6 The role of temperature in NBTI characterization

Having evaluated and summarized fundamental features of NBTI degradation and recovery in the previous chapters, this chapter recalls the drawbacks of conventional characterization techniques and introduces a new hardware tool, enabling us to overcome previously strict experimental limitations regarding temperature. The new experimental approach is based on in-situ polyheaters which enable us to switch the temperature of the device in a very fast and defined way. Having broadened one’s mind to the possibility of switching the temperature at arbitrary points of time, the polyheater technique opens up unprecedented experimental capabilities for NBTI characterization.

This chapter addresses the calibration procedure of the polyheater tool, investigates its capabilities and demonstrates dedicated experimental setups which become feasible once having a well calibrated and stable temperature switching tool at hand. Having embedded the polyheater in the measurement software environment, the technique allows to run stress/recovery experiments with variable temperature. From these experiments new fundamental features of NBTI arise, helping to clarify conflicting issues in literature and allowing to draw new conclusions which finally lead to a more consistent microscopic picture of the degradation and the recovery mechanism.

6.1 Fast heating and cooling using in-situ polyheaters

In this section the in-situ polyheater measurement technique is introduced and its power for device characterization and reliability issues is discussed. Furthermore, the calibration procedure and performance of the polyheater tool is elaborated. A particular emphasis is put on the accessible temperature range, the heating and cooling dynamics as well as on the impact of the temperature gradient between heater, active device and thermo chuck. Once calibrated, the polyheater technique provides a reliable solution for fast and arbitrary temperature switches and offers the possibility to reach device temperatures far beyond the operating range of conventional thermo chuck systems [154].

6.1.1 Hardware assembly and polyheater design

Poly resistors surrounding a silicon device can be used to perform fast in-situ heating on a single device on wafer level which is commonly applied in time-critical fast wafer level reliability (fWLR) monitoring [155, 156, 157, 158, 159]. The main advantage of the polyheater is that it provides an elevated stress temperature without the use and the limitations associated with a conventional heating system like a thermo chuck. Although, this alone is already a valuable feature, it does not even begin to explore the multitude of possibilities one finds in a more scientific use of the tool. By correct calibration and automation of the polyheater-device system, the temperature becomes a quasi arbitrary experimental parameter which can be switched easily by more than within a couple of seconds. For such an application conventional thermo chuck systems are unsuitable because they are slow and their heating/cooling durations depend strongly on the difference to the target temperature. Furthermore, when attempting to keep the junction biases applied during the temperature switch, it is a mandatory requirement not to lose probe needle contact. Since heating and cooling of a wafer on a thermo chuck involves considerable thermal expansion of wafer, needles and pads, this request cannot be fulfilled over a wide temperature range without continuous manual readjustments. As opposed to heating the whole wafer on the thermo chuck, in-situ heating by poly wires is very local. Hence, there is no thermal expansion of needles and pads, which saves us from losing mechanical contact during the temperature switch.

Once calibrated and implemented in the software, the polyheater feature opens up unprecedented possibilities for device characterization and reliability testing. Its application potential is thereby way beyond the scope of NBTI characterization. The concept of in-situ heating by implanted poly wires has been taken up also for instance for thermo cycling [160] or for performing on chip high temperature annealing of irradiated PMOS dosimeters [161].

A common challenge of in-situ heating can be found in the fact that the device we want to heat is in most cases a distance away from the actual heating source. Consequently, the poly wires are always hotter than the tested structure itself, which results in a temperature gradient between radiator, device, and ambient. From a technology point of view the distance between the polyheater wires and the active areas of the device must be large enough to prevent a direct current flow between the individual components. However, the larger the distance between the heater and the device, the higher is the thermal resistance of the system and the more power has to be applied to the wires in order to generate a certain elevated device temperature. Furthermore, the time delay for restoring thermal equilibrium must also be taken into account as we switch the heater on or off abruptly. The farther the heater is away from the device, the longer it takes to restore thermal equilibrium. Thus, in order to find the optimal distance between the heating source and the active device for a particular application, the above specified points have to be considered carefully.

