Experimental data (nominal sheet resistance
New contemporary applications of thick resistive films are inducing the need to investigate their behaviour under various stressing conditions. On the other hand, there is a growing interest in noise measurements as means of thick‐film resistor quality and reliability evaluation and evaluation of degradation under stress. For these reasons, this chapter presents effects of mechanical, electrical and simultaneous mechanical and electrical straining on performances of conventional thick‐film resistors that are analysed from micro‐ and macro‐structural, charge transport and low‐frequency noise aspects.
- thick‐film resistors
- mechanical straining
- high voltage pulse stressing
- gauge factor
- noise index
Present miniaturization trends and ongoing usage of thick‐film resistors in sensitive telecommunications equipment have induced the need to investigate their reliability under various straining conditions. The most of the published data dealt with effects of mechanical straining on performances of these complex heterogeneous systems using the piezoresistive effect in thick resistive films for strain gauge realization [1, 2]. On the other hand, performances of standard thick resistive films subjected to unwanted mechanical straining [3–5] have not been sufficiently investigated despite the fact that mechanical straining may take place during all phases of resistor realization, examination and application. In case of high‐voltage pulse stressing, the most of the papers investigated effects of trimming of thick resistive films by energy of high‐voltage pulses [6–8] and behavioural analysis of surge thick‐film resistors . Influence of electrical straining on the reliability of conventional thick resistive films has been seldom investigated. Little attention has particularly been paid to examining effects of the simultaneous impact of these two types of straining with respect to their contrasting effects on resistor performances. In addition, standard low‐frequency noise measurements [10–13] are being recognized as useful tools in reliability analysis of thick‐film resistors subjected to various straining conditions. For these reasons, this chapter focuses on performance analysis of mechanically, electrically and simultaneously mechanically and electrically strained thick‐film resistors based on compositions with three different volume fractions of conducting phase, using standard resistance and low‐frequency noise measurements as valuable indicators in reliability evaluation of thick resistive structures under a wide range of extreme working conditions.
2. Mechanically strained thick‐film resistive structures
Thick resistive films have been known for their piezoresistive properties for more than 40 years. Over the years, strain gauge applications have been topics of the most of the available published data. At first, only the basic piezoresistive characteristics of thick resistive films were examined. Later on, new resistive sensing elements emerged based on novel thick‐film inks designed for each specific application [14, 15]. On the other hand, standard thick‐film resistors are being continuously used in contemporary electronic equipment that requires high functional capability, improved reliability and environmental stability. These up‐to‐date applications induced the need to examine performances of standard mechanically strained thick‐film resistive structures [5, 16].
Sensitivity of a certain material to mechanical strain is referred as the gauge factor. In case of thick‐film resistive structures, gauge factor (
The relation between strain and resistor position on the substrate can be given by the equation :
Schematic presentation of mechanically strained thick‐film resistor is given in Figure 1.
Mechanical straining causes a reversible resistance change in thick‐film resistors [5, 16]. The reversible resistance change is partially due to change in resistor geometry but mainly due to micro‐structure changes. According to 3‐D planar random resistor network model , transport of electrical charges in thick‐film resistive materials takes place via a complex conductive network formed during firing by sintering metal‐oxide particles (usually combination of RuO2 and Bi2Ru2O7) immerged in the glass matrix. During the sintering process, a number of conducting chains is being formed. These chains consist of clusters of particles (particles that are in contact) and neighbouring particles separated by thin glass barriers (metal-insulator-metal or MIM units). Therefore, the current flow is being determined by metallic conduction and tunnelling through glass barriers. The micro‐structure of thick resistive films, determined by the ratio of the conducting and insulating phase, also determines conducting mechanisms present in the film. Performed experiments , illustrated by data given in Table 1, showed that gauge factor values are greater for resistors realized with compositions with higher sheet resistances, that is, resistor compositions with smaller volume fractions of conducting phase have greater
3. Electrically strained thick‐film resistive structures
Different conditions of thick‐film resistor application that induced the need to investigate their behaviour under stress also brought to attention the importance of high‐voltage pulse stressing. The most of the available data dealt with trimming of thick resistive films by the energy of high‐voltage pulses [6–8], a trimming method based on internal discharges using both thick‐film resistor terminations as electrodes for applying the high‐voltage energy to the resistor body. Also, several papers explored properties of low‐ohm thick‐film surge resistors  that serve as protection of communication systems. However, little attention has been paid to the influence of high‐voltage pulse stressing on structure and noise performances of conventional thick‐film resistors [20, 21].
