Design of a scanning gate microscope for mesoscopic electron systems in a cryogen

12 Pages·2014·2.2 MB·English

Design of a scanning gate microscope for mesoscopic electron systems in a cryogen-
free dilution refrigerator
M. Pelliccione, A. Sciambi, J. Bartel, A. J. Keller, and D. Goldhaber-Gordon

Citation: Review of Scientific Instruments 84, 033703 (2013); doi: 10.1063/1.4794767
View online: http://dx.doi.org/10.1063/1.4794767
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REVIEWOFSCIENTIFICINSTRUMENTS84,033703(2013)
Design of a scanning gate microscope for mesoscopic electron systems in
a cryogen-free dilution refrigerator
M.Pelliccione,1,2 A.Sciambi,1,2 J.Bartel,2,3 A.J.Keller,3 andD.Goldhaber-Gordon2,3
1DepartmentofAppliedPhysics,StanfordUniversity,348ViaPuebloMall,Stanford,California94305,USA
2StanfordInstituteforMaterialsandEnergySciences,SLACNationalAcceleratorLaboratory,
2575SandHillRoad,MenloPark,California94025,USA
3DepartmentofPhysics,StanfordUniversity,382ViaPuebloMall,Stanford,California94305,USA
(Received29January2013;accepted23February2013;publishedonline12March2013)
Wereportonourdesignofascanninggatemicroscopehousedinacryogen-freedilutionrefrigera-
torwithabasetemperatureof15mK.Therecentincreaseinefficiencyofpulsetubecryocoolershas
madecryogen-freesystemspopularinrecentyears.However,thisnewstyleofcryostatpresentschal-
lengesforperformingscanningprobemeasurements,mainlyasaresultofthevibrationsintroduced
bythecryocooler.Wedemonstratescanningwithroot-mean-squarevibrationsof0.8nmat3Kand
2.1nmat15mKina1kHzbandwidthwithourdesign.UsingCoulombblockadethermometryona
GaAs/AlGaAsgate-definedquantumdot,wedemonstrateanelectrontemperatureof45mK.©2013
AmericanInstituteofPhysics.[http://dx.doi.org/10.1063/1.4794767]
I. INTRODUCTION pulsing high pressure helium gas through the pulsetube ata
frequencyontheorderof1Hz.Therefore,thenatureofvibra-
Scanning probe microscopy has been used as a very tionsinthesystemismuchdifferentthanthoseinaLHebased
powerfultooltoinvestigatemesoscopicsystemsatcryogenic system, where the vibrations from the thermal bath are a re-
temperatures.1–3 In particular, scanning gate microscopy sultoftheboilingliquidcryogen.Inthispaper,wepresentour
(SGM), which typically involves scanning a conductive designofascanninggatemicroscopeina“cryogen-free”di-
AFM or STM tip over a sample, has shown the ability lutionrefrigerator.Webuiltthismicroscopetoperformmea-
to probe branched electron flows through a quantum point surementsaimedatrealizinglocaltunnelinginhighmobility
contact4,5 and to image Coulomb islands of an Aharonov- 2D electron systems using a technique called “virtual scan-
Bohm interferometer.6 Many SGM measurements are per- ningtunnelingmicroscopy”(VSTM).27,28
formed at liquid helium temperatures, but there has been a
strong interest in performing SGM in a dilution refrigerator,
which is desirable for improved energy resolution for spec-
II. SYSTEMDESCRIPTION
troscopicmeasurements,aswellasforinvestigatingphysical
effectsthatareabsentathighertemperatures. TheSGMishousedinsideaLeidenCryogenicsCF-650
Inrecentyears,anumberofgroupshavedevelopedscan- dilution refrigerator, with a base temperature of 10 mK and
ning probe systems operating at dilution refrigerator tem- 650 μW of cooling power at 120 mK with no experimental
peratures, typically at or below 100 mK.7–19 Most systems payload.Precoolingto3.3KisprovidedbyaCryomechPT-
described in the literature are housed in traditional “wet” 415 pulse tube cryocooler driven by a CP1010 helium com-
cryostats that utilize liquid helium (LHe) as a thermal bath. pressor, which itself provides 1.35 W of cooling power at
However, with the increasing cost and scarcity of liquid he- 4.2Kwiththeremotemotoroption.Asuperconductingvec-
lium,manynewcryostatsarenow“dry”systemsinthesense tormagnetfromAmericanMagneticscapableofapplying9T
thatthereisnoliquidheliumbathtoprovidecoolingto4.2K. perpendiculartothesampleor3Tparalleltotheplaneofthe
A LHe bath is instead replaced with a cryocooler, typically sample is integrated into the system and cooled by the pulse
a pulse tube,20,21 which can provide conductive cooling to tube. The entire system is housed inside an acoustically and
approximately 3 K. A traditional dilution unit based on the electricallyshieldedroombuiltbyETS-Lindgren,whichhas
circulation of a 3He/4He mixture is then used to reach tem- 45dBofRFattenuationat1GHz.Allelectricalpenetrations
peraturesontheorderof10mK.Thesenewsystemsaretyp- into the room pass through pi filters from Spectrum Control
icallyreferredtoas“cryogen-free”becauseoftheabsenceof (56-725-003and1289-004)whichattenuate70dBat1GHz.
a LHe bath, although the systems do still rely on a 3He/4He Thebodyofthescanneriscomposedofthreecoarsesteppers
mixture similar to a traditional dilution system. Dry systems (ANPx101andANPz101)andapiezoscanner(ANSxyz100)
offer significant advantages over wet systems, including no fromAttocubeSystemsmadeofGrade2titanium.
