SME
University Physics III: Waves, Optics & Modern · Problem type
The longest wavelength a semiconductor absorbs
Use this for “Silicon has a band gap of 1.12 eV. What is the longest wavelength it absorbs?”
Diagram
λₘₐₓ = 1,107 nm: infrared.
c = λₘₐₓ × f
299,800,000 m/s = 1,107 nm × 2.708 × 10¹⁴ Hz
This is an example. Type your own values to start a new problem.
λₘₐₓ (nm)
=
1,240
eV·nm
Eg (eV)
f
Frequency at the edge
worked out (not typed) · Hz
Formulas
λₘₐₓ
=
1,240
Eg
1,107
=
1,240
1.12
f
=
2.998 ×
10
8
λₘₐₓ ×
10
-9
2.7079 ×
10
14
=
2.998 ×
10
8
1,107 ×
10
-9
Assumptions
•
A photon is absorbed only when its energy lifts an electron across the gap, hf ≥ Eg; longer waves pass through.
•
hc = 1240 eV·nm and c = 2.998 × 10⁸ m/s; visible light runs from about 380 nm (violet) to 750 nm (red).
•
The same edge sets the color an LED of that material gives off.
Step-by-step
WE KNOW
Eg = 1.12 eV
FIND
longest wavelength absorbed (λₘₐₓ), frequency at the edge (f)
Step 1 · Find longest wavelength absorbed (λₘₐₓ)
Use λₘₐₓ = 1,240 ÷ Eg
The
photon
that
carries
just
Eg
has
λ
=
hc
Eg
;
any
longer
wave
carries
less
and
is
not
absorbed.
λₘₐₓ
=
1,240
1.12
λₘₐₓ = 1,107.14 nm → infrared: every visible photon is absorbed, so the material looks dark.
Step 2 · Find frequency at the edge (f)
Use f = 2.998 × 10⁸ ÷ (λₘₐₓ × 10⁻⁹)
Light’s speed over the wavelength in meters: the lowest frequency absorbed.
f
=
2.998 ×
10
8
1,107.14 ×
10
-9
f
=
2.7079 ×
10
14
Hz
Check
Put the numbers back in. Both sides should match.
1,107.14
=
1,240
1.12
✓
2.7079 ×
10
14
=
2.998 ×
10
8
1,107.14 ×
10
-9
✓
Topic check
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