J . Phys. Chem. 1989, 93, 5717-5721
5717
Particulars on all parameters appearing in this equation can be found in ref 2. The quantities ai(JTK) are the coefficients of expansion of the asymmetric top rotational eigenfunctions IJTM) in the chosen (either oblate or prolate) symmetric top basis set (1JKM):K= -J, ...,J). The subscripts on these coefficients indicate that the rotational eigenstates of the ground and excited electronic states will in general be different due to differing rotational constants. The four rotational symmetry species (++, +-, -+, and - in Dennison’s notation)38 are distinguished by restrictions on the properties of the ai coefficients, and through them, the radiative f(Jb J I , J’l, 703 TI. 7’1) = selection rules are implicitly contained in eq B2. Specifically, only C C D ~ ~ ( L I ) ( @0,, o)(-I)Jo+JI+J’I+KI+K”I+K’~+~I+QI+Q~even or only odd K terms that are either symmetric or antisymqiq’iqz4’i LI KIK‘IK‘’IK”‘IK~~‘o metric in K may contribute to the eigenstates of a given species. x (2 J 0 + 1)(2JI + 1)(2J’I + 1)(2L1 + l)ao(JoroKo)ao(Jo~oKb~ X These properties of the ~ ( J T Kenable ) one to prove that for ara, (JlrlKl)al(J’,7’1 K ; ) a l (JIrl K”l)al(J’IT’]K”’J X bitrary dipole directionsf(Jo, J , , J’l, T ~ T,, , T’,) and f ( J o , J’l,J , , T ~ T,’ ~ T, ~ are ) real and equal. (This is a generalization of the relation given in ref 2 for dipoles along principal axes.) This fact ensures that I is real and modulated solely by cosine terms. It has also been used to advantage for the efficient evaluation of eq 1 1 191 KO -K’l J; 9’1 1 K’o Jo)x 9’2 - 92 -4‘2 92 BI. Registry No. Ar, 7440-37-1; Ne, 7440-01-9; He, 7440-59-7; He,, 12184-98-4; fluorene, 86-73-7; trans-stilbene, 103-30-0; anthracene, 120- 12-7.
its thermal population. Within the brackets is a summation over all pairs of excited-state rotational levels that are reached via excitation from a given ground-state level. Each such pair gives rise to an interference term that is modulated at a beat frequency proportional to the energy difference between the levels. y is the radiative lifetime of the excited state. The dependence of the intensity on time and temperature are shown explicitly in the three exponentials. Only the angle between the excitation and detection polarization vectors is important and appears in the expression for the Fourier amplitudes of the interference terms:
)(
”)(
Line Shape in Normal Metal Tunneling Spectroscopy K. W. Hipps* and Susan Leenov Peter Department of Chemistry, Washington State University, Pullman, Washington 99164-4630 (Received: January 23, 1989)
The variation of line shape in inelastic electron tunneling spectroscopy (IETS) with temperature and modulation voltage is studied. Only normal metal tunneling is considered. Tunneling spectra were obtained from junctions of the type AI-A1203-KSCN-M, where M, the top metal, was Pb or T1. The data presented cover the temperature region from 4 to 77 K. The experimental variation in line shape with modulation voltage ranging from 1.5 to 30 mV is also reported. A simplified line-shape function (Gaussian) is shown to satisfactorily predict line widths and peak intensities over a wide range of experimental conditions. The half-width at l / e height of a single line is given by A, where A = [ ( a l k T ) 2+ + 1 ’ 2 ] 1 / 2a,l = 3.3, a2 = 0.62, k = 0.0862 mV/K, r is the intrinsic line width in millivolts, and Vr is the 0 to peak modulation amplitude. This formula works best when 8kT 2 Vf.