He loss and the capacity for a large experimental volume at The design of the system does not incorporate a top-
basetemperature. loading probe, instead a sample is loaded into the system
Asignificantdisadvantageofapulsetubebasedcryostat by disassembling the outer vacuum can, inner vacuum can,
isthevibrationintroducedbythecryocooler.22–25 Althougha and radiation shields. The cooldown time for the system
pulsetubehasnomovingmechanicalpartsatlowtemperature fromroomtemperaturetobasetemperatureisapproximately
likeaGifford-McMahoncryocooler,26coolingisachievedby 36 h, and it takes about 30 min to disassemble the system
0034-6748/2013/84(3)/033703/11/$30.00 84,033703-1 ©2013AmericanInstituteofPhysics
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033703-2 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
once warm to access the sample. The absence of a probe in- fridge back and forth. As a result, we anchored the motor to
creases the turnaround time for changing samples, but sim- oneofthesupportlegsofthefridge,butonafoambasethat
plifiesthedesignconsiderablybecauseiteliminatesthespace dampsvibrationsfromthedirectanchoring.
constraintssetbythediameterofaprobe.Moreimportantly, Ifthemotordoesnotturnsmoothly,thevibrationsofthe
it allows one to add significantly more mass to the scanning motor can add to the vibrations generated by the helium gas
stage to improve vibration damping. The mixing chamber pulses.WefoundthatthemotordriversuppliedbyCryomech
plateis340mmindiameterwitha125mmclearanceabove (IM483)wasfarfromideal,generatingvibrationsinthestep-
thetopofthemagnet,whichgivesamplespaceforlowtem- per motor at 140 Hz and higher harmonics. The 140 Hz
peraturewiringandRFfiltering. vibrations are a result of the design of the stepper motor;
Before presenting the specifics of the system design, it thesteppermotorhas200stepsperrevolution,andthemotor
will be important to briefly describe the nature of vibrations turnsat0.7Hz(onefullrotationyieldstwogaspulsecycles),
introducedbythepulsetube.Toachievecooling,thehelium and(200stepsperrevolution)×(0.7revolutionspersecond)
gas pressure in the pulse tube must be pulsed at a particu- =140stepspersecond.Thevibrationsarearesultofthena-
larfrequencysetbythedimensionsofthepulsetubeandthe tureofthesteppermotordrivegeneratedbytheIM483.
thermodynamics of the cooling cycle. For the PT-415 pulse The cold head motor is a 4-wire bipolar stepper motor,
tubeusedinthissystem,thepulsefrequencyis1.40Hz,and and the ideal drive for a smooth rotation of the motor is a
the gas pressure oscillates between 80 psi and 300 psi. The sinusoidalcurrentthroughthewindings.Atypicalmicrostep-
gaspulsesaresharpinthatthevibrationspectrumisreminis- pingdriver,suchastheIM483,discretizestheidealsinusoidal
centoftheFourierspectrumofasquarewave,withharmonics currentintomicrostepsapproximatingasinewave,resulting
measurabletowellabove1kHz.TheintegratedRMSvibra- in sharp steps of current through the motor windings and a
tions up to 1 kHz on the mixing chamber plate are approxi- jerkyrotation.Wealsofoundthismotordrivetobeasignif-
mately2μmintheverticalzdirectionand6μminthelateral icant source of radiated EMI due to a rapid change in cur-
directions x and y. More details regarding the vibrations are rentthoughthemotorwindings,whichhaveaninductanceof
presentedinSec.IV. 15 mH per winding for this motor. The magnitude of the
One straightforward way to reduce the vibrations from pickup will depend on the specific orientation and type of
the pulse tube is to mechanically decouple it from the rest wiringinstalled,butweobservedEMIinthe10kHzto1MHz
of the system.22 In our system, the pulse tube is bolted to a rangewithanamplitudeabove10mVoncoaxialcablingin-
copper plate in the cryostat, which provides not only good stalledinthefridge.
thermal anchoring but also good mechanical anchoring. Re- These problems can be improved dramatically by using
placingthisjointwithamechanicallyfloppyconnectionusing alinearmicrosteppingmotordriver,whichlinearlyrampsthe
copperbraidsorstrapswouldhelpwithvibrationsbutwould current between microsteps instead of abruptly changing it.
alsocompromisecoolingpowerbecauseoftheincreasedther- We modified the cold head motor to be driven by a custom
mal resistance of the joint. The PT-415 pulse tube provides LNX-Glinearmotordriver(PrecisionMotionControl,Inc.),
only1.35Wofcoolingpowerat4.2K,whichissignificantly whichreducedtheamplitudeof140Hzvibrationsatthemix-
less than a LHe bath. Introducing a thermal impedance be- ing chamber plate by an order of magnitude. There is also
tweenthepulsetubeandcryostatwouldeffectivelylowerthis nomeasurabledifferenceinthenoiseonfridgewiringwhen
value. We have chosen not to isolate the pulse tube in this comparingthenoisewiththecoldheadmotoroffandwiththe
manner because of the cooling requirements of our vector coldheadmotoronbeingdrivenbythelineardriver.
magnet.
Although we chose not to modify the thermal anchor-
ing of the pulse tube to the cryostat, there are a few impor-
III. SGMDESIGN
tantpointstohighlightregardingthecoldheadmotor.Forthe
PT415pulsetube,thecoldheadmotorisasmallsteppermo- The design of the SGM was chosen to attenuate vibra-
torthatturnsavalvewhichcyclesbetweenthehighandlow tionsfromthepulsetubeasmuchaspossible.Thisisaccom-
pressure helium reservoirs supplied by the helium compres- plished passively by implementing a low-pass spring stage
sor. Vibrations from the rotation of this motor are important in series with a mechanically stiff scanning stage, which
becausethemotorneedstobelocatedclosetothepulsetube will attenuate relative vibrations between the scanning tip
toavoidasignificantlossincoolingpower.Weusetheremote and the sample. A diagram of the total ensemble is shown
motoroptionforthePT415pulsetubewhichallowsthemotor in Figure 1 and consists of three main sections; the “spring
tobeseparatedfromthepulsetubebyabout30cm.However, stage,”asetofsix11in.×5in.×0.125in.phosphorbronze
thisreducesthecoolingpowerofthepulsetubefrom1.5W (PhBr) plates clamped together that hang via beryllium cop-
to 1.35 W at 4.2 K, and as such should not be moved much per (BeCu) springs from the mixing chamber plate; the cold
furtherawaytoavoidcompromisingmorecoolingpower. finger,agold-plated4NOFHCcopperassemblythatextends
Themountingoftheremotemotorisalsoimportantbe- to the center of the magnet; and the scanner mounted at the
cause the flexible helium line between the motor and pulse end of the cold finger. The spring stage consists of six sepa-
tube expands and contracts as the helium pressure changes. rateplatesbecausewecouldnotlocateasupplierofphosphor
Forexample,wefoundthatmountingtheremotemotorona bronze who could provide one plate with the desired thick-
platform separate from the fridge resulted in significant lat- ness.Thecoldfingerisdesignedtohaveavariableheightso
eralvibrations,causedessentiallybythemotor“rocking”the the sample can be adjusted to rest in the field center of the
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033703-3 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
of the phosphor bronze plates is chosen to be approximately
6kg,aschoosingalargemasshelpsreducetheamplitudeof
vibrationsfromthepulsetube.Ideally,onewouldchoosethe
resonantfrequencyofthisstagetobeconsiderablylowerthan
theresonantfrequencyofthepulsetubeforgoodattenuation.
