An integrated mid-infrared, far-infrared and terahertz optical Hall effect instrument

3.2 MB·

by  P. Kühne

An integrated mid-infrared, far-infrared and terahertz optical Hall effect
instrument
P. Ku¨hne,1,a) C. M. Herzinger,2 M. Schubert,1 J.A. Woollam,2 and T. Hofmann1
1)Department of Electrical Engineering and Center for Nanohybrid Functional Materials,
University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
2)J. A. Woollam Co., Inc., 645 M Street, Suite 102, Lincoln, Nebraska 68508-2243,
USA
(Dated: 22 January 2014)
We report on the development of the first integrated mid-infrared, far-infrared and terahertz optical Hall
effect instrument, covering an ultra wide spectral range from 3 cm−1 to 7000 cm−1 (0.1–210 THz or 0.4–
870 meV). The instrument comprises four sub-systems, where the magneto-cryostat-transfer sub-system en-
ables the usage of the magneto-cryostat sub-system with the mid-infrared ellipsometer sub-system, and the
4 far-infrared/terahertz ellipsometer sub-system. Both ellipsometer sub-systems can be used as variable angle-
1
of-incidence spectroscopic ellipsometers in reflection or transmission mode, and are equipped with multiple
0
light sources and detectors. The ellipsometer sub-systems are operated in polarizer-sample-rotating-analyzer
2
configurationgrantingaccesstotheupperleft3×3blockofthenormalized4×4Muellermatrix. Theclosed
n
cycle magneto-cryostat sub-system provides sample temperatures between room temperature and 1.4 K and
a
magneticfieldsupto8T,enablingthedetectionoftransverseandlongitudinalmagneticfield-inducedbirefrin-
J
gence. Wediscusstheoreticalbackgroundandpracticalrealizationoftheintegratedmid-infrared,far-infrared
1
and terahertz optical Hall effect instrument, as well as acquisition of optical Hall effect data and the corre-
2
sponding model analysis procedures. Exemplarily, epitaxial graphene grown on 6H-SiC, a tellurium doped

] bulk GaAs sample and an AlGaN/GaN high electron mobility transistor structure are investigated. The se-
l
l lectedexperimentaldatasetsdisplaythefullspectral,magneticfieldandtemperaturerangeoftheinstrument
a
and demonstrate data analysis strategies. Effects from free charge carriers in two dimensional confinement
h
- andinavolumematerial,aswellasquantummechanicaleffects(inter-Landau-leveltransitions)areobserved
s and discussed exemplarily.
e
m
. I. INTRODUCTION magnetic wave’s polarization state.4 Experimentally the
t
a Mueller matrix is measured by generalized ellipsometry
m
The optical Hall effect (OHE) is a physical phe- (GE).5–12 During a GE measurement different polariza-
- nomenon, which describes transverse and longitudinal tion states of the incident light are prepared and their
d
n magnetic field-induced birefringence, caused by the non- change upon reflection from or transmission through a
o reciprocal magneto-optic response of electric charge car- sample is determined.
c riers. The term OHE is used in analogy to the classic, An OHE instrument conducts GE measurements on
[ electrical Hall effect,1 since the electrical Hall effect and samples in high, quasi-static magnetic fields, and de-

1 certain cases of OHE observation can be explained by tects the magnetic field induced changes of the Mueller
v extensions of the classic Drude model for the transport matrix.13 Though several instruments with partial OHE
2 of electrons in matter (metals).2,3 For the OHE, Drude’s instrument characteristics were described in the litera-
7 classic model is extended by a magnetic field and fre- ture, most instruments did not fulfill all criteria for an
3 quencydependency,describingtheelectron’smomentum OHE instrument. Nederpel and Martens developed in
5 under the influence of the Lorentz force. As a result 1985asinglewavelength(444nm)magneto-opticalellip-
.
1 an antisymmetric contribution is added to the dielec- someterforthevisiblespectralrange,buttheinstrument
0 tric tensor ε(ω), whose sign depends on the type of the providedonlylowmagneticfields(B ≤50mT).14In2003
4 free charge carrier (electron, hole). The non-vanishing Cˇerneetal. presentedamagneto-polarimetryinstrument
1
off-diagonal elements of the dielectric tensor reflect the (B ≤ 8 T) for the mid-infrared spectral range (spec-
:
v magneto-optic birefringence, which lead to conversion of tral lines of CO2 laser),15 and in 2004 Padilla et al. de-
Xi p-polarized into s-polarized electromagnetic waves, and veloped a terahertz-visible (6 to 20000 cm−1) magneto-
vice versa. reflectance and -transmittance instrument (B ≤ 9 T).16
r
a TheOHEcanbequantifiedintermsoftheMuellerma- Whilebothinstrumentsprovidehighmagneticfields,and
trix,whichcharacterizesthetransformationofanelectro- contain polarizers and photo-elastic-modulators, these
instruments were not designed to record Mueller ma-
trix data (GE). The full 4 × 4 Mueller matrix in the
terahertz-mid-infrared spectral range (20 to 4000 cm−1)
a)Electronicmail: can be measured by an instrument described in 2013 by
[email protected];(http://ellipsometry.unl.edu/)
2
composition, are shown. The MIR OHE data of the
Stanislavchuket al.,17 butheretheinstrumentisnotde- same epitaxial graphene sample is used to demonstrate
signedforexperimentswiththesampleinmagneticfields. the operation of the MIR ellipsometer sub-system of
The first full OHE instrument developed in 2006 by the integrated MIR, FIR and THz OHE instrument,38
Hofmann et al. for the far-infrared (FIR) spectral range over the full available magnetic field range of the instru-
(30 to 650 cm−1) provided magnetic fields up to 6 T ment. The magneto-optic response of free charge carri-
and allowed sample temperatures between 4.2 K and ers and quantum mechanical inter-Landau-level transi-
roomtemperature.18ThisfirstOHEinstrumenthassince tions is observed, and their polarization selection rules
been successfully used to determine free charge carrier obtainedtherefromarebrieflydiscussed. ATe-doped, n-
properties,19–24 including effective mass parameters for type GaAs substrate serves as a model system for the
a variety of material systems.22,25–28 Later, OHE ex- FIR spectral range of the FIR/THz ellipsometer sub-
periments were conducted in the terahertz (THz) spec- system. The OHE signal originating from conduction
tral range,29 but were limited to room temperature and band electrons in a bulk material is discussed, and the
low magnetic fields (B ≤1.8 T).30–33 Since the magni- concentration, mobility, and effective mass of the con-
tudeoftheOHEdependsonthemagneticfieldstrength, duction band electrons is determined. Finally, OHE
highermagneticfieldsfacilitatethedetectionoftheOHE. data from an AlGaN/GaN high electron mobility tran-
Furthermore, the sensitivity to the OHE is greatly en- sistor structure (HEMT) from the THz spectral range of
hanced by phonon mode coupling,34,35 surface guided the FIR/THz ellipsometer sub-system is presented and
waves27 and Fabry-P´erot interferences.31,36 Since these analyzed.36 The data was recorded at different tempera-
effects appear from the THz to the mid-infrared (MIR) tures between T = 1.5 K and room temperature, repre-
spectral range, depending on the structure and mate- senting the full sample temperature range of the instru-
rial of the sample, it is necessary to extend the spec- ment.
