Assume that the surface concentration of phosphorus being diffused in silicon is 10²¹ atoms/cm³. We need to design a process, known as the pre-deposition step, such that the concentration of P (c₁ for step 1) at a depth of 0.25 micrometer is 10¹³ atoms/cm³. Assume that this is conducted at a temperature of 1000°C and the diffusion coefficient of P in Si at this temperature is 2.5 x 10^-14 cm²/s. Assume that the process is carried out for a total time of 8 minutes. Calculate the concentration profile (i.e., c₁ as a function of depth, which in this case is given by the following equation). 

Use different values of x to generate and plot this profile of P during the predeposition step.

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c₁(x, t) = cs 1- erf Cs X [;)] 4Dt