Therelativelylowpulsefrequencyof1.40Hzmakesthisdif-
ficult, and the spring stage does not act as an ideal low-pass
filter for the pulses. It does, however, serve to attenuate vi-
brations at higher harmonics of the pulse frequency, as will
be shown in Sec. IV. It is also important that the resonance
of the spring stage does not lie on a harmonic of the pulse
frequency,orelsevibrationscouldbeamplified.
Thespringconstantofthespringstageisapproximately
1.75 N/mm at room temperature. This value may change
when the stage is cooled due to thermal contraction of the
BeCu and a change in the shear modulus. Given the shear
modulusG,springdiameterD,wireradiusd,andnumberof
activecoilsN ,thespringconstantisgivenby29
a
FIG.1. SchematicdrawingoftheSGMsuspendedfromthemixingchamber
plate. Gd4
k = .
8N D3
a
magnet. A photograph of the SGM is shown in Figure 2(a), Forcopperalloys,theshearmodulustypicallyincreasesabout
withaclose-upimageofthescannerinFigure2(b). 8%fromroomtemperatureto4K,30andforBeCuthethermal
contractionisabout0.3%overthesametemperaturerange.31
Tofirstorder,thespringconstantatlowtemperatureisthen
A. Springstage
(1.08)(0.997)4
k(4K)≈ k(300K)≈(1.077)k(300K).
The choice of mass and spring constant for the spring (0.997)3
stage is restricted by the dimensions of the system, par-
This increase in spring constant will lead to an increase in
ticularly the 125 mm clearance between the bottom of
theresonantfrequencyofthespringstage,whichinourcase
the mixing chamber plate and the top of the magnet. The
√resonant frequen(cid:2)cy of this stage is given by f =(2π)−1 may lie within the bandwidth of the second harmonic of the
k/m=(2π)−1 g/x ,wherex istheequilibriumexten- pulsetubeat2.80Hz.AswillbeshowninSec.IV,vibrations
eq eq measuredonthespringstagedonotexhibitastrongenhance-
sion of the springs. The lowest resonant frequency achiev-
ment at 2.80 Hz, indicating that the spring stage is not am-
able for the spring√stage given the dimensions of the space
is f =(2π)−1 g/(125mm)=1.41Hz. Since the un- plifyingthevibrationsatthisfrequency.Also,ascanbeseen
min inFigure2(a),theBeCuspringsarewrappedinTeflontape.
stretched length of the springs and thickness of components
Thisprovidesdampingtothespringswithouttransmittingtoo
are non-negligible, the maximum extension of the springs is
muchextravibration.Wefoundempiricallythattwolayersof
less than 125 mm, and the actual resonant frequency of the
Teflon tape (MS-STR-4) yielded the lowest vibrations at the
stageinFigure2(a)is2.63Hzatroomtemperature.Themass
scanner;extralayersoftapemadethespringsmorerigidand
increasedthevibrationstransmitted.
B. Thermalanchoring
Suspending the scanner via springs involves making a
tradeoffbetweenthermalanchoringandmechanicalstiffness.
Good thermal contact is achieved by rigidly anchoring the
scanner to the mixing chamber plate, but this configuration
resultsintip-samplevibrationsthatareunacceptablylargefor
ourmeasurements.Whentestedinthisconfigurationwithour
scanning cage, we observed over 200 nm peak-to-peak mo-
tion of the tip relative to the sample, with motion correlated
with gas pulses from the pulse tube. This could perhaps be
improvedwithamorerigiddesignforthescanningcagethat
housesthepiezoscanner,butthestiffnessismostlikelylim-
itedbythelowerrigidityoftheAttocubecoarsesteppersand
FIG.2. (a)PhotooftheSGMmountedonthemixingchamberplateofthe piezoscannercomparedtothecopperscanningcage.
CF650dilutionrefrigerator.(b)Photoofthescanningstagemountedatthe
The design of this system has been biased towards
bottomofthecoldfinger.Thesampleisseatedfacingdowninthechipsocket,
andthetiprestsontopofastackofcoarsesteppersandapiezoscanner. achievinglowvibrationattheexpenseofthermalanchoring.
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033703-4 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
to an annealing procedure that improves the residual resis-
tanceratio(RRR)atlowtemperatures.34
C. Responseinamagneticfield
Integrating the spring supported SGM with a magnet
presents a number of additional challenges. Since the spring
stageisnotwellmechanicallyanchoredtotherestofthesys-
tem, extra care needs to be taken when operating in a large
magneticfieldtoavoidforcesthatcanleadtosignificantmo-
tion. This starts with choosing appropriate materials; avoid-
ing not only ferromagnetic materials but also materials with
a large paramagnetic or diamagnetic response. This is espe-
cially true at base temperature where the magnetic suscepti-
bility χ can follow a Curie-like χ∝T−1 dependence. Mate-
rialsthatsuperconductshouldalsobeavoidedifpossiblebe-
causetheirmechanicalresponsewillbesimilartoadiamagnet
FIG.3. Coolingpowerversustemperatureforthemixingchamberandthe withχ =−1untilthemagneticfieldexceedsthecriticalfield
scanner.Thecoolingpoweratthescannerisreducedasasideeffectofme- ofthematerial.