tral range covered by OHE instrumentation. An OHE The manuscript is organized as follows, in section II
instrument for the MIR, for example, can detect the dielectric and magneto-optic dielectric tensors are intro-
magneto-optic response of free charge carriers enhanced duced, a brief theoretical overview on Mueller matrices
by phonon modes present in the spectral range above and GE data-acquisition is given, and general GE data
600 cm−1, which applies to many substrate materi- analysis procedures are introduced. Section III gives a
als, e.g., SiC,34,37,38 Al2O3,28,39 or GaN,40 as well as detailed description of the experimental setup, while in
to many materials used for thin films, e.g., III-V ni- section IV data acquisition and data analysis procedures
tride semiconductors Al1−xGaxN,35,41 Al1−xInxN42 or for OHE data are discussed. Examples of experimen-
In1−xGaxN.28,42 In addition, inter-Landau-level transi- talresults,demonstratingtheoperationoftheintegrated
tions can be studied in the MIR spectral range43–46 with MIR, FIR and THz OHE instrument, are presented and
a MIR OHE instrument.38 The extension to the THz discussed in section V, which is followed by a short sum-
spectral range enables the detection of the OHE in sam- mary in section VI.
ples with low carrier concentrations.18,31 Furthermore,
the strongest magneto-optic response can be observed at
the cyclotron resonance frequency, which typically lies II. THEORY
in the microwave/THz spectral range for moderate mag-
netic fields (few Tesla) and effective mass values compa-
The evaluation of physical relevant parameters from
rable to the free electron mass.
the OHE requires the experimental observation and
Inthisarticle,wepresentanOHEinstrument,covering
quantification of the OHE, and a physical model to an-
an ultra wide spectral range from 3 cm−1 to 7000 cm−1
alyze OHE data. Experimentally, the OHE is quantified
(0.1–210 THz or 0.4–870 meV), which combines MIR, in terms of the Mueller matrix M 47,48 by employing
FIR and THz magneto-optic generalized ellipsometry in OHE
generalizedellipsometry(GE).Thephysicalmodelwhich
a single instrument. This integrated MIR, FIR and
is used to analyze the observed transverse and longitudi-
THzOHEinstrumentincorporatesacommerciallyavail-
nal magneto-optic birefringence of the OHE is based on
able, closed cycle refrigerated, superconducting 8 Tesla the magneto-optic dielectric tensor ε (B), which is a
magnet-cryostatsub-system,withfouropticalports,pro- OHE
function of the slowly varying external magnetic field B.
vidingsampletemperaturesbetweenT =1.4Kandroom
If, among other parameters, the magneto-optic dielec-
temperature. Theellipsometersub-systemswerebuiltin-
tric tensor of a sample is known, experimental Mueller
houseandoperateintherotating-analyzerconfiguration, matrices M can be modeled from ε (B) using the
capable of determining the normalized upper 3×3 block OHE OHE
relation
of the sample Mueller matrix.
The operation of the integrated MIR, FIR and THz M (ε (B)). (1)
OHE OHE
OHE instrument is demonstrated by three sample sys-
tems. Combined experimental data from the MIR, FIR Thisrelationisingeneralnotinvertibleanalytically, but
and THz spectral range of a single epitaxial graphene can be used to determine the magneto-optic dielectric
sample, grown on a 6H-SiC substrate by thermal de- tensor from experimental Mueller matrix data through
non-linearmodelregressionanalysis.49Dielectrictensors,
3
time harmonic electromagnetic plane wave with an elec-
Muellermatrixcalculus, generalizedellipsometryinclud- tric field E → Eexp(iωt) with angular frequency ω, the
ing data acquisition, as well as data analysis will be ad- time derivative of the spatial coordinate of the charge
dressed in this section. carrier is x˙ = vexp(iωt), where v is the velocity of the
charge carrier. With the current density j=nqv Eq. (4)
reads
A. Magneto-optical dielectric tensors
(cid:20) (cid:21)
E= 1 im (cid:0)ω2I−ω2I−iωγ(cid:1)j+(B×j) , (5)
The optical response of a sample is here described by nq qω 0
the dielectric tensor ε. If the dielectric tensor of the
samplewithoutamagneticfieldisgivenbyε andthe where n is the charge carrier density. With the Levi-
B=0 Cevita-Symbol (cid:15) 54, the conductivity tensor σ, the di-
changeofthedielectrictensorinducedbyamagneticfield ijk
B by εB, the magneto-optic dielectric tensor describing ethleectdriiecleccotnrisctatnentsεo0r,faonrdchuasringegcEar=rieσrs−s1ujbajnedctεto=thiεe10ωexσ-
the OHE, can be expressed as
ternal magnetic field B can be expressed as
ε (B)=ε + ε . (2)
OHE B=0 B ε = nq2 (cid:2)m (ω2−ω2−iωγ )−iω(cid:15) qB (cid:3)−1 . (6)
The magneto-optic response of the sample described by ik ε0 ik 0 ik ijk j
ε usually originates from bound and unbound charge
B a. Polar lattice vibrations (Lorentz oscillator)
carriers subjected to the magnetic field and is caused
For isotopic effective mass tensors the cyclotron fre-
by the action of the Lorentz force. The magneto-optic
response is anisotropic, and non-reciprocal in time.12,50 quency ωc = q|mB| can be defined. For the mass of the
Thus,thecorrespondingmagneto-opticcontributionsχ vibrating atoms of polar lattice vibrations, the cyclotron
+
and χ to the permittivity tensor χ=ε−I, where I is frequency is several orders of magnitude smaller than
−
the3×3identitymatrix,originatefromtheinteractionof for effective electron masses, and can be neglected for
right- and left-handed circularly polarized light with the the magnetic fields and spectral ranges discussed in this
