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Explain why a semi conductor acts as an insulator at 0K.

In an intrinsic semiconductor the number of free carriers i.e. holes and electrons is very less at room temperature. At any temperature above absolute zero, there will be some electrons which are excited across the band gap into the conduction band and which can support current flow. While at absolute zero, the band gap (also called forbidden gap) is large and no free electron is present to conduct electricity.

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at 0 K , electrons do not have sufficient energy to jump from valence band to conduction band and therefore it act as an insulator .
as the temperature increases , electrons get energy to pass from valence band to conduction band making it to conduct . as the temperature increases further more  and more electrons get energy and crosses the forbidden energy gap increasing the conductivity .
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In semiconductors resistivity decreases exponentially with temperature . Resistivity is given by 
               p= p0 eEg/kT​     
where k is bolyzmann's constant , Eg is energy gap.
At 0K value of resistivity is zero .so semiconductor behaves as insulator at 0K
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sorry there is boltzmann 's constant
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