In a given n-type silicon material, the donar concentration is 1 atom ...
The donor consecration will be calculated first. As there are 1 atoms per 2 x 10
8 silicon atoms, there will be
donor atoms per met
3. This density of doner
N
d = 2-5 x 10
20 per m
3We know that Fermi level will coincides with the edge of conduction band if N
d = N
c, where
with
But given that effective mass of the electron is equal to its true mass, i.e.,
m
e* = m
eso that
N
C = 4.82 x 10
21 x T
3/2Putting it equal to N
d, we get
or
T = 0.14 K
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In a given n-type silicon material, the donar concentration is 1 atom ...
Given information:
- N-type silicon material
- Donor concentration: 1 atom per 2 * 10^8 silicon atoms
- Density of atoms in silicon: 5 * 10^28 atoms/m^3
Explanation:
The given information allows us to calculate the concentration of donor atoms in the silicon material. Let's calculate it step by step.
Step 1: Calculate the number of silicon atoms per unit volume
Given that the density of atoms in silicon is 5 * 10^28 atoms/m^3, we can calculate the number of silicon atoms per unit volume as follows:
Number of silicon atoms per unit volume = density of silicon * volume
Number of silicon atoms per unit volume = (5 * 10^28 atoms/m^3) * (1 m^3)
Number of silicon atoms per unit volume = 5 * 10^28 atoms
Step 2: Calculate the donor atom concentration
Given that there is 1 donor atom per 2 * 10^8 silicon atoms, we can calculate the donor atom concentration as follows:
Donor atom concentration = (1 donor atom / 2 * 10^8 silicon atoms) * (5 * 10^28 silicon atoms)
Donor atom concentration = 0.25 * 10^20 donor atoms
Step 3: Determine the temperature at which the Fermi level coincides with the edge of the conduction band
At absolute zero temperature, the Fermi level lies at the highest occupied energy level in the material. As the temperature increases, some electrons gain enough energy to move from the valence band to the conduction band, creating holes in the valence band.
At a certain temperature, called the Fermi temperature (T_F), the Fermi level aligns with the edge of the conduction band. Beyond this temperature, the Fermi level will be above the conduction band edge, indicating the presence of free electrons in the conduction band.
In the given question, the donor concentration is given, but the Fermi temperature is not directly provided. However, we can deduce from the given information that the Fermi temperature is very low (0.14 K) compared to the usual operating temperatures of silicon-based devices.
Therefore, the correct statement is option 'B': Temperature at which the Fermi level coincides with the edge of the conduction band is 0.14 K.