MEASUREMENT OF THE TUNNELING AND HOPPING PARAMETERS IN Ru 02 THICK FILMS

Thick film resistors containing a mixture of ruthenium oxide (RuO) and lead borosilicate (Pb have been produced on alumina [(AI 03).96 (MgO).04 substrates. The temperature coefficient of resistivity (TCR) of these films has been measured for different particle size and concentration (weight percentage) of the conductor particles. The TCR was found to be a function of temperature in all the films included here. From the measured values of negative TCR the tunneling parameter a and hopping parameter were determirred. These results suggest that hopping is important for the low concentration films. For films with positive TCR only parameter a could be determined. The parameter a increased but the parameter decreased with temperature for the present films.

Thick film resistors containing a mixture of ruthenium oxide (RuO) and lead borosilicate (Pb have been produced on alumina [(AI 03).96 (MgO).04 substrates. The temperature coefficient of resistivity (TCR) of these films has been measured for different particle size and concentration (weight percentage) of the conductor particles. The TCR was found to be a function of temperature in all the films included here. From the measured values of negative TCR the tunneling parameter a and hopping parameter were determirred. These results suggest that hopping is important for the low concentration films. For films with positive TCR only parameter a could be determined. The parameter a increased but the parameter decreased with temperature for the present films. In an earlier paper we have investigated the possibility of tunneling and hopping mechanism in RuO2 thick film resistors. Our conclusion in that paper was that while both the mechanisms are possible in a thick film resistor for electronic conduction, hopping becomes more important with low concentration t of RuO2 particles. In this paper we will report a detailed experimental study of RuO: thick trim resistors with a view to understanding the behavior of various tunneling and hopping parameters and their relationships. In this context we will also examine the various theories for the conduction fHere, by concentration we mean weight percentage. 124 N.C. HALDER AND R.J. SNYDER mechanism in RuO thick film resistors.
Thick films are fabricated z by means of a screen printing process using a paste containing a mixture of a conductive material, a glass, a binder and a thinner. A definite pattern of interest is first made and printed on a ceramic substrate. This process is repeated with the resistor pattern using the resistor paste. The paste is usually printed on the substrate and fired to form a glaze. The resistors are finally trimmed to proper values for the resistances.
We define the temperature coefficient of resistivity (TCR) by (R -R) x 10 6 ' (T-T) x R ppm/deg (1.1) where R1 is the resistance at T1, R: is the resistance measured at T:, and R is the average resistance. However, for the temperatur dependence study, we will use In the above expression, TCR is found by measuring resistance Ro at 0C and resistance R at temperature T (TCR is defined as the change in resistance per R per degree from 25C to 125C for Department of Defense work). The ideal resistor should have a TCR equal to zero. We will first measure the TCR of RuOz films with various particle sizes and concentrations of the conductor particles. We will then use these results to compute some important parameters so as to understand the theoretical models proposed earlier for thick film resistors. We believe it will be possible to see how barrier height, activation energy and hopping parameter influence the TCR. This study will help in the development of a resistor ink with smaller TCR and greater stability, z 2. EXPERIMENTAL MEASUREMENTS

Sample Preparation
The paste or ink used in this investigation consisted of a conductive material (RuO), a binding material which is a fine glass powder (lead borosilicate), and organic binder (ethyl cellulose) and a volatile solvent (pine oil). The organic binder held RuO and glass particles in suspension before firing and provided a proper fluid characteristic for screen printing. Samples with three different particle sizes were obtained from Electro Materials Corporation of America (EMCA), who also mixed them in proper proportions with other ingredients.
The actual resistor consisted of two conductor pads with the film printed between them. The pattern was made in two parts: one for the pad and the other for the film as shown in Figure (a). The original pattern was drawn to a scale of five to one making the initial pattern five times larger than the desired resistors. The conductor and resistor patterns were cut separately since they were printed and fired at two different stages. Finally the aspect ratio (length/width) was maintained unity.
The substrate was produced by grinding AlO3 to a 2 to 3 micron ) grain size, mixing with magnesium oxide (MgO) and an organic material. This paste-like substance was smoothed, cut to the desired size and fired at 2200C. The finished substrate was 96% AlO3 and 4% MgO. The substrates, printed with the conductor pattern, were dried in air for about fifteen minutes at 150C temperature. Finally, the substrates were placed in a nichrome belt furnace for about twenty-eight minutes to heat at a temperature of 850C for eleven minutes. An identical procedure for printing and firing was used for the resistor ink. However, after each resistor was printed, the screen was washed with alcohol and water and then dried with compressed air. The final form of the resistor is shown in Figure (b).

