The term "integrated" is borrowed from the semiconductor industry and is used in a similar way. An integrated circuit is a grouping of elements which are formed and interconnected on a common substrate to form a functional network. An integrated resistor network is similarly defined as a grouping of resistive elements formed and interconnected on a common substrate.

Although it is not implicit in the definition, it is generally understood that the elements are produced by deposition on, or reaction with, the substrate, and that the patterns are produced by phototlithographic imaging, followed by selective removal of unwanted materials.

The resistors in a given network, being quite small and in close proximity, are exposed to nearly identical conditions during processing. Similarly, each network on the wafer or substrate is exposed to virtually the same conditions. Because several wafers are processed together, at the same time and in the same equipment, uniformity is bestowed upon the entire lot - to hundreds or thousands of individual units. An added benefit of integrated construction is the integrity of the interconnections, which are inherently more reliable than the man-made connections of discrete component construction.

• Extremely close matching of all elements in a network, insuring close tracking over temperature and throughout life.
• Very small, high density, multi-element networks which save printed circuit board real estate
• Hermetic construction practical in a variety of standard contemporary formats
• Repeatable and consistent characteristics part-to-part and lot-to-lot
• Very low inductance
• Outstanding reliability - fewer man-made interconnections
• No thermoelectric effects
• Installed costs no more than discretes - often less

Thin Film technology employs photolithographic precision patterning to give the designer a wide range of resistance values in the smallest possible area. This provides a choice of minimizing the size of the component or increasing the number of resistive elements in the same space, The total resistance achievable in a given area is dictated primarily by the sheet resistance of the film material and the patterning. However in actual designs, the maximum area utilized is reduced because of space required for termination pads, internal conductors, special trimming features, and pin-out constraints.

Thin film resistive materials cover a normal sheet resistance range of 50 to 1000 ohms/square which results in an available resistance range for individual resistors from a few ohms to several megohms. The highest precision is normally found in the range 100 ohms to 100K ohms.

When low resistance elements are incorporated in precision networks, the small but unavoidable resistances of the leads and conductive patterns on the chip and in the package must be taken into consideration. These lead effects can be minimized, but not completely eliminated, by proper design, processing, package selection and assembly. However special attention must be given to the setting of specifications, particularly with regard to realistic tolerances on resistance and tracking, and to the method of their measurement.

Modern laser systems are capable of adjusting resistors to very close tolerances on either an absolute or relative basis: 0.01% and 0.005% respectively. Furthermore, the responsible manufacturer will actually "guard band" the trimming so that the internal specification will be tighter than the release specification.

The closer the required tolerance, the more carefully the resistor must be designed to achieve a tight distribution, well within the tolerance limits, with a cost effective trimming speed. One of the ways this is achieved is to provide special trimming geometries. These features reduce the sensitivity of the resistor to the amount of material being removed by the laser, allowing successively higher accuracy to be obtained. These features utilize additional substrate area, which sometimes requires trade-offs between cost and performance.

One of the features which distinguishes modern thin film technology for use in precision networks is the electrical and mechanical stability of the films. This is important because closely trimmed resistors must endure the sometimes stressful conditions of assembly without significant drift. This again emphasizes the inherent advantages of integrated construction over individual discrete resistors, since any changes which do occur will be common to all resistors in the network, thus preserving the ratios precisely as trimmed.

The temperature coefficient of resistance is the measure of resistance change as a function of the ambient temperature. It is defined as the unit change of resistance per unit change in temperature, and is commonly expressed as parts per million per centigrade degree (ppm/°C). It is the property by which resistors are most often characterized or differentiated. Historically, discrete resistors, including those made from films, were graded by lots according to TCR value. The relatively recent use of sputter deposition to control film composition, together with related improvements in processing, have resulted in the so-called "third generation" thin film products with TCRs consistently less than 5 ppm/°C, absolute.

TCR is usually determined experimentally by measuring the resistance at several temperatures and calculating the rate of change over the appropriate temperature interval, e.g. 25°C to 125°C. If the resistance changes linearly with temperature, the TCR is a constant, regardless of the temperature interval. However, when it is not linear, as is the case for the commonly used nickel/chromium alloys, the TCR is expressed as the slope of the line connecting two points on the resistance vs. temperature curve, e.g. 25°C and 125°C. In other words, it is the average TCR over the interval. The more non-linear the relationship, the poorer the approximation of the average.

It is absolutely crucial in specifying TCR that the temperature interval be clearly specified as well.

The procedure outlined in MIL-STD-202 Method 304 is often referenced as a standard for measuring TCR. In this method, average TCRs are calculated for a series of intervals between 25°C and -55°C and between 25°C and 125°C. The highest value is recorded as the TCR. This reflects the full military operating range, but may result in overspecification for components having a different or narrower operating temperature interval.

