Steps of finding the solutions of heat-dissipated problems.
Junction temperature is the highest operating temperature of the actual semiconductor in an electronic device. In operation, junction temperature is higher than the case temperature and the temperature of the part’s exterior. The difference is equal to the amount of heat transferred from the junction to case multiplied by the junction-to-case thermal resistance. When designing integrated circuits, predicting and calculating the chip junction temperature is a very important task. This chapter describes how to derive the junction temperature from the thermal transport model.
- junction temperature
- thermal resistance
- thermal conduction
- thermal convection
- thermal radiation
From the small integrated circuits in 1960 to the development of today’s large and ultra-high-speed integrated circuits, the package density has increased from only several electronic components to billions of electronic components per chip. Because of this high package density, the combination directly causes a serious designing problem, and it will also increase the heat dissipation of the chip per unit volume or area. If the cooling method is not properly designed, this overheated high-density package chip will result in a high junction temperature. As a result, it will have a negative effect on the functions, the reliabilities, and the life of the electronic chip. Usually, a high-speed integrated circuit is the most expensive element of the whole package. If the chip continues to suffer from the effect of high heat, it will cause the speed to slow down or be damaged; therefore, the solution of the heat-dissipated problem should not be underestimated. In electronics manufacturing, integrated circuit packaging is the final stage of semiconductor device fabrication, in which the tiny block of semiconducting material is encased in a supporting case that prevents physical damage and corrosion. The case, known as a “package,” supports the electrical contacts that connect the device to a circuit board. The junctions of the chip are used by wire connecting on the package housing. These wires are then connected to other components through the wire on the printed circuit board (PCB). Therefore, for many integrated circuit products, packaging technology is a very important stage. Using chip as the main product such as random access memory (RAM) or dynamic RAM (DRAM), packaging technology not only can guarantee the separation of the chip and the outer world but also can prevent chip circuit from losing its function caused by the corrosion of the impurities in the air; also, the wellness of the packaging technology directly concerns the designing and producing of the PCB connected with the chip. This leads to the deeply influential of the chip’s performance. However, if the thermal impedance of the package is too high, the junction temperature will also be raised to a high level. According to the report, once the junction temperature is raised to approximately 10°C, half of the component life will be reduced . if the average life span is 30,000 to 50,000 hours, it is also implied that 15,000 to 25,000 hours of usage time will be decreased and result in the chip efficiency’s sharp decline. This chapter is mainly focused on the theoretically export system manufacturers’ topmost concern, junction temperature (
2. Theoretical derivation of the junction temperature
The following are the logical ways to think of the solutions to counter heat-dissipated problems.
2.1. Questions in Table 1
|A||What is the thermal model in this problem? Is it thermal conduction in ?|
Or thermal convection in ?
Or thermal radiation in ?
|B||Fluid? Is liquid? Or gas?|
|C||Can the fluid be compressed or not ?|
We usually supposed it is not compressible fluid.
|D||Are the fluid properties related to the temperature?|
|E||What is the status of the fluid?|
Is it laminar flow  or period cycle flow in ?
Or turbulent flow in ? Or transient in?
|F||What is the length of calculating Re’s characteristic?|
By tube diameter or by plate length or by obstacle height? Or others
|G||What is the effect of the viscosity in this problem ?|
How about the boundary layer ? What is mechanical loss? And others?
At this step, readers should have a good physical explanation for solving the questions. From steps A to G, we can be closer and see clearly the answer to the question.
