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Question

The number of silicon atoms per m3 is 5×1028. This is doped simultaneously with 5×1022 atoms per m3 of Arsenic and 5×1020 per m3 atoms of Indium. Calculate the number of electrons and holes.
Given that ni=1.5×1016m3. Is the material 𝑛-type or 𝑝-type?

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Solution

Step 1: Find the number of electrons.
Hint: Arsenic is pentavalent dopant and Indium is trivalent dopant.
Given,
Number of silicon atoms =5×1028 atoms per m3
Number of Arsenic atoms, nAs=5×1022 atoms per m3
Number of Indium atoms,
nIn=5×1020 atoms per m3
As we know, Arsenic is pentavalent dopant and Indium is trivalent dopant.
So, holes of Indium atoms are balanced by electrons of Arsenic atoms.
No of electrons,
ne=nAsnIn
ne=(5×1022)(5×1020)
ne=4.95×1022

Step 2: Find the number of holes.
Formula used: nenh=n2i
Given,
intrinsic concentration,
ni=1.5×1016m3
The electron and hole concentration in a semiconductor in thermal equilibrium is given by,
nenh=n2i
Number of holes, nh=n2ine
nh=(1.5×1016)24.95×1022
nh=4.54×109
Here, ne>>nh
Therefore, material is n-type.
Final answer : 4.95×1022,4.54×109; n-type.

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