eV, 2Eg ¼43.00 eV [56]. The 40.8 eV lines which are most intensive of the HeII radiation are close to the electron–electron scattering threshold in solid Ne and fit, thus, the expected minimum of the photoemission line shape. Moreover, comparison of the 21.22 eV HeI and 40.8 eV HeII photon fluxes reported in the literature [54,57,58] shows that the latter one is 1–3 orders below the former one, making negligible contribution to the photoemission from solid Ne. In order to understand the difference in the temperature dependence, Figs. 3 and 4, of the photoemission caused by irradiation from open Ne and He discharge sources, we next analyze significant features in the Ne emission spectrum and compare those to the ones in the He spectrum just described above. Based on the data by Sansonetti and Martin [49], 61.563 nm NeI line fairly well falls into the n¼2(3/2) Ne absorption band, while 59.183 and 58.991 nm NeI lines fall into n¼3(3/2) and n¼3(1/2) bands, respectively. The Ne discharge emission spectrum contains also very intense NeII lines which correspond to the photon energies above the threshold for photoelectron emission. Paresce et al. [53] measured NeII irradiation close to 46 nm to be one order in magnitude above the NeI lines near 59 nm and markedly larger in intensity compared to the 61.6 nm NeI line. The 46 nm emission turned out to be as intense as the well known, most intense 73.6 nm NeI UV line. Masoud et al. [59] studied vacuum ultraviolet emissions from a cylindrical dielectric barrier discharge (C-DBD) excited by radio frequency power at 13.56 MHz in pure Ne in the 60–90 nm region. The most prominent VUV emissions that were observed from low-pressure Ne plasma (10 Torr) were the Ne resonance lines at 73.59 and 74.37 nm. The spectrum in Fig. 2 of the paper [57] shows no signs of 61–62 nm emission lines thus testifying their low intensity. In Ref. [57], the most intense Ne discharge spectrum lines were found those of NeI at 73.59 and 74.37 nm, and NeII lines at 46.07 and 46.24 nm. Also emission at 41 nm contributed markedly to the spectrum. One, therefore, believes that weak NeI lines which fall into the exciton bands make only small contribution to the photoelectron yield from solid Ne, while the major effect comes from the NeII overthreshold irradiation. Contrary to the Ne discharge, the He discharge provides strong light emission which enables the electron ejection through the sample excitation into the exciton bands. This inference is supported by the above different temperature dependences of the photoelectron yield

23.09 53.70 HeI 400

26.82 46.24 NeII 500

26.92 46.07 NeII 1000

30.46 40.71 NeII 120

30.55 40.59 NeII 150

40.81 30.38 HeII 1000

under the action of the open Ne and He discharges. Thus, in the case of Ne discharge the usual intrinsic photoemission above the threshold, i.e., E4ETh, takes place. When the solid Ne sample is subjected to the action of the He discharge in the excitonic range En ¼ 1 ≤E≤ETh , the extrinsic photoemission occurs. Here extrinsic means that the photoemission process is mediated by energy transfer of the exciton to the boundary from where a photoelectron is released. Table 2 lists energies, wavelengths, and relative intensities of the He and Ne discharge photons most contributing to the electron photoemission from solid Ne. In various studies of the photoelectron yield from RGS, the extrinsic photoemission is attributed to the exciton diffusion to the gold substrate (the emitter electrod) followed by electron ejection from the electrode. It is also believed that the extrinsic photoemission may originate from exciton-induced impurity photoionization. However, in some investigations, the effects from a substrate and impurities were analyzed and their contribution to the photoemission was shown to be negligible. O′Brien and Teegarden [60] measured the photoelectric yield for thin films of xenon and krypton subjected to the light irradiation from 7.5 to 11.7 eV. Emission was observed below threshold in both materials. Because of the reason that no impurities were optically observed in the films, they concluded that, in the above region of the spectrum, the emission occured after interaction of the excited states of the crystal with a defect left. The authors suggested no model of the defect lefts. Pudewill et al. [51] examined different mechanisms of the extrinsic photoemission from solid Ne. They excluded the impurity effect and electron ejection from the electrode. Ionization of excitons at the insulator-vacuum interface was favored as an explanation for the extrinsic photoemission. Kraft et al. [61] found photoconductivity in solid Kr samples after excitation of the Kr bulk and surface excitons. They discussed possible mechanisms by which free charge carriers can be produced though only bound charge carrier states have been excited. The authors excluded diffusion to the electrodes and explained the finding under the assumption of a Poole–Frenkel effect in the electrical fields produced by surface charges generated during the irradiation. Since the experimental technique applied in the present study involves no metal substrate and makes use of thick sample films, one believes that the measured photoemission yield has nothing to do with the substrate ionization through the energy transfer process. Direct photoemission from the impurity states above the impurity threshold as well as the exciton enhanced ionization of the impurities in the bulk cannot also be considered as a serious possibility of the extrinsic photoemission. Indeed, in such a way one could not expect the different temperature dependencies for