Through an understanding of the effects of alloy composition and the ability to carefully control processing, it is possible to "tailor" the resistance vs. temperature curve to product TCRs that are a) negative over the entire range, b) positive over the entire range, or c) negative in the low end, positive at the high end, with a relatively flat "zero TCR" sector in a range about room temperature. This can be used to advantage for equipment operating in the vicinity of room temperature or otherwise requiring temperature compensation.

Most applications in which precision thin film networks are employed depend upon achieving and maintaining close relative resistance values.

Thus relative changes in resistance within a network, called "tracking," are very important. Thin film networks excel at tracking. There are several different aspects of tracking which are important to understand and differentiate.

RULE OF THUMB FOR TRACKING INTEGRATED NETWORKS VS DISCRETE REGISTORS In discrete resistors, tracking between a matched pair may be as great as twice the specified absolute TCR. So for a TCR of 0 ±2.5 ppm/%deg;C the tracking may be as much as 5 ppm/°C. With integrated film networks, the tracking is independent of the absolute TCR, and usually far better. For example, tracking of less than 2 ppm/°C can be readily obtained when absolute TCRs are within the range of ±25 ppm/°C.

TCR tracking is defined as the difference between the TCRs of a pair of resistors over a given temperature interval. Achieving close TCR tracking in discrete resistors is difficult and places severe burdens on the manufacturing process to produce to a very close absolute TCR limit. By contrast, the integrated construction of thin film networks assures extremely close TCR tracking because the resistors are produced as a group under nearly identical process conditions. Moreover, the resistors are small and in close proximity on the surface of a common substrate of high thermal conductivity, which keeps them at or near the same temperature in operation.

Nevertheless, process and material variations can occur which produce small, but measurable, differences in the TCRs of neighboring resistors on the same wafer. Process variables which may affect this include: non-uniform film deposition, substrate defects, thermal gradients during annealing, and non-uniform stresses. Design can also play a role. However by employing state-of-the-art process controls, measuring equipment and techniques, TCR tracking can be controlled to within a few tenths of a part per million, per degree, given the proper circuit and chip configuration and packaging.

A factor which results in the apparent TCR tracking being higher than the "true" tracking on the presence of a common tap lead having a measurable resistance (r).

where TCR (r) is the TCR of the common lead material, typically metallic. For example: a 1 kilohm resistor having a TCR of 8.9 ppm/°C connected to a 2 kilohm resistor with a TCR of 8.5 ppm/°C, and a shared output lead of resistance 0.1 ohm with TCR (r) of 4000 ppm/°C will exhibit TCR tracking

The extraneous contribution by the common lead (0.2 in the case above) disappears in the event that critical ratios are specified and measured according to voltage division rather than resistance ratio.

Some circuits operated in a mode whereby current is switched off and on in one resistor, which is matched to a reference resistor carrying a constant current. In this case, even though the resistors may have identical TCRs and the substrate may be at a uniform ambient temperature, the resistances will differ in value as a result of self heating. (Strictly speaking this is not a true "tracking" requirement in as much as the resistors of interest are subjected to different stresses.) This difference will be governed by the absolute TCRs of the two resistors. In these applications, which are not uncommon, the resistors should have as low an absolute TCR as possible in the operating temperature region*, and the resistors should be designed as close together as possible to minimize the temperature differences between them.

*See diagrams on shaping the TCR curve

Resistors are frequently employed as voltage dividers. In this case, and where precise tolerances are involved, it is more appropriate to deal with voltage ratios than with resistance ratios. There are three important aspects of voltage ratios that should be understood in comparison with resistance ratios. They are: the voltage ratio itself, the tolerance of the voltage ratio, and voltage ratio tracking.

Ideally, the voltage drop across a pair of resistors is determined by the ratio of resistance values: R1/(R1 + R2). When the resistance values are not equal, the voltage ratio will differ from that calculated from the apparent (measured) resistance values by an amount which is governed by the resistance of the common lead. This deviation can be quite significant, especially with low value resistors.

For a 10 kilohm resistor in series with a 1 kilohm resistor, having a common "tap" lead with 100 milliohms resistance, the two ratios will differ by 75 ppm:

Voltage Ratio Calculated From Apparent Resistance:

Voltage Ratio Measured Directly:

For a 1K ohm resistor in series with a 100 ohm resistor, 100 milliohm tap resistance will produce a difference in the respective ratios of more than 800 ppm!

This illustrates the importance of specifying the proper operating parameter.