Introduction Inelastic electron tunneling spectroscopy has been extensively used to study vibrational’” and e l e ~ t r o n i c ~transitions ,’~ in species adsorbed on the insulator of various metal-insulator-metal (MIM) devices. Because the tunneling spectral lines broaden dramatically with temperature,lslO.llmost of the work to date has been performed at, or below, 4 K. Recently, however, we have become ( I ) Lambe, J.; Jaklevic, R. C. Phys. Reu. 1968, 165, 821. (2) Klein, J.; Leger, A.; Belin, M.; Defourneau, D. Phys. Reu. B 1973, 7 , 2336. (3) Hansma, P. K. Phys. Rep. C 1977, 30, 145. (4) Tunneling Spectroscopy: Capabilities, Applications, and New Techniques; Hanmsa, P. K., Ed.; Plenum Press: New York, 1982. (5) Weinberg, W. H. Vib. Spectra Struct. 1982, 11, 1. (6) Vibrational Spectroscopy of Molecules on Surfaces; Yates, J. T., Madey, T. E., Eds.; Plenum Press: New York, 1987. (7) Hipps, K . W.; Mazur, U. J. Am. Chem. S o t . 1987, 109, 3861. (8) Hipps, K . W.; Mazur. U.J . Phys. Chem. 1987, 91, 5218. (9) Hipps, K. W.; Mazur, U. Surj. Sci., in press. ( I O ) Jennings, R. J.; Merrill, J. R. J . Phys. Chem. Solids 1972, 32, 1261. ( I I ) (a) Kirtley, J.; Hansma, P. K . Phys. Reu. B 1976, 13, 2910. (b) Walmsley, D. G.; Floyd, R. B.; Read, S. F. J. Phys. C 1978, 11, L107.
0022-3654/89/2093-57 17$0l S O / O
interested in the use of IETS for studies a t 77 K and above. Our interest lies in two areas: ( I ) the use of infusible j u n ~ t i o n s ~ ~ ~ ~ * l ~ as chemical sensors, and (2) spectroscopic studies performed by scanning tunneling m i c r o ~ c o p e ’ ~near J ~ 77 K. In order to proceed in both these areas, we needed a simple but accurate method for predicting IETS line widths and intensities under conditions of varying modulation voltage and temperature. A search of the tunneling literature provided significant insights, but no solution to our problem. Lambe and Jaklevic’ first predicted the functional and form of the IET intensity variation with temperature,f( 0, showed that it was in rough agreement with the observed line width of a CH stretching mode at 77 K. Jennings and MerrillIo studied the temperature variation of three hydrocarbon bands in the 0 to 30 K temperature range. They found that the full width a t half-maximum of these bands varied approximately as [(5.4kn2 Wo2Io5 , where Wo2is the non-temperature-dependent contribution to the width. For later reference we note that a Gaussian
+
(12) Jaklevic, R . C. J . Electrochem. S o t . 1979, 126, 1549. (13) Heiras, J. L.; Adler, J . G. Appl. Surf. Sci. 1982, 10, 42. (14) Baratoff, A,; Persson, B. N. J . Vac. Sci. Technol. 1988, A 6 , 331. (15) Smith, D.; Kirk, M . D.; Quate, C . F. J. Chem. Phys. 1987, 86, 6034.
0 1989 American Chemical Society
5718
The Journal of Physical Chemistry, Vol. 93, No. 15, 1989
band having a full width a t half-height of 5.4kT is the same as a Gaussian having a half-width a t l / e height ( H W E H ) of 3.2kT. Klein et aL2 provided an analysis of the role of the modulation voltage in determining the measured line, m( V f ) ,but they did not test their formulation quantitatively. Kirtley and Hansma'la combined Jaklevic and Lambe's temperature-dependent shape function with Klein et al.'s modulation function and the BCS density of states to compute the low-temperature (1.1 and 4.2 K) and low modulation voltage line shapes of junctions having one or two superconducting electrodes. Their calculations agreed very well with their experimental data but did not address the case of normal metal tunneling. Somewhat later, Walmsley and coworkers'Ib measured the line shape of the 410-cm-' band of phenol a t 0.07 K . Their analysis was very similar to that of Kirtley and Hansma,lIa This was the situation as we found it. Based on the above work, it is expected that the normal metal tunneling line shape will be a convolution of three factors, the temperature-dependent function of Jaklevic and Lambe, the instrumental function of Klein et al., and the intrinsic line shape of the transition studied. This expectation, however, did not satisfy our need. First. Kirtley's'Ia convolution line shape had not been tested for normal metals or temperatures above 4 K. Second, the computations involved in performing the triple convolution did not satisfy our need for a simple rapidly evaluated function. Our experience with tunneling spectra