(a) If 5 × 10¹⁷ phosphorus atoms per cm³ are add to silicon as a substitutional impurity, determine the percentage of silicon atoms per unit

Question

(a) If 5 × 10¹⁷ phosphorus atoms per cm³ are add to silicon as a substitutional impurity, determine the percentage of silicon atoms per unit volume that are displaced in the single crystal lattice.
(b) Repeat part (a) for 2 × 10¹⁵ boron atoms per cm³ added to silicon.

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Doris 4 years 2021-07-24T02:00:45+00:00 1 Answers 200 views 1

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  1. vankhanh
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    2021-07-24T02:02:16+00:00
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    Answer:

    (a) In the single crystal lattice,0.001 % of silicon atoms per unit volume that displaced.

    (b)In the single crystal lattice,4\times 10^{-6} \% of silicon atoms per unit volume that displaced.

    Explanation:

    Unit cell:

    • 8 atoms at the corners at \frac18 each cell
    • 6 atoms in the face at \frac12 each in cell.
    • 4 atoms within cell.

    Total number of atoms per unit cell of silica is  (8\times \frac18+6\times \frac12+4)=8 .

    Dimension of unit cell is 5.43\times 10^{-8}\ cm.

    The volume occupied by a single Si atom in the crystal structure is

    V_{si}=\frac{a^3 \ cm^3/cell}{\textrm{Number of atom per cell}}

        =\frac{(5.43\times 10^{-8})^3\ cm^3 /cell}{8 \ atoms /cell}

       =2\times 10^{-23} cm^3/atom

    The concentration of Si atom is

    n_{si}=\frac{1}{V_{Si}}

       =\frac{1}{2\times 10^{-23}\ cm^3/atom}

      =5\times 10^{22} atom/cm^3

    (a)

    n_P=5\times 10^{17} \ atom/cm^3

    PCT=\frac{n_P}{n_{Si}}\times 100

            =\frac{5\times 10^{17} \ atom/cm^3}{5\times 10^{22}\ atom/cm^3}\times 100

            =10^{-3}\%

           =0.001 %

    In the single crystal lattice,0.001 % of silicon atoms per unit volume that displaced.

    (b)

    n_b=2\times 10^{15}\ atom /cm^3

    PCT=\frac{n_b}{n_{Si}}\times 100

            =\frac{2\times 10^{15} \ atom/cm^3}{5\times 10^{22}\ atom/cm^3}\times 100

            =4\times 10^{-6} %

    In the single crystal lattice,4\times 10^{-6} \% of silicon atoms per unit volume that displaced.

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