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Yu.A. Dmitriev / Physica B 428 (2013) 53–64

the extrinsic and intrinsic photoemission yields because originally free electrons appear in the conduction band of the bulk in both processes. Moreover, almost all our experiments with doped solid Ne showed degradation of the photoemission yield with increase in the impurity content. This effect was observed using such dopants as He, CH4, O2, CO. Fig. 7 shows ECR signal of free electrons emitted from solid Ne subjected to the action of the open Ne discharge source. The sample temperature was 4.2 K. Additional gaseous CO flow was passed to the substrate avoiding the discharge. The dopant pressure at the warm end of the matrix channel is identified by numbers at the top of each record. We suggest also the possible contribution to the yield of surface charges through the Poole–Frenkel effect to be negligible. Indeed, the surface charges cannot accumulate in our experiment because the surface of the growing sample renews constantly. One, thus, comes to the conclusion that the extrinsic photoemission in the “solid Ne–He discharge” experiments originates from ionization of excitons at the insulator-vacuum interface due to the negative affinity of solid Ne. The n ¼4 exciton in solid Ne can be described in terms of the hydrogenic Wannier–Mott exciton model based on the effective mass approximation. This simple model has been applied successfully to describe the n≥2 states in pure rare gas solids [56]. The exciton radius can be calculated from rn ¼

ε0 n 2 μ

ð8Þ

where ε0 is the static dielectric constant and μ is the reduced effective mass of the exciton 1 1 1 ¼ þ μ me mh

ð9Þ

with me and mh as effective mass of the electron and hole, respectively. The radii obtained for the n ¼1 Ne states are 1.17 Å (j¼3/2) and 1.19 Å (j¼1/2) [62]. Based on Eq. 8, the radius of the n ¼4 exciton can be estimated as 19 Å being far above the nearest neighbor distance in solid Ne of 3.156 Å. The exciton, thus, is free to move through the crystal. Previously, the Wannier–Mott excitons were found to be the dominant source of photoelectron emission from negative electron affinity diamond for near band gap excitation up to 0.5 eV above threshold [63,64]. The authors concluded that the exciton-derived emission must result from exciton dissociation at

Fig. 7. ECR signal of free electrons emitted from solid Ne subjected to the action of the open Ne discharge source. The sample temperature is 4.2 K. Additional gaseous CO flow was passed to the substrate avoiding the discharge. The dopant pressure at the warm end of the matrix channel is identified by numbers at the top of each record. The high-field line of the N-atom EPR triplet gives an idea of how the ECR amplitude decreases with increasing impurity concentration in solid Ne.

