Math Problem Statement
Consider a silicon semiconductor doped with 5 x 10^16 cm β 3 phosphorus atoms at 300K. The intrinsic carrier concentration of silicon is π π = 1.5 Γ 10^10 cm^ β3 . Calculate: The electron concentration π is _____ cm^-3 . and the position of the Fermi level relative to the intrinsic Fermi level E Fi is _____ eV .
4.5 x 10^3 and 0.388 5 x 10^16 and 0.388 5 x 10^16 and 0.126 4.5 x 10^3 and 0.126
Solution
To solve this problem, we need to calculate two quantities:
- The electron concentration in the silicon semiconductor.
- The position of the Fermi level relative to the intrinsic Fermi level .
Given Data:
- Doping concentration (phosphorus atoms).
- Intrinsic carrier concentration .
- Temperature .
- Silicon is an n-type semiconductor (since it is doped with phosphorus, which donates electrons).
Step 1: Calculate the electron concentration .
For an n-type semiconductor, the electron concentration can be approximated as:
This is because in an n-type semiconductor, the majority carrier concentration (electrons) is approximately equal to the donor concentration when the doping is not too high and the temperature is not too low.
Thus:
Step 2: Calculate the position of the Fermi level relative to the intrinsic Fermi level .
The shift in the Fermi level relative to the intrinsic Fermi level can be calculated using the formula:
Where:
- is Boltzmann's constant, .
- .
- .
- .
Substitute the values:
Calculate the argument of the logarithm:
Now, take the natural logarithm:
Now calculate :
Final Answer:
- Electron concentration :
- Position of the Fermi level :
The correct option from the choices given is:
Option: and
Would you like any further explanations or details?
Relative Questions:
- How does doping concentration affect the position of the Fermi level in a semiconductor?
- What is the significance of the intrinsic carrier concentration in semiconductors?
- How does the Fermi level shift for p-type semiconductors?
- Why is the Fermi level important in understanding the electrical properties of semiconductors?
- How does temperature affect the Fermi level in semiconductors?
- What assumptions are made when calculating the electron concentration in an n-type semiconductor?
- How would the calculations change if the semiconductor were heavily doped?
- What happens to the Fermi level in intrinsic semiconductors?
Tip:
In semiconductor physics, always check whether the doping concentration significantly exceeds the intrinsic carrier concentration; this will help you determine if the majority carrier concentration is approximately equal to the doping level.
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Math Problem Analysis
Mathematical Concepts
Semiconductor Physics
Carrier Concentration
Fermi Level
Formulas
Electron concentration in n-type semiconductor
Fermi level shift formula
Theorems
-
Suitable Grade Level
Undergraduate
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