Download Single-electron transport and the new standard for electrical current

IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Single-electrontransport
andthenewstandard
forelectricalcurrent
HansjörgScherer
PTBdepartment2.6„Electricalquantummetrology“
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Talkoutline
• SIunitsystemandtheampere
• Single-electroncurrentsourcesingeneral
(‘classical’and‘modern’devices....)
• Future“quantumampere”realisaMonbasedon
single-electrondevices:Conceptsandchallenges
• Recentdevelopmentsandadvances
• Conclusions&outlook
2
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
SystèmeInterna-onald'Unités(SI)-since1960
TheampereistheSIunitofelectriccurrent
andistheelectricalbaseunit.
3
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
SIdefiniBonoftheampere
Theampereisthatconstantcurrentwhich,if
maintainedintwostraightparallelconductorsof
infinitelength,ofnegligiblecircularcross-secMon,
andplaced1metreapartinvacuum,would
producebetweentheseconductorsaforceequal
to2x10–7newtonpermetreoflength.
ThisdefiniMon
•  definesthevaluesforthemagneBc
constant(µ0≡4π⋅10–7N/A2)and
fortheelectricconstantε0=1/µ0c02
•  usestheacMonofforcefromelectrical
currents(m,kg,s→A)
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H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
RealisaBonoftheSIampere
e.g.witha“currentbalance”
(m,kg,s→A)
RelaMveuncertainty∼10-7(0.1ppm)
5
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Electricalunits:Formerly...
RealisaMon
kg
s
m
µ0,ε0
Current 0.1 Voltage
Balance ppm Balance
A
Wab 0.01 Calculable
Balance ppm Capacitor
V
V⋅A
F
R∝1/ωC
Ω
6
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Electricalquantumeffects(since1990)
JosephsonEffect,discovered1962byBrianD.Josephson
Un=n⋅fJ⋅ h
2e
JosephsonconstantKJ=2e/h
KJ-90=483597.9GHz/V
Quantum-HallEffect,discovered1980byKlausvonKlitzing
Ri=
1 h
⋅ 2
i e von-KlitzingconstantRK=h/e2
RK-90=25812.807Ω
7
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Electricalunits:Formerlyandtoday
RealisaMon
kg
s
m
µ0,ε0
Current 0.1 Voltage
Balance ppm Balance
A
Wab 0.01 Calculable
Balance ppm Capacitor
V
V⋅A
F
R∝1/ωC
RepresentaMon
Ω
KJ-90,RK-90
Josephson
Effect
U∝f/KJ
8
Reproducibility
be_erthan
0.001ppm
QuantumHall
Effect
U/I∝RK
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Electricalunits:Formerlyandtoday
RealisaMon
µ0,ε0
SI
RepresentaMon
KJ-90,RK-90
notSI!
9
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
RevisionoftheSI:RedefiniBonoftheunits
Plannedbythe“ConférenceGénéraledesPoidsetMesures”
andimpendingfor2018:
DefiniMonsforallSIbaseunits
willenMrelybebasedon
fixednumericalvaluesfor
fundamentalconstants
(h,e,kB,NA,c,...)
→ Thiswillrestorecoherence
betweenthe“convenMonal”
electricalunitsandtheSI
10
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
RedefiniBonoftheSIampere
ResoluMon1ofthe24thCGPM(2011):
“TheInternaMonalSystemofUnits,theSI,
willbethesystemofunitsinwhich...
theelementarychargeeis
exactly1.60217X×10-19coulomb...”
Single-electrontransport(SET)devices
areconsideredthe‘silverbullet’soluMon
fortherealisaMonthenewampere:
•  itallowsthemostdirectunitrealisaBonusingthe
physicaldefiniMonofcurrentI=dq/dt,
exploiMngthesimpleandevidentrelaMonISET=e⋅f
•  itinvolvesonlyonefundamentalconstant(e),
nottwo(e&h),asJosephson-/QHE-basedrealizaMonsdo.