the diamond vacuum interface. Despite of the fact that a significant component of the total photoabsorption is the excitation of the “free” conduction band (CB) electrons, they observed no contribution from the CB of diamond to the total electron yield from threshold to hv¼ 6.1 eV. The mechanism responsible for quenching of CB emission was attributed to band bending and/or wave vector conservation. Upwards band bending at the surface produces an electric field which repels CB electrons, yet has little effect on uncharged carriers such as excitons [63,64]. The indirect band gap of diamond has implications for the escape probability of CB electrons since the electron emission from a perfect surface requires, in addition to conservation of energy, conservation of the component of the electron wave factor (k//) in a direction parallel to the emission surface [63,65]. In this case momentum tangential to the surface is conserved while normal momentum is altered by interaction with the crystal as a whole. It is believed that this may be quite generally true whenever clean surface of high perfection can be produced [65]. The conservation laws require that the magnitude of the negative electron affinity be large [63,64]. This consideration suggests that CB electrons are hindered from electron escape. Moreover, the wave factor of the emitted electrons should have a large k// component. It was found, however, that the angular distribution of the observed emission was directed along the surface normal with a broad angular width [64]. The authors suggested that extrinsic effects, such as surface roughness, could play an important role in the emission phenomena. Our observation of the electron photoemission from solid Ne reveals some striking similarities in the emission peculiarities between the diamond and Ne. Indeed, having analyzed our data on the emission yield versus impurity concentration [19,21] we came to the conclusion that the probability of the electron escape from the perfect Ne surface (terrace site) is rather low and the majority of the yield comes from electrons which escape the sample from atomic step sites (step edges). Thus, the surface roughness, indeed, plays a role. One could suggest now that some of the electrons having the wave vector perpendicular to the surface readily escape the sample, while emission of electrons which have momentum components parallel to the surface is hindered. The latter electrons travel in solid Ne along the surface for some distance before reaching the step edge. As a result, these electrons having, thus, the momentum perpendicular to the step edge are capable of escaping the sample. The electrons traveling under the surface are partly trapped by shallow and deep traps or recombine with positive ions. Frankowski et al. [66] found electrons in the shallow traps in solid Ne located at the sample top layer of 10– 20 μm. In our experiment, new layers of solid Ne appear again and again during condensation. That is why the surface traps cannot be saturated, while the trapped electrons appear eventually in the bulk and, hence, are lost for the emission. These processes of the electron scavenging result in that some (possibly, the most) part of the CB electrons reaching the sample surface provide no contribution to the emission yield. Because of the strong temperature dependence of the photoelectric yield, Fig. 4, one would suggest that the exciton assisted emission due to the HeI 58.43 nm irradiation is far above the emission of the CB electrons due to the HeI 53.70 nm irradiation. Moreover, we have found that the ECR signal intensity in the “solid Ne–He discharge” experiment is at least an order of magnitude above the intensities in “solid Ar (Kr)–He discharge” and “solid Ne–Ne discharge” experiments. This observation corroborates the suggestion about high efficiency of the photoemission driven by irradiation into the Ne exciton bands by He discharge VUV light. The effect of the impurity-induced quenching of the electron emission found in Refs. [19] (He), [21] (CH4), and the present study (CO), may be very tentatively attributed to the possible upwards band bending upon impurity adsorption on the step edges.

Yu.A. Dmitriev / Physica B 428 (2013) 53–64

In order to understand the temperature dependence of the photoyield found in the “solid Ne–He discharge” experiment, Fig. 4, we consider a three-step model [64,67] consisting of (a) bulk excitation, absorption of light generates photoexcited carriers; (b) transport of the carriers to the surface region; and (c) escape of the electrons from the surface into the vacuum. The general case for the photoelectric emission from solid Ne under the excitation from the He open discharge source is when the emission occurs as the result of both electron and exciton transport to the surface. Following Ref. [64], we allow, in such a case, for two independent transport and escape steps to describe the behavior of excitons and electrons respectively. The total electron yield is given by the sum of the two components Y ðhν; T Þ ¼ ∑Y i ; where Y i ¼ P i ðhν; TÞ