sample,respectively.13,22Withoutlossofgenerality,ifthe paper. Therefore, the dielectric tensor of polar lattice
magneticfieldBispointinginthez-direction,thepolar- vibrations εL can be approximated using Eq. (6) with
ization vector P=ε χE can be described by arranging B = 0. When assuming isotropic effective mass and
0
theelectricfieldsintheircircularlypolarizedeigensystem mobility tensors, the result is a simple harmonic oscilla-
E =(E +iE ,E −iE ,E )=(E ,E ,E ) by P = torfunctionwithLorentzian-typebroadening.53,55,56 For
e x y x y z + − z√ e
ε χ E = ε (χ E ,χ E ,0), where i = −1 is the materials with orthorhombic symmetry and multiple op-
0 e e 0 + + − −
imaginaryunit.18,51 TransformingP backintothelabo- ticalexcitablelatticevibrations,thedielectrictensorcan
e
ratorysystemthechangeofthedielectrictensorinduced be diagonalized to
by the magnetic field takes the form:18,5152
 
εL 0 0
x
1 (χ++χ–) i(χ+−χ–) 0 εL =0 εLy 0 , (7)
εB = 2−i(χ+−χ–) (χ++χ–) 0 . (3) 0 0 εLz
0 0 0
where εL (k ={x,y,z}) is given by57
k
Note, under field inversion B→−B, the polarizabilities
fcnohorannl-edgfitea-.gaεonBndailsriwognhittlhy-hadaninatdgi-eosdnyamclimricfeuχtlra+ircl=yoffpχo−dl,aiaraginzodendaolltihgeelhertmwiniesnteetrsis-. εLk =ε∞,kjY=l1ωω22++iiωωγγTLOO,,kk,,jj−−ωωLT22OO,,kk,,jj , (8)
where ω , γ , ω , and γ denote the
LO,k,j LO,k,j TO,k,j TO,k,j
k ={x,y,z} component of the frequency and the broad-
1. Classic dielectric tensors (Lorentz-Drude model)
ening values of the jth longitudinal optical (LO) and
transverse optical (TO) phonon modes, respectively,
Chargedcarriers, subjecttoaslowlyvaryingmagnetic
while the index j runs over l modes. Further details can
field obey the classical Newtonian equation of motion
be found in Refs. 26, 57–60, and a detailed discussion of
(Lorentz-Drude model)53
the requirements to the broadening parameters, such as
Im{εL}≥0, in Ref. 40.
mx¨+mγx˙ +mω2x=qE+q(x˙ ×B), (4) k
0 b. Free charged carriers (extended Drude model)
Forfreechargedcarriersnorestoringforceispresentand
where m, q, µ = qm−1γ−1, x and ω represent the
0 the eigenfrequency of the system is ω =0. For isotropic
effective mass tensor, the electric charge, the mobility 0
effective mass and conductivity tensors, and magnetic
tensor, the spatial coordinate of the charged carrier and
fields aligned along the z-axis Eq. (6) can be written in
the eigenfrequency of the undamped system without ex-
theformεD (B)=εD +εD,withtheDrudedielectric
ternal excitation and magnetic field, respectively. For a OHE B=0 B
tensor for B =0
ω2
εD =− p I=εDI, (9)
B=0 ω(ω+iγ)
4
upon change of the coordinate system or the interaction
with a sample, optical element, or any other matter5,47
q
whereω = nq2 istheplasmafrequency, andεD isthe
p mε0 3
isotropic Drude dielectric function. The magneto-optic S(out) =XM S(in), (j =1...4), (12)
contribution to the dielectric tensor εD for isotropic ef- j ij i
B i=1
fectivemassesandconductivitiescanbeexpressed,using
Eq. (3), through polarizability functions for right- and where S(out) and S(in) denote the Stokes vectors of the
left-handed circularly polarized light
electromagnetic plane wave before and after the change
ofthecoordinatesystem,oraninteractionwithasample,
εD
χ =− , (10) respectively. NotethatallMuellermatrixelementsofthe
± 1∓ ω+iγ
ωc GE data discussed in this paper, are normalized by the
!
element M , therefore |M |≤1 and M ≡1.
where ω = q|B| is the isotropic cyclotron frequency. 11 ij 11
c m
2. Mueller matrix and OHE data
2. Non-classic dielectric tensors (Inter-Landau-level
transitions)
The Mueller matrix can be decomposed in 4 sub-
matrices, where the matrix elements of the two off-
The dielectric tensor εLL describing a series of inter- h i h i
Landau-level transitions cBan be approximated by a sum diagonal-blocks MM1233 MM1244 and MM4311 MM3422 only deviate
of Lorentz oscillators. The quantities χ in Eq. (3) are from zero if p-s-polarization mode conversion appears,
±
then expressed by while the matrix elements in the two on-diagonal-blocks
h i h i
M11 M12 and M33 M34 mainly contain information
χ± =e±iφXω2−ω2Ak−iγ ω , (11) abMo2u1tMp2-2s-polarizMa4t3ioMn44mode conserving processes. p-s-
k 0,k k polarization mode conversion is defined as the transfer
of energy from the p-polarized channel of an electromag-
where A , ω , and γ are amplitude, transition energy,
k 0,k k neticplanewavetothes-polarizedchannel,orviceversa.
and broadening parameter of the kth inter-Landau-level
Polarization mode conversion can appear when the p-s-
transition, respectively, which in general depend on the
coordinate system is different for S(in) and S(out)64, or
magneticfield. Thephasefactorφwasintroducedempir-
when a sample shows birefringence, for example. In par-
ically here to describe the experimentally observed line
ticular, polarization mode conversion appears if the di-
shapesofallMuellermatrixelements. Forinter-Landau-
electric tensor of a sample possesses non-vanishing off-
level transitions in graphite or bi-layer graphene we find
diagonal elements. Therefore, in Mueller matrix data
φ = π/4, and for inter-Landau-level transitions in single
from optically isotropic samples, ideally all off-diagonal-
layer graphene φ=0.
blockelementsvanish,while,forexample,magneto-optic
Note that for φ = 0, the polarizabilities for left
birefringence can cause non-zero off-diagonal-block ele-
and right handed circularly polarized light are equal
ments in the Mueller matrix.
