Domain free high field superlattice transport

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by  T. Feil

Domain free high field superlattice transport
T. Feil, H.-P. Tranitz, M. Reinwald, and W. Wegscheider
Institut fu¨r Experimentalphysik, Universit¨at Regensburg, 93040 Regensburg, Germany
(Dated: February 2, 2008)
Thefundamentalconditionforoperatingasuperlattice(SL)asaBlochoscillatorisahomogeneous
electric field alignment under large applied bias. This can be done by combining the nonlinear
5
minibandtransportchannelwithaparallelshuntchannel,connectedthroughlateraltransport. We
0
reporthereaboutthefirstrealizationofsuchaSL-shuntsystem. Withthecleaved-edge-overgrowth
0
(CEO)methodwecombineanundopedsuperlattice,whichactsastheshunt,withatwo-dimensional
2
(2D) cleaved-edge surface superlattice channel. Our results confirm the long predicted current-

n voltage-characteristic (I-V) of a SL in a homogeneous DC electric field. Excitation experiments in
a theGHzregimeshowthatourshuntapproachalsoworksinthepresenceofanexternalACelectric
J
field. Thedeviceconceptopensaclearpathtowardstherealization ofasolidstateBlochoscillator.

3
2 PACSnumbers: 73.21.Cd,72.20.Ht,73.50.Mx

] a)
r experimentalrealization
e 500
theoreticalsuggestion
h WhenEsakiandTsu[1]proposedthefabricationofSL A]
ot structures,they showedthatthese shouldexhibit alarge [m400 combinedI-V
. regionofnegative-differentialconductance(NDC)dueto nt
at the occurance of Bloch oscillations [2], [3]. Since they re300
m found Bloch frequencies in the terahertz (THz) range, ur shuntI-V
C200
- they suggested to use the SL as a solid state source in D-
d this regime. Semiclassical calculations of the dynamic S100
n conductivityofaSLbyKtitorovet al. [4]confirmedthat
o 0 SLI-V
c theSLactsasagainmediumforallfrequenciesuptothe
[ Bloch frequency. About twenty years after these initial 0.0 0.1 0.2 0.3 0.4 0.5
SD-Voltage[V]
1 predictions, experiments, successfully revealing the for- b)
v mation of Wannier-Stark ladders in biased SLs [5], and 4 s(w)combined
0 resolvingBlochoscillationswiththehelpoftime domain 3
5 spectroscopy[6], [7], [8], were performed. The excitation
5 of a biased doped SL [9] also showed the theoretically s02 s(w)shunt
01 predictedTHzresonancesinthephotoconductivityofthe ()/s 1
5 SLsample. TheoreticalfindingsbyWillenberget al. [10] Re
0
0 extendtheKtitorovresultstoawiderangeofSLparam-
t/ eters and electric field and temperature regions. It was -1 gainresonance
a alsopossibletoconfirmthetheoreticallypredictedshape s(w)SL
m -2
of the gain curve, by deriving the dynamic conductivity
- from time domain spectoscopy results [11]. Recently, a 0.0 0.5 1.0 1.5 2.0
d w/w
direct observation of the crossover from loss to gain in B
n
o a biased super-SL sturcture was successfully performed FIG. 1: (a) Current-Voltage-characteristics of the shunt, the
c [12], measuringthe change intransmissionof a super-SL SLandthecombinedsystemsuggestedin[14]comparedwith
v: array,when bias was applied to the structure during the theexperimental realization. Addingtheshunt tothe super-
i THz excitation. lattice makes the overall conductivity positive and no insta-
X bilitiesoccur. (b)Iftherealpartofthedynamicconductivity
Nevertheless there exists no successful realization of an
r issmallerthanthemaximumgainattheresonanceoftheSL,
a active solid state Bloch oscillator up to now. The main thenthecombinedsystemstillexhibitsgainclosetotheBloch
obstacle in achieving such a device, is the instability of frequency;adapted for our samples from [14].