Li ðhν; TÞαi ðhν; TÞ 1 þ Li ðhν; TÞαðhν; TÞ

ð10Þ

Here, i – excitons or electrons, αex ðhν; T Þ and αel ðhν; T Þ the absorption coefficient for transitions in which the final state lies in the exciton or conduction bands, respectively. The total absorption coefficient will be sum of these two: αðhν; T Þ ¼ αex ðhν; T Þ þ αel ðhν; T Þ. Li are the carrier diffusion lengths which should be a property of the bulk crystal, and Pi is surface escape probabilities. First we consider whether the temperature dependence of the position of the n ¼ 4 exciton band in solid Ne may effect markedly the absorption of the HeI 58.43 nm line. Previously, the temperature dependence of the shape of the resonance band Γ(3/2) was found in solid Xe [68,69]. The resonance luminescence spectrum shifts towards lower energies with increase with temperature (the temperature coefficient is 0.7 meV K
1). To the best of our knowledge, similar effects have not been reported for other rare gas solids, suggesting that the dependence (if any) in those cryocrystals is more subtle than in Xe. However, if one assumes that the temperature coefficient for Ne is approximately that of Xe than the lowering of the sample temperature by 2 K, Fig. 4, would provide the band shift towards the higher energies by only 1.1 meV, which is far below the n ¼1 band width of 200 meV [50]. For the n≥2 exciton states Saile and Koch [50] estimate the half-widths of roughly 100 meV. In the weak coupling approximation, the kinetic energy of exciton is determined by its mass mex_¼me_+mh, and hence the half-width of the exciton band along the Γ-direction for ℏ2 π 2 excitons with n≥2 can be estimated as BexEMA ¼ 2m 2 eV [62,70]. ex a Then, for Ne, one obtains mex ¼m0+4.7m0 ¼5.7m0, BexEMA ¼ 0.3 eV [62,70]. Thus, the possible temperature shift of the absorption band in solid Ne cannot affect the absorption coefficient and, hence, cannot account for the observed temperature dependence of the photoelectric yield, Fig. 4. Next, one may suppose that the decrease of the photoelectron yield is due to temperature dependence of the exciton diffusion length. For the migration of free excitons, two limiting cases of energy transfer should be considered. (A) The limiting situation for weak exciton-lattice coupling involves coherent transfer characterized by the exciton group velocity. This idealized state of affairs is not realized in real life as exciton-scattering mechanisms due to phonons, structural imperfections, etc., prevail even in pure crystals [56]. Coherent exciton transport should be envisioned in terms of a mean free path Λ, which considerably exceeds the lattice spacing a, i.e., Λca. (B) Incoherent exciton transport occurs when the exciton scattering by phonons, disorder, etc., is strong, and the exciton mean free path is comparable to the lattice spacing Λ≅a. Exciton transport is now characterized by a diffusion coefficient D which is related to the diffusion length ℓ by ℓ ¼ ðDτÞ1=2 where τ is the exciton lifetime [56]. The weak or strong scattering

61

character is reflected in the exciton absorption lineshape. The experimental absorption spectra for n ¼1 excitons in Ar, Kr and Xe reveal a linewidth of 80 meV, while for the excitons in solid Ne the width is of several hundreds meV (see discussion above). The increase of the linewidth for Ne presumably reflects the transition from the weak scattering limit in Ar, Kr, and Xe towards the strong scattering situation [56]. Saile and Koch [50] point out that the estimate of roughly 200 meV for the widths in solid Ne is in favor of localized-exciton states (strong-scattering case). It is believed, however, that in case of Ne, the situation is still on the verge of weak scattering [56]. In any event, the exciton transport in Ne is incoherent and characterized by a diffusion coefficient D. The kinetic parameters of an exciton in the case when the energy transfer is realized by free excitons in the process of their diffusion motion arising from phonon elastic scattering was analyzed in Refs. [62,69]. It was shown, for the case of thermalized (thermal) excitons and in the limit of T 4 2ms2 ;

ð11Þ

that the free exciton diffusion path length, lph ðTÞ, varies as T lph ðTÞ ¼ vk τph ðTÞ ¼

