Two-dimensional electrons on the helium film—solid neon system

Two-dimensional electrons on the helium film—solid neon system

Surface Science I 13 ( 19X2) 4 19-422 North-Holland Publishing Compnny TWO-DIMENSIONAL NEON SYSTEM Received I4 July I9X I : accepted ELECTRONS fo...

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Surface Science I 13 ( 19X2) 4 19-422 North-Holland Publishing Compnny



I4 July I9X I : accepted


for publication


26 Augwt


Tw-dimensional electrons on thin films of helium adsorbed on solid neons arc atudicd. It i.\ shown that electrons are atably trapped on the film. moving with high mobility. When the film i\ thin. the electron mobility is governed by gas atom scattering and aurfacc roughncas scattering At a moderate film thickncas. a dccrrase of the mobility was observed. which may be interpreted in terms of a “polaron”. an electron with surface deformation.

Electrons on a helium film constitute a two-dimensional system similar to those on the bulk liquid helium, but with some differences as follows. (i) Since the image force on an electron from the substrate is strong, the bound level for the electron on the film is deep compared with that on the bulk liquid helium [ 11. (ii) For an appropriate region of film thickness, the strong image force may cause localization [2], a more drastic change in the electronic state. This localization is caused by the self-trapping of an electron in a small dimple of the helium film and will be called a “polaron” in analogy to the case of small polaron in ionic crystals. (iii) The accessible electron density for this system is much higher [3] than that for bulk liquid helium 2 X 109/cm’. The stable existence of electrons on helium film was pointed out soon after the discovery of surface electrons on the bulk liquid helium [4]. However. no experimental investigation on such a system has appeared in the literature up to date. In this paper, we report our experiment of the electrons on helium film realized in an electron-helium film-solid neon system [5]. It is shown that electrons are stably trapped and move with high mobility on the helium film. The experimental set up is shown in the inset of fig. 1. Solid neon is grown by the Bridgman method. The solid surface is located l-2 mm above the lower electrode. After the neon crystal is prepared, the whole system is immersed in the liquid helium bath, and helium gas is introduced into the vessel. The number 8 of the helium film layers adsorbed on a solid surface is known to depend on the gas pressure P as d3 =D[Tln(P,,/P)]-‘, 0039-6028/82/0000~0000/$02.75

0 1982 North-Holland

where P,, is the saturated vapor pressure, T the temperature measured in K and D is a constant which depends on the substrate [6]. For neon, D is a number of a few tens, though the accurate value is not known. The principle of the mobility measurement is the same with that in ref. [7]. Electrons are fed from a tungsten hot cathode. An ac electric field of 100 kHz is applied on one of the upper electrodes and in phase and out of phase components of the signal are detected at the pick-up resistor R. Electrons once bound were found to stay on this system for hours in spite of the disturbance due to the evacuation or feed of the helium gas. When the electron density is below a critical value, which depends on the roughness of the neon surface, we could not detect the signal of electrons. Thus, the measurements were performed at an electron density above this critical value. The electron mobility is measured at liquid helium temperatures as a function of the helium gas density N,;. The typical charge density studied is about 7 X 10X/cm’ with attracting electric field of 1000 V/cm. In fig. 1. we show the mobility p as a function of NC; for electrons on several neon crystals at 4.2 K. The effect of changing N,; is two-fold: change in the film thickness and in the density of scattering centers for electrons. While the experiment in

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I. Electron mobility agaimt the gas pre~surc (gas density) for several neon crystals at 4.2 K absolute value of mobility is estimated by magnetoresiatance at a point indicated in the figure. solid line shows the mobility due to gas atom scattering. The inset is the electrode arrangement the measurement.

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fig. 1 covers a wide range of No, the change in the film thickness is small, because in this region where P/PO =Z 0.4, the film is only one or two layers thick. Thus, the behavior of mobility is considered to be dominated by the change in the scattering due to gas atoms. to the inverse of the For No below 2 X tOZ’/cm”, p--r which is proportional scattering time 7, is expressed as p -- ’ tJy.q--’ ’ =: q; 1 + q 1,


q; “Ap, where 7,; represents the scattering time due to gas atoms and 7s which is independent of NCj is due to the surface roughness. We found that 7Cidepends only on N,; and is independent of the temperature. The value of 7r; is about l/3 of that for electrons on the bulk liquid helium. Saitoh [S] gave an expression for the scattering time 7o for two-dimensional electrons as 7; = 1.47 x lo-l3





where Lris the range of the electron wave function normal to the surface. For an electron on a very thin helium film over the neon crystal, b is estimated to be about 19 A while it is about 78 A for b&k liquid helium [I J_ This gives rise to the value of Q which is smaller by a factor 19/78 ^c lj4 compared to the case of electrons on bulk liquid helium. Thus, the experimental results in fig. 1 can be well interpreted in terms of eq. (2) with the additional scattering due to the surface roughness. When A& is increased above 2 X 102*,/cm3, p deviates from the relation of eq. (1) decreasing rapidly. This is considered due to the formation of bubblelike states, a two-dimensional analogue of the state observed in the threedimensional electron helium gas system. Fig. 2 is the ~1versus No curve at T = 2.02 K. In the gas pressure below 20 Torr, where the film is only one or two layers thick, p is well represented by eq. (1). In the vicinity of the saturated vapor pressure, there appears a region where interesting structures appear in the curve. With increasing P, the mobility first rises and after having a maximum, it drops to l/4 of the maximum value. Then, it rises again steeply. Since ni, is neariy constant Through this region, the structures should be ascribed to the change in the film thickness which grows with increasing P. When the film becomes thick, ft in eq. (2) increases from 19 to 78 A. Then, the mobility will increase with film thickness approaching the value for the bulk liquid helium. The steep rise of p at the highest pressure region is ascribed to this mechanism. The problem is the low mobility dip. It is possible that the electron-ripplon scattering becomes very strong in this intermediate region because of strong image force on the electron. A more fascinating interpretation of this phenomenon is the forma-

tion of a polaron, an electron with surface deformation. Whether the polaron is stable or not is determined by the balance of the image force on the electron. surface tension of the helium film and Van der Waals force on the helium film from the substrate. Then polaron will be possible in a region of appropriate film thickness [9]. VVe could not observe the mobility drop above the X transition temperature. However, it may be because a unifornl film is hard to attain in this temprrature region.