the electric field in a region of NDC. This phenomenon
is well known from the Gunn effect [13]. Any fluctua- SL structure. Consequently, in order to realize an active
tion in the electron density along the device, when it is Bloch oscillator device one has to overcome the problem
biased in the NDC region, leads to a growth of the fluc- of domain formation. One such attempt is the super-
tuation and a redistribution of the electric field in do- SL structure employed in [12], in which individual SL
mains of small and large magnitudes. This destroys the sections are so short that full grown domains cannot be
equidistant Stark-ladder. In contrast, the homogeneous formed. Under THz excitation this resulted in a homo-
electric field along the device is an essential requirement geneous field distribution across about 75 percent of the
presentinalltheoreticalcalculationspredictinggainina device. Another approach towards avoiding the problem
2
of instabilities was theoretically suggested by Daniel et a) V VSD+
al. [14]. The authors propose to combine the SL with a
sinidtehsehsutnattircestirsatnosrpwohrticrhegaicmtsea.sTahneeirlepcrtoripcofisealldisstsaubmilmizear- usunpdeorplaetdt ibceulk VSD{- n++ contact layer barrier contact
rthizeedovienrafilglucroend1u.ctTivhietyapdodsititioivneoinf tthhee srheguinmtecaonf NmDaCke. acting as a shunt GaAs gate
Numerical simulations show that the shunt can stabilize n++ contact layer Al n++ VGate
theelectricfielddistributioninsidetheSLuptoalength
Substrate
scale of a few microns. In the dynamic transport regime
one tries to arrange the structure in a way, that the real 2D surface superlattice channel
part of the dynamic conductivity of the shunt increases b) 14 c) 80000
thecombinedconductivity,butissmallenoughsuchthat 70000
the gain resonance of the SL becomes smaller but is still eV] 7 2m/Vs]60000 fSorshocumibllnoaintkisooenvts-doefHaas-
present, as drawn in figure 1b. [m 0 D=3meV [c50000
ISnLt-shhisunletttseyrstweemretphoarttptrhoevfiidrestssauchcoemssofguelnreeoauliszafiteioldnodfisa- Energy-7 D=9meV 05nnmmwweellll mobility234000000000000 fromPosition
tributionacrosstheSL.Molecularbeamepitaxialgrowth -14 ofNDCpeak
10000
on the sidewall of an undoped SL employing the CEO 0 p/d k 2p/d 0
method [15] allows us to combine the shunt and SL SL 0wel5l0w1i0d0th15[0A]200
withatomicprecisionandwithoutproblemsarisingfrom FIG.2: (a)Schematicdrawingofthesamplestructure. In(b)
the theoretically calculated bandstructures along the surface
poorly defined or contaminated interfaces. Since our ge-
SLareplottedfor0nmand5nmcleaved-edgewellwidths,to-
ometry also results in direct control of the SL channel
getherwithasimplecosinefit. (c)Anincreaseinthecleaved-
density, a complete separation of the two transport con-
edge well widths leads to a strong increase in themobility of
tributions is possible. Thus, for the first time we can thesurface SL.
experimentally confirm the long and often predicted I-
V-characteristic of a superlattice under stable high field
conditions. The device gives entrance to a theoretically fieldtransportstudies. Magnetotransportmeasurements
wellstudied,butexperimentallysofarinaccessibletrans- revealedanadjustable2Dchanneldensitybetween0and
portregime. TheresponseoftheSL-shuntsystemstoan 6×1011cm−2 for gate voltages between 0 and 7 V (500
external high-frequency (HF) field confirms the forma- nm barrier width). Figure 2(b) shows the bandstructure
tion of a domain free field distribution. of the 12/3 SL structure for cleaved edge well widths
We realize the SL-shunt system with the CEO method of 0 nm and 5 nm, calculated with the self-consistent
which, in the GaAs/AlGaAs system, allows the atomi- Schr¨odinger-Poisson-Solvernextnano3 [16]. Our calcula-
cally precise combination of two different growth steps tionsshowanincreasingminibandwidthforthickerwells,
(figure 2(a)). In a first molecular-beam-epitaxy process but at the same time the inflection point moves towards
wegrowanundopedGaAs/Al0.3Ga0.7AsSL structurein the brillouin zone boundary and almost completely dis-
between two n+-GaAs layers on a semi-insulating [001] appears for the 20 nm well. These findings are in agree-
GaAssubstrate. TheundopedSL,whosetransportprop- ment with differently based numerical calculations for
erties can be modified by the doping concentration in equivalent structures [17]. Although the gaps to higher
the n+-layers, acts as the shunt in our structure. This lying states appear rather small, the simulations show
layer sequence is then cleaved in situ along the [110] that these states belong to minibands formed from ex-
direction and is overgrown with a GaAs well, followed cited subbands of the gate induced confinement poten-