4ℏs ; 3λT


1

ð12Þ

where s is for the longitudinal sound velocity, λ is a dimensionless scattering parameter, τph(T) is for the diffusion time, and ms2 is a measure of the kinetic energy of the lattice vibrations. The diffusion characteristics τph(T) and lph(T) describe the exciton motion in a crystal in the form of a wave package with group velocity vk. For Ne, 2ms2 ¼ 1.58 K [69] and, hence, the condition (11) is met. The diffusion path length of the thermalized excitons is independent of the wavenumber, Eq. (12). Of particular importance is the process of energy transfer by non-thermalized (“hot”) excitons. It was shown [62,69] that for non-thermalized excitons with high wave-vectors the diffusion coefficient appears to be independent of temperature and exciton wave-vector. However, when the temperature is sufficiently high the value of lph is given [69] by the same formulae (12). Thus, in general, the exciton path length in solid Ne is expected to increase with decreasing the sample temperature and, therefore, cannot account for the observed temperature dependence of the photoelectron yield, Fig. 4, which thus to be attributed to the exciton ionization at the sample surface. The photoabsorption penetration depth, 1/α, of solid Ne is [51] 33 Å at 17.5 eV (n¼1 exciton state). The absorption coefficient greatly decreases for larger photon energies. In the exciton band n¼4, the absorption depth can be estimated from Fig. 1 Ref. [51] as about 600 Å. Diffusion length, L, for free n¼ 1, 1′, 2 excitons in solid Ne was measured to be 25007500 Å [51,56]. It is interesting to note that the quantitative analysis of the extrinsic photoemission from solid Kr shows a pronounced energy dependence of the diffusion length [56]. The diffusion length rises from L≅30 Å in the low energy tail of the n¼1 exciton to L≅300 Å for the n¼2 exciton. A question is discussed as to whether this monotonic increase of the length does reflect a transition from incoherent strong scattering motion at low energies to coherent motion at higher energies. In solid Ne, smaller scattering is also expected to occur for high energy excitons which may result in diffusion lengths greater than 2500 Å. One concludes then that the Lα product appreciably exceeds unity, so the three-step model, Eq. (10) reduces to Y ¼ P ex ðhν; TÞ

ð13Þ

Thus, the above consideration of the absorption and diffusion characteristics confirms the suggestion that the observed temperature dependence of the photoelectron yield is governed by the process of the exciton ionization at the solid-vacuum interface.

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The fact that the impurity He has no effect on the photoyield is further evidence that the nature of the photoemission observed in the “solid Ne–He discharge” experiment is not that of the photoexcited CB-electron-transport to the surface. It is believed that, in solid Ne, the excitons with n≥2 promptly relax into the lower n¼1 free exciton state. The electronic relaxation time from the initial state of the n¼2 exciton to the first order excitonic state is estimated to be ∼10
13 s. On the other hand, the large diffusion length of the n¼2 exciton testifies that the high energy excitons have large velocity and large enough life time to diffuse long distances in the solid. Hirayama and Arakawa [71] studied desorption induced by electronic transitions in the RGS by selective excitation of valence excitons. They subjected solid Ne to VUV irradiation spanning from 55 nm to 75 nm. Measuring time-of-flight spectra of desorbed metastable Ne atoms at exciton wavelengths corresponding to the bulk B2 (n¼ 2) excitons, the authors found an additional shoulder in the higher energy side in the B2 spectrum. This shoulder was suggested to be a contribution of Nen in the 2p54s state. This finding evidences that the n¼2 exciton does appear at the surface before relaxation to the n¼1 state. Inoue and co-authors reported observation of the visible luminescence which corresponds to the transition between 3p and 3s free excitons in solid Ne [72]. Kloiber and Zimmerer [73] studied desorption of neutral Ne atoms following selective excitonic excitation of solid Ne by VUV photons. They found the crucial role of excitons concerning transport of excitation energy from the bulk to the surface, and the microscopic desorption mechanism itself. The highly excited n¼ 4, 4′excitons contribute markedly to the total desorption yield, while they play only a minor role in desorption of metastable (3P2, 3P2) and excited 3P1 atoms [73]. On the contrary, the excitation into the n¼1, 1′bands of the solid Ne accounts for the major part of the partial desorption yields of the above atoms. Thus, one concludes that the free excitons in n¼4, 4′ reach the surface before being converted into the lower n¼1, 1′ states. The process of the exciton ionization at the solid-vacuum interface is not known in detail. It is generally agreed that because of the dipole nature of the surface-vacuum interface and the polar nature of the electron–hole pair, one may reasonably expect strong exciton-lattice coupling, which results in phonon emission during excitation breakup at the surface [64]. Electron-emitting exciton breakup then becomes a many-body problem with emission of not only a free electron, but also multiple phonons and a hot hole. The temperature dependence of the solid Ne phonon spectrum may be responsible for the observed temperature dependence of the photoyield in the “solid Ne–He discharge” experiment. In the “solid Ne–Ne discharge” experiment, the CB electrons are the major carriers. The VUV NeII 46 nm and 41 nm photons from the Ne discharge incident on the solid Ne sample excite CB electrons with energies 27.0 eV and 30.2 eV, respectively. These values are far below the threshold energies of the electron– electron scattering in solid Ne. In that case, the electron mean free path is of very large value. Escape length of electrons in solid Ne was estimated to be ≈3500 Å [51], i.e not less than the diffusion lengths of the excitons. The absorption coefficient of the solid Ne at photon energies above 25 eV shows only slight dependence on the photon energy [74] and the penetration depth may be estimated for the NeII lines as close to 300 Å [53]. Again, the three-step model, Eq. (10) reduces to surface effects, Eq. (16): Y ¼ P el ðhν; TÞ