Measurement of the Temperature Coefficient of Resistivity
The thickness of the film were traced using a Sloan Dektak MDC-9000 system. The resistances of the films were measured simultaneously using a parallel connection as shown in Figure 2. A standard oven operating in the temperature range of 25 ,x, 300C was found suitable for this work. The connecting wires showed no significant change of resistance as temperature changed, and were negligibly small (0.3 1.7 ohms)compared to the resistances of the films. The resistances were recorded with a five-digit Keithley 174 multimeter. This instrument used a current of lmA for 3 k2 and for 3 M2 films. These currents were too small to introduce any additional thermal effect.
The temperature was increased gradually in steps of about 15C and was allowed to stabilize for about ten minutes upon reaching the desired temperature.

X-Ray Diffraction Measurements of the Thick Films
The x-ray diffraction patterns of the thick films were recorded on a vertical Philips diffractometer using the fiat sample focusing condition. 3 The Ni-filtered CuKal radiation was 126 N.C. HALDER AND R.J. SNYDER TABLE IDENTIFICATION OF SAMPLES Please note that these were commercial samples which were obtained from EMCA with these specifications. Therefore, the composition and size could not be changed more uniformly.
used. The x-ray beam was collimated through divergence slit and passed through 0.006 receiving flit. Each diffraction peak was scanned at 1.0 per minute scanning speed and recorded at 60 inches per hour paper chart speed. Intensity scale, baseline and time constant were held constant for all samples, since a comparison of peak height, or intensity, and the broadening of the peaks would be made later. Because of the importance of peak tails, care was taken to collect the background level over a sufficiently large angular spread on either side of the peak maximum. All available peaks were recorded.
A blank substrate was also run in order to sort out the peaks due to alumina substrate alone.  Table I. The results of the measurements are illustrated in Figures 3-4. The x-ray data are tabulated in Table II. We used Eq. (1.2) to calculate our TCR reflecting T1 30C and Tz 250C. The plots in Figure 3 show two types of effects: (i) change of resistance with temperature, and (ii) change of resistance with thickness when concentration and particle size are kept constant. Similarly, Figure 4 illustrates: (i) change of resistance with concentration when thickness and particle size are kept constant, and (ii) change of resistance with particle size when thickness and concentration are kept constant.

Negative and Positive TCR
We see from the slopes of plots in Figure 3(a) that the TCR is negative for 2% concentration films. These plots are designated as al and a2. Instead of the usual rise, these plots show a decrease. If these results were to follow the tunneling model as proposed by Pike and Seager, a resistance minimum should occur at some temperature Tin. Here we do not find such an effect for 2% film with 2.2 and 3.1/a particles. The plots of measured TCR are shown in Figure 5. These values are rather large and may not be suitable for 1 Table III. practical use in the microcircuits, e However, these numbers suggest that the effective resistances of these films are predominantly due to tunneling as opposed to metallic condition as observed in pure metallic films. inversely proportional to thickness. The TCR of these films are positive implying that Tm is below 25C. In the present investigation, the 2% films have the highest resistance, the 12% have a fairly high resistance and the 16% have a value somewhat less than that of the 12%. This dependence on concentration has been verified by others. 7 -9 Figures 4(a) through 4(d) show the temperature dependence of resistance as functions of particle size and concentration. It is seen that, at these fairly high concentrations 10 (12% and 16%), smaller particle size films have higher resistance.

