Diffusion current in a circuit containing semiconductor but no electric source

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Please I need help to understand how diffusion current can occur in a circuit that contains an N-type or P-type semiconductor without being connected to an electric souce such as a battery.And how can both drift and diffusion current occur when the circuit is connected to a battery?
 
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Diffusion current will be a transient at the time of making of a p-n junction. You won't be able to measure it then.