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Diffusion constant = Mobility*Thermal Voltage 

            *Where,Thermal voltage = T/11600*

From above equation it is clear that Diffusion constant should increase with rise of temperature as it is Directly Proportional to Thermal voltage. On other hand Mobility Decrease with rise of temperature because of high Kernel vibration with rise in temperature that will reduce Diffusion constant. I am not able to conclude Whether Diffusion constant should increase or decrease with temperature.

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    \$\begingroup\$ The diffusion constant should be constant. If temperature goes up, the mobility should go down. \$\endgroup\$
    – b degnan
    Commented Mar 31, 2016 at 11:54
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    \$\begingroup\$ In other words, you cannot adjust the diffusion constant. It is a physical constant that depends on the property of the material or laws of physics. (Similar to the gravitational constant). You can adjust temperature. And you can calculate how mobility changes with temperature. But you cannot change the diffusion constant. \$\endgroup\$
    – user57037
    Commented Apr 3, 2016 at 21:16

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The Einstein relationship for semiconductors is:

 D   =   kT
---     ---
 u       q

which describes the relationship between the diffusion constant D, and mobility u.

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