On the modeling of the transient thermal behavior of semiconductor devices

Accurate, Pre-RTL Temperature-Aware Design Using a Parameterized, Geometric Thermal Model

“…With a finite silicon thickness, the heat generated from a block cannot be fully spread before reaching the back surface of the die, causing a larger thermal resistance and also a longer thermal time constant. This difference in silicon thermal time constant leads to slower transient temperature changes in HotSpot which models larger blocks and grid cells than the model in [11] which models tiny transistors.…”

“…With the semi-infinite silicon assumption, heat can be fully spread within silicon before reaching the back surface of the silicon substrate, leading to a smaller thermal resistance and also a shorter thermal time constant. On the contrary, the HotSpot model aims at granularities coarser than transistors, and the block size or grid size are usually comparable with or greater than the die thickness, rendering the boundary conditions assumed in [11] not valid. With a finite silicon thickness, the heat generated from a block cannot be fully spread before reaching the back surface of the die, causing a larger thermal resistance and also a longer thermal time constant.…”

“…This "by-construction" nature also makes the thermal model parameterized and allows designers to explore hypothetical designs easily without building prototypes. Regarding transient thermal modeling, another previous work [11] approaches the topic analytically at a finer granularity-the transistor level. Since the size of a transistor is much smaller than the die thickness, silicon can be modeled as semi-infinite, which greatly simplifies the boundary conditions and makes an analytical transient heat transfer solution possible.…”

Analytical Solutions of the Diffusive Heat Equation as the Application for Multi-cellular Device Modeling – A Numerical Aspect

“…In used formalism each term correspond to 8 image sources. The solution for semi-infinite domain [6] can be also achieved from (7) by taking (m,n,p)=(0,0,0) and neglecting some of the remaining elements. To investigate the properties of STGF solution, as previous, the thermal impedance in the middle of the centered heat source has been calculated utilizing different number of terms and the obtained curves are depicted in Fig.…”

“…Let consider two such solutions of the problem described by (2); namely (6) and (7) called the Large Time Greens Function solution (LTGF) [1,4] and the Small Time Greens Function Solution (STGF) [4,6] (known also as the image method approach), respectively. The both are in a form of complex series but the difference between the formulas are so large that one can expected that their application in the considered thermal model cannot be equivalent from the point of view both computation effort and computation complexity.…”