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A silicon semiconductor slab has absorption coefficient of 102 cm-1 at wavelength of 1 μm. If 90% of the incident flux is to be absorbed then the thickness of the slab required is:
- a)0.23 mm
- b)0.0105 mm
- c)0.10 mm
- d)0.0045 mm
Correct answer is option 'A'. Can you explain this answer?
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A silicon semiconductor slab has absorption coefficient of 102 cm-1 at...
Understanding Absorption in Semiconductors
To determine the thickness of a silicon semiconductor slab required to absorb 90% of the incident flux at a wavelength of 1 µm, we can use the formula related to the absorption coefficient and thickness.
Key Formula
The relationship is given by:
I = I0 * e^(-αx)
Where:
- I is the transmitted intensity
- I0 is the incident intensity
- α is the absorption coefficient (in cm-1)
- x is the thickness (in cm)
Given Values
- Absorption coefficient (α) = 102 cm-1
- Percentage of flux absorbed = 90%
- Therefore, transmitted flux (I/I0) = 10% = 0.1
Calculating Thickness
Set up the equation for the required absorption:
0.1 = e^(-102x)
Taking the natural logarithm of both sides:
ln(0.1) = -102x
Solving for x:
x = -ln(0.1) / 102
Calculating -ln(0.1):
- ln(0.1) ≈ 2.3026
Now substitute back:
x ≈ 2.3026 / 102
This gives:
x ≈ 0.0226 cm
Converting to mm:
x ≈ 0.226 mm
This is approximately 0.23 mm, aligning with option 'A'.
Conclusion
The required thickness of the silicon semiconductor slab to achieve 90% absorption of incident flux at 1 µm is approximately 0.23 mm. Thus, option 'A' is correct.
To determine the thickness of a silicon semiconductor slab required to absorb 90% of the incident flux at a wavelength of 1 µm, we can use the formula related to the absorption coefficient and thickness.
Key Formula
The relationship is given by:
I = I0 * e^(-αx)
Where:
- I is the transmitted intensity
- I0 is the incident intensity
- α is the absorption coefficient (in cm-1)
- x is the thickness (in cm)
Given Values
- Absorption coefficient (α) = 102 cm-1
- Percentage of flux absorbed = 90%
- Therefore, transmitted flux (I/I0) = 10% = 0.1
Calculating Thickness
Set up the equation for the required absorption:
0.1 = e^(-102x)
Taking the natural logarithm of both sides:
ln(0.1) = -102x
Solving for x:
x = -ln(0.1) / 102
Calculating -ln(0.1):
- ln(0.1) ≈ 2.3026
Now substitute back:
x ≈ 2.3026 / 102
This gives:
x ≈ 0.0226 cm
Converting to mm:
x ≈ 0.226 mm
This is approximately 0.23 mm, aligning with option 'A'.
Conclusion
The required thickness of the silicon semiconductor slab to achieve 90% absorption of incident flux at 1 µm is approximately 0.23 mm. Thus, option 'A' is correct.
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A silicon semiconductor slab has absorption coefficient of 102 cm-1 at wavelength of 1 μm. If 90% of the incident flux is to be absorbed then the thickness of the slab required is:a)0.23 mmb)0.0105 mmc)0.10 mmd)0.0045 mmCorrect answer is option 'A'. Can you explain this answer?
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