(χ =χ ), and εLL is diagonal.
+ – B Here,wedefineOHEdataasMuellermatrixdatafrom
an OHE experiment [Eq. (1)] with magnetic field ±B
B. Mueller matrix calculus, GE and data acquisition M± =M(ε +ε ). (13)
OHE B=0 ±B
1. Stokes vector/Mueller matrix calculus Furthermore, we define the derived OHE datasets δM±
as difference data between the Mueller matrix datasets,
The real-valued Stokes vector S has four measured at the magnetic field ±B and the correspond-
components61, carries the dimension of an inten- ing zero field dataset
sity, and can quantify any polarization state of plane
electromagnetic waves. If expressed in terms of the δM± =M± −M
p- and s-coordinate system62, its individual compo- OHE 0 (14)
=∆M(ε ,ε ),
nents can be defined by S = I + I , S = I − I , B=0 ±B
1 p s 2 p s
S = I −I , and S = I −I , with I , I , I ,
3 45 −45 4 σ+ σ− p s 45 where M = M(ε ) is the Mueller matrix of the zero
I , I , and I being the intensities for the p-, s-, 0 B=0
−45 σ+ σ− fieldexperimentand∆M(ε ,ε )isthemagneticfield
+45◦, -45◦, right- and left-handed circularly polarized B=0 ±B
induced change of the Mueller matrix. This form of pre-
light components, respectively.5,63
sentation is in particular advantageous in case the mag-
The real-valued 4×4 Mueller matrix M describes the
netic field causes only small changes in the Mueller ma-
change of electromagnetic plane wave properties (inten-
trix, and provides improved sensitivity to magnetic field
sity, polarization state), expressed by a Stokes vector S,
5
dependent model parameters during data analysis. An-
other form of presentation for derived OHE data is
C. Data analysis
δM+±δM− = ∆M(ε ,ε )
B=0 +B (15)
Ellipsometry is an indirect experimental technique.
±∆M(ε ,ε ),
B=0 −B Therefore, in general, ellipsometric data analysis invokes
model calculations to determine physical parameters in
which can be used to inspect symmetry properties of
dielectrictensorsorthethicknessoflayers,forinstance.71
magneto-optic Mueller matrix data, and can help to im-
Sequencesofhomogeneouslayerswithsmoothandparal-
prove the sensitivity to magnetic field dependent model
lelinterfacesareassumedinordertocalculatethepropa-
parameters during data analysis.
gationoflightthroughalayeredsample,bythe4×4ma-
trix formalism.7,12,47 To best match the generated data
with experimental results, parameters with significance
3. Mueller matrix data acquisition (GE)
are varied and Mueller matrix data is calculated for all
spectral data points, angles of incidence and magnetic
Rotating element ellipsometers can be classified
fields. During the mean square error (MSE) regression,
into two categories:47 (i) rotating analyzer ellipsome-
the generated Mueller matrix data MG is compared
ters(RAE)6,47,65,66inpolarizer-sample-rotating-analyzer ij,k
with the experimental Mueller matrix data ME and
(PSA ) or rotating-polarizer-sample-analyzer (P SA) ij,k
R R
their match is quantified by the MSE
configuration, capable to measure the upper left 3 ×
3 block of the Mueller matrix; (ii) rotating compen- v
satorsellipsometers(RCE)47,65,67–70 inpolarizer-sample- MSE=uut 1 X4 X4 XS MiEj,k−MiGj,k!2 , (17)
rroottaattiinngg--ccoommppeennssaattoorr--asanmalpylzee-ran(aPlySzCerR(AP)CorSAp)olcaornizfiegr-- 9S−K i=1j=1k=1 σMiEj,k
R
uration, capable to measure the upper left 3×4 or 4×3
where S, K and σ denotes the total number of data
block of the Mueller matrix, respectively. MiEj,k
points, thetotalnumberofparametersvariedduringthe
The Mueller matrices of a polarizer P, analyzer A,
non-linear regression process, and the standard devia-
compensator C(δ) with phase shift δ, coordinate rota-
tion of ME , obtained during the experiment, respec-
tion along beam path R(θ) by an angle θ, and of the ij,k
tively. For fast convergence of the MSE regression, the
sample M are given by
Levenberg-Marquardt fitting algorithm is used.72 The
 1 1 0 0  MSE regression is interrupted when the decrease in the
1 1 1 0 0 MSE is smaller than a set threshold and the determined
P=A =   ,
2 0 0 0 0  parameters are considered as best model parameters.