11
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
SETcurrentsources
“Classical”devices:SETpumpsmadefrom
ultra-smalltunneljuncBons(metal)
Ø J.Pekolaetal.,“Single-electroncurrentsources:Towardarefineddefini?onoftheampere”,Rev.Mod.Phys.85,
1421-1472(2013)
12
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
SETcurrentsources
“Classical”devices:SETpumpsmadefrom
ultra-smalltunneljuncBons(metal)
Energy
PotenMal
V1
V2
V3
Gate
voltage
RCMmeconstantoftunneljuncMons:
f≤100MHz⇒I=e⋅f≤16pA(1.6⋅10-11A)
13
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
SETcurrentsources
“Modern”devices:SETpumpsmadefrom
‘dynamicquantumdots’(semiconductor)
GaAsheterostructure
+Schobkycontacts(gates)
f∼1GHz
⇒I=e⋅f∼160pA
Ø B.KaestnerandV.Kashcheyevs,“Non-adiaba?cquan?zedchargepumpingwithtunable-barrierquantumdots:
areviewofcurrentprogress”,Rep.Prog.Phys.78,103901(2015)
14
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
FutureSET-based“quantumampere”realisaBon
Electrical
current
SETcurrentsources
(state-of-the-art)
Metrologyneeds
Level
fmax∼1GHz
⇒Imax∼160pA
I∼1µA
Accuracy
Dominatedby
Uncertainty∼0.1ppm
orbeber
(staMsMcal)single(cf.‘old’electromechanicalSI
electrontransfererrors!
ampererealisaMons)
15
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
FutureSET-based“quantumampere”realisaBon
SETcurrentsourcesgeneratesmallcurrents!
⇒ Required:CurrentamplificaBonand
measurementmethods(highlyaccurate)
SETcurrentsourcesaresubjectto
single-electrontransfererrors!
⇒Required:Error(ac)counBngschemes
16
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
FutureSET-based“quantumampere”realisaBon
Fordetailssee:
hbp://www.ptb.de/emrp/qu_ampere.html
17
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
FutureSET-basedquantumcurrentstandards
SETcurrentsourcesgenerate
smallcurrents!
⇒Required:CurrentamplificaBon
andmeasurementmethods
SETcurrentsourcesaresubjectto
single-electrontransfererrors!
⇒Required:SETerror(ac)counBng
schemes
18
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
State-of-the-artin100pAmeasurements
• CommercialpAmmeters
offeraccuraciesofnotbeberthan10ppm,
limitedbygaininstabiliMes
• CryogenicCurrentComparators(CCCs)
arealternaMvehigh-accuracycurrent
amplificaMontechniques,
butinthelow-flux(smallcurrent)regime
theysufferfromnoiserecMficaMoneffects
⇒ NovelconceptsandinstrumentaBonarenecessary!
Wanted:Ahandy(mobile),non-cryogenic,single-box
tabletopelectrometerwithsuperioraccuracy!
19
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
‘Ultrastablelow-noisecurrentamplifier’(ULCA)
Measures100pAwith0.1ppmtotaluncertaintyinabout10hours!
Ø D.Drungetal.,“Ultrastablelow-noisecurrentamplifier:anoveldeviceformeasuringsmallelectriccurrents
withhighaccuracy”,Rev.Sci.Instrum.86,024703(2015)
Ø D.Drungetal.,“Improvingthetraceablemeasurementandgenera?onofsmalldirectcurrents”,IEEETrans.
Instrum.Meas.64,3021–3030(2015),open-access
hbp://ieeexplore.ieee.org/xpl/arMcleDetails.jsp?arnumber=7132759
20
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CCCsystemforcalibraBonoftheULCA
SQUIDelectronics
hCCC:
it
w
n
o
B
a
r
b
li
a
ULCAc
.1ppm
0
<
y
t
in
a
t
r
e
c
n
Totalu
Digitaldualchannel
currentsource
andbridgevoltmeter
Comparatorwithbinary
windingarrangement
(12-bitor14-bit)and
SQUIDnulldetector,in
superconduc?ngscreen
Liquidhelium
bathfor
comparator
probe
ments,
PTB develop ilable
y a va
commerciall
Ø D.Drungetal.,“Ultrastablelow-noisecurrentamplifier:anoveldeviceformeasuringsmallelectriccurrents
withhighaccuracy”,Rev.Sci.Instrum.86,024703(2015)
Ø D.Drungetal.,“Improvingthetraceablemeasurementandgenera?onofsmalldirectcurrents”,IEEETrans.