chanicallydecouplingthescannerfromthepulsetube.Afittothepredicted
Ifalloysareused,itisimportanttoknowthespecifical-
quadraticdependenceofcoolingpowerontemperatureisplottedalongwith
loycompositionsincethemagneticresponsecanvarysignifi-
experimentallymeasuredvalues.
cantlywithsmallchangesinelementalcomposition.Consider
for example the various alloys of brass. Pure alloys of brass
The scanner is heat sunk to the mixing chamber plate with arealloysofcopperandzinconly(e.g.,C23000andC26000),
two4NOFHCcopperfoils,each5milsthick.Tomeasurethe but most common alloys of brass include a non-negligible
effective cooling power at the scanner, heat is applied to the amount of lead (2.5%–3.7% for C36000).35 Lead is added
scannerandthetemperatureismeasuredbothonthescanner to improve the machinability of the brass, but unfortunately
andonthemixingchamberplate.Theresultofthismeasure- has a large effect on the magnetic response. Unleaded brass
mentisshowninFigure3.Thebasetemperatureofthemixing alloys have volume magnetic susceptibilities on the order of
chamberis14.5mKandthebasetemperatureofthescanner χ ∼10−5 at4K,butleadedbrassalloyscanhaveχ ∼10−2
is15.4mK.At1μWofheatapplied,thetemperatureofthe at 4 K with only a few percent of lead added.36 The leaded
scanner increases to 35 mK, and the mixing chamber tem- brassalloysalsotendtohavemorerelaxedconstraintsforthe
perature increases to 16.4 mK. The cooling power Q˙ versus concentration of ferromagnetic elements including iron and
temperatureTcanbeextractedwithaquadraticfit,32 nickel,althoughtheyarenotexplicitcomponentsofthealloy.
(cid:3) (cid:4) From our experience, it can be difficult to identify the alloy
Q˙ −Q˙ =a T2−T2 ,
0 0 compositionofaunknownbrasspart,assuppliersofcompo-
whereQ˙ isthebackgroundheatloadontherespectivestage. nents cannot always guarantee a specific alloy. However by
0
farthemostcommon alloychosenformachined brassprod-
Using the quadratic fitting, when the scanner is at 100 mK
uctsistheleadedC36000.37 Unlessthesusceptibilityischar-
ithasacoolingpowerof11μW,andthetemperatureofthe
acterized with a low temperature SQUID, it is better to only
mixingchamberplateis31mK.
usepartswherethealloyisknown.Tothisend,allanchoring
This is a considerable reduction in cooling power, but
hardwareincludingscrews,nuts,andboltsusedontheSGM
heatloadstypicallygeneratedbytheANSxyz100piezoscan-
havebeenmachinedoutofphosphorbronze(C51000),which
ner during large area scans are manageable at this scale. For
hasasusceptibilityofχ =−5.6×10−6 at4K.36
example, a 30 min long raster scan over an area of 3 μm
× 3 μm dissipates a power of about 1 μW due to losses in Asanexample,considerthebehaviorofthespringstage
if it were machined out of leaded brass instead of phosphor
thescanpiezos.ThepowerPdissipatedinapiezoelectricele-
bronze. The force on a homogeneous material with volume
mentundertheinfluenceofasinusoidaldriveV sin(2πft)is
magneticsusceptibilityχ andvolumeV inthepresenceofa
givenby33
fieldB(cid:6) =B(z)zˆis
P =2πfCV2tanδ, F(cid:6) =∇(m(cid:6) ·B(cid:6))
where C is the piezo capacitance and tanδ is the dissipa- = χV ∇(B(cid:6) ·B(cid:6))
tionfactorduetodielectriclossinthepiezoelectricmaterial. μ (1+χ)
0
(cid:5) (cid:6)
Therefore,theheatloadfromthescanningpiezosscaleslin-
χV ∂B
early with scan speed and quadratically with voltage or dis- = 2B zˆ.
μ (1+χ) ∂z
placement. If a lower temperature is required during a scan, 0
thiscanbeachievedbyscanningeithermoreslowlyorovera Although the fringing fields of the magnet are not aligned
smallerarea.Ifalargercoolingpowerisrequired,thecopper along the zˆ direction throughout the entire volume of the
heatsinkscouldbereplacedwith5Ncopper,orbesubjected spring stage, we can make this assumption to simplify the
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033703-5 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
calculation.Forcesinthelateraldirectionsshouldcanceldue r4 andquicklybecomesinsignificantforpartswithsmalldi-
tosymmetrysincetheSGMiscenteredalongtheaxisofthe mensions.Forexample,thecoldfingerdesignincludesashaft
solenoid.FromsimulationsprovidedbyAmericanMagnetics, with a diameter of 5/16 in. that rests inside the bore of the
whenthesolenoidisenergizedto9T,thevalueofthezcom- magnet. Even though it experiences a larger field and larger
ponent of the fringe field at the center of the spring stage is field gradient in this volume than the spring stage, the ra-
0.6Twithagradientof0.1T/cminthezdirection.Forphos- dius is small enough that the force it would experience in a
phor bronze (C51000, χ = −5.6 × 10−6) this gives a force magnet quench is not significant. The strong dependence on
F=36mN,butforleadedbrass(C36000,χ =1.4×10−2) dimensioniswhythisistypicallynotaconcernforcoldfin-
this gives a force F = 89 N. Therefore, motion of the brass gersmountedinprobebasedsystems.Therestrictiononsize
plate would be significant enough to cause a touch between imposed by the probe precludes the use of parts with lateral
the SGM and the fridge (51 mm) where it is not significant dimensionslargerthanafewinches.Inthosecases,themain
forthephosphorbronze(21μm). motivationforreducingeddycurrentsistoreducetheheating
A similar calculation needs to be performed for the ti- associated with the dissipation of eddy currents in the mate-
tanium in the coarse and fine positioners, which experience rials. Eddy currents can also be reduced by cutting holes or
larger fields and field gradients than the spring stage. They slitsintoaparttoimpedeeddycurrentflow.Thisisshownin
aremachinedofGrade2titanium38withχ =1.5×10−4.Ti- Figure 1 for the spring stage and the larger diameter copper
tanium will also superconduct at base temperature, although partsinthecoldfinger.