0 0 0 0 The sensitivity and possible correlation of the varied
parameters is checked and, if necessary, the model is
 1 0 0 0 
changed and the process is repeated.73–75
0 1 0 0
C(δ) =   ,
 0 0 cosδ −sinδ
0 0 sinδ cosδ
(16) III. INTEGRATED MIR, FIR AND THZ OHE
 1 0 0 0  INSTRUMENT
0 cos2θ sin2θ 0
R(θ) =  j j  ,
 0 −sin2θj cos2θj 0  Figure 1 shows (side view) the integrated MIR, FIR
0 0 0 1 andTHzOHEinstrumentwithitsfoursub-systems: (A)
M M M M  the MIR ellipsometer sub-system, (B) the FIR/THz el-
11 12 13 14
M M M M lipsometer sub-system, (C) the magneto-cryostat sub-
M =  21 22 23 24  ,
M M M M  system, and (D) the magneto-cryostat transfer sub-
31 22 33 34
M M M M system. In order to utilize the magneto-cryostat sub-
41 42 43 44
system with the MIR or the FIR/THz ellipsometer sub-
respectively. Execution of the matrix multiplication systemthemagneto-cryostattransfersub-systemwasin-
characteristic for the corresponding ellipsometer type47 stalled. The integrated MIR, FIR and THz OHE in-
shows that, due to the rotation of optical elements, the strument contains multiple light sources and detectors,
measuredintensityatthedetectoristypicallysinusoidal. and covers a spectral range from 3 cm−1 to 7000 cm−1
Fourier analysis of the detector signal provides Fourier (0.1–210 THz or 0.4–870 meV). Both ellipsometer sub-
coefficients,whichareusedtodeterminetheMuellerma- systems can be operated without the magneto-cryostat
trix of the sample (see sec. IVA). sub-system, in a variable angle of incidence ellipsometry
mode76 (Φ = 30◦...90◦). Figure 2 shows a schematic
a
overview (top view) of all major components in the inte-
grated MIR, FIR and THz OHE instrument.
6
FIG. 1. Technical drawing (side view) of the integrated MIR, FIR and THz OHE instrument. The instrument has four sub-
systems,(i)theMIRellipsometersub-system,(ii)theFIR/THzellipsometersub-system,(iii)themagnet-cryostatsub-system,
and (iv) the magneto-cryostat transfer sub-system. The magneto-cryostat transfer sub-system holds both ellipsometers and
serves as a translation system for the magnet-cryostat sub-system, which can be used with the ellipsometer sub-systems. The
total dimensions of the integrated MIR, FIR and THz OHE instrument are 160 cm × 450 cm × 115 cm (h×w×d).
a source selection and beam focusing assembly (R ) and
1
a rotation stage assembly (P -b -St ), respectively. The
1 1 1
beam steering plane mirror assembly (m ) is composed
1
A. MIR ellipsometer sub-system ofanopto-mechanicmountandaplanefirstsurfacegold
mirror.78 Thesourceselectionandbeamfocusingassem-
The upper part of Fig. 2 shows a schematic drawing bly (R ) comprises two sub-assemblies (detailed draw-
1
(top view) of the optical configuration of the MIR sub- ing: Fig. 3 a), the rotatable plane mirror sub-assembly79
systemoftheintegratedMIR,FIRandTHzOHEinstru- (stepper motor, axis extension, mechanic mount for axis
ment. The MIR ellipsometer sub-system is composed of extension, opto-mechanic mount for mirror, plane first
(i)theMIRsourceunit,(ii)thepolarizationstateprepa- surface gold mirror78) and the beam focusing off-axis
ration unit, (iii) the MIR goniometer unit, and (iv) the paraboloidstagesub-assembly(opto-mechanicmountfor
polarizationstatedetectionunit. Tominimizeabsorption paraboloid, gold surface 90◦ off-axis paraboloid with an
due to water vapor, the complete beam path of the MIR effective focal length of f = 350 mm80), which focuses
e
ellipsometer sub-system is purged with dried air.77 Due the beam onto the sample position. The focused beam
to the high magnetic stray-fields (see Fig. 4), all opto- then reaches the rotation stage assembly (P -b -St )
1 1 1
mechanical components in the polarization state prepa- which has a nominal angular resolution of 0.045◦. The
ration and detection units were designed and manufac- rotationstageassembly(detaileddrawing: Fig.3b)con-
turedwithoutferromagneticmaterials(withexceptionof tains a KRS-5 substrate based wire grid polarizer (P ),
1
the stepper motors). which is mounted in a hollow tube, which is fitted into
The MIR source unit of the MIR ellipsometer sub- two polymer bearings with glass balls, which are held by
system is a Bruker Vertex 70 Fourier-transform-infrared analuminumblock. A48-toothpolymergearismounted
spectrometer (Fig. 2: MIR-FTIR) with a silicon carbide to the hollow tube, and is connected via a Kevlar tim-
globar light source (spectral range 580–7000 cm−1). Af- ing belt (b ) to a 12-tooth polymer gear on a stainless
1
ter being collimated, the light beam passes the interfer- steel shaft (gear ratio: 1:4), leading to the stepper mo-
ometer (potassium bromide (KBr) beam splitter), is re- tor (St ). After passing the rotation stage assembly, the
1
flectedbyaplanemirror, andexitstheMIRsourceunit. polarized and focused beam leaves the polarization state
The beam enters the polarization state preparation preparation unit.
unit. Inside the polarization state preparation unit the The beam is then reflected by, or transmitted through
beampassesabeamsteeringplanemirrorassembly(m ), the sample (S ). The sample can be mounted on a sam-
1 1
7
A: Analyzer
B: Bolometer
b: Timing Belt
BWO: Backward Wave
Oscillator Source MIR-FTIR
Ch Chopper Wheel
DTGS:DTGS Detector
FTIR: Bruker V70 FTIR St1
g: Golay Cell In
Detector
G: Goniometer Unit MIR
In: Input Port (for R
m 1
additional light 2 m sub-system
sources) b P 1
1 1
MCT: HgCdTe Detector
MCT
m: Plane Mirror o
M1,M2:Closed-Cycle 8T M1 A1 1 o2
Magnet-Cryostat
R DTGS
in Position 1&2 S 2 1
1
o: G90o°l dF Oirsfft- SAuxirsfa-ce b2 St2
Paraboloid G o B
1 3 1
P: Polarizer
PR: Polarization State
Rotator
R: Source Selection, 0 10 20 30 40cm
Beam Focusing
Assembly
S: Sample
St: Stepper Motor
FIG. 3. a) Technical drawing of the source selection and
beam focusing/beam collimation and detector selection as-
St BB2 o7 G2 sfoecmubsliinegs/(bRea1−m4 cinollFimiga.t2io)n. aEnadchdseoteucrtcoerseselelecctitoionnaansdsebmebamly
5 bb
5 is composed of a rotatable plane mirror sub-assembly [plane
S FIR/THz
g DTGS2 RR4 2 first surface gold mirror (mr), opto-mechanic mount for mir-
o6 mAA2 M2 sub- ror (Tm), opto-mechanic mount for axis (TA), axis with
7 system stepper motor and encoder wheel (Str)] and a collimat-
o ing off-axis paraboloid stage sub-assembly [opto-mechanic
5 m P2 b4 m mount for paraboloid (Tp), 90◦ first surface gold off-axis-
6 5
RR paraboloid (or)]. b) Technical drawing of the rotation stage
0 10 20 30 40cm 3 assemblies for polarizers and analyzers (here depicted: rota-
tionstageassemblyforpolarizeroftheFIR/THzellipsometer
sub-system,P -b -St inFig.2). Thestagescompriseanalu-
St b 2 4 4
4 3 minum frame, two plastic bearings with glass balls (Ba), a
St3 m3 shaftwhichcanholduptotwowiregridpolarizers(P2),two
FIR-FTIR m4 PR Ch bgeealtrs(b[1)2atnedetahn(aGx1is2)leaandding48toteaestthep(pGe4r8)m],otaorKwevitlharenticmodinegr
4
wheel (St ).
