Heat generation in integrated circuits

<h2 id="joule-heating">Joule heating</h2>
<p><a href="/facts/Joule_heating/eANEHVzP">Joule heating</a> is a predominant heat mechanism for heat generation in integrated circuits<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> and is an undesired effect.
</p>
<h2 id="propagation">Propagation</h2>
<p>The governing equation of the physics of the problem to be analyzed is the heat diffusion equation. It relates the flux of heat in space, its variation in time and the generation of power.
</p>

∇
        
          (
          
            κ
            ∇
            T
          
          )
        
        +
        g
        =
        ρ
        C
        
          
            
              ∂
              T
            
            
              ∂
              t
            
          
        
      
    
    {\displaystyle \nabla \left(\kappa \nabla T\right)+g=\rho C{\frac {\partial T}{\partial t}}}

<p>Where 
  
    
      
        κ
      
    
    {\displaystyle \kappa }
  
 is the <a href="/facts/Thermal_conductivity/qWnSG3nQ">thermal conductivity</a>, 
  
    
      
        ρ
      
    
    {\displaystyle \rho }
  
 is the density of the medium, 
  
    
      
        C
      
    
    {\displaystyle C}
  
 is the specific heat
</p>

k
        =
        
          
            κ
            
              ρ
              C
            
          
        
        
      
    
    {\displaystyle k={\frac {\kappa }{\rho C}}\,}

<p>the <a href="/facts/Thermal_diffusivity/dRa1aeHY">thermal diffusivity</a> and 
  
    
      
        g
      
    
    {\displaystyle g}
  
 is the rate of heat generation per unit volume. Heat diffuses from the source following equation ([eq:diffusion]) and solution in a <a href="/facts/Homogeneous/y84KQJxl">homogeneous</a> medium of ([eq:diffusion]) has a <a href="/facts/Gaussian_distribution/UapjjPyQ">Gaussian distribution</a>.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Thermal_simulations_for_integrated_circuits/MIWuDH5w">Thermal simulations for integrated circuits</a></li>
<li><a href="/facts/Thermal_design_power/Idcy26tM">Thermal design power</a></li>
<li><a href="/facts/Thermal_management_(electronics)/6WPm3enf">Thermal management in electronics</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Ogrenci-Memik, Seda (2015). <i>Heat Management in Integrated circuits: On-chip and system-level monitoring and cooling</i>. London, United Kingdom: The Institution of Engineering and Technology. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9781849199353. <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/934678500">934678500</a>.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>T. Bechtold, E. V. Rudnyi and J. G Korvink, "Dynamic electro-thermal simulation of microsystems—a review," Journal of Micromechanics and Microengineering. vol. 15, pp. R17–R31, 2005 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Heat generation in integrated circuits open-in-new

Heat generation in integrated circuits