Instrum.Meas.64,3021–3030(2015),open-access
hbp://ieeexplore.ieee.org/xpl/arMcleDetails.jsp?arnumber=7132759
21
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CCCandULCA:EffecBveinputcurrentnoise
102
√SI (fA/√Hz)
14-Bit CCC @ 17000 turns
101
ULCA @ 3 GΩ
100
10-3
10-2
10-1
100
101
f (Hz)
Ø D.Drungetal.,“Ultrastablelow-noisecurrentamplifier:anoveldeviceformeasuringsmallelectriccurrents
withhighaccuracy”,Rev.Sci.Instrum.86,024703(2015)
Ø D.Drungetal.,“Improvingthetraceablemeasurementandgenera?onofsmalldirectcurrents”,IEEETrans.
Instrum.Meas.64,3021–3030(2015),open-access
hbp://ieeexplore.ieee.org/xpl/arMcleDetails.jsp?arnumber=7132759
22
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
High-accuracySETcurrentmeasurements
ULCA
23
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
f=545.45MHz
T=0.1K
B=16T
on/offcycle
PumpcurrentI/pA
PumpcurrentI/pA
High-accuracySETcurrentmeasurements
Time/s
VExit/mV
Ø  F.Steinetal.,“Valida?onofaquan?zed-currentsourcewith0.2ppmuncertainty”,APL107,103501(2015)
24
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
High-accuracySETcurrentmeasurements
8
4
World
recordin
accuracy!
2
Plateauxdatamean:
(I-e⋅f)/(e⋅f)=
(-0.094±0.194)ppm
0
inpartspermillion
ΔI=(I-ef)/(ef)
6
≈4-6hoursintegrationtimeperpoint
≈1hourintegrationtimeperpoint
Fitoftheroreticalmodel
-2
-4
-6
Uncertaintybarstype-Aonly(k=1)
-380
-375
-370
ExitgatevoltageinmV
-365
Ø  F.Steinetal.,“Valida?onofaquan?zed-currentsourcewith0.2ppmuncertainty”,APL107,103501(2015)
25
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
FutureSET-basedquantumcurrentstandards
SETcurrentsourcesgenerate
smallcurrents!
⇒Required:CurrentamplificaBon
andmeasurementmethods
SETcurrentsourcesaresubjectto
single-electrontransfererrors!
⇒Required:SETerror(ac)counBng
schemes
26
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
TransfererrorsinSETpumps
Example:SETpumpsbasedontunneljuncMons
27
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
TransfererrorsinSETpumps
Example:SETpumpsbasedondynamicalquantumdots
28
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CounBngsingle-electrontransfererrors
ISET=〈n〉⋅e⋅fwith〈n〉≈1
〈n〉incl.uncertainty(!)
mustbequanMfied
foranymetrological
SETpump +SETdetector applicaMon/experiment!
(QuantumMetrology
Triangle,SETcurrent
standard,...)
Keyidea:
Tocountnoteveryelectron(waytoofast!),
butjustcounttheerrors(muchmorerare)!