2.2. Quantization and removal of unimportant parameters
The goal of this step is to think about every item of the question (or concept) to gain a deeper understanding. For example,
2.3. Establishment of the governing equation
The definition of the governing equation is using other variables to define an unknown item. If we only consider the heat transfer mechanics of the single chip on the PWB, take Figures 1 and 2, for example, during the heat transfer mechanism. The chip and the board both have thermal conductance, thermal convection, and thermal radiation. At this point, we can notice some of the characteristics of the heat transfer processes: (A) Multiple heat transfer processes, a high level of thermal coupling (heat source and sink). (B) Large-scale thermal spreading effect. If we consider all the heat transfer mechanism between each PWB, such as in Figure 3, then we need to also consider the thermal conductance coupling problem from the PCB. Among thermal convection, they include (i) material on the board, (ii) thermal convection and thermal radiation between each adjacent boards, and (iii) thermal coupling between the main board and the daughter card. Among radiation coupling, they include (a) material on the board and (b) adjacent boards. What needs to be paid attention of is when there is thermal coupling between the outer heat source and the chip heat itself. The heat received from the critical chip is not less than the heat source chip itself. Figure 4 presents a schematic diagram between the heat source chip and the critical chip of the motherboard and the outer heat source. Thus, to solve the heat-dissipated problem, we should not only pay attention to the temperature on the heat source of chip itself but also need to know problems such as the heat accumulation locations and the other chip influences.
2.4. How to analyze the influences of the thermal coupling
Thermal coupling makes it hard to analyze, if we do not include the thermal coupling in the calculation, and the results will not be accurate. Because of the thermal coupling natural properties, we need to consider the environment, chassis, PWB, component (module), chip, and parts (diodes, transistor) etc., when analyzing conducting a solution that can explain the thermal effect. Usually, there are three ways to solve either the key component or the heat source chip’s heat-dissipated problem (see Figure 5). One of them is using the integral method, that is, a closed-form solution. However, this method can necessarily not be used on every energy conservation. The second method is using the differential method, the so-called numerical analysis. Numerical analysis needs a special mathematical skills technique. It needs someone who has studied numerical analysis to write a program that includes grids definition, module establish, numerical analysis model, converging problem, boundary condition definition, etc. This needs to educate talented people, and most of the companies are unwilling to invest in here. But on the other hand, usually there are also software packages in the market, such as ice pack, fluent, ANSYS, and Flotherm. However, all these software packages cost more than USD 30,000 or 40,000. Not everyone can afford it, and most companies cannot even buy it—these are some of the difficulties what companies are facing. The third solution is measure it by experiment. The experiment is then separated into two kinds. One is the actual measurement that uses the real system with the samples attached to it to measure the data such as temperature. Although this is a very reliable way, it spends a lot of manpower and time, and the cost is expensive. Cooler manufacturers commonly do not use this solution. For example, Intel published the next-generation CPU, but there are supplier problems on these equipment, such as power supply, main board, south bridge, north bridge, hard disk, and DRAM. Cooler manufacturers can only solve the CPU’s heat-dissipated problems, and they really cannot wait until all these peripheral accessory devices are ready because it will take too much time and cost too much. Therefore, the actual measurement is only used in system manufacture, such as in HP, DELL, ASUS, ACER, and Lenovo. The second way of the experiment is the Dummy experiment, also known as Dummy heater. It is commonly used by the industry. For example, because we wanted to know what the thermal resistance of the cooler is, we only have to place the cooler on the heating copper block with which it has the same area and then measure the difference temperature between the heat copper block and ambient temperature then divide by the input power to get the thermal resistance of the cooler. The experiment does not have any complex problems. The only thing that we need to be aware of is the sensors’ correction, measuring the position and boundary condition.
2.5. Theoretical derivation of the junction temperature (
2.5.1. Consider a control volume around the outside of the component and lead pin
Take the control volume on the external chip and wire as in Figure 6.
