Psi or Theta: Which One Should You Choose? By Roger Stout, Senior Research Scientist, ON Semiconductor, Technology Development, Advanced Packaging, Phoenix Many device data sheets now list both of these thermal characterization parameters, but to ap- ply them accurately in power-supply designs, engineers must understand the subtle difer- ences in how these terms are defned. ver the years, standards organizations have But recognizing certain limitations of these standards, undertaken numerous eforts to standardize EIA and JEDEC later came along and defned their own the test methods that are used to characterize standards for measuring the performance of semiconductor the thermal performance of semiconductor devices. In the process, they clarifed the applicability and devices. Groups such as Semiconductor narrowed the scope of the existing theta terms for thermal OEquipment and Materials International (SEMI), the Elec- resistance, while also creating a new set of thermal charac- tronic Industries Alliance (EIA) and the Joint Electron terization parameters, symbolized by the Greek letter psi Device Engineering Council (JEDEC) have developed (Ψ). As with theta, the psi terms usually carry subscripts several standards or specifcations that defne methods of that refect measurement conditions. measuring a variety of thermal characterization parameters. As the EIA/JEDEC standards describe, the psi and theta For example, the SEMI organization drafed standards terms are related but have diferent meanings and impli- for measuring the thermal resistance of ceramic packages, cations for use. Now that both terms are appearing more integrated circuit packages and semiconductor packages frequently on device data sheets, it’s imperative that system under diferent environmental and test conditions. Tese designers understand the distinctions between the terms standards defned the familiar theta (q) terms for thermal and how these terms are defned, so that they understand q q resistance such as JA and JC . how the device vendors are characterizing their parts. Theta (Greek letter ) Psi (Greek letter Ǡ ) TLOCATION X – TLOCATION Y TLOCATION X – TLOCATION Y XY = ǠXY = PowerPATH X-Y PowerTOTAL DEVICE Heat in Heat in y y ?? x x We know the actual We only know the heat along the path total device power Fig. 1. Theta defned, showing that you have to know the heat fowing Fig. 2. Psi defned, showing that when you don’t know the heat fowing along the specifc path from location x to location y to properly use along the specifc path from location x to location y, and all you know the term. is the total heat into the system, you have a psi, not a theta. Power Electronics Technology March 2008 20 www.powerelectronics.com 0308OnSemi-Figure 2 0308OnSemi-Figure 1 THERMAL CHARACTERIZATION From these defnitions, it should be clear that it is very TJ difcult to defne a thermal parameter that’s going to apply to a package under all circumstances. Yet, for some reason, JB (path down JCtop (path device manufacturers — even the ones following these stan- to board) through case top) constant at 20 constant at 80 dards — tend to gloss over this fact in their data sheets. However, in the industry at large there was a recognition Package T T Environment B C that the SEMI standards were inadequate. Consequently, in the early 1990s, EIA/JEDEC (www.jedec.org), the developer BA (board CtopA (case to air resistance) vary path resistance) of standards for the solid-state industry, drafed its own from 1 to 1000 constant at 500, comprehensive thermal standards. or 20 timesǰ BA As can be seen in the following excerpt from JESD51-2 “Integrated Circuits Termal Test Method Environmental TAMB Conditions — Natural Convection (Still Air),” published in 1995, JEDEC recognized the same issues as SEMI: Fig. 3. Four-resistor network illustrates how psi values change depending “Te purpose of this document is to outline the environ- on the external environment, even when the package is constant. mental conditions necessary to ensure accuracy and repeat- q ability for a standard junction-to-ambient ( JA) thermal Tis article will frst review, in some detail, the nuances of resistance measurement in natural convection. Te intent q the standards themselves. It will then illustrate, by using a of JA measurements is solely for a thermal performance relatively simple0308OnSemi-Figure system model, 3 why these seemingly subtle comparison of one package to another in a standardized diferences in defnitions between theta and psi are, in fact, environment. Tis methodology is not meant to and will profound. Armed with that knowledge, designers can make not predict the performance of a package in an application- more accurate predictions about the thermal performance specifc environment.” of the semiconductor devices in their systems. So, how did JEDEC improve the situation? In my view, the most signifcant improvement was the defnition of Thermal Parameters Defned some new terms. In particular, farther into JESD51-2, Many of the now-familiar thermal-resistance param- § 4.3 