indicates that most tunneling bands are Gaussian, especially when the modulation voltage is not much greater than IOkT. Thus, it should be possible to develop a much simpler line-shape function. The course we follow in this article reflects these needs and observations. W e will fit the normalized instrument response function [convolution off( r ) with m( Vf)] to a Gaussian dependent on two parameters. This Gaussian shape function will then be used to predict the modulation and temperature dependence of lines in the IETS of the SCN- ion. Additionally, we will fit the Gaussian line shape to our experimental data and then compare the resulting parameters to those obtained by the former procedure. Experimental Section Tunnel junctions were prepared in a diffusion pumped, liquid nitrogen (LN2) trapped, vacuum system. Junctions were of the type AI-AI,O,-KSCN-M, where M = Pb or TI. The aluminum strip ( 1 X 50 mm) was deposited a t 4 X Torr to a thickness of 0.1 bm on a clean Pyrex microscope slide. Oxidation was accomplished in an ac discharge plasma (0.1 mTorr of 0,) for a period of 2 min. The vacuum system was opened and the devices were spin-doped with a solution of 0.5 g / L K S C N (Baker analytical reagent grade) in water. The slide was returned to the vacuum system and four cross strips (2 X 20 mm) of 0.1 bm thick top metal were deposited. The device was then wired to a sample rod using indium solder and cooled to the desired temperature. Typical junction resistances ranged from 30 to 1500 ohms. Temperatures of 4.2 and 77 K were obtained by immersion in liquid helium and LN2, respectively. A few samples were also measured a t 8.7 K, obtained by positioning the sample above the helium liquid level. This temperature was determined by a sensor mounted on the block holding the slide. In the case of Pb top metal junctions, the devices were sandwiched between two S m C o magnets (Edmunds Scientific No. 030779) during spectral measurement. These magnets have a sufficiently intense magnetic field to quench the superconductivity of Pb. They were in place at all measurement temperatures. The TI top metal and AI base metal are not superconducting in the temperature region studied and no magnets were used with TIcoated junctions. Data were obtained both as (d2V/dp) and as normalized tunneling intensity [NTI], (d21/dVZ)(dV/dZ) on a spectrometer described in detail el~ewhere.'~J' Because of the slow variation in conductance with bias voltage present in the junctions studied, the differences in observed line shape were not significant. Each (16) Hipps, K . W . ; Maiur, U . Reu. Sei. Insrrum. 1988, 59, 1903. ( 17) Hipps, K. W. ReG. Sci. fnstrum. 1987, 58, 265.
Hipps and Peter of the spectra presented represent the sum of from 9 to 100 scans. For the purposes of line-shape analysis, it was often necessary to remove the elastic tunneling contribution to the tunneling s p e c t r ~ m .This ~ was done by fitting a low-order polynomial to the spectral areas adjacent to, and bracketing, the bands of interest. This polynomial "background" function was then subtracted from the experimental data. Other than this procedure, the data were not mariipulated in any way (i.e., they were not smoothed or digitally filtered). Experimentally, the modulation voltage was measured as a true root mean square (trms) value. Theoretically, it is the 0 to peak value that is of importance. In what follows, V, will indicate the trms value while VFwill indicate the 0 to peak value. Vf = Vr2L/z. The conversion between units of wavenumbers (cm-I) and millivolts (mV) was made through the use of the relationship I mV = 8.066 cm-I. Theoretical Section Three factors are expected to play a significant role in determining the observed line shape. The line has a natural shape, N ( V-V,), which we here suppose is Gaussian. As indicated in eq I , N( V-V,) is centered a t bias voltage V, and has a half-width
N ( v - ~ o )= ( N o / ( r ~ ' ' ~ )exp(-((V) Vd/V2)
(1)
at l / e height of r ( H W E H = I'). The area under the band is No. The second factor is due to thermal smearing of the Fermi surface. Lambe and Jaklevic' represented it as f(x), as in eq 2,
f ( x ) = ( 1 /kT)eX[(x- 2)eX + (x
+ 2)]/[(eX -
(2)
where x = ( V - V,)/kTand k = 0.0861 63 mV/K. The last factor, given by eq 3, is the modulation voltage dependent term? m( V,Vf). 8(V? m(V,Vf)=
P)3/2
3TVf4
for
IVl