The layout of an active transistor surrounded by a polyheater system and placed on a thermo chuck is illustrated schematically in Fig. 6.1. Depending on the ground temperature of the thermo chuck, a certain power has to be applied to the heater in order to reach a specified device temperature. From a layout point of view the heater should overlap the device considerably in order to guarantee a homogeneous temperature distribution over the whole active device area. The theoretical determination of the polyheater and the device temperature as a function of the power is very difficult [162] since considerable simplifications are required due to the fact that various back-end layers and materials usually have non-linear thermal conductivities [163]. In the following subsections an experimental procedure is presented, allowing to determine the power supply which is necessary to bring an active transistor to a certain device temperature. Thereby, we evaluate both the heater and device temperature which enables us to estimate the temperature gradient between poly wires and active device. Furthermore, we extract the transient heating and cooling characteristics for different target temperatures and discuss effects that may delay the restoration of thermal equilibrium and destabilize an adjusted temperature.

6.1.2 Calibration of heater and device temperature

In order to extract the polyheater and device temperature as a function of the applied power, we call on an appropriate temperature dependent parameter of the material. In the case of the highly doped poly silicon wire, the temperature dependent electric resistance () would be such a parameter. In the case of the MOS transistor the forward current of the source/bulk diode or the source/drain current (around the threshold voltage of the device) can be used as an appropriate thermometer. For reliability issues, the source/drain current () is the preferred reference since it directly reflects the temperature of the interface between the silicon substrate and the gate oxide. This interface is of major interest because most studies suggest this region to be the location of concern for NBTI.

For the initial calibration we heat the wafer on the thermo chuck from -60 °C to 300 °C and record the poly resistance () and the drain current () of our PMOS device at selected temperatures, cf. Fig. 6.2 (a). The sense currents and voltages must be chosen carefully in order to prevent self-heating during the measurement. Within the scanned temperature range the increase of the poly resistance and the drain current can be fitted very well by a polynomial of first (linear) or of second-order. From a physical point of view, the increase in the poly resistance can be explained by a reduction of the carrier mobility due to enhanced lattice scattering at higher temperatures while the increase in the drain current is originated in an enhancement of the concentration of thermally activated inversion carriers (). Having determined the coefficients of the polynomial fit, we can calculate the poly and device temperature from and , respectively, when a power is applied.

In Fig. 6.2 (b) the poly resistance and the drain current is illustrated as a function of the power supply (). In this example the chuck temperature was -60 °C. When applying zero watts ( = 0), the poly resistance and the drain current correspond exactly to their values extracted for -60 °C in Fig. 6.2 (a). As we increase the power supply from 0 toward 6, the poly resistance and the drain current grow simultaneously. In order to provide enough time for restoring thermal equilibrium, the power supply steps must be moderate. In the analysis () can be converted into the temperature of the polyheater () and () into the device temperature ().

The temperatures as a function of the power supply are illustrated in Fig. 6.3 (a). As can be seen, when applying a heater power of 6 at a chuck temperature of -60 °C, one may reach a device temperature of approximately 175 °C. This corresponds to a maximum temperature range of = 235 K. Naturally, the correlation between the heater power and the accessible device temperature depends on the particular poly design. The higher the supplied power, the further the poly and the device temperature drift apart. For example, at a poly temperature of 150 °C the device temperature is just 125 °C. This is caused by the vertical temperature gradient between the heater and the device, cf. Fig. 6.1.

From the slope one can determine the individual thermal resistances. In Fig. 6.3 (b) the thermal resistances and of our particular heater design are depicted for different chuck temperatures. Obviously, and increase as the ambient temperature increases. This means that less power has to be applied at higher ambient temperatures in order to bridge the same temperature range . This is due to the non-linear thermal conductivity of silicon. In fact, the thermal conductivity decreases as the temperature increases [162, 163, 164]. Consequently, the dissipated heat by the poly wires is distributed to a smaller area the higher the temperature. Due to the more concentrated power dissipation, poly and device heating become more efficient at higher chuck temperatures.

