376 IEEE TRANSACTIONS ON PARTS, HYBRIDS, AND PACKAGING, VOL. PHP-12, NO. 4, DECEMBER 1976

REFERENCES 121 G. N. Ellison, “The effect of some composite structures on the

[l] .V. L. Hein and V. D. Lenzi, “Thermal analysis of substrates and thermal resistance of substrates and integrated circuit chips,”

integrated circuits,” presented at the 1969 Electronic Com- IEEE Trans. Electron Devices, vol. ED-20, pp. 233-238, Mar.

ponents Conf. 1973.

‘On the Interpretation of Noise in Thick-Film Resistors

J. A. RINGO, MEMBER, IEEE, E. H. STEVENS, MEMBER, IEEE, D.A. GILBERT, MEMBER, IEEE

Abstract-Noise in thick-film resistors is interpreted by comparison to experimental and theoretical results previously reported for noise in metals and semiconductors. This com- parison provides an explanation for the observed dependence of noise on the thick-film-resistor geometry and the IOO-fold increase- in noise amplitude over that of metals and semi- conductors. This comparison indicates that mobile-charge interactions with traps are an inherent feature of charge trans- port in thick-film resistors.

Noise in thick-film resistors has long been recognized as an important parameter for characterizing thick-film materials and noise data are usually provided by the vendor when promoting a given resistor system. Little has been done, how- ever, to relate I/f noise in thick-film materials to a similar type of noise observed in other materials such as semiconductors or metals.

Extensive studies of noise in metals and semiconductors have led to the basic postulate that I/f noise is inversely proportional to the total number of charges contributing to conduction as expressed by the relation

(1)

where I is the average sample current under constant applied voltage, N is the total number of mobile charges in the sample,

Manuscript received April 30, 1976; revised July 30, 1976. J. A. Rjngo is with the Department of Electrical Engineering,

Washington State University, Pullman, WA. E. H. Stevens was with the Department of Electrical Engineering,

University ‘of Idaho, Moscow. He is now with the Joint Center for Graduate Study, Richland. WA.

D. A. Gilbert was with the Department of Electrical Engineering, University of Idaho, Moscow. He is now with the Naval Weapons Center, China Lake, CA.

f is the frequency in hertz, and (Y is a dimensionless empirical constant.

Hooge and Hoppenbrouwers have reviewed the data from well-defined homogeneous samples and concluded that (I) with a value of about 2 X 10v3 for o applies to both metals and semiconductors [ 11, [2]. Recently, Van Der Ziel has provided some theoretical justification for the postulate by showing that an expression similar to (I) results when fluctua- tions in the number of mobile charges are caused by charge communication with traps 131.

Through suitable substitutions for N in (1). the basic I/f noise postulate can be expressed in two alternate forms which will facilitate its comparison to experimental data. Material sheet resistivity, resistance, sample geometry, and effective charge mobility are related to N by (2) and (3). Substitution of (2) into (I) yields the alternate form given by (4); substitu- tion of (3) into (1) yields the alternate form given by (5):

Ps = L W/qN (2) R = psL/W = L 2/qpN

< (!?L)2 > = (%) (E) I LW f

< (y > = (ciqp) +$5. In the above equations, ps is the material sheet resistivity, q

is the electronic charge, /-I is the effective mobility, and L and W are the length and width, respective!y, for a resistor of resistance R.

When aq,up, is held constant, it follows from (4) that the I/f noise is inversely proportional to the resistor surface area if it is inversely proportional to N. Extensive measurements made in other laboratories on a variety of thick-film systems have indicated that I/f noise in thick-film resistors tends to be

RING0 eta/.: INTERPRETATION OF NOISE IN THICK-FILM RESISTORS 379

ps’l00Kn/o

Fig. 1. Normalized mean-square noise current in thick-film resistors versus R/L2. The test samples were fabricated from DuPont BIROX 1451 material. These data show that I/f noise is inversely propor- tional to N.