29
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CounBngsingle-electrontransfererrors
Idea(1992)andfirstpioneeringexperiments(1994)byNIST:
“Electron
”
d
r
a
d
n
a
t
S
nce
a
t
i
c
a
p
a
C
C o u n Mn g
30
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CounBngsingle-electrontransfererrors
...inthe“ElectronCounMngCapacitanceStandard”byPTB
SETpump
UFB
Qisl
Electrometer signal / e
V1
V2
V3
V4
SETelectrometer
“shu_le
pumping”
slow
@2.5Hz
n
o
t
s
e
t
y
Fidelit pump
T
E
S
e
th
1.0
0.0
38
39
40
41
42
43
Time / s
31
44
Ø B.Camarotaetal.,“Electron
Coun?ngCapacitanceStandard
45 withanimprovedfive-junc?onRpump”,Metrologia49,8-14
(2012)
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
CounBngsingle-electrontransfererrors
...inthe“ElectronCounMngCapacitanceStandard”byPTB
SETpump
UFB
Qisl
V1
V2
V3
V4
SETelectrometer
“shu_le
pumping”
fast
@2.5MHz
Electrometer signal / e
-46
-47
39errorsin1049s
⇒Γerror=0.038s-1
-48
-49
-50
-51
RelaBvetransfererror
=0.038s-1/2.5MHz
=0.015ppm
-52
-53
-54
0
5
10
15
Time / min
32
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
BUT...notsuitableforSETcurrentstandard
SETpump
SETelectrometer
Schemedoesnotallowtocontactpumpdrainsidebycurrentlines
becausehighstraycapacitanceof‘drainwire’deterioratessingleelectronresoluMonofdetector(SETelectrometer=SETtransistor)
33
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
BUT...notsuitableforSETcurrentstandard
SETpump
SETelectrometer
Schemedoesnotallowtocontactpumpdrainsidebycurrentlines
becausehighstraycapacitanceof‘drainwire’deterioratessingleelectronresoluMonofdetector(SETelectrometer=SETtransistor)
⇒CounMngsingle-electrontransfererrorsmustbedoneina
separateevaluaMonphase,whichisdifferentfromthe
‘currentsourcing’operaMonmode!
34
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
AdvancedSETerroraccounBngscheme
SETelectrometers
SETpumps
• AllowscontacMngthecircuitwithoutimpairingsingle-electron
resoluMonofthedetectors
• AllowstocountSETerrorswhilepumpingunidirecMonally:
‘insitu’erroraccounBng ‘Self-referenced’SETcurrentsource
• FurtheradvantagesbycorrelaBonanalysisofdetectorsignals!
Ø  M.Wulf,“Erroraccoun?ngalgorithmforelectroncoun?ngexperiments”,PRB87,035312(2013)
35
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
‘Self-referenced’SETcurrentsource:device
SETpumps
(GaAs)
SETdetectors
(Al-AlOx-Al)
1µm
Ø L.Frickeetal.,“Coun?ngSta?s?csforElectronCaptureinaDynamicQuantumDot”,PRL110,
126803(2013)
Ø L.Frickeetal.,“Self-referencedsingle-electronquan?zedcurrentsource”,PRL112,226803(2014)
36
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
‘Self-referenced’SETcurrentsource:firstresults
Signaturesofmissed-cycleevents
50-foldaccuracyenhancement
byerroraccounBng(but:f∼30Hz)
Ø L.Frickeetal.,“Self-referencedsingle-electronquan?zedcurrentsource”,PRL112,226803(2014)
37
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
Conclusions&outlook
...onthechallengesregarding
“futureSET-basedquantumcurrentstandards”:
• SET-generatedcurrentlevelandaccuracy:
100pAwith∼0.1ppmwithinreach,
1nAwith<0.1ppmenvisaged(silicon-basedSETpumps?)
• SETerroraccounBng:
...ismandatoryformetrology!SchemesforsoluMonsexist
(demonstrated&validated),butneedopMmizedimplementaMons
(high-speedoperaMon,usingrf-SETdetectors,...)
• Small-currentmeasurementandamplificaBon:
ThenovelULCAinstrumentissuperiortoCCC-basedsystems,
offeringunparalleledperformanceforapplicaMonsinsmallcurrentmetrology(SET,andmore!)
38
H.Scherer:Single-electrontransportandthenewstandardforelectricalcurrent
IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2016.
KRYO 2015 tutorial presentation. Not submitted for publication.
...thankstoallinvolvedcolleaguesfromfourPTBdepartments
inBraunschweigandBerlin!
•  QuantumElectronics(PTBdepartment2.4)
•  SemiconductorPhysicsandMagneBsm(PTBdepartment2.5)
•  ElectricalQuantumMetrology(PTBdepartment2.6)
•  CryophysicsandSpectrometry(PTBdepartment7.2)
Physikalisch-Technische Bundesanstalt
Braunschweig and Berlin
Bundesallee 100
38116 Braunschweig
Hansjörg Scherer
Telefon: 0531 592-2610
E-Mail: [email protected]
www.ptb.de