BWO o 4
4
reflectiontypemeasurementscanonlybeconductedata
FIG. 2. Schematic drawing (top view) of the in-house
Φ =45◦angleofincidence. Adetaileddescriptionofthe
built, variable angle-of-incidence spectroscopic ellipsometer a
sub-systems, used for magneto-optic measurements in the magneto-cryostatsub-system, itssamplemount, andthe
wavelength range from 3 to 8000 cm−1. In the top part optical window configuration is given in section (IIIC).
theFourier-transform-infraredspectroscopybasedMIRellip- The beam then enters the polarization state detection
someter sub-system is depicted while the lower part shows unit, which is mounted to the rotatable arm of the MIR
thecombinedFIR/THzellipsometersub-system. Theclosed- goniometer unit (G ). The polarization state detection
1
cycle 8T magnet-cryostat sub-system can be moved between unit contains a rotation stage assembly (A -b -St ), a
1 2 2
the two ellipsometer sub-systems (M1 or M2) utilizing the
beam collimation and detector selection assembly (R ),
magneto-cryostat transfer sub-system (not depicted). 2
and three beam focusing/detection assemblies (o -MCT,
1
o -DTGS ando -B ). Therotationstageassembly(A -
2 1 3 1 1
b -St ) is equivalent to the one in the polarization state
2 2
preparation unit (P -b -St , Fig. 3 b), but in the polar-
ple holder, attached to the MIR goniometer unit (G ) 1 1 1
1
ization state detection unit the KRS-5 substrate based
(commercially available 2-circle goniometer 415, Huber
wiregridpolarizerservesastheanalyzer(A )oftheMIR
Diffraktionstechnik),orinsidethemagneto-cryostatsub- 1
ellipsometer sub-system. The beam collimation and de-
system(M1). Ifthemagneto-cryostatsub-systemisused,
tector selection assembly (R ) is composed of two sub-
2
8
B. FIR/THz ellipsometer sub-system
The lower part of Fig. 2 shows a schematic drawing
(top view) of the optical configuration of the FIR/THz
ellipsometer sub-system of the integrated MIR, FIR and
THz OHE instrument. The FIR/THz ellipsometer sub-
system can be divided in five units: (i) the FIR source
unit, (ii) the THz source unit, (iii) the polarization state
preparationunit,(iv)theFIR/THzgoniometerunit,and
(v) the polarization state detection unit. For measure-
ments in the FIR spectral range, the FIR/THz ellip-
someter sub-system is operated in analyzer-step mode,63
while for measurements in the THz spectral range the
FIG. 4. Technical drawing of the FIR/THz ellipsometer sub- FIR/THz ellipsometer sub-system is operated in contin-
systemoftheintegratedMIR,FIRandTHzOHEinstrument uously rotating analyzer mode. To minimize absorp-
(MIR ellipsometer sub-system not shown) and the magneto-
tion due to water vapor, the complete beam path of
cryostat sub-system. A cutout view of the magneto-cryostat
the FIR/THz ellipsometer sub-system can be purged
sub-system (blue cylinder, top, center) shows the supercon-
with dried air.77 Due to the high magnetic stray-fields
ducting magnet coils, the variable temperature inset (VTI)
(see Fig. 4), all opto-mechanical components in the THz
and the sample. The three cutout prolate ellipsoids (green)
represent the spacial positions at which the magnetic stray source unit, polarization state preparation unit and po-
field is less than 0.1, 0.025 and 0.01 T. The beam path is larization state detection unit were designed and manu-
indicated in red. facturedwithoutferromagneticmaterials(withexception
of the stepper motors and the THz source).
The FIR source unit of the FIR/THz ellipsome-
ter sub-system is a Bruker Vertex V-70 FTIR-
spectrometer (Fig. 2: FIR-FTIR). The spectrometer
assemblies: the rotatable plane mirror sub-assembly and
is equipped with a silicon beam splitter but otherwise
the collimating off-axis paraboloid stage sub-assembly
identical to the spectrometer used as MIR source unit in
(gold surface 90◦ off-axis paraboloid, f = 350 mm).
e the MIR ellipsometer sub-system.