inversely proportional to the surface area 141, [51. It follows from (5) that when cuqp is held constant the I/f noise is proportional to R/L 2 if it is inversely proportional to N. Implied in this R/L2 parameter is the direct dependence of noise on the sheet resistance ps. Noise measurements were then made on thick-film test resistors which were fabricated under carefully controlled screening and firing conditions to insure that c~q/~ remained constant. The firing of these resistors was done at a peak temperature of B50°C and the processing closely followed the recommendations of the thick-film-paste manufacturer. The noise data from these test resistors, which are plotted in Fig. 1, indicate that the I/f noise is proportional to R/L2 as predicted. These noise measurements were made using a low-noise preamplifier followed by a commercial wave analyzer. The effective noise bandwidth was 6 Hz. The nor- malized mean-square noise current was then computed from the averaged wave-analyzer output using the appropriate scale factors. This experimentally observed dependence of noise on the inverse resistor area and on the R/L2 parameter (even though the latter observation was limited to a single resistor paste) lends strong support to the fact that the I/f noise postulate applies to thick-film materials as well as to metals and semiconductors.

It also should be noted that according to (4), noise in resistors of equal area should be directly proportional to the sheet resistance if the factor aqp is constant. Noise data from a number of thick-film-resistor material systems are plotted versus ps in Fig. 2. It is clear from Fig. 2 that noise is propor- tional to ps only for a limited sheet resistance range in DuPont 7800 materials; for all other material systems noise is not proportional to ps. From this observation we may either conclude that 1) the basic postulate expressed by (1) is incor- rect or 2) that the factor o#~ does not remain constant as ps increases, implying that the conduction process in thick-film materials changes as the sheet resistance changes. In light of the previously cited experimental evidence, we feel that the latter conclusion is both logically and physically sound.

0

:

s c -10

3 z 2 -20

0 DUPONT 1400 0 ESL - 2800 0 ESL- 2800-C

-30 A DUPONT 7800 0 PLESSEY EM0 G .02 II01

4 -I-- THEORETICAL SLOPE

-40 I I I I I IO I02 IO’ IO4 105 IO6

SHEET RESISTIVITY ps (A/o)

Fig. 2. Noise figure versus ps for resistors fabricated from a number of thick-film material systems. It is predicted from (4) that the slope of these data will, be similar to the slope of the dotted line. These data show that the charge-transport process is a function of ps.

A value for the factor oqu which appears in (4) and (5) can be determined from the noise data shown in Fig. 1. The data indicate that a/~ is approximately 1 cm2/V.s for this thick-film material. Taking the maximum estimate for effective mobility as 3.1 cm2/V.s, which is the Hall mobility for single-crystal Ru02, yields a minimum value of about 0.3 for (Y inthick-film materials [9]. This value of (Y for thick-film materials is more than 100 times larger than the value found for metals and semiconductors; this observation may provide valuable in- formation about charge transport in thick-film resistors as discussed below.

In metals and semiconductors; l/f noise results from fluc- tuations in the number of mobile charges due to interactions with traps which are localized at crystal imperfections or at the sample surface. Since traps in metals,and semiconductors are localized, only a small fraction of mobile charges are affected, and the small value of 2 X 10W3 results for the l/f noise parameter ff.

Charge in thick-film resistors, however, is transported through a complicated interconnected network of conducting filaments [ 121 , [13] . These filaments are formed by the sinter- ing of small glass-coated metal-oxide particles [14]. In addi- tion, since the temperature dependence of resistance in thick- film materials and single crystals of the parent metal oxide differ greatly, it follows that the charge-transport process in thick-film resistors and single crystals of the parent metal oxide differ greatly [I 1 I, [I51 . This temperature dependence of resistance implies that charge transport in thick-film re- sistors is determined by properties of the interfacial regions between adjacent metal-oxide particles and not by’ properties of the parent metal oxide. The large a value suggests that the capture and release of charges from traps is an inherent feature of charge transport through these interfacial regions.

