Download Optical properties of silicon at low temperatures

Optical properties of silicon at low
temperatures
J. Komma, G. Hofmann, C. Schwarz, D. Heinert, P. Pastrik,
R. Nawrodt
Institut für Festkörperphysik, Friedrich-Schiller-University Jena
04.10.2012
ELiTES meeting 2012
Friedrich-Schiller-Universität Jena
Outline
• motivation
• absorption processes in semiconductors
• electronic absorption
• thermal heating
• temperature dependence of the refractive index of silicon
– measurement principle and experimental setup
– acquired data
– results
Julius Komma
Optical properties of silicon at low temperatures
2 / 14
Friedrich-Schiller-Universität Jena
Motivation
silicon is one material of interest for optical components for future
detectors
• dn/dT is needed for calculations of:
– thermal lensing
– thermo-refractive noise
• for the design of the cryogenic parts of future detectors the optical
absorption is needed (thermal equilibrium, cooling power,…)
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Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Absorption processes inside a semiconductor
conduction
band
valence
band
inter band absorption
(band-band abs.)
Julius Komma
intra band absorption
(free carrier abs.)
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Phonon assisted band-band absorption
• band band absorption
conduction
band
phonon
photon
valence
band
58 meV
phonon dispersion and density of states
for silicon [1]
[1[ Phonon dispersion of silicon and germanium from first-principles calculations
Wei and Chou
Julius Komma
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Electronic absorption
due to phonons absorption below the energy gap is possible
2
10
1
absorption [1/cm]
10
0
10
silicon photodiode
1-phonon edge
-1
10
-2
10
-3
10
2-phonon edge
Gap
-4
10
0.90
0.95
1.00
1.05
1.10
photon energy [eV]
Julius Komma
1.15
1.20
photodiode inside
a sample holder
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Temperature dependent absorption
• for lower
temperatures
phonons freezing
out (beginning with
the higher energy
phonons)
 absorption
below the gap is
getting smaller
100
10
absorption [1/cm]
1
300 K
220 K
150 K
100 K
50 K
3K
0.1
0.01
1E-3
1E-4
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
photon energy [eV]
Julius Komma
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Absorption measurement in brewster angle
• for p-polarised light there is
no reflection on a surface if
the angle of incident is the
brewster angle
• so all light can be used for
the measurement without
losses because of reflected
light
• scattered light causes
problems inside a cryostat
Julius Komma
P0
Ptrans
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Thermal absorption measurement
• one sample of high purity to
measure the absorption of
silicon between 5 and 300 K
• the upper sample is doped,
so we expect a higher
absorption due to free
carriers. With lower
temperatures the
absorption is expect to
become smaller, when the
number of free carriers
decreases
doped sample
pure silicon
cover
base
setup to measure two samples inside a cryostat
Julius Komma
Optical properties of silicon at low temperatures
9 / 14
Friedrich-Schiller-Universität Jena
Setup for dn/dT measurement
• with the continuous helium flow cryostat it is possible to measure
from <4 K up to 325 K
• sample thickness: 0.3 … 14 mm
Julius Komma
Optical properties of silicon at low temperatures
10 / 14
Friedrich-Schiller-Universität Jena
Extracting of dn/dT from exp data
Ir =
𝐼0
,
1+ 𝜋2/ 4𝐹2sin2 𝜃
𝜃=
2𝜋𝑛𝑙
𝜆
interference maximum ↔ ∆𝜃= 𝜋
∆𝜃= 𝜋
1.0

𝑑𝑛
𝑑𝑇
=
𝜆
2𝑙 Δ𝑇
0.8
− n T 𝛼(T)
110-4 1/K
110-6 1/K
(𝑙 = 14 𝑚𝑚, 𝑇 = 300 𝐾)
IR norm.
0.6
0.4
0.2
0.0
310.0
312.5
315.0
temperature [K]
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Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Data at low temperatures
1.0
0.8
IR norm.
0.6
0.4
0.2
0.0
0
10
20
30
40
50
60
temperature [K]
• problem: only a small change of n at low temperatures  only a
few fringes
• dn/dT  0 for T  0 (3rd law of thermodynamics)
Julius Komma
Optical properties of silicon at low temperatures
12 / 14
Friedrich-Schiller-Universität Jena
dn/dT (1/K)
Results for dn/dT
10
-3
10
-4
10
-5
our data [1]
Frey [2]
10
-6
10
-7
10
-8
10
-9
ET design study
20K: 3.5E-6 1/K [3]
0
50
100
150
200
250
300
temperature [K]
[1] Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures.
Komma et al.
[2] Temperature-dependent refractive index of silicon and germanium
Bradley J. Frey et al.
Julius Komma
[3] The Einstein gravitational wave Telescope conceptual design study
M. Abernathy et al.
Optical properties of silicon at low temperatures
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Friedrich-Schiller-Universität Jena
Summary
• The absorption inside a semiconductor consists of band-band and
free carrier parts
• band-band absorption can be measured with a photodiode
– phonon assisted absorption below the gap energy
• both processes together can be observed due to thermal heating
• dn/dT was measured over a wide temperature range (5 … 300 K)
𝑑𝑛
𝑑𝑇
= 1.5𝑥10-6 1/K @20K and 8𝑥10-8 1/K @10K
Acknowledgements: This work was supported by the German science foundation within the SFB TR7.
Julius Komma
Optical properties of silicon at low temperatures
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