Voltage Ratio Tolerance - The tolerance assigned to a given voltage ratio also differs markedly from the related tolerance on the resistance ratio. The major amount of this difference is set forth by the first term of the following equation. It is also affected by the common lead resistance, as given by the second term in the equation.

Voltage Ratio Tracking - The relationship between the TCR tracking and Voltage Ratio (VR) tracking is more complex. If the common lead resistance is zero, the relationship is simply:

However, when the common lead resistance (r) is measurable, the apparent TCR tracking is higher than the "true" tracking, as shown earlier, and the Voltage Ratio tracking is lower.

The VR tracking is always less (better) than TCR tracking.

The effects described in the previous sections are reversible: the changes are not permanent and will disappear when the temperature returns to the starting point. There are, however, irreversible effects.

As discussed earlier, most precision resistor networks are used in a ratio mode. They have been trimmed to tight tolerances and carefully engineered to track within these tight initial tolerances with regard to resistance or voltage ratios. But this is meaningless unless these tolerances can be preserved throughout the life of the network. This requires maximum film stability. It is notable that recent advances in materials and processes have resulted in improving the stability of thin films to unprecedented levels, approaching those previously obtainable only with foils.

Extensive long-term stability testing of nickel/chromium alloys has shown conclusively that the rate of change of resistance with time is a single valued function of substrate temperature. This is a mathematical way of stating that temperature is the only variable—whether it is induced by power loading or simply by the ambient. Moreover, it has been determined experimentally that the stability measured at a higher temperature may be confidently extrapolated to lower temperatures and longer times according to classical kinetic equations.

Although the term "stability tracking" is not traditionally used, we may think of permanent changes in a pair of matched resistors as stability tracking. In contrast to TCR tracking, where close tracking is independent of the absolute TCR, stability tracking is somewhat dependent on the absolute stability. The more stable a pair of resistors, the less they will change in absolute value and in relationship to each other. Here again, the advantages of integrated construction are evident: all resistors in the network tend to have similar changes during life, and resistance ratios change far less than absolute values.

Because thin film precision networks are not generally used in high power applications, methods for establishing the maximum power ratings are not as critical as in general purpose networks. However, limits must be set and this is best done by establishing upper temperatures limits.

Zero Power Temperature (sometimes called the maximum operating temperature) is the maximum temperature at which the part can be operated, for a specified time (usually 1000 hours), without excessive change (usually defined in relationship to the initial tolerance), expressed in percent. For a thin film network required to maintain a 0.1% tolerance, this zero power temperature would be 150ÞC. At this temperature, a resistor might exhibit a change of the order of 500 ppm absolute or 100 ppm relative to others in a network. If the maximum initial tolerance required were 0.01%, a more appropriate zero power temperature would be 125ÞC. These levels are for hermetically-enclosed parts. If packaged non-hermetic, the parts would be given lower temperature rating.

Full Power Rating - Rated power is generally accepted as that power which is required to raise the surface temperature of a part above some ambient temperature, usually 70ÞC, to the zero power temperature. This is expressed in watts-full power. A power derating curve is used to determine limits at intermediate temperatures.

Special consideration must be given to the rating of individual resistors within a network, since the final surface temperature of an individual resistor will differ greatly depending upon whether other resistors in the network are under power. Although it is difficult to generalize, proper network design will account for these potential variations be arrangements providing uniform power density.

As indicated above, although the power levels in closer-tolerance precision networks are usually set lower, because chip dimensions are small, the power density can be high. A typical design level is 25 watts/in2 for very precise networks, but thin films are capable of sustaining remarkably high levels of power density as much as 200 watts/in2 without jeopardizing their integrity. As a final consideration, allowance must be made for the fact that packages vary widely in thermal resistance.

Voltage Coefficient of Resistance and Current noise

These two characteristics, which may be quite a serious drawback in resistors made from composite materials such as cermets or polymers, can be generally ignored with thin film precision networks because the magnitudes are so small. This is one of the major advantages of monolithic thin film materials.

Voltage coefficient of resistance is the unit change in resistance per unit change in voltage expressed as ppm/volt. It is a measure of the non-ohmic behavior, and in thin films, reaches identifiable levels only in the megohm range, where it has been measured at about 0.1 ppm/V.

Current noise is characterized and measured using a standard instrument developed by the Quantek Company. For thin films, a typical value would be less than - 35 dB.

Thermoelectric effects

Thermoelectric voltages may be generated if the terminations of resistors are at different temperatures. This can be a real problem with discrete resistors, where thermal gradients can exist over the relatively large dimensions. In thin film networks, all resistors are at or near the same temperature, as a result of their small size and the heat spreading effects of the thermally conducting substrate. Thermoelectric effects on thin films are typically < 0.1µ V/°C