In many cases one is not interested in the thermal resistance and in the heating characteristics, making the calibration procedure for a single target temperature much less laborious. In principle, it is sufficient to determine one single target drain current at a certain target temperature. Therefore, we heat the thermo chuck to the desired temperature and record the corresponding target current at an arbitrary operating point (i.e. the threshold voltage of the device). When later (at a lower chuck temperature) determining the power supply necessary to reach this elevated target temperature, we simply increase the power supply incrementally while measuring the drain current in parallel at the same operating point as before. Once the measured drain current corresponds exactly to its calibrated target value, the required power supply is found.

6.1.3 Maximum accessible temperature range

A remarkable application of the polyheater technique can be found in the ability of reaching device temperatures far beyond the scope of conventional thermo chuck systems. For instance, an ultra high target temperature can be reached when providing additional heating power at the maximum temperature range accessible by the thermo chuck. This feature enables us for example to determine activation energies of NBTI induced defects in a much wider temperature range than provided by our thermo chuck.

However, the calibration procedure of the polyheater in the high temperature regime (beyond the scope of the thermo chuck) requires more effort. This is because we cannot determine a target drain current in a temperature regime which is not accessible by the thermo chuck. Furthermore, previously established thermometers like the drain current change their temperature dependent characteristics as the semiconductor becomes intrinsic.

The high temperature calibration is illustrated in Fig. 6.4. In Fig. 6.4 (a) the same experiment as in Fig. 6.2 (b) was performed, however, this time at a chuck temperature of 150 °C. As we increase the power supply at an ambient temperature of 150 °C, the heater resistance () and drain current () initially show a similar behavior as observed in Fig. 6.2 (b). Both parameters increase regularly until we reach a power supply of approximately 3. According to the thermal resistance of 55 (cf. Fig. 6.3 (b)), 3 applied at a ground temperature of 150 °C should elevate the device temperature to approximately 315 °C. Beyond this temperature range the doped silicon substrate becomes intrinsic which changes the current/voltage characteristics and temperature development of the drain current significantly. As can be seen in Fig. 6.4 (a), between 3 and 5 the drain current begins to deviate from its linear temperature dependent relationship (cf. Fig. 6.2 (a)) and can therefore no longer serve as a reliable thermometer. On the other hand, the poly resistance abides by its regular development which validates still for poly temperature extrapolation.

In Fig. 6.4 (b) we have determined the interface temperature of the device for an increasing power supply in two different ways. The first way is simply linked to the thermal resistance evaluated in Fig. 6.3 (b) for 150 °C. According to at 150 °C, the device temperature should increase by 55. We can use this result to calculate the device temperature in a straight-forward manner. The second way is a little bit trickier. From the poly resistance, which still follows its regular development in the high temperature regime, we can extrapolate at first the poly temperature as a function of the power supply. In a second step the device temperature is calculated from the poly temperature. The procedure is similar to the one demonstrated in Fig. 6.3 (a), however, this time for a chuck temperature of 150 °C. As can be seen in Fig. 6.4 (b), the results of both methods agree very well and give similar device temperatures with a maximum discrepancy of about . We remark that at a chuck temperature of 150 °C one is able to exceed device temperatures up to 400 °C which is far beyond the scope of most industrial thermo chuck systems. At the moment we turn off the heater, the temperature drops back to 150 °C almost immediately. The detailed heating and cooling dynamics of the heater-device system are investigated in the next subsection.

