Comments are made on the model of electron injection into SiO₂ proposed by Berglund and Powell. Their assumptions on electron scattering, disregarding the change of the escape cone with the distance from the emitter, lead to serious underestimation of the injected current. Two alternative models of electron injection, based solely on elastic scattering are discussed and do not predict the experimental results. We suggest that observed field dependence of the injected current into SiO₂ indicates that energy relaxation associated with the injected electrons is responsible for the voltage dependence of the current

Silver, M.

Smejtek, Pavel

PDXScholar (Portland State University)

Portland State UniversityPDXScholarPhysics Faculty Publications and Presentations Physics10-1-1971Comment on Electron Scattering in the Image Potential WellPavel SmejtekPortland State UniversityM. SilverLet us know how access to this document benefits you.Follow this and additional works at: http://pdxscholar.library.pdx.edu/phy_facPart of the Physics CommonsThis Article is brought to you for free and open access. It has been accepted for inclusion in Physics Faculty Publications and Presentations by anauthorized administrator of PDXScholar. For more information, please contact pdxscholar@pdx.edu.Citation DetailsSmejtek, P., & Silver, M. Comment on Electron Scattering in the Image Potential Well. J. Appl. Phys. 43, 2451 (1972).COMMUNICATIONS 2451 maximum if one electrode, say at x = 0, is blocking, since charge compensation by carrier transport in op-posite directions is prevented. Integration of Poisson's equation, with P=O, gives aD[O, to, T(to)] = - a;: [1 -xld]p[x, to, T(to)] dx<S. (8) In view of Eq. (7) one has Q = aD. Therefore, the fro-zen-in charge, as defined by Eq. (1), is always smaller than the net volume charge. Q might be vanishingly small. Charge inj ection and trapping in an isotropic medium having an intrinsic Ohmic conductivity a(T) gives i=IlP*E+aE, where p* is the concentration of free charge and 11 is the carrier mobility. If, at one temperature, a is sufficiently high, IlP*la«l, i=(JE, and J=O in view of Eqs. (4) and (5). While III a might be independent of T, IlP* I a is not, since p* depends on detrapping time which is a function of temperature. Therefore, the above inequality might be fulfilled at one temperature but not at some other where one would have J '* O. Any asymmetry, like heat-ing in a temperature gradient or unequal distribution of traps, makes a dependent on x and thus prevents J from becoming zero. In the absence of retrapping and of macroscopic hetero-geneities of structure capable of creating a spatial asymmetry, charge release from a si.ngle trapping lev-el produces small external currents because currents to opposite electrodes compensate eaeh other. 7 Only if carriers have been trapped in asymmetrically filled multiple levels does one record significant charge values in the external circuit. It can also be shown that such a system is not charge invariant. lB. Gross and L. F. Denard, Phys. Rev. El6, 26 (1944); C. Bucci and R. Fieschi, Phys. Rev. Letters 12, 16 (1964). zB. Gross, J. Electrochem. Soc. 115, 37El (1968); Appl. Opt. Suppl. 3, 17El (1969); Northern Electric Co. (Canada) Report No. TO 145, 1970 (unpublished). 3R. Gerson and J. H. Rohrbaugh, J. Chern. Phys. 23, 12 4(1955); M.M. Perlman, J. Appl. Phys. 42,2645 (1971). J. van Turnhout, Polymer J. (Japan) 2, 173 (1971). 5G. Jaffe, Ann. Physik 16, 217 (1933); 16, 249 (1933). 6B. Gross, An. Acad. Brasil. Ci. 17, 219> (1945); H. Kallmann andR. Rosenberg, Phys. Rev. 97, 1596 (1955). 