Doping refers to placing a different atom into the crystal lattice of another. O

Question

Doping refers to placing a different atom into the crystal lattice of another. One way to accomplish this is by diffusing one atom, called the dopant, into the lattice of another, which is called the host lattice. The simplest requirement is that the dopant be small enough to fit into the open space within the host lattice In this problem, we will assume that all of the atoms are spherical and and their volume is given by 4 3 where r is the radius of the spherical atom. 6. Consider gallium as the host lattice. Gallium crystallizes in a simple cubic lattice shown below. " (a) If the radius of a Ga atom is 210 pm, determine the volume of empty space in the unit cell shown (b) Given the following atoms and their respective volumes, which of these atoms could be used to dope below crystalline gallium. Table of Dopant Sizes Unit Cell of Gallium Dopant Dopant Volume (pm)- 4.65 x 107 .07 x 107 .60 x 107 4.40 x 107 Sn As In

Explanation / Answer

Radius of a Ga atom, R = 210 pm = 0.21 nm

In simple cubic lattice,

Volume of unit cell = (2R)3 = 8 R3

No. of atoms of Ga per unit cell = 1/8 * 8 = 1

a)

Volume of Ga atoms in unit cell = Volume of 1 Ga atom * No. of atoms of Ga per unit cell

= 4/3 * * R3 * 1

Volume of empty space in unit cell = Volume of unit cell - Volume of Ga atoms in unit cell

= 8 R3 - 4/3 * * R3

= 3.81 R3

= 3.81 * (210 pm)3

= 3.53 x 107 pm3

b)

Dopant atoms that occupy volume less than volume of empty space in unit cell only could be used.

Only P atom has volume = 3.07 x 107 pm3 < 3.53 x 107 pm3

P atoms could be used to dope crystalline gallium.

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