Both sub-assemblies are equivalent to the source selec-
tionandbeamfocusingassemblyinthepolarizationstate
The THz source unit comprises five assemblies: the
preparation unit (Fig. 3 a), but are used in reverse order
THz source and THz-beam collimation assembly (Fig. 2:
to first collimate and then redirect the beam to one of
BWO-o ), the optical chopper assembly (Ch), the beam
the three beam focusing/detection assemblies using the 4
steering plane mirror assembly (m ), polarization state
rotatablemirror.78 Eachbeamfocusing/detectionassem- 3
rotator assembly (PR-b -St ), and the beam steering
bly contains a beam focusing off-axis paraboloid stage 3 3
plane mirror assembly (m ). The THz source and THz-
sub-assembly and a detector sub-assembly. All detector 4
beam collimation assembly contains a THz source sub-
sub-assemblies contain an opto-mechanic mount and a
assemblyandaTHz-beamcollimatingoff-axisparaboloid
detector. The beam focusing off-axis paraboloid stage
stage sub-assembly. The THz source sub-assembly is
sub-assemblies (o ) are composed of an opto-mechanic
1-3 composed of an opto-mechanic mount and the backward
mount and a 90◦ off-axis paraboloid with an uncoated
wave oscillator (BWO) THz source (Microtech). The
goldsurface. Thefocallengthsoftheoff-axisparaboloids
BWO source emits THz radiation with a high brilliance
are matched to the corresponding detector. The off-
(bandwidth ∼2 MHz) and a high output power (∼0.1–
axis paraboloids (o , o ) for the liquid nitrogen cooled
1 2 0.01 W). The THz radiation is almost perfectly linearly
HgCdTe-detectorsub-assembly(MCT)andthepyroelec-
polarized and the orientation of the polarization is fixed
tric,solidstatedeuteratedtriglycinesulfatedetectorsub-
in space. The base frequency range of the BWO is 107–
assembly(DTGS ),eachhaveaneffectivefocallengthof
1 177 GHz, which can be converted to higher frequency
38 mm (1.5 in). The off-axis paraboloid o for the liquid
3 bands using GaAs Schottky diode frequency multipliers.
heliumcooledbolometerdetectorsub-assembly(B )81,82
1 The spectral range accessible by the BWO can be ex-
has an effective focal length of 190.5 mm (7.5 in). The
panded to 220–350 GHz (×2 multiplier), 330–525 GHz
signal of the used detector is fed back into the MIR-
(×3 multiplier), 650–1040 GHz (×2 and ×3 multiplier)
FTIR-spectrometer to record interferograms. For more
and 980–1580 GHz (double ×3 multiplier). For further
information on the data acquisition and processing see
details on the BWO based THz source and THz ellip-
section IIC.
sometry are given in Ref. 29 and references therein. The
THz radiation from the BWO is collimated by the THz-
beamcollimatingoff-axisparaboloidstagesub-assembly,
composed of an opto-mechanic mount and a 90◦ off-axis
paraboloid(o )withanuncoatedgoldsurfaceandanef-
4
9
fective focal length f = 60 mm. The THz-beam then
e
reaches the optical chopper assembly (Ch), which con-
tains an opto-mechanic mount and a 3 bladed optical
chopper, driven by a linear motor. The 3 bladed optical
chopperisrotatedwithafrequencyoff =3.8Hz,result-
c
inginaopticalchoppingfrequencyoff =11.4Hz,which
o
is close to the optimal frequency response of the Golay
cell detector (f ∼ 12–15 Hz). After interaction with
opt
THz-beam steering plane mirror assembly (m ) (opto-
3
mechanic mount and plane first surface gold mirror78),
theTHz-beamisredirectedtothepolarizationstaterota-
torassembly(PR).Thepolarizationstaterotatorassem-
bly (Fig. 5) is an odd-bounce image rotation system.83
The polarization state rotator is designed to rotate the
polarization state of an incoming electromagnetic beam
azimuthally in a non-deviating, non-displacing fashion
(with respect to the incoming electromagnetic beam di-
rection), and is used to pre-align the polarization direc-
tionoftheTHz-beamwiththepolarizingaxisofthewire-
FIG. 5. Technical drawing of the polarization state rotator
gridpolarizerinthepolarizationstatepreparationunit.84 assembly, used in the THz source unit of the FIR/THz ellip-
Thepolarizationstaterotatorassemblyiscomposedofa someter sub-system to pre-align the polarization direction of
steppermotor(St )witha12-toothpolymergear,which the linearly polarized THz-beam with the polarizing axis of
3
is connected to a 48-tooth polymer gear (gear ratio: 1:4) the polarizer in the polarization state preparation unit. The
viaaKevlartimingbelt(b ),rotatingaPEEKcage(PR) odd-bounce image rotation system83 is composed of a frame
3
which contains three opto-mechanic mounts with plane with an opto-mechanic alumina mount (F), a stepper motor
first surface gold mirrors78 (rotation axis parallel to the with encoder wheel (St3), a 12 teeth gear (G12), connected
byaKevlartimingbelt(b )toa48teethgear(G ). The48
incoming and outgoing THz-beam). After reflection on 3 48
teethgearisgluedtoarotatablePEEKcage(PR)whichcom-
a THz-beam steering plane mirror assembly (m ) (opto-
4 prises 3 opto-mechanic mounts with plane first surface gold
mechanic mount and plane first surface gold mirror78), mirrors (m ),78 and is mounted into the alumina mount (F)
r
the THz-beam leaves the THz source unit.
by two plastic bearings with glass balls (Ba).
The polarization state preparation unit contains four
assemblies: a FIR-beam steering plane mirror assem- lenesubstratebasedwire-gridpolarizers(P ),butisoth-
2
bly (m6), a THz-beam steering plane mirror assem- erwiseidenticaltotherotationstageassemblyinthepo-
bly (m5), a source selection and beam focusing assem- larizationstatepreparationunitoftheMIRellipsometer
bly (R3), and a rotation stage assembly (P2-b4-St4). sub-system (Fig. 3 b). The beam then leaves the polar-
The FIR- and THz-beam steering plane mirror assem- ization state preparation unit.
blies (m6,5) are identical and both are composed of The beam is then reflected by, or transmitted through
an opto-mechanic mount and a plane first surface gold thesample(S ). Thesamplecanbemountedonasample
2
mirror.78 The plane first surface gold mirrors redirect, holder, attached to the FIR/THz goniometer unit (G )
2
dependingonthespectralrangetheFIR/THzellipsome- (commercially available, 2-circle goniometer 415, Huber
ter sub-system is operated in, the FIR- or THz-beam to Diffraktionstechnik),orinsidethemagneto-cryostatsub-
the source selection and beam focusing assembly. The system(M2). Ifthemagneto-cryostatsub-systemisused,
source selection and beam focusing assembly (R3) com- reflection type measurements can only be conducted at
prises two sub-assemblies, the rotatable plane mirror Φ = 45◦ angle of incidence. A detailed description of
a
sub-assembly and the beam focusing off-axis paraboloid themagneto-cryostatsub-system, itssamplemount, and
stage sub-assembly, which are equivalent to those in the theopticalwindowconfigurationisgiveninsectionIIIC.