High voltage pulse stressing of thick resistive film causes irreversible resistance change. Experimental data obtained by extensive investigations of performances of thick‐film resistors subjected to this type of straining [20, 21] showed that behaviour under strain strongly depends on sheet resistances of resistor compositions used. Resistors based on compositions with low sheet resistances exhibit macro‐structural changes that result in irreversible resistance increase. Lack of micro‐structural changes is a consequence of the dominant conducting mechanism, conducting through clusters of conducting particles. High‐voltage treatment leads to burning and evaporation of the resistive layer. Resistor volume is reduced causing the significant resistance and noise index increase (Figure 2).
Resistors realized using compositions with medium values of sheet resistances exhibit initial resistance decrease followed by the significant resistance increase during high voltage pulse stressing (Figure 3). Lower pulse amplitudes lead to resistance decrease due to changes in conducting mechanisms, metallic conduction through conducting particles and sintered contacts and tunnelling through glass barriers. High‐voltage treatment affects charges captured by traps present in thin glass layers between neighbouring conducting particles or the trap concentration increases  due to existence of impurities introduced in insulating layers during firing. In addition, a minor resistance decrease may occur due to the conversion of single chain from non‐conductive to conductive state. High‐voltage treatment induces electrical field inside MIM unit that is insufficient to provoke dielectric breakthrough and therefore decrease of the resistance due to the increase in a number of contacts between neighbouring particles does not occur. Measured resistances substantially increase when the pulse voltage reaches the critical point when macro‐structural changes occur. High‐voltage treatment leads to burning and evaporation of the resistive layer thus reducing its volume and causing significant resistance increase similar to the one seen in resistors based on compositions with low sheet resistances. Since the low‐frequency noise in thick‐film resistors is the consequence of electrical charge transport fluctuations, noise index values are in agreement with resistance behaviour (Figure 3). Due to high voltage treatment, conduction is being modulated by electrical charges captured by traps that are not directly involved in conduction, thus altering the height of the potential barriers of MIM units. For these reasons, measured noise index values are more sensitive to changes on micro‐structural level than resistance.
Established correlation between structural properties and low‐frequency noise can also be illustrated using noise spectra measurements (Figure 4). The fitting of experimental results for current noise spectra and the following theoretical relation can be performed:
The first term is the thermal current noise given by:
Normalized noise amplitude
When thick‐film resistors based on high sheet resistance compositions are concerned, due to a low volume fraction of the conducting phase, dominant conduction mechanism is tunnelling through glass barriers. Stressing causes pronounced micro‐structural changes, changes barrier resistances and causes significant resistance decrease similar to the ones seen in resistors based medium sheet resistance compositions. Experimental data showed that noise index values are in agreement with resistance behaviour exhibiting an increase of
4. Simultaneous mechanical and electrical straining
Investigations of mechanical and electrical straining of thick‐film resistors showed that these two types of straining have opposite effects on behaviour of these complex nanostructures [5, 20, 21]. Examining effects of the simultaneous impact of mechanical and electrical straining on thick‐film resistors  is of particular interest for sensitive equipment exploitation since simultaneous mechanical and electrical straining may affect resistors capability to withstand high‐voltage treatment.