6.1.4 Heating and cooling dynamics

In this subsection we elaborate on the time dependent heating and cooling dynamics of the device as a heating voltage/power is applied or removed, respectively. The chuck (ambient) temperature was -60 °C during these experiments. By applying a certain heating voltage to the poly wires, the device temperature quickly elevates and stabilizes after a couple of seconds. On the other hand, when removing the heating voltage, the device cools down immediately. In order to determine the exact heating voltage necessary to reach a certain device temperature, the heater was calibrated in advance. The output of this initial calibration were 8 different heating voltages appropriate to heat the device from -60 °C to -40/-20/0/25/50/75/100/125 °C. In the experiments illustrated in Fig. 6.5, a heating voltage is abruptly applied while recording in parallel the heater current for 100. After this 100 heating period the supply voltage was removed abruptly recording again the heater current in parallel for another 100. From the heating voltage and current characteristics the time dependent power dissipation of the heater is calculated.

As can be seen in Fig. 6.5 (a), when turning the heater on, it takes up to 1 until the maximum power dissipation is reached. This delay time is mainly limited by the finite speed of the voltage source. Using our particular heater design, heating voltages up to 34 are required in order to overcome a temperature range of 185 K (-60 °C 125 °C). After the voltage source has stabilized (> 1), the heater power tends to decrease slightly for a couple of seconds. This is because some time is needed to restore thermal equilibrium between heater, wafer, and thermo chuck. Consequently, the initial power decrease is more significant the larger the temperature difference between heater and chuck. When turning the heater off, the heater power vanishes within approximately 1. Again, this 1 is originated in the finite speed of the voltage source.

In Fig. 6.5 (b) the same experimental sequence as in Fig. 6.5 (a) was performed but this time the drain current of the device was recorded as a representative for the interface temperature. By using the results of Fig. 6.2 (a) one can calculate the evolution of the device temperature from .

As can be seen in Fig. 6.5 (b), when turning the heater on abruptly, it takes up to 10 until the device has stabilized at its calibrated target temperature. The larger the temperature difference, the longer it takes to reach the target temperature. The larger time delay is due to the finite time interval necessary to restore thermal equilibrium a distance away from the actual heating source. The shoulder visible in the evolution of during heating is due to the power decrease illustrated in Fig. 6.5 (a). We remark that although heater power and heater temperature reach a maximum 1 after turning the heating voltage on, the device temperature does never exceed its target value due to the delayed thermal coupling between the polyheater and the device. This is an important aspect since we do not want to subject the device to an elevated pre-stress at the moment the heater is turned on. When turning the heater off, the situation is similar as during heating. It takes a couple of seconds until the excess heat generated by the polyheater can be removed by the thermo chuck. Following Fig. 6.5 (b), we come to the conclusion that at -60 °C ambient temperature, any temperature switch up to 200 K can be executed safely within a time interval of maximal 10. In fact it takes approximately 0.1 to reach the target temperature by 3, 1 to obtain a 1 accuracy and after 10 the target temperature is adjusted by 0.1 which corresponds to the measurement resolution as well.

6.1.5 Summary of the polyheater features

In the previous subsections the features and performance of the in-situ polyheater measurement technique was demonstrated. The temperature calibration procedure for determining the poly temperature and device temperature was elaborated in detail for different ambient temperatures and power supplies. The thermal resistances of the polyheater and the device were found to depend on ambient temperature which is consistent with the non linear thermal conductivity reported for silicon. It was shown that a temperature range of more than 200 K can be bridged by additional power supply provided by the polyheater. In particular, the ability of reaching device temperatures far beyond conventional thermo chuck ranges was pointed out. A thorough study on the heating and cooling dynamics of the device has revealed that a maximum time of 10 is needed to switch the temperature within an interval of 200 K with a maximum precision of 0.1 K. Thereby, the heating and cooling procedure was found to be nearly independent of the difference between ambient temperature (chuck temperature) and target temperature. Equipped with this features the polyheater tool exhibits a remarkable and unique tool for device reliability testing and characterization purposes which will be applied in the following sections for NBTI investigation.