ð14Þ

This inference is in line with the observation of the photoelectron emission in experiments on doped solid Ne [18,19,21,25]. 4. Conclusion Study of the electron emission property of solid Ne finds that the photoemission from pure Ne is governed by the surface

processes. The effect is due to the exceptionally large path lengths of free excitons and CB electrons in the bulk. Comparative study of the temperature dependencies of the photoelectron yield in the “solid Ne–Ne discharge” and “solid Ne–He discharge” experiments revealed two different mechanisms, intrinsic and extrinsic, responsible for the electron emission in these experiments: escape of the electrons photoexcited into the conduction band, in the former one, and exciton assisted emission, in the latter one. The intrinsic emission from solid Ne shows no temperature dependence in the range 2–4.2 K, while the extrinsic one is temperature dependent: the photoyield is found to decrease with decreasing sample temperature. Our previous studies show an effect which sample temperature has on the photoelectron yield in “solid Ar–He discharge” and “solid Kr–He discharge” experiments [75,76]. The threshold energies for photoelectron emission, 13.9 eV and 11.9 eV, in pure Ar and Kr, respectively [56], are far below the photon energies of the most intense HeI VUV lines at 58.43 and 53.70 nm. Hence, intrinsic photoelectron emission takes place in these systems. The electrons are, thus, promoted into the conduction band upon absorption of the discharge light by the solid Ar and Kr samples. Apart from the case of intrinsic photoemission in solid Ne, the photoyield from Ar and Kr subjected to the action of the He discharge rapidly increases with decrease of the sample temperature. The measurements were performed in the temperature ranges, for Ar, 1.9–4.2 K, and, for Kr, 2.2–4.2 K [75,76]. The temperature dependence of the ECR signal intensity can be fairly well fitted by a liner function A(T)/A(T0)¼
a(T
T0)+b. Here, T0 is 1.9 K and 2.2 K for Ar and Kr, respectively, while a and b constants were obtained in the fitting procedure. The electron mean free paths for the electron energies below the threshold for the electron–electron scattering are about 1000 Å in pure Ar and Kr solids [74]. The scattering onset was reported to be, in Ar, 24.5 eV [77], and, in Kr, 20.5 eV [77] and 21.5 eV [78]. Thus, the CB electrons generated under the photoexcitation from the VUV He discharge source are expected to travel long distances in Ar and Kr. The photoabsorption penetration depth, 1/α, at the relevant photon energies can be estimated from the absorption coefficient [77] as, for Ar, 200 Å, and, for Kr, 120– 170 Å. One would suppose, therefore, that the surface processes are predominant in the photoemission from solid Ar and Kr as well as they are in the case of solid Ne. In respect of the surface processes influencing the electron ejection, solid Ar might be suggested to behave similarly to solid Ne because of the negative electron affinity of both cryocrystals: for Ne,
1.3 eV, and for Ar,
0.3 eV [56]. With lowering temperature, the adsorption of He atoms increases which results in the drop of the photoelectron yield in the “solid Ne–Ne discharge” experiment with doping He. However, the opposite temperature dependence of the yield is observed in the “solid Ar–He discharge” experiment, which correlates with the dependence found in the “solid Kr–He discharge” experiment. We suggest that, in solid Ar and Kr, the temperature dependence is actually governed by the transport properties of these solids for the CB electrons. Indeed, the solid Ne is known to demonstrate the largest electron escape length of hot electrons in a solid [51]. The electron transport properties of the rare gas solids were compared in Ref. [56]. Hot electron current from an Au substrate was plotted versus thickness of the RGS overlayer. For the layer thicknesses above 50 Å, Ar, Kr, and Xe show gradual but considerable decrease in the yield, while the yield from Ne keeps constant. The decrease of the yield in the heavier solid gases was attributed to trapping of electrons at grain boundaries, at dislocations and at impurities. Because of the lowest melting temperature of Ne, 24.6 K, as compared to those of Ar, 83.8 K, and Kr, 116.0 K, the Ne condensate is of greater structural quality, i.e. has a much lower density of imperfections than Ar and Kr obtained at the same liquid-helium temperatures