with a small critical field39 of H ≈ 5 mT. For our design,
c
the forces on the titanium in these situations are negligible,
yielding motion less than 100 μm. In addition to titanium,
D. Tuningforkcantilevers
anysolderusedinconstructioncouldsuperconduct andgive
unwantedmotion.Theonlysolderusedinthisdesignissilver OperatingtheSGMintopographicmodeisnecessaryto
solder in the cold finger; however, the solder used (Silvaloy orient the location of the tip over the region of interest on a
A-56T; 56% Ag, 22% Cu, 17% Zn, 5% Sn) has been shown sample.Thisrequiresaschemethatallowsforameasurement
nottosuperconduct40 downto35mK.Lead-tinsoldershave of the force (or force gradient) that the tip experiences. The
been avoided in the design, all joints in electrical wiring are most common method to accomplish this in AFM is a laser-
eithercrimpedorpress-fit. based scheme, where a laser spot is reflected off the back of
Inadditiontomagneticsusceptibility,onemustalsocon- the cantilever, and the deflection of the laser is registered on
sidertheresponseoftheSGMduringmagneticfieldsweeps, a photodiode. For cryogenic scanning probes, there are two
andintheworstcaseintheeventofamagnetquench.Arapid maincomplicationswiththismethod:alignmentandheating.
change in magnetic field will induce eddy currents in com- Ifthereisnoopticalaccesstothesamplefromroomtempera-
ponents with low electrical resistivity. Eddy currents in the ture,maintainingalignmentofthelaserandcantileveratcryo-
presenceofamagneticfieldcanresultinforcesthatmovethe genictemperaturescanbedifficult,althoughnotimpossible.
SGM,andinthecaseofamagnetquenchpossiblycausedam- Residualheatingfromlaserilluminationisthelargerproblem
age. Theforceon ahomogeneous materialofcircular cross- atdilutiontemperatures,andforourmeasurementswewould
section in the presence of a time-varying magnetic field ori- liketokeeptheheatloadonthescannerunder1μW.Thisre-
entednormaltothecircularcross-sectionisgivenby stricts the laser intensity and the signal-to-noise ratio for the
topographic measurement. In addition, mesoscopic samples,
πtr4dB
|F|≈ |∇B|, includingthoseintheGaAs/AlGaAsmaterialsystem,aretyp-
8ρ dt icallylightsensitive,42 andanyunnecessaryexposuretolight
where r is the radius of the circular cross-section, t is the atcryogenictemperaturesshouldbeavoided.
thickness, and ρ is the electrical resistivity. To calculate the For these reasons, self-sensing cantilevers are of inter-
forceonthespringstageinamagnetquench,assumeithasa est for cryogenic SGM since the use of a laser or other
circular cross-section, and 1 s elapses from full field to zero lightsourceisnotnecessary.Themostcommonself-sensing
field.Thetimetoreachzerofieldisconservativelyestimated methods are piezoresistive cantilevers43 and tuning fork
usingtheinductanceofthemagnetL=32Handthenormal cantilevers.44–47 Piezoresistivecantileversarefabricatedwith
stateresistanceR≈30(cid:7),althoughinanactualquenchdiodes a piezoresistive element in the cantilever that changes resis-
across the magnet leads will also be active. Using the low tanceasthecantileverisstressed.Althoughthefabricationof
temperatureelectricalresistivityofphosphorbronze(ρ=8.8 thesetypesofcantileversismorecomplicatedthantraditional
×10−8 (cid:7)m),31 thisgivesaforceF≈4N,whichwillmove siliconcantilevers,ameasurementoftheresistancechangeof
theSGMbutisnotenoughtodamageit.Werethespringstage thepiezoresistorisrelativelystraightforward.Adrawbackof
insteadmadeof4NOFHCcopper(ρ =1.6×10−10 (cid:7)m),41 piezoresistivecantileversforSGMinadilutionrefrigeratoris
the force would become F ≈ 2300 N. This is a conservative theheatdissipatedbythepiezoresistor.Typicalsensitivitiesof
estimatefortheforcebecausethespringstagewillheatupas piezoresistve cantilevers are a few ppm change in resistance
aresultofthemagnetquench,whichwillincreasetheelectri- pernanometerofdeflection,andpowersontheorderof1mW
calresistivityandreducethesizeoftheeddycurrents. aredissipatedinthepiezoresistortoachieveasuitablesignal-
Theforceduetoeddycurrentsisaconcernforanypart to-noiseratioforimaging.43Thispowerismanageableat4K
made of OFHC copper, since it has a low electrical resistiv- orevenina3He-basedcryostatbutbecomesproblematicbe-
ity at cryogenic temperatures. However, this force scales as low100mK.
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033703-6 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
fork leads. The resonant frequency of the tuning fork after
fabricationistypically30–31kHz,slightlylowerthanitsorig-
inalresonance,withaQaround750inambientconditionsand
7500atlowtemperatureinvacuum.
IV. VIBRATIONS
Thevibrationsinthesystemaredominatedbythepulse
tube.Tocharacterizetheoverallvibrationfloorofthesystem,
it is instructive to use a geophone, which is simply a small
FIG.4. Photographsofassembledtuningforkcantilevers.(a)Topviewof
magnet hanging from a spring coaxially inside a solenoid.
thetuningforkanchoredtoasapphirediskwithsilvercontactpads.(b)Top
viewofthecantileverandtipepoxiedtotheendofthetuningforkwitha When there is relative motion between the magnet and the
Ti/Auevaporatedtracetomakeelectricalcontacttothetip. solenoid, a voltage will be induced in the solenoid propor-
tional to the velocity of the magnet for small displacements.
