A.L. Palisoc

Thermal analysis of integrated circuit devices and packages

The integrated circuit device is modeled as a four-layer structure with multiple heat sources located on the surface of the first layer and with the fourth layer representing the device package. Each layer is assumed to have the same rectangular dimensions. Using the separation of variables, an analytical solution for the temperature at any location inside and on the boundaries of the structure is derived. Based upon the solution obtained, a computer program, Thermal, has been written in Fortran. Characteristics of the solution were studied, and several representative device structures were analyzed. The results of the simulation show how the device thermal resistance is affected by the die-bonding layer properties, the electrodes on the chip surface, and the heat spreader at the bottom surface of the chip. A FET power device was also analyzed to illustrate the very narrow hot zones produced on the chip surface, suggesting that the thermal measurement techniques must have adequate spatial resolution to measure the peak temperatures accurately. The lateral spread of heat flux into the regions of the package extending beyond the chip dimensions was studied using the boundary element method. An iteration technique based on the analytical solution has also been developed to account for the effect of this lateral heat spread. The corrected temperature using this iteration technique agrees to within 3.7% with that obtained using the boundary element method. >

Thermal analysis of solid-state devices using the boundary element method

Thermal analysis of two-dimensional and three-dimensional two-layer device structures have been carried out using the boundary element method (BEM). The resulting thermal profiles for two different device structures agree very well with those obtained using analytical solutions. This agreement indicates not only the accuracy of the BEM but also the correct derivation of the analytical solutions. >

Transient thermal study of semiconductor devices

An analytical three-dimensional transient temperature solution of a two-layer semi-infinite plate structure with embedded heat sources is discussed. The thickness of the second layer is assumed to extend to infinity. By incorporating the method of images this solution can be used to approximate the structure with finite second-layer thickness. Exact temperature can also be obtained for the rectangular lateral boundaries by the use of the method of images. The correct derivation of the solution is verified by comparing it with the result of the steady-state temperature solution. A computer program has been written based upon the solution and the method of images. A variety of device structures have been studied. Results on the thermal risetime and the effect of the second-layer medium have been obtained. The software is particularly useful for devices operating under pulsed or switching conditions. >

Real-time thermal design of integrated circuit devices

A novel method for real-time thermal design of integrated circuits is presented. The method uses a multiple regression technique whose input is the thermal profile due to a unit heat source over an infinite multi-layered plate structure. The unit profile in two dimensions is calculated using the Fourier integral solution and matched to an equation having several parameters. The temperature profiles of rectangular device structures having the same layered composition are computed by superposing the profiles generated by the matched equation, shifted in position according to the source location and weighted by the source power. By using the proposed approach, it is possible to reduce the CPU time required by a factor of several hundred thousand compared to analytical approaches and numerical techniques. As a result, it is possible to perform IC (integrated circuit) thermal design at the chip level. >

Exact thermal representation of multilayer rectangular structures by infinite plate structures using the method of images

Using the method of images and the analytical temperature solution to the multilayer infinite plate structure, the thermal profile over finite rectangular multilayer integrated circuit devices can be calculated exactly. The advantage of using the image method lies in the enhanced capability of arriving at an analytical solution for structures where analytical solutions do not apparently exist, e.g., circular or arbitrarily oriented rectangular sources over multilayered rectangular structures. The new approach results in large savings in computer CPU time especially for small sources over large substrates. The method also finds very important applications to integrated circuit devices with heat dissipating elements close to the edge boundaries. Results from two examples indicate that the edge boundaries of a device may also be utilized to remove heat from it. This additional heat removing capability should have important applications in high power devices.