Let us apply the energy balance equation to the body of the component and device power dissipation is “
Converting all the
220.127.116.11. Using Stefan-Boltzmann’s law to change the thermal radiation of the chip into temperature
where σ=Stefan-Boltzmann’s constant=5.669×10−8 W/m2 K4,
18.104.22.168. Using Newton’s cooling law to change the thermal convection of the chip into temperature
22.214.171.124. Using Newton’s cooling law to change the thermal convection of the lead into temperature
126.96.36.199. Using Fourier’s cooling law to change the thermal conduction of the chip into temperature through air gap between chip and board
Substitute the above into Eq. (1):
In Eq. (8),
2.5.2. Consider a control volume around the inside of the component
Assume a chip inside as shown in Figure 7, according to energy conservation
188.8.131.52. Using Fourier’s cooling law to change the inner thermal conduction of the chip into temperature
184.108.40.206. Using Fourier’s cooling law and Newton’s cooling law to change the thermal conduction and thermal convection of the chip and lead into temperature
As shown in Figure 8, the conduction heat transfer within the body of the component
Plugging all the thermal conduction equation and thermal convection into above equation, we obtain:
In Eq. (13), the junction temperature is what we need, but there are two unknown temperatures, such as
2.5.3. Consider a control volume around the air flow channel without considering adjacent heat source
Consider a control volume around the air flow channel as shown in Figure 9. The conduction heat transfer from component to board
From Eq.(1), with energy conservation of airflow channel:
……With energy conservation of air flow channel:
It is reasonable that all the power generation from the component should be carried away by the air flow. If not, the board temperature, the case temperature, and the junction temperature will be increased. However, Eq. (18) cannot help to solve the board temperature; therefore, we need to seek another control volume to solve
2.5.4. Consider a control volume around the board
Consider a control volume around the board as in Figure 10, where
Energy balance for the steady-state condition:
In Figure 11, the conduction heat transfer from component to board
After obtaining a first estimate of the board temperature and assuming that the heat is uniformly distributed over the board, neglect
Hence, we have a first estimate of Tb.
2.5.5. Solve for
TC, Tb, and TJ
220.127.116.11. Method 1
R th, JCcan be obtained from the vendor:
18.104.22.168.2. If Rth,JC is unknown
In the case of duct flow, from Eq. (26), we need to obtain
In duct flow, the ambient temperature is the average temperature of the air inlet temperature and air exit temperature:
However, in Eq. (30), the heat transfer coefficient
22.214.171.124. Method 2
The definition of thermal resistance
The thermal convection resistance from chip surface to ambient
Therefore, the total thermal resistance
The thermal resistance
The case temperature
2.5.6. Consider a control volume around the air flow channel with adjacent heat source
Now, if we want get a more accurate expression for the board temperature
Because we have
Figure 14 shows the flow chart solution for
The goal of the thermal designer is to minimize the thermal resistance of the chip. Equations and analysis procedures are provided in this chapter to assist the designer in understanding the thermal characteristics of chip devices and the thermal performance of related materials. The methods are useful for the approximations of the chip junction temperature. In the meantime, the permissible dissipated powers of chip can be estimated as well.
Bogatin E., Roadmaps of Packaging Technology. Chapter 6, In: Chip packaging: Thermal requirements and constraints, D. Potter and L. Peters, editors, Integrated Circuit Engineering Corporation, 1997, pp. 6-1. Available at: http://www.smithsonianchips.si.edu/ice/cd/PKG_BK/title.pdf.
Holman J.P., Heat Transfer, 7th ed., McGraw-Hill Publishing Co., Singapore, 1992, pp. 2–10.
Rolle K.C., Heat and Mass Transfer, 1st ed., Prentice-Hall, Upper Saddle River, NJ/Columbus, OH, 2000, pp. 205–228.
Kern D.Q., Process Heat Transfer, McGraw-Hill Book Co., New York, 1976, pp. 62–84.
Goldstein R.J., Fluid Mechanics Measurements, University of Minnesota, 1983, pp. 51–60.
Byron Bird R., Stewart W.E., and Lightfoot E.N., Transport Phenomena, John Wiley Sons, Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin, USA, 1960, pp. 56–61.
E. Benjamin Wylie Victor L. Streeter, “Fluid Transients Systems”, Prentice-Hall Inc A Simon & Schuster Company, Englewood Cliffs, NJ, USA, 1993, pp.287–305.
Whitaker S., Fundamental Principles of Heat Transfer, Library of Congress Cataloging in Publication Data, 1977, pp. 273–303.
Holman J.P., Experimental Methods for Engineers, 7th ed. Mc-GRAW-Hill Book Co., Singapore, 2001. pp. 432–434.
Schlichting H., Gersten K., Krause E., Oertel Jr. H., and Mayes C., Boundary-Layer Theory, 8th ed. Springer, 2004. ISBN 3-540-66270-7.