WeusegeophonesfromGeoSpaceLP,modelGS-11Dwitha
We have chosen to implement a tuning fork based can- natural resonance frequency of 4.5 Hz. Geophones become
tilever scheme for topographic imaging. Tuning fork can- less sensitive below their natural resonance because exter-
tilevershavesufficientforcesensitivitytoachieveatomicres- nal vibrations result in a common mode motion of both the
olution under suitable conditions.44–46 Although we do not magnetandsolenoidwellbelowtheresonantfrequency.This
need atomic resolution imaging for our measurements, the yieldsapracticallowerlimitof1Hzfordetectablevibration
very high force sensitivity of tuning forks is desirable. The usingthisparticulargeophone.Thismodel,however,isquite
interaction force between the tip and sample is measured ei- compactandeasilyfitsinsidethesystemformeasurementsat
therwithamplitudeorfrequencymodulatedtechniques,√with roomtemperatureandlowtemperature.
anultimatedeflectionsensitivityontheorderof10fm/ Hz Figure5showstheresultofavibrationmeasurementin
at 4 K.46 This is a result of the high quality factor Q of the theverticaldirectionwithageophoneonthemixingchamber
tuning fork, which can exceed 20000 in vacuum and at low plateatroomtemperature,comparingthevibrationswiththe
temperature.46Anotherconsequenceofthehighqualityfactor pulse tube on and off. The effect of the pulse tube on vibra-
at cryogenic temperatures is low power dissipation. We typ- tions is dramatic. We define the integrated RMS vibration I
ically operate the tuning fork with powers much less than 1 betweentwofrequenciesf andf as
1 2
(cid:7)
nW,whichisnegligiblysmallforourmeasurementsandhas (cid:8)
nomeasurableeffectonthetemperatureofthescanner. I(f ,f )= f2[S(f)]2df,
1 2
AnimageofatuningforkcantileverwithattachedAFM
f1
tipisshowninFigure4.ThetuningforksarefromIQDFre-
where S(f) is the amplitude spectral density. Integrating the
quency Products (LF A103C) and have a nominal resonant
data in Figure 5 from 1 Hz to 1 kHz gives an RMS vibra-
frequency of 215 = 32768 Hz. We fabricate cantilevers in
tion of 1.9 μm on the mixing chamber plate in the vertical
the qPlus configuration, where one prong of the tuning fork
directionwiththepulsetubeon.ThedatainFigure5areonly
is held fixed and the other prong is free to vibrate. The tun-
plottedto100Hztoclearlyshowthefullwidthathalfmaxi-
ingforkismountedtoa7.5mmdiametersapphirediskwith
cyanoacrylate glue (Krazy glue),47 where sapphire is chosen
for its high thermal conductivity at low temperature for an
electricalinsulator.Electricalcontactismadetothetwoleads
ofthetuningforkwithsilverpaint,whichisusedbothtoex-
citethemechanicalresonanceofthetuningforkandtoapply
a voltage to the SGM tip when performing a scanning gate
measurement.
In the zoomed view in Figure 4, the AFM tip and sili-
con cantilever can be seen mounted to the end of the upper
prong of the tuning fork. The tip is attached by first plac-
ing a drop of fast-setting epoxy (Devcon 14250) at the end
of the tuning fork. Next, the cantilever and silicon base chip
it is attached to are anchored to a micromanipulator stage,
which is used to controllably lower the cantilever onto the
epoxy.Afterabout1mintheepoxyhaspartiallyset,andthe
stage is lowered further until the cantilever snaps off the sil-
iconbasechip.Thetipsused(MikroMaschDPE14)arepre-
coatedinPtwitha30nmtipradiusandhaveaspringconstant
FIG.5. Vibrationsintheverticaldirectiononthemixingchamberplateas
of 6 N/m. A shadow mask is then used to evaporate Ti/Au
measured with a geophone at room temperature. Harmonics of the pulse
(20 nm/30 nm) on the end of the tuning fork to electrically
frequency (1.40 Hz) are clearly visible in the spectrum when the pulse
connect the Pt-coated cantilever with one of the Ag tuning tubeison.
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033703-7 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
FIG.6. Vibrationsintheverticaldirectiononthemixingchamberplateand FIG.7. Tip-samplevibrationswhilescanningat15mK.TheintegratedRMS
springstagewiththepulsetubeonatroomtemperature.Above10Hz,there vibrationbetween1Hzand1kHzat15mKis2.1nm.
isasignificantattenuationofthepulsetubeharmonicsatthespringstage.
mumoftheresonantpeaks,approximately25mHz.Aniden- tuningforkresonance.Theresponseofthetuningforkisthen
ticalmeasurementforthehorizontalvibrationgivesanRMS measured with a phase locked loop, and any variation in the
amplitudeof6.4μmand6.0μminxandy,wherethex-axis resonantfrequencyisaresultofrelativedisplacement(vibra-
is defined parallel to the helium line that connects the pulse tion)betweenthetipandsample.Theextensionofthezpiezo
tube to the remote motor. Similar spectra were also taken at is simultaneously oscillated at a known frequency and am-
3.3 K after recalibrating the geophone at this temperature;48 plitude for calibration purposes, in this case 1.0 nm RMS at
thevibrationsarequalitativelysimilarandthetotalRMSvi- 25Hz.Theelectricalresponseofthetuningforkcanthenbe
brationchangesonlybyafewpercent.Theharmonicsofthe convertedintoavibrationamplitudebycalibratingthepower
pulsefrequency(1.40Hz)aremeasurablewiththegeophone underthepeakintheFourierspectrumat25Hz.