Thermal properties of the multilayer infinite plate structure

Using the double Fourier integral transform method, the analytical temperature solutions to the single‐layer and multilayer structures with infinite lateral dimensions have been derived. For the single‐layer structure, temperature dependence of the thermal conductivity has been taken into account using the Kirchhoff transformation. The use of discrete rectangular heat sources rather than circular heat sources on the top surface of the structure makes this model particularly useful for the thermal analysis of common solid‐state and integrated circuit devices and packages. For studying the thermal properties of a large class of solid‐state device geometries, this model can be utilized to approximate actual devices with reasonable accuracy. The general device geometries for which this model can be employed to represent the actual devices are determined. Compared with the model where the finite extent of the chip lateral dimensions is considered, the present model is much more computationally efficient for ca...

Thermal properties of five‐layer infinite plate structures with embedded heat sources

The analytical three‐dimensional temperature solution of a five‐layer anisotropic plate structure with infinite lateral boundaries and with embedded heat sources has been derived. By incorporating the method of images, this solution can be utilized to obtain the exact solution of a five‐layer structure with rectangular lateral boundaries and with embedded heat sources. Consequently, this solution constitutes the most general analytical expression reported so far. The solution is in the form of a double Fourier integration. To carry out the integration effectively, the characteristics of the transformed temperature in the Fourier domain have been studied. Subsequently, an integration algorithm has been developed for the efficient numerical integration of the double Fourier inverse transform for temperature calculation. In comparison with the double Fourier series solution of rectangular structure, the solution reported here is not only much more computationally effective but also more general. Besides ther...

A general integration algorithm for the inverse Fourier transform of four-layer infinite plate structures

An integration algorithm is presented for the effective and accurate integration of the thermal and electrostatic solutions of a four-layer plate structure with infinite lateral boundaries. By using the method of images, the effect of the finite lateral boundaries of a rectangular structure can be taken into account. As a result, the solution of the infinite plate structure can be utilized to represent exactly the solution of a rectangular structure. The rectangular structure solution is an infinite double Fourier cosine series. A large number of terms has to be summed for accurate temperature calculation, resulting in a prohibitively long CPU time for structures with small sources. The solution of the infinite plate structure, on the other hand, is an inverse double Fourier cosine integration. The integrand decreases very rapidly with the spatial frequencies alpha and beta . However, it is also highly oscillatory, as the location of temperature calculation is remote from the source. Consequently, general-purpose integration routines require long CPU time and produce uncertain results. By using the integration algorithm developed, it is possible to reduce the CPU time by a factor of 10 and at the same time obtain more accurate results. In comparison with the infinite Fourier series solution of the rectangular structure, the CPU time is reduced by a factor of 100 to 1000 with the use of the integral solution incorporated with the integration algorithm. >

Thermal design of integrated circuit devices

An analytical solution derived by the authors (1986) for the thermal analysis of multisource, four-layer ICs has been useful in simulating device thermal properties. However, in the simulation of structures with large chip-to-heat-source size ratios, the computer program based on the exact solution requires a substantial amount of CPU time, making it impossible to carry out real-time thermal design of ICs having large numbers of small heat sources. A method is presented for the computer-aided thermal design of ICs in real time. This method uses a multiple regression technique whose input is the thermal profile due to a unit heat source over a multilayered unit structure. The profile in two dimensions is matched to an equation having several parameters. The temperature profiles of other devices having the same layered structure is computed by superposing the profile generated by the matched equation, shifted in position according to the source location and weighted by the source power.<<ETX>>

Thermal Analysis of Semiconductor Devices

To produce a device, three major aspects of the device operation and fabrication must be studied. The first aspect is the transport of charge carriers, namely, electrons and holes, inside the device. The second one is the process by which the devices are fabricated, and the third is the dissipation of heat from the devices to its environment. The study of carrier transport is commonly referred to as device physics, device modeling or device simulation. Over the past four decades, analytical techniques have been utilized to study devices with simple geometries [1–3]. Later, when the device structures became more complicated, two-dimensional numerical analyses based upon the finite difference method [4–6] have been used. Meanwhile, the three-dimensional finite element technique has also been developed to solve the nonlinear transport equations numerically for devices operating under steady state and transient conditions [7].