by an Al0.3Ga0.7As barrier and a n+ GaAs layer act- tial. Since the spatial overlapbetween these subbands is
ing as a gate contact for the surface superlattice chan- vanishingly small, no signigicant tunneling between the
nel. The thickness of the cleaved edge well determines lowest lying miniband and the excited ones is expected
the bandstructurepropertiesandmobilities,whereasthe and also not observed in the experiment. The miniband
thickness of the gate barrier controls the ratio between width of the 12/5 SL with the 5nm cleaved-edge well is
source-drain-voltage (SDV) and gate bias. Two differ- 3.5 meV
ent SL systems with 25 periods of 15 nm length and 60 TheI-V-characteristicsofourdevicesdepictedinfigure3
periods of 17 nm length were used for the samples. In are measured at liquid helium temperature. An increas-
both cases the SL well width was 12 nm, while the bar- ingvoltageV isappliedbetweenthecontactlayersofthe
riers were 3 nm and 5 nm. For further reference we will SL,while the currentthroughthe deviceandthe voltage
call these 12/3 SL and 12/5 SL structures. The cleaved drop VSD across the sample are measured as indicated
edge wellthickness was variedbetween0 nm and20 nm. in figure 2(a). In the inset of figure 3(a) a comparison
Those, with 5 nm well width and a gate barrier thick- between the I-V traces taken for zero applied gate bias
nesses of 100 nm and 500 nm, were chosen for the high- andafterthegatewasmechanicallyremovedshows,that
3
a)
thegatecontrolindeedallowsustoseparatebetweenthe 500
I-VU =0V 700
twotransportchannels. Sincetheshuntchannelaloneal- I-VGGaatteeremoved 600A]m 12/5Slnoshunt,
rqeuaedsytiorneporefspenotsssibtrlaenisnpsotartbitlhitrioeusgihnatnhisuncdhoapnendelShLa,sthtoe [A]m400 345000000urrent[ nn+2Dl=a3yxe1r=0111xc1m0-127cm-3
be addressed. The experimental results show no abrupt nt300 120000D-C
iwnistthabailvitoiletsaguepdtroopStpaerrkSsLplpitetriniogds,,othfemeonreertghyaans2so5cmiaetVed. Curre200 0.0 0.1S0D.2-V0o.3lta0.g4e0[.5V]0.6 0.7 0 S1n2/=52S.5Lx,1b0a1r1rcimer-=2500nm
The inset of figure 3(b) shows the combined results for 2D
D- n+layer=4x1017cm-3
transportthroughboth the shunt and the surface super- S100
lattice. The CEO method leads to a very flexible sam-
12/5SL,barrier=100nm
ple design and allows the realization of different ratios 0 n =2.5x1011cm-2,n+layer=4x1017cm-3
2D
between the magnitude of the two transport channels.
0.0 0.1 0.2 0.3 0.4 0.5
While the shunt dominates the shape of the 12/3 SL SD-Voltage[V]
b)
sample, the contributions are more equal for the 12/5 240
SL. After subtraction of the shunt transport from the 220 A]1000 12/3SL,scaledby1/3
200 [m
I-V-characteristic of the combined system, the current A]180 ent500 12/5SL
carriedby the surface superlattice is recoveredand plot- m160 urr
[ C
ted in figure 3. The trace follows the long and often nt140 SD- 0
e120
predicted shape. For small electric fields, transport is rr100 0.0 0.1SD0-.2Vo0l.t3ag0e.4[V0].5 0.6
essentiallyohmic. With increasingbias,the electrondis- u
C 80 n=0-6x1011cm-2
tributionstartsto feelthe non-linearityofthe dispersion D- 60
and the current saturates. Beyond this point electrons S 40
20
increasingly start to Bloch oscillate and the transport
0
gradually decreases. In order to emphasize the impor-
-20
tanceoftheshuntchannel,figure3(a)alsoshowsanI-V-
0.0 0.1 0.2 0.3 0.4 0.5
characteristic of a sample with no such stabilizer. This SD-Voltage[V]
was achieved by reduced doping in the n+ layers, for
which a finite minimum voltage is needed to inject car- FIG. 3: (a) Current through the surface SL of different 12/5
riers into the SL. For this sample a typically observed SL structures. The dots show a shunt free system which re-
currentplateau due to field inhomogeneties is measured. sults in an inhomogeneous electric field distribution. The
The instability occurs at a source-drain- to gate volt- squaresshowthetransportinastructurewitha500nm wide
gate barrier. The resulting I-V-characteristic agrees excel-
age ratio of about 5 percent. Such high gate voltages
lently with the semiclassical fit (grey line). A thinner gate
are necessary to avoid a strong influence of the sample
barrier (triangles) leads to quenching effects for increasing
bias on the gate induced confinement [18]. This fact is
SD-voltage. (b) Current through the surface SL of a 12/3
also stressed by the comparison of the 12/5 SL samples SL sample for channel densities from 0 to 6×1011cm−2 in
with 100 nm and 500 nm thick gate barriers also shown steps of 1011cm−2. The observed saturation in transport is
in figure 3(a). There, the current of the thin gate bar- theoretically expected.
