An analytical model for the upper bound on temperature differences on a chip

ABSTRACT

The main contribution of this work is an analytical model for finding the upper bound on the temperature difference among various locations on the die. The proposed model can be used in many applications, such as estimation of maximum temperature variations on the die and estimating the maximum placement error in temperature sensor placement algorithms. The model also identifies the conditions under which these maximum temperature variations might happen, which is very helpful for generating test data for thermal stress tests and for augmenting different benchmarks. Experiments show that maximum temperature differences can be underestimated as much as 9°C. Based on this model, a temperature sensor placement algorithm is also proposed which is able to guaranty a maximum temperature error due to placement of the sensor. The ability of the proposed model to estimate point to point maximum temperature difference can improve the efficiency and accuracy of the sensor placement technique so that we can reduce the number of thermal sensors needed by about 16% on average.

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INDEX TERMS

Primary Classification:
  B. Hardware
  B.8 Performance and Reliability
      B.8.0 General

Additional Classification:
  C. Computer Systems Organization
  C.4 PERFORMANCE OF SYSTEMS
      Subjects: Modeling techniques; Performance attributes

General Terms:
Measurement, Performance, Reliability

Keywords:
sensor placement, temperature, temperature difference, temperature variation, thermal management