7J. Lindmayer, J. Appl. Phys. 36, 196 (1965). Comment on Electron Scattering in the Image Potential Well* M. Silver and P. Smejtek University of North Carolina, Chapel Hill, North Carolina 27514 (Received 22 October 1971) Comments are made on the model of electron injection into SiOz proposed by Berglund and Powell. Their assumptions on electron scattering, disregarding the change of the escape cone with the distance from the emitter, lead to serious underestimation of the injected current. Two alternative models of electron injection, based solely on elastic scattering are discussed and do not predict the experimental results. We suggest that observed field dependence of the injected current into SiOz indicates that energy relaxation associated with the injected electrons is responsible for the voltage dependence of the current. Recently, Berglund and Powell l reported on the field dependences of photoinjected carriers into Si02 • Exper-imentally, the current was found to be proportional to exp( -xml"A), where x m= (e/4€.E)1/2 is the position of the maximum in the potential due to the image and applied field. In order to explain these results, Berglund and Powell assumed that only those electrons which are emitted within the escape cone at the electrode and which reach the maximum in the potential without mo-mentum exchange scattering, or which remain in this small cone after scattering, can contribute to the cur-rent. This assumption which does yield a current pro-portional to exp( - xm/"A) is not correct theoretically, be-cause it does not take into account the fact that the escape cone increases rapidly with distance. Conse-quently, the model seriously underestimates the cur-rent. Figure 1 illustrates how the escape cone varies as a function of distance. An examination of Fig. 1 shows that electrons originally in the small escape cone at x = 0, if scattered at a dis-tance x away from the electrode, have a reasonably large probability of remaining in the escape cone and, therefore, these electrons are not returned to the cath-ode. Also, electrons outside the small escape cone at x = 0, but with enough momentum to reach x, may be scattered into the large escape cone at x. Because of this argument, we conclude that agreement between the Berglund and Powell model and experiment is acciden-tal. The problem including the change of the escape cone has been treated by Young and Bradbury. 2 They show that . . [lLw (x)dX l x dx' ] J=J. 1- --- exp -- w(x') , • 0 "A l!tJ'S' 15 0 "A l!tJ'S' EI (1 ) where j; is the injection current from the emitter; the probability of return is 1 [ ( rp(x) )1/2J w(x)=2 1- Em+rp(x) forx;~xm' and where rp(x) is the height of the remaining barrier at x, Em is the excess energy of the electron over the barrier in the absence of an applied field, and 15 is the polar angle of scattering. J. Appl. Phys., Vol. 43, No.5, May 1972 Downloaded 21 Sep 2012 to 131.252.4.4. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions2452 COMMUNICATIONS 2 _______ !S.i~e-.!.!~ __________ _ + 5 10 15 20 25 30 35 40 45 50 0 __ ------- x(A) .2 Potential > .4 ~ ,., 2' ., c: W c: 2 U ., w 1.2 1.4 1.6 (a) <J<J()()OO Escape Cone (b) FIG. 1. (a) Energy diagram for electrons injected into image potential well near a metal-insulator surface. (b) The escape cone for electrons having an average energy of + O. 2 eV as a function of x for a scattering event at x. The barrier height is 2 eV. Notice how rapidly the escape conoe increases with x. An electron scattered, for example, at 20 A has much greater probability of remaining in the escape cone than an electron scattered at x= O. The Young and Bradbury model which is based on elec-trons experiencing only momentum exchange scattering is not satisfactory either because it is essentially a single-scattering model. Calculations of the current using the correct image and applied potential in Eq. (1) yield a current practically independent of applied electric field E and A over a wide range. For example, a current cal-culated to result from the injection of l-eV electrons into the medium with A= 100 A is about 3% of the in-jected current for 70 < xm < 700 A. One might argue that a correction to the Young and Bradbury model might give j -exp( - Xm!A) if one in-cluded multiple momentum exchange scattering and no energy relaxation. This calculation has not been tried but should give similar results as a solution to the dif-fusion equation when the mean free path (MFP) is very small. In order to show the inadequacy of purely diffu-sive and