states: eters were originally defned by the SEMI organization. “... Te junction-to-top center-of-package thermal charac - Ψ Tree standards in particular are worth noting. In quoting terization parameter, JT , is calculated using the following Ψ excerpts from these standards, I have italicized certain pas- equation: JT = (TJss - TTss)/ PH. ... Te relationship between q sages to highlight some of their limitations. the junction-to-ambient thermal resistance, JA , and the 1. SEMI G30-88 “Test Method for Junction-to-Case junction-to-top center-of-package thermal characterization Ψ q Ψ Ψ Ψ Termal Resistance Measurements of Ceramic Packages.” parameter, JT , is described by: JA = JT + TA , where TA Tis test method deals only with junction-to-case or mount- equals thermal characterization parameter from top surface ing surface measurements of thermal resistance and limits of package-to-air (°C/W). ... Te thermal characterization Ψ Ψ itself to heatsink and fuid bath testing environments. Te parameters, JT and TA , have the units °C/W but are math- heatsink mounting method for measuring junction-to-case ematical constructs rather than thermal resistances because thermal resistance is a conservative measure of the package’s not all of the heating power fows through the exposed case Ψ ability to transfer heat to the ambient environment, because surface. ... Also, TA is very dependent on the application- heatsinking is provided only on one side of the package, specifc environment.” whereas the fuid bath mounting method has the potential It took another decade, but the logical extension of Ψ to for equally cooling both sides of the package. other points of interest was codifed in 2005, when JEDEC 2. SEMI G38-0996 “Test Method for Still- and Forced-Air published JESD51-12 “Guidelines for Reporting and Using Junction-to-Ambient Termal Resistance Measurements Electronic Package Termal Information,” and in which can of Integrated Circuit Packages.” Tis test method deals be found, among other statements: only with junction-to-ambient measurements of thermal “... Te purpose of the JESD51 standards is to compare resistance and limits itself to still- and forced-air convection the thermal performance of various packages under stan- testing environments. dardized test conditions. While standardized thermal test 3. SEMI G68-0996 “Test Method for Junction-to-Case information cannot apply directly to the many specifc ap- Termal Resistance Measurements in an Air Environment plications, the standardized results can help compare the for Semiconductor Packages.” Te measurement results are relative thermal performance of diferent packages. A more usually diferent from the results obtained by testing in the meaningful comparison is possible if the test conditions are fuid bath environment described in SEMI G30-88 and in understood along with the factors afecting package thermal SEMI G43-87 “Test Method for Junction-to-Case Termal performance. Brief discussions of key topics are included Resistance Measurements of Molded Plastic Packages,” not in this guideline.” Ψ summarized here. Within the guidelines, it is noted that JB was not in- Power Electronics Technology March 2008 22 www.powerelectronics.com THERMAL CHARACTERIZATION q temperature. It can be approximated using JCtop , measur- 1000 ing the heatsink temperature in the application as close to 900 the package interface as possible, and accounting for the 800 temperature diference across the heatsink to case interface. JA — var brd only (°C/W) 700 — var airflow Alternatively, some suppliers may provide a junction-to- JA JA 600 Ψ e, sink JS thermal parameter that may be used analogously 500 Ψ Ψ to JT , recognizing that the JS value is dependent on the 400 package-to-heatsink interface.” 300 Thermal resistanc 200 A Closer Examination 100 Figs. 1 and 2 introduce a very generic “thermal system” 0 that illustrates what’s diferent between the defnitions of q 110 100 1000 and Ψ. Referring to Fig. 1, if you can defne the path along PC-board thermal resistance, BA (ºC/W) which heat fows and quantify the heat along that path, only Fig. 4. Four-resistor network (of Fig. 3) results in these widely then can you call it q. With this restriction, it may be seen varying U values, even when the package contribution is fxed. q q JA that the traditional defnitions of JA and JC are applicable. q Regarding JA, all the heat that can fow must originate at cluded in the natural 0308OnSemi-Figureconvection standard 4 because it had the junction and end up at ambient (even if the path isn’t not yet been defned, but that it may be added in the future. pinned down, at least you know the heat can’t sneak away JESD51-12 further went on to clarify some existing termi- to somewhere not encompassed by the system). Regarding q q q nology, in particular JC and JB : JC, you can presume that something approaching 100% of q q “Te conduction thermal resistances JCx and JB are total device heat is fowing out through the heatsink, which measured with nearly all of the component power dissipa- it is supposed to do.