Structural Analysis by Thickness and X-Ray Measurement
In Figures 6(a) and 6(b) are shown the thickness traces obtained with SLOAN Dektak Model 9000. The thickness measurement indicates a significant amount of surface irregularities. It is found that resistors with smaller concentration had much smoother surfaces than the ones with higher concentration. The profile is very smooth although the thickness does vary a great deal. Additionally, the surface irregularities appear to be propor- As stated previously the diffraction peaks due to the alumina substrate and the lead borosilicate glass were identified by analysis of the x-ray spectra. No peaks due to RuO2 were found in the 2% film. The 12% and 16% resistors do show, however, some small peaks not attributable to the substrate or the lead borosilicate glass. The peak intensity and peak numbers increased with increase of concentration. The observed half widths of the films are inversely proportional to the particle size if we assume that there is no particle strain.

Resonance Tunneling and Parameter
According to the Pike-Seager theory we expect to see a resistance minimum (or conductance maximum) at T m. In the present experiment this could perhaps occur above 250C. This minimum depends on several factors, most critically on the barrier resistance with positive curvature. A simple tunneling, which is also called 'resonance tunneling', can give such a minimum. Introducing 7 for TCR, we write as in our previous paper (1 + bT) 6 (4.2) whereas, from the exact definition of a' we can easily get  TABLE III   TCR results From Figure 3 From Figure 4 at 112C at 112C We can now calculate a for all the films using the data listed in Table III. These values of a are found in the range 2.28 2.30. We find that these calculated a s, specifically for the low concentration films, do not compare with the value 0.7 ,x, 0.75 as suggested by As has been reported earlier there are two possibilities for an electron to tunnel through. For narrow barriers, the result is a simple tunneling, as where an electron with less kinetic energy may cross the barrier quantum mechanically without going through any intermediate hopping step. This is in fact what happens in the resonance tunneling and has been discussed in the Pike-Seager theory. It should be mentioned here that this theory allows (i) the effects of the presence of impurities (resonant centers) in the barrier, and (ii) the correction factor due to the finite size of the metal oxide particles. However, for wide barriers, there is another form of tunneling, the phonon assisted hopping, a6,a7 which involves a number of intermediate hopping steps before the electron can pass through these barriers. We will now address ourselves to this possibility.

Phonon Assisted Hopping and Parameter
In the present paper we will follow the work of our previous paper and denote the barrier resistance as Rb and hopping resistance as Rp; then the effective barrier resistance as RB may be written either in the parallel mode or in the series mode. Thus for parallel mode the TCR equation will be We shall now examine the implication of these derivations.   Figure 9. We also show the behavior of a with 3' at mean temperature of 112 C in Figure 10. From this study it is seen that films with large a have small and vice versa, a tends to increase but tends to decrease with temperature. This study further points out that the parallel mode is more likely than the series mode. The series mode results of film 3a2 in Table IV are not to be accepted for this reason. It should be mentioned here that the temperature dependence of a and/3 are not the same. As pointed out before, phonon assisted hopping is a form of tunneling. However, resonance tunneling does no.t directly depend on temperature. Its dependence comes mainly from the Fermi-Dirac distribution function that describes the occupancy of the electron states, whereas the hopping does depend on the temperature in a direct way.
We may now summarize the results of this investigation. Films with larger particle size had higher resistance than those with smaller particle size. For low concentration films resistance decreased as temperature increased indicating a Tm somewhere above 250C.
These were explained by extending the tunneling model to phonon assisted hopping. The results of the present study seem to confirm the Pike and Seager model in the high concentration films but not necessarily in the low concentration films. The tunneling parameter a and hopping parameter 3 are both affected by temperature. The nature of the temperature dependence, however, is not the same. It is further noted that the particle size and concentration are the two most critical parameters which influence the behavior of the resistor. The distribution of particle size depends very much on the preparation technique and firing process, which in turn, fixes the resistance minimum at Tin.