source selection and beam focusing assembly in the po- The beam then enters the polarization state detection
larization state preparation unit of the MIR ellipsome- unit, which comprises a rotation stage assembly (A -
2
ter sub-system (Fig. 3 a). Depending on the orienta- b -St ), a beam collimation and detector selection as-
5 5
tion of the plane first surface gold mirror78 in the rotat- sembly (R ), and three beam focusing/detection assem-
4
able plane mirror sub-assembly, either the FIR- or THz blies (m -o -g, o -DTGS and o -B ). The beam is
7 5 6 2 7 2
beam is directed to beam focusing off-axis paraboloid routed through the rotation stage assembly for the an-
stage sub-assembly (gold surface 90◦ off-axis paraboloid, alyzer of the FIR/THz ellipsometer sub-system, which
fe =350mm). Thefocusedbeamisthenroutedthrough contains two polyethylene substrate based wire-grid po-
therotationstageassembly,whichcontainstwopolyethy- larizers (A ), but is otherwise identical to the rota-
2
10
tion stage assembly in the polarization state detection
unit of the MIR ellipsometer sub-system (Fig. 3 b).
The rotation stage assembly for the analyzer of the
FIR/THz ellipsometer sub-system can be operated in
step mode for FIR measurements63 or in continuous
rotation mode for THz measurements. The beam is
then collimated (gold surface 90◦ off-axis paraboloid,
f = 350 mm) and redirected to the selected detector
e
by the beam collimation and detector selection assem-
bly (R ), identical to the beam collimation and detec-
4
tor selection assembly in the polarization state detec-
tion unit of the MIR ellipsometer sub-system (Fig. 3
a). The beam focusing and Golay-cell-detector assem-
bly(m -o -g)containsabeamsteeringplanemirrorsub-
7 5
assembly(m )(opto-mechanicmount,planefirstsurface
7
goldmirror78),abeamfocusingoff-axisparaboloidstage
sub-assembly (o ) (opto-mechanic mount, gold surface
5
FIG. 6. Technical drawing of the sample (S) and its holder,
90◦ off-axis paraboloid, f = 60 mm), and a Golay-cell
e including the sample heater, capsuled in a copper block (H).
detectorsub-assembly(g)(opto-mechanicmount,Golay-
Thesampleisthermallycoupledtothevariabletemperature
cell detector). The beam focusing and DTGS detector
inset (VTI) by a static exchange gas (UHP-He) surrounding
assembly (o -DTGS ) comprises a beam focusing off-
6 2 thesample. Theinner,0.35mmthick,diamondwindows(W)
axis paraboloid stage sub-assembly (o6) (opto-mechanic are wedged and were glued to their stainless steel window
mount, gold surface 90◦ off-axis paraboloid, fe = frames (C) by a two component epoxy (G).
38 mm), and a solid state deuterated triglycine sulfate
detector sub-assembly (DTGS ) (opto-mechanic mount,
2
Bruker Vertex V-70 DTGS detector). Alternatively, the
beamfocusingandbolometerdetectorassembly(o -B ), B =8Twithaninhomogeneityoflessthan0.3%canbe
7 2
composed of a beam focusing off-axis paraboloid stage achieved. The magnetic field can be reversed and points
sub-assembly (o ) (opto-mechanic mount, gold surface towards one of the optical windows. Therefore, for re-
7
90◦ off-axisparaboloid, f =190.5mm)andthebolome- flection type OHE measurements, the magnetic field lies
e
ter detector sub-assembly (B ) (opto-mechanic mount; within the plane of incidence and forms an angle of 45◦
2
commercially available, liquid helium cooled bolometer with the sample norma√l. This leads to a magnetic field
detector, Infrared Laboratories Inc.), can be used. For component Bc = |B|/ 2 perpendicular to the sample
THz measurements the bolometer or the golay cell de- surface.
tector can be chosen, while for FIR measurements only The primary cooling cycle comprises a pulse tube
the bolometer or the DTGS detector provide frequency cooler (SRP-082, SHI Cryogenics), high pressure helium
responses fast enough to record interferograms. lines and a helium compressor (F-70, Sumitomo Heavy
Industries). Ultra-high-purity helium (UHP-He) gas at
high pressure is provided by the helium compressor, and
C. Magneto-cryostat sub-system guided by a high pressure helium line to the pulse tube
cooler. The pulse tube cooler is thermally coupled to
The central piece of equipment of the integrated the superconducting magnet coils and allows to cool the
MIR, FIR and THz OHE instrument is the commer- magnet coils to temperatures of T ≈ 3.1 K. The pulse
cially available, superconducting, closed cycle magneto- tube cooler also pre-cools the UHP-He in the secondary
cryostat sub-system (7T-SpectromagPT, Oxford Instru- cooling cycle. The UHP-He gas is then guided back to
ments)withfouropticalports(Fig.4). Thedesignofthe the helium compressor by a high pressure helium line,
integrated MIR, FIR and THz OHE instrument allows and is reused.
the usage of the magneto-cryostat sub-system with the The secondary cooling cycle uses UHP-He gas to cool
MIR and the FIR/THz ellipsometer sub-system by em- thesample. TheUHP-Hegasintheclosedcycle,iscircu-
ploying the magneto-cryostat transfer sub-system. The latedbyanoil-free,dryscrollpump(XDS-10,Edwards).
magneto-cryostat sub-system can be subdivided into the When the sample is at base temperature, the UHP-He
magnet head, the primary cooling cycle, the secondary gas leaves the outlet of the scroll pump at a pressure
coolingcycle,thesampleholderandtheopticalwindows. of ∼ 0.5 bar, and is pumped through a zeolite and a
The magnet head contains two magnet coils, which liquidnitrogentrap,inordertoextractpossiblecontam-
are mounted around the sample position and are fabri- inants leaking into the closed cycle. The UHP-He gas
cated in a split-coil pair design. In a spherical volume of then passes a distiller spiral, which is thermally coupled
10mmdiameteraroundthesample,magneticfieldsupto tothepulsetubecooler(primarycoolingcycle),andcon-