, 380 IEEE TRANSACTIONS ON PARTS, HYBRIDS, AND PACKAGING, VOL. PHP-12, NO. 4, DECEMBER 1976

ACKNOWLEDGMENT [71

f81

Dl

[IO1

[III

C. Huang and S. J. Stein, “Thick film resistors for high yield processing,” Electra Science Labs, Inc., Pennsauken, NJ. --, “Thick film resistors for glass substrates,” in Pr&. Elec- tronic Components Conf., 1973. DuPont Electronic Products, Commercial Products Information A-66898, Wilmington, DE, Aug. 1969. M. Greenfield and R. Delaney, “A new thick-film resistor system,” in NEPCON Proc., Feb. 1973. W. D. Ryden and A. W. Lawson, ” Electrical transport proper- ties of Ir02 and RuO2,” Phys. Rev. 6, vol. 1, no. 4, pp. 1494-l 500, 1970. R. W. Vest, Purdue Research Foundation, Semi-Annual Tech. R.ep. for the period 1 /I I72 to 6/30/72. APRA Grant DAHCl5- 70-G 7. pp. 7-8. Aug. 1972. P. W. Polinski, “Stability of thick-film resistors under high electromagnetic stress,” Solid-State Technology, pp. 31-58, May 1973. R. W. Vest, Purdue Research Foundation, Semiannual Tech. Rep. for the period 7/l/71 to 12/31/71, ARPA Grant DAHCI 5-70-G7, pp. 3-21, Feb. 1972. --, Purdue Research Foundation, Semiannual Tech. Rep. for the period 7/l/73 to 12/31/73. APRA Grant DAHC15-73-G8, p. 14, Feb. 1974.

The noise data shown in Fig. 1 are from the measurements made on test samples provided by the Thick-Film Prototypes Group, Tektronix Laboratories.

REFERENCES

[II F. N. Hooge, “i/f noise is no surface effect’,” Physics Letters, vol. 29A, pp. 139-140, Apr. 1969.

[21 F. N. Hooge and A. M. H. Hoppenbrouwers, “l/f noise in continuous thin gold films,” Physica, vol. 45, pp. 386-392, 1969.

[31 A. Van Der Ziel, “Proof of basic semiconductor flicker noise formula,” Solid State Electronics, vol. 17, pp. 11 O-l 11, 1974.

[41 C. Y. Kuo and H. G. Blank, “The effects of resistor geometry on current noise in thick-film resistors,” in Proc. /SHM Symp. pp. 153-160, 1968.

[51 C. W. H. Bristow, W. L. Clough, and P. L. Kirby, “The current noise and non-linearity of thick film resistors,” presented at the Int. Microelectronics Symp.; 1971.

[Cl DuPont Thick-Film Handbook; Specification 1400-10 A- 83586, Wilmington, DE, Oct. 1972.

[I21

[I31

[141

[151

Prevention of Bridging Failure in Mercury Switches JAMES E. BENNETT, MICHAEL P. VAN DER WIELEN, WALTER E. ASBELL, AND M. ROBERT PINNEL

Abstract-Service failures of sealed mercury switches in relays may occur by “sticking” or by “bridging.” Analyses by scanning-electron-microscope microprobe and by X-ray dif- fraction revealed that bridging failures in certain make-before- break-type switches can be due to the accumulation of par- ticles of NiHg4 in the mercury which, because of increased viscosity, may form a quasi-steady bridge be.tween the movable and fixed contacts.

inhibits the dissolution of nickel and the subsequent formation

Doping of the mercury with copper and tin was proposed as a solution to the bridging problem based on the analysis of failed switches and the knowledge gained from previous studies of liquid-mercury/solid-metal interactions [I] .

The results of an accelerated laboratory test and a field trial comparing the electrical characteristics of undoped and doped switches confirm that the failure mechanism is thermally acti- vated. The undoped switches were prone to bridging failure. Prevention of bridging failure in doped switches is attributed to the preferential formation of a tin-bearing layer which

Manuscript received May 24, 1976; revised June 30, 1976. The authors are with Bell Laboratories, Columbus, OH 43213.

of a viscous slurry of NiHg4 in mercury.

INTRODUCTION

Mercury relays, used in telephone equipment, occasionally fail due to the “sticking” or “bridging” of the enclosed switches. The switches used in these relays generally consist of movable and fixed metallic contacts in a sealed glass envelope containing mercury. The contacts are wetted by the mercury, which is drawn into a ribbon between the movable (armature) and the fixed contacts when the switch is magnetically actuated. Depending on the design configuration, the mercury ribbon may or may not break before closure between the armature and the other fixed contact. Failure has been ob- served in break-before-make-type switches due to “sticking,” where the armature does not release or is slow to release from a fixed contact. “Bridging” failure has been observed in make- before-break-type switches in which the mercury ribbon does not break or is slow to break after closure.

In a previous paper [I], certain aspects of dissolution and precipitation at liquid-mercury/solid-metal interfaces were