field-driven motion, for the explanation of the experimental results, 1 we have solved the continuity-of-current equation for a very simple model potential. To make the problem as easy as poSSible, yet keep the main feature that there is a barrier of finite magnitude and extent, we have chosen the potential shown in Fig. 2. In region 2, we assume a small field so that the con-centration of carriers is constant and they have an aver-age kinetic energy of %kT at xm ' In this case the current follows the simple Thomson picture, 3 and (2) where E2 is the electric field in region 2. To specify the current j, we must solve the continuity-of-current equa-J. Appl. Phys., Vol. 43, No.5, May 1972 tion in region 1. In region 1 we assume only momentum exchange scattering, and therefore j = - D(x)1E - n /11 (x )E1 ; (3) the boundary condition at x = 0 is jt = in(O)v(O) + j, (4) where j I is the injection current from the electrode, v(O)=[(2!m)(%kT+eE1x m )]1/2, and El is the electric field in region 1. The diffusion coefficient and the mobility are functions of x because the kinetic energy is a fune-tion of x in region 1, i. e. , D(x)= k(x)..\ and /1(x) = eA! mv(x), where v(x)= {(2!m)[%kT+ eEI(xm _X)]}1/2. Equation (4) can now be solved, yielding i= [1+ v(O) (kT+teEIXm)3/2 +!%kT+eE1x m jl 4ilzE2 kT 4 eEIA (k T + teEIXm _ 1 )J-l x\ kT ' (5) which is approximately equal to (6) As is obvious, Eq. (5) does not yield an exponential of the form exp( - Xm!A) and, therefore, the assumptions regarding the importance of momentum exchange scat-tering are not justified. In a similar experiment using hot-electron injection from a tunnel cathode into liquid helium, Silver et al. 4 and Onn and Silver5 also experimentally obtained a cur-rent proportional to exp( -Xm!A). They proposed a model involving rapid energy relaxation in the region of xm ' In this case A is the diffusion length of the hot electrons during their thermalization time and not the MFP for momentum exchange scattering. This model applies at low temperatures or at very short energy relaxation times, Electron energy Electron potential energy ® FIG. 2. Energy diagram for electrons inj ected into a hypothetic potential well near a metal-insulator surface. Downloaded 21 Sep 2012 to 131.252.4.4. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsC OMM UNIC ATIONS 2453 We submit that energy relaxation is also a reasonable assumption to explain the experimental results obtained by Berglund and Powell, and therefore they are not deriving the MFP for momentum exchange scattering, but rather a factor proportional to (O"pO"/)-1/2, where O"p is the cross section for momentum exchange scattering and 0"/ is the energy relaxation scattering cross section. We wish to thank Professor Martin Pope of New York University for calling our attention to the paper by Berglund and Powell. *Work supported by the Army Research Office, Durham, N. C. IC.N. Berglund and R.J. Powell, J. Appl. Phys. 42, 573 (1971) . 2L.A. Young ani N.E. Bradbury, Phys. Rev. 43, 34 (1933). 3J. J. Thomson and G. P. Thomson, Conduction oj Electricity Through Gases (Cambridge U. P., Cambridge, England, 1928), p. 466. 4M.Silver, D.G. Onn, P. Smejtek, and K. Masuda, Phys. Rev. Letters 19, 626 (1967). 5D.G. Onn and M. Silver, Phys. Rev. 183,295 (1969); D.G. Onn and M. Silver, Phys. Rev. A3, 1773 (1971). Sputtering of Iron by Fast Neutrons T.S. Baer and J.N. Anno University of Cincinnati, Cincinnati, Ohio 45221 (Received 30 August 1971; in final form 13 January 1972) The atomic sputtering by fast neutrons incident upon a thin iron foil target was determined by measuring the activity of radioactive iron atoms collected during continuous exposure of the target to a fast neutron flux of 4. Ox 1012 neutrons/cm2 sec. The sputtering ratio (atoms of iron sputtered per fast neutron crossing the surface of the target) was found to be (5.7 ± 0.8) x 10-3, assuming an isotropic neutron flux. This paper reports the measurement of sputtering from the surface of an iron target exposed to fast neutrons. The experimental technique was similar to that used in a previous study of the sputtering from a gold target. 