up to 1 kHz, although the spectral weigh√t of harmonics near TheresultofthemeasurementisshowninFigure7,with
1kHzissmall,ontheorderof10−5 μm/ Hz. thecalibrationsignalat25Hzremoved.TheintegratedRMS
A comparison of the vibrations on the mixing chamber vibrationbetween1Hzand1kHzintheverticaldirectionat
plate and spring stage highlights the function of the spring 3.3 K is 0.8 nm; a similar measurement at 15 mK gives an
stage in the SGM design and is shown in Figure 6. At 5 Hz RMS vibration amplitude of 2.1 nm, with the increase due
and below, the spring stage gives almost no attenuation of tomixtureflowingthroughthedilutioncircuit.Ameasureof
the vertical vibrations on the mixing chamber. Over a full horizontalvibrationscanbeachievedbyrepeatedlyscanning
1 kHz bandwidth, the vertical RMS vibration amplitude on over a sharp step edge with the caveat that the response of
thespringstageismodestlyreducedto0.58μm,downfrom the feedback circuitry can artificially broaden edges of fea-
1.9 μm at the mixing chamber plate. For the horizontal vi- tures on the surface. Using this method we can put a con-
brations,theRMSamplitudeisreducedto1.53μmand1.48 servative limit of 10 nm RMS on the size of horizontal vi-
μm for the x and y axes, respectively. But most of the re- brations. These vibrations are manageable for scanning gate
maining vibration is at low frequencies, below 10 Hz. The measurements,wherethetipistypicallyscannedatleast10–
higherharmonicsofthepulsetubevibrationaresignificantly 20 nm above the surface when gating. Example topographic
attenuated, up to a factor of 103 at 100 Hz. The main role andscanninggateimagesareshowninFigure8.
ofthespringstageistoattenuatevibrationforfrequenciesat Ifasignificantlylowervibrationfloorisneededforscan-
or above the resonant frequency of the body of the scanner. ning, as would be required for STM measurements, the first
The series combination of a “low-pass” spring stage and a modificationtothisdesignwouldbetomechanicallydecou-
“high-pass” rigid scanner body is what ultimately allows for ple the pulse tube from the fridge as much as possible given
therelativetip-samplevibrationstobelow. thecoolingpowerconstraintsofthesystem.Forasystemwith
We now turn to a direct measurement of vibrations be- a large superconducting magnet, this would require a design
tween the tip and the sample while scanning. This measure- that allows for good thermal contact to the magnet while si-
ment is performed by operating the SGM in tapping mode, multaneouslyprovidingamechanicallyfloppycontacttothe
where the tip is in intermittent contact with the surface, at a scanner.Anotherimprovementthatcouldbemadeistheintro-
largeamplitudewithnoheightfeedback.Forthesemeasure- ductionofactivevibrationcancellation.Sincethepulsetube
ments,thepeak-to-peakoscillationheightofthetipis50nm. vibrationsareregular,onecouldimplementaschemethatac-
Vibrations that are much smaller than the large 50 nm exci- tivelymeasuresvibrationsatthescanningstageandcompen-
tation will produce an approximately linear response in the satesforthemthroughthemotionofthescanningpiezos.
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033703-8 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
in a cryostat and the presence of a pulse tube factors into
these considerations for our SGM. One source of noise that
is significant in cryogen-free systems is triboelectric or mi-
crophonicnoise,whichistheresultofaphysicalvibrationof
thecable.Forshieldedcabling,vibrationscanleadtofriction
betweentheinner/outerconductors andthedielectric,which
candumpchargeontheconductorsandappearasexcesscur-
rent noise in a sensitive measurement. In a pulse tube based
system, the hallmark of triboelectric noise is a peak in the
noise spectrum at the pulse frequency. In fact, when making
measurementsofvibrationsasdescribedinSec.IV,onemust
takecarenottoconfusetriboelectricnoisefortip-samplevi-
brations.Thesecanbediscriminatedbycomparingthenoise
spectrum with the tip in tapping contact and retracted from
thesurface.
A. Samplewiring
The sample wiring can be divided into two main sec-
tions; wiring from room temperature to the mixing chamber
andwiringfromthemixingchambertothescanner.Between
roomtemperatureandthemixingchamber,thereare8coaxial
cables with a 36 AWG CuNi (C71500) inner conductor and
0.025 in. outer diameter braided CuNi shield from Calmont
Wire & Cable. These coaxial cables have a graphite coating
between the dielectric and outer shield to help reduce tribo-
electric noise. Care must be taken when using these cables
to avoid shorts between the graphite and the inner conduc-
torneartheconnectors.Thereisanadditionalsetof24PhBr
twistedpairlinesinaCuNisheathfromroomtemperatureto
the mixing chamber. These cables lead into a set of filtering
andheatsinkingstagesonthemixingchamber,oneofwhich
is shown in Figure 9. After this stage, all cabling between
the mixing chamber and scanner is coax with a Ag plated
Cu32AWG7/40strandedinnerconductorandAgplatedCu
braided shield from Calmont (3007-4876-10-11). The sam-
ple is mounted on a chip carrier from Kyocera (PB-44567),
andthechipsocketisfromPlastronics(P2032S-A-AU)with
BeCu pins, as can be seen in Figure 2(b). Both the chip car-
rierandchipsocketarecustombuiltwithnon-magneticma-
terials,andarefreeofferromagneticunderlayersbeneaththe
goldcontacts.
When considering voltage biased AC measurements,
it is important to keep the pin-to-pin capacitance low to
FIG.8. Exampletopographicandgatescans.(a)Opticalimageofadevice
basedonaGaAs/AlGaAsbilayer2Delectronsystem.27Theactiveregionof
thedeviceliesbetweenthesourceanddraingateswherethe2D-2Dtunnel
conductanceismeasured.(b)Topographicimageoftheregionoutlinedin
yellowin(a).(c)Virtualscanningtunnelingmicroscopy(VSTM)imageof
theregionoutlinedinredin(b).Thechangeintunnelconductancewithos-
cillatingtipheightisplottedintheimage.Thetipwasheld300nmabovethe
devicewitha30nmRMSoscillationand−6Vappliedtothetip.
V. WIRINGANDFILTERING
The wiring and low temperature filtering implemented FIG.9. LowtemperatureRFfilteringandheatsinkingstage.(a)Thelower
in the SGM were chosen to optimize measurements of halfofthestagecontainsEccosorbfoamforfilteringabove1GHz.Multipole
large sample impedances (>1 G(cid:7)) encountered in tunnel- discreteRCfiltersmountedonsapphireprovideheatsinkingintheupper
halfofthestage.(b)Close-upimageoftheRCfiltersmountedonsapphire.
ing measurements.27 A number of different factors help de-
Thesapphireisanchoredtotheboxwithtwobrassscrewsthatalsoprovide
termine the type of wiring and filtering that is implemented groundcontactfortheRCfilters.