Yu.A. Dmitriev / Physica B 428 (2013) 53–64

of a substrate. In our experiments all gases were condensed on the 4.2 K substrate. In Refs. [51,56], the Ne thin films were prepared by condensing the gas onto a gold substrate at 5 K, while Ar and Kr films [56,77] were obtained at the gold substrate temperature of 10 K. Thus, the Ne deposition temperature [51,56] was close to that of the present experiment, while the Ar and Kr ones were sufficiently higher. One would suppose, therefore, that the Ar and Kr samples used in the present study have greater density of structural imperfections and, hence, reveal shorter electron escape length compared to the solids studied in [51,56]. Indeed, in an EPR study of H atoms trapped in quench-condensed Kr films [79], we have found that samples obtained at the substrate temperature of 6.5 K are markedly more disordered than samples deposited at 10.5 K. Thus, in our Ar and Kr experiments, the condition Lel ðhν; TÞαðhν; TÞc1 is, probably, not fulfilled and the transport of the CB electrons may contribute to the temperature dependence of the photoelectron yield in these solids through the elastic and inelastic electron–phonon scattering. Solid rare gases have only acoustics phonons with energies smaller than 10 meV. Because of the small energy losses for emission of acoustic phonons in the electron-scattering event, the scattering only increases the path of the electron to the surface in a random walk process [77]. With increasing path, the probability of trapping electrons at the defects of the cryocrystal increases, thus decreasing the escape depth. Earlier Gullikson [8] studied hot-electron diffusion lengths in thin films of Ne, Ar, and Xe. Measurements of the secondary-electron escape probability have been used to determine the escape depth. The electrons were generated with X-rays. Surprisingly, the diffusion length for Ar turned out to be very short compared to that value for Ne and close to the diffusion length for Xe: 0.45 μm, 25 μm, and 0.23 μm respectively. In Xe, the electron lifetime (the lifetime of an electron before it is trapped) could be the time required for a hot electron to lose enough energy so that its kinetic energy drops below the Xe positive electron affinity. However, for both Ar and Ne the electron affinity is negative. The author suggested that trapping at defects limited the electron lifetime for Ar. The suggestion was confirmed by the observation of effects of the film growth temperature on the escape length: films grown at lower temperatures had shorter diffusion lengths. The present experiment with CO doping corroborates our previous finding that impurities with negative electron affinity, Ea, hamper the electron emission. Fig. 7 shows large suppression of the photoelectron yield from solid Ne which occurs upon increasing gaseous CO, Ea ¼
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