In the case of medium and high sheet resistance compositions, resistance changes of thick resistive films exposed to high‐voltage treatment are caused by changes in the micro‐structural level  that result in decreasing resistance values. In a case of thick‐film resistors subjected to mechanical straining, resistance changes are caused by changes in physical dimensions and more dominantly by changes on micro‐structural level resulting in increasing resistance values [5, 16]. On the other hand, simultaneous mechanical and electrical straining has opposing effects on performances of thick‐film resistors . The ratio of conducting and insulating phase determines sheet resistances of thick resistive films and accordingly micro‐structural properties and charge transport conditions. When compositions with a high content of conducting phase are in question, metallic conduction is the dominant conducting mechanism. When the simultaneous impact of these two types of straining are in question, they have opposing effects on tunnelling through insulating layers of MIM unit and accordingly on barrier resistances. In a case of applied mechanical straining, widths of glass barriers are being altered. On the other hand, applied electrical straining affects glass barrier heights. Taking into account the fact that tunnelling is not a dominant conducting mechanism when thick‐film resistors with low sheet resistances are concerned, the lack of micro‐structure changes is expected. Simultaneous mechanical and electrical straining cause changes in the macro‐structure. High‐voltage pulse stressing causes visible vaporisation of resistive layers. It decreases volumes of resistors and therefore significantly increases their resistances. Gauge factor changes exhibit increase following the shapes of curves of the resistance changes due to resistor degradation. Noise index values are in agreement with resistance behaviour and show significant increase confirming the fact that noise parameters are very sensitive to structural changes of thick‐film resistors, more sensitive than resistance changes (Figure 8).
In a case of resistor compositions with medium sheet resistances, conduction incorporates both tunnelling through glass barriers and metallic conduction. Change of barrier resistance results in decreasing resistance values that is being succeeded by increasing resistance values caused by alterations on macro‐structural level analogous to ones observed in low sheet resistance compositions.
In the case of high sheet resistance resistor compositions, small conducting/isolating phase ratio determines dominant conducting mechanism‐tunnelling through glass barriers. This small volume fraction of conducting phase leads to pronounced micro‐structure changes, changing barrier resistances and causing significant resistance decrease. Gauge factor changes show an increase with the applied straining as well as noise index values. Experimental results for relative resistance, gauge factor changes and noise index for simultaneously mechanically and electrically strained 100 kΩ/sq thick‐film resistors are given in Figure 10.
Sources of low‐frequency noise in thick resistive films are correlated to charge transport mechanisms ; metallic conduction is correlated to resistance fluctuations of contact resistivity and particle resistivity and tunnelling through glass barriers is correlated to noise due to modulation of the Nyquist noise and fluctuations induced by existence of traps in insulating layers of MIM units. Figure 11 shows experimental results for current noise spectrum before and after simultaneous electrical and mechanical straining of thick resistive films whose experimental results for relative resistance, gauge factor and noise index changes are given in Figure 9 . Presented data demonstrate that changes on micro‐structural level cause initial resistance decrease. Changes on macro‐structural level have an opposing effect. Initial resistance decrease is being followed by resistance increase, thus reaching the initial resistance value.
In order to fully comprehend effects correlated to a current noise of simultaneously strained thick resistive films, the fitting procedure was implemented based on experimental data presented in Figure 11 and theoretical relation (4). As an illustration, the fitting and experimental results for the curve (4) in Figure 11, together with contributions of different kinds of noise sources in the total current noise spectrum, are given in Figure 12.
In the total current noise spectrum, dominant 1/
It can be seen that parameter
In the fabrication of precise and reliable up‐to‐date communication systems stability and precise resistance values of widely utilized conventional thick‐film resistors are of great importance. Different conditions of their application induced the need to investigate their behaviour under stress, especially under influence of mechanical and electrical straining. Mechanical straining leads to reversible resistance change due to change of charge transport conditions. It predominantly affects tunnelling through glass barriers by changing barrier widths. Electrical straining leads to irreversible resistance change due to barrier height alteration. Simultaneously, mechanically and electrically strained resistors are affected in two opposing manners; mechanical straining reversibly alters barrier widths while electrical straining irreversibly affects barrier heights. Having in mind that tunnelling through glass barriers is primarily affected by simultaneous straining; an impact of the simultaneous straining can be optimally evaluated using resistors with medium sheet resistances that include both metallic conduction and tunnelling through glass barriers. Results presented in this chapter can be viewed as an experimental verification of correlation between resistance, gauge factor and low‐frequency noise parameters (noise index and current noise spectra) and changes with resistor degradation due to the impact of these three types of straining. Furthermore, they can be seen as validation of earlier presumptions [24, 25] that standard resistance, noise spectrum and noise index measurements are valuable tools in reliability evaluation of thick resistive films.
The authors would like to thank the Ministry of Education, Science and Technological Development of the Republic of Serbia for supporting this research within projects III44003 and III45007.