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033703-9 Pelliccioneetal. Rev.Sci.Instrum.84,033703(2013)
avoid a capacitive shunt across the device that has a com- net, the stray fields from our magnet satisfy this constraint.
parable impedance to the device at the measurement fre- It has also been shown to thermalize well down to 25 mK
quency, which for us is typically below 100 Hz. For a 1 G(cid:7) with comparable filtering performance at room temperature
sample impedance and 100 Hz measurement frequency, and low temperature.50 To mount the Eccosorb foam in the
this requires a pin-to-pin capacitance much smaller than filterbox,apieceoffoamiscutintosmallsegmentswithdi-
[2π(100Hz)(1G(cid:7))]−1 ≈1.6pF.Thisrequirestheuseofin- mensionssuchthattwosegmentsplacedsidebysideareafew
dividually shielded cables, which is why we chose to have millimeters wider than the filter box enclosure. A 36 AWG
eight lines be coaxial from room temperature to the sample. copperwireisthenplacedinbetweenthesesegments,andthe
The typical capacitance between two sample pins connected assemblyiscompressedintothefilterbox.Thisallowsthedi-
tothecoaxialcablingisabout1fF,limitedonlybythegeome- electrictofullysurroundthewire,aswellasprovidethermal
tryofthechipcarrierandchipsocket.Itisalsoimportantthat anchoringbetweenthefoamandthefilterbox.
these coaxes have low triboelectric noise, as this will appear The upper half of the box contains a 0.5 mm thick sap-
ascurrentnoiseintheconductancemeasurement.Thetwisted phire substrate on which a 3 stage RC filter and meander
pairwiringisusedforapplyingvoltagestogates,wherelow tracesarepatterned,asshowninFigure9(b).Themetaltraces
pin-to-pincapacitanceislesscrucial. onthesapphireareTi/Au(5nm/200nm)whichwasannealed
The Attocube coarse positioning stages require special at 450 ◦C for 60 s after deposition. Meander traces are in-
considerationbecausethereisalimitontheDCresistanceof cluded before and after the RC filters to help heat sink the
thecablingforproperstepperoperation.Atlowtemperature, trace.TheRCfiltersareeach200(cid:7)with100pF/10pF/1pF
thepiezosinthestepperstypicallyhaveabout150nFofca- capacitors from ATC. The inline resistance of the RC stages
pacitance.Theslip-stickmotionreliesonapplyingafastvolt- alongwiththemeandertracesisapproximately700(cid:7)atroom
agepulsetothepiezotorapidlyexpandorcontractthepiezo temperature,whichchangesbylessthan5%atbasetemper-
toovercomestaticfriction.Atotallineresistanceoflessthan ature. The measured attenuation of the completed stage is
5(cid:7)isneededforoperationtoavoidasignificantRCfiltering showninFigure10,alongwiththepredictedresponseinclud-
ofthepulse,butusingcoppercablewouldpresentalargeheat ingparasiticcapacitances.ThedataweremeasuredwithaHP
loadtothemixingchamberandisthereforeavoided.Tomain- 83650BRFsignalgeneratorandAgilentE4404spectruman-
tainlowDCresistancewhilestillprovidingasmallheatload alyzer and are corrected for losses from cabling outside the
to the mixing chamber, superconducting coaxial cables with filterbox.TheRCfiltersareomittedfortheAttocubecoarse
aNbTiinnerconductorandCuNiouterconductor(CoaxCo., positioningstagestomaintainalowDCresistance.However,
Japan, SC-033/50-NbTi-CN) are used between the still and Eccosorbfoamisstillusedtofiltertheselinesabove1GHz,
mixing chamber. From room temperature to the still, semi- andsapphireisstillusedforheatsinkingtheselines.
rigid coaxial cables with a Ag plated BeCu inner conductor To maintain a strong thermal connection between the
and CuNi outer conductor are used, which have a resistance sampleandtheheatsinkingstagesonthemixingchamber,no
of about 1 (cid:7) each. A separate coaxial cable is used as the solderisusedinthedesignoftheheatsinkingstagesorinthe
stepper ground, as tying the stepper ground directly to the pathfromtheheatsinkstothesample.Allelectricalconnec-
fridge ground resulted in a cross-coupling between the slip- tionsaremadeeitherbycrimping,pressfitting,orwithsilver
stickdriveandthesample. epoxy (Epo-Tek H20E) in this region. Lead-tin solders will
superconductatthesetemperatures,whichwillactaseffective
B. RFfilteringandheatsinking
To effectively thermalize the coaxial cables to the mix-
ing chamber, the inner conductor should be broken out of
thecoaxandheatsunkseparatelyfromtheoutershield.The
stagedesignedtodothisisshowninFigure9(a),whichfilters
eight lines. This stage provides both heat sinking of the in-
nerconductorandelectricalfilteringabove1MHz.Sevenof
thesestagesaremountedinthesystemtofilterthe32sample
lines and all lines associated with the Attocube coarse step-
persandpiezoscanner.EachstageismachinedoutofOFHC
copper and MCX connectors are used for the inputs and
outputs.
There are two main sections to each filtering stage. The
inputisalongthebottomofFigure9,andthelowerhalfofthe
boxprovidesfilteringabove1GHzusingadielectricthatbe-
comeslossyinthisfrequencyrange.49,50 Thedielectricused
is Eccosorb foam (MFS-117), which has been shown to be
asuitablereplacementfortraditionalcopperpowderfilters49
FIG.10. AttenuationoftheRFfilteringstageversusfrequency.Themea-
atmagneticfieldsbelow0.1T.Sincethesefiltersarelocated
suredresponseisplottedaspointsandthepredictedresponseisplottedasa
at the mixing chamber plate and not in the bore of the mag- solidline,whichaccountsforparasiticsofdiscretecomponents.
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