introduce
Thermal management is crucial in package selection to ensure high product reliability. A good thermal assessment requires a combination of analytical calculations, empirical analysis, and thermal modeling. The challenge lies in determining whether a particular integrated circuit is reliable at high temperatures. Without following specific analytical methodologies, a reliable answer is impossible. In DC-mode operation, parameters such as thermal resistance (θJA) and junction temperature (θJC) are important. Thermal resistance, as the reciprocal of thermal conductivity, measures the temperature difference by which an object or material resists heat flow. Junction temperature, on the other hand, is a critical factor in the semiconductor thermal analysis of bipolar transistors, MOSFETs, and rectifiers. Currently, this term is used for all power supply devices, including IGBT devices. In AC mode or when LEDs are driven by MOSFETs using PWM modulation, it is necessary to define transient thermal data. The question we should answer is: how long can a chip operate at a certain power level before encountering thermal problems? In the following paragraphs, we will attempt to determine the thermal equations related to power consumption so that the junction temperature of the chip can be predicted as a function of time. This approach will be applicable to any type of chip. Based on these equations, an RC equivalent circuit model (easily simulated using SPICE) will be defined to represent the transient thermal characteristics of the IC.
Thermodynamics
The relationship between temperature and time stems from two main laws: Newton's law of cooling and the law of conservation of energy.
Where TB is body temperature, TA is ambient temperature, and KA is a proportionality constant.
Where P is the power applied to the body, m is the mass, and c is the specific volume. Newton's laws state that the rate of heat loss from the body is proportional to the temperature difference between the body and the environment. On the other hand, the law of conservation of energy states that energy cannot be created or destroyed, but can only be changed from one form to another or transferred from one object to another. As mentioned above, thermal resistance is the first factor to be analyzed: it can be easily found in the IC datasheet. Calculations should be performed under conditions of thermal equilibrium.
thermal model
At this point, a physical mathematical model should be defined so that the above equations can be applied. A schematic layout of chips mounted on a PCB is shown: involving different materials, including epoxy resin, chips, and packaging. The model we will analyze is based on the direction of heat flow: heat flows from an external source to the mold (when the main heat source is external) and from the mold to the environment (when the main heat source is external).
In the first case, we will solve the differential equation (dT B/dt) with respect to TB calculated in the second paragraph. When the heat source is external, the preceding formula can be used to estimate the chip temperature (at both the package and chip level). An example is a MOSFET near a high-current chip, which dissipates a significant amount of heat. We can now consider another case where the body generates heat on the chip and dissipates it into the environment through the epoxy resin and the package. To solve this system, it is necessary to define differential equations for all three components.
Where T<sub>Bi</sub> (i = 1, 2, and 3) are the instantaneous temperatures of the body (chip, epoxy resin, and encapsulation). The term P represents the power transferred from one object to another (e.g., P<sub>12</sub> is the power transferred from object 1 to object 2), while PG is the source power. Considering the expression for the power P of a single object and applying the Laplace transform, we obtain the following three differential equations for each object.
Where Ti is the integration constant, mi is a function of ki, and θij is the thermal resistance from object i to object j. To solve the equations mentioned above, we need to know all the parameters. To avoid tedious calculations, we can try to implement the model as a simple RC network so that the differential equations can be solved using circuit analysis software (Spice) by determining the relevant parameters.
The main idea is to model the differential equation obtained in the previous section using a passive RC circuit to simulate the power generated on the chip. The voltage across the capacitor represents the initial temperature of the chip (C1), epoxy resin (C2), and package (C3). VA represents the ambient temperature, while IS (the current flowing into capacitor C1) is the power generated on the chip. Replacing VC1 with TB1, VC2 with TB2, VC3 with TB3, and IS with PG, we obtain the following differential equation:
Mold temperature measurement
Different techniques can be used to perform die temperature measurements. One of these utilizes the forward voltage drop of an ESD diode. To ensure measurement accuracy is within permissible limits, the selected ESD diode should not have a large parasitic resistance. Furthermore, it is recommended to place the diode very close to the hottest spot on the chip. If you choose to use the Rds(on) of a FET as a temperature indicator, you must ensure that the FET is in off-mode at the measurement point. Rds(on), or on-resistance, represents the internal resistance of the transistor when it is in the on-state (VGS = 0). The ESD diode is connected between the chip pin and the supply voltage and has direct polarization. Since we obtain the voltage across the diode from the measurement, we must also consider the relationship between the voltage across the diode and the temperature.
RC network measurement
The MAX16828/MAX16815 LED drivers will be used to test the model just described. These chips can operate at voltages up to 40V with only a few external components. The MAX16828 provides a maximum LED current of approximately 200 mA. Both drivers are intended for automotive applications such as sidelights, exterior lights, backlights, and indicator lights. To obtain a direct indication of the die temperature, the DC voltage of the internal ESD diode connected between the DIM and IN pins was measured. The draw current was approximately 100 μA, resulting in a voltage change of approximately 2 mV/K.
The configuration ensures accurate temperature readings and estimates with an error of approximately ±10 mV. To calculate KA and θJA, the chip should be heated with a hot air gun. Die temperature can be monitored by measuring the diode voltage.
in conclusion
Analyzing die temperature using a full-chip thermal model is crucial for identifying and mitigating potential thermal risks. Experimental results obtained using Maxim drivers demonstrate the effectiveness of this model. Spice allows for easy simulation of RC networks to readily indicate the transient temperature of an IC. This model is applicable to any chip and allows for the definition of operating modes to avoid overheating.