1 The radioactive Fe59 atoms produced by the thermal-neutron (n, y) reaction with Fe58 were collected on alu-minum-covered quartz plates located near the iron tar-get and, from the measured activity, the sputtering ra-tio was determined. The apparatus used for the sputter-ing-ratio determination is sketched in Fig. 1. The over-all length of the evacuated quartz tube containing the experimental components was 14 cm. The collector plates, consisting of high-purity Spectrosil quartz with an approximately 500-A-thick 99.9999% pure aluminum coating, were 5 cm in diameter and 0.16 cm thick. The target was a 3-mil-thick (0. 0076-cm) iron foil, with 1 cm2 of exposed surface area. The collector plates were spaced 1 cm apart. With this geometry essentially all sputtered atoms are collected. The quartz tube was evacuated to 10-6 Torr and posi-tioned adjacent to the core of the Battelle Research Reactor for a six-day irradiation. The average thermal neutron flux was determined from the activation of the target foil to be (8.96 ± O. 50)x 1012 neutrons cm2 sec. From this measured flux and the known time of exposure (six days), the fraction of the sputtered atoms in the form of Fe59 was determined. Aluminum, nickel, and iron cadmium-covered foils (threshold detectors) were used to determine the fast neutron flux. The data were fit to a proton-moderated integral fast neutron spec-trum, resulting in a fast flux determination of (4.0 ± O. 4) x 1012 neutrons/cm2 sec above 0.1 MeV. From the mea-sured Fe59 activity on the collectors, the fraction of the sputtered atoms in the form of Fe59 at the end of irradi-ation, the counter efficiency, and the decay time be-tween irradiation and counting, the total number of atoms sputtered was determined. The sputtering ratio A was then determined from (1) where Ns is the number of sputtered atoms, Cp, is the fast neutron flux, S is the iron target surface area, and t is the irradiation time. An ordinary polycrystalline iron target was used. Earlier experiments with gold showed only a small effect of target crystallinity on the sputtering ratio. 2 After a decay time of approximately fi.ve weeks after the irradiation (to allow for the decay of short-lived radioisotopes), the sputtered atoms and the aluminum covering on the two collector plates were removed by washing in a heated 6N HCI bath. AppJrOximately 10 mg of iron carrier was added to the soluti.on from each plate and the iron was precipitated from the solutions by the addition of concentrated ammonium hydroxide. The preCipitates were then centrifuged, washed, and slur-ried into steel planchets for drying. Alter drying, the planchets containing the sputtered atoms were counted by a Ge-Li detector for 8x 104 sec eaeh and the result-ing spectrum was analyzed to determine the quantity of iron sputtered to the collector plates. The Fe59 activity found on the primary collector (the plate opposite the target) was 8.86 ± 0.58 diSintegrations/sec as deter-mined by the 1. 29-MeV decay y of Fe~,9 and 7. 75±0. 45 diSintegrations/sec as determined by the 1. lO-MeV de-cay y of Fe59, where the activities have been corrected for the decay time from the end of the irradiation to the time of counting and for counter efficiency. An average of the two values was taken as the iron activity. The Fe59 activity found on the secondary collector was 9.36 ± 0.70 diSintegrations/sec (1. 29-MeV y) and 9.37 ± 0.55 diSintegrations/sec (1. 10-MeV y). The activities of the two plates being nearly equal indicates a sticking frac-tion for iron on aluminum of apprOximately O. 5. 1. Appl. Phys., Vol. 43, No.5, May 1972 Downloaded 21 Sep 2012 to 131.252.4.4. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

Comment on Electron Scattering in the Image Potential Well

Crossref

http://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1122&context=phy_fac

Comment on Electron Scattering in the Image Potential Well

Abstract

Similar works

Full text

Available Versions

PDXScholar (Portland State University)

Crossref