rier sample drops quickly towards zero, which is largely
caused by the fact that the increasing source-drain volt-
age reduces the confinementpotential atthe top contact characteristics of the 12/3 SL sample for densities up to
andthereforecausesanincreasinglyinhomogeneousden- 6×1011cm−2 in steps of 1011cm−2. For higher densities
sityandfielddistributionalongthesurfaceSL.The12/5 a saturation of the overall transport is observed. This
SL sample I-V is fitted with the Esaki Tsu prediction is theoretically expected from the filling of the 2D mini-
I ∼ 1+ωωB2ττ2, where the peak current was adjusted to band[18]andconfirmsourtheoreticallycalculatedband-
B
the experimental value and a series resistance of about structure. Small densities still show a more pronounced
500 Ω was included, which was independently confirmed current drop due to the density reduction caused by the
bymagneto-resistancemeasurements. Analmostperfect source-drainvoltage increase.
agreement between experiment and theory is found for From the current peak position scattering times of 350
thistrace,butthesimpletheoreticalresultdoesnotwork fs and 500 fs, respectively, are extracted for the 12/5
equally well for other densities or the 12/3 SL sample. SL and 12/3 SL structures, assuming ωBτ = 1 at the
This is attributed to the fact, that a possible increase in peak. Since the miniband width is smaller than the
the electronic temperature for large electric fields has to longitudinal optical phonon energy of 36 meV in GaAs,
be considered[19] and that the device and measurement prominently accoustic phonon scattering contributes to
setupdoesnotallowadirectdeterminationofthevoltage the inelastic scattering processes and is responsible for
applied to the surface SL. In figure 3(b) we plot the I-V- the overall transport along the surface SL. Moreover, as
depicted in figure 2(c) an increase in the cleaved-edge
4
140 firmed. Exciting the samples with GHz radiation also
static
120 6dBattenuation follows the semiclassically expected behavior. Although
] 4dBattenuation the response is still quasistatic, due to the short relax-
A
m100 3dBattenuation ationtimes, the presentedstructureis animportantfirst
2dBattenuation
nt[ 80 1dBattenuation steptowardstherealizationofanacitvesolid-stateBloch
0dBattenuation oscillator. The remaining influence of the gate struc-
e
rr 60 ture on the measured traces can be further reduced by
u
C thicker gate barriers or completely avoided by switching
40
- to a modulation doped structure. Moreover, the bet-
D
S 20 ter achievable mobilities in the 2D surface SL compared
to 3D SL transport offer the advantage of a more pro-
0
nounced gain maximum below the Bloch frequency.
-20
We would like to thank S. J. Allen for very fruitful
0.0 0.1 0.2 0.3 0.4 0.5 0.6
SD-Voltage[V] discussions and gratefully acknowledge financial support
by the DFG via SFB348 and by the BMBF, contract
01BM918.
FIG. 4: The plot shows the DC transport characteristics of
a 12/5 SL structure excited at 65 GHz for increasing input
power. The grey lines are plotted from the evaluation of a
semiclassical theory. The smaller experimental valuesare at- [1] L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61 (1970).
tributedtoan increased electron temperaturenot considered [2] F. Bloch, Z. Phys. 52, 555 (1928).
in thetheory. [3] C. Zener, Proc. Roy.Soc. (London) A 145, 523 (1934).
[4] S. A. Ktitorov, G. S. Simin, and V.Y. Sindalovski, Sov.
wellwidth shows a strongincrease ofthe mobility. Since
Phys. Solid State 13, 1872 (1972).
theelectronicsystemistherebyshiftedawayfromtheSL
[5] E. E. Mendez, F. Agullo-Rueda, and J. M. Hong, Phys.
structure,thisindicatesstrongelasticscatteringbyinter- Rev. Lett.60, 2426 (1988).
faceroughness,whichisalsoobservedinconventionalSL [6] J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E.
transport. This elastic interface roughness scattering is Cunningham, T. Meier, G. von Plessen, A. Schulze,
responsiblefor the relativelyshortrelaxationtimes mea- P.Thomas,andS.Schmitt-Rink,Phys.Rev.B46,R7252
sured and, since it strongly dominates over the inelastic (1992).
[7] C.Waschke,H.G.Roskos,R.Schwedler,K.Leo,H.Kurz,
scattering, also for an observed large reduction of the
and K.K¨ohler, Phys.Rev.Lett. 70, 3319 (1993).
peak current [19].
[8] T. Dekorsy,P.Leisching, K.K¨ohler, and H.Kurz,Phys.
Finally we studied the response of our SL/shunt system Rev. B 50, R8106 (1994).
to an externally applied HF field Fω. The 12/5 SL sam- [9] K. Unterrainer, B. J. Keay, M. C. Wanke, S. J. Allen,
plewasmountedinsideawaveguidewhichwasfittedwith D. Leonard, G. Medeiros-Ribeiro, U. Bhattacharya, and
an ajustable short at its end. It was then excited with M. J. W. Rodwell, Phys.Rev.Lett. 76, 2973 (1996).
a Gunn-oscillator operating at 65 GHz, mounted with [10] H. Willenberg, G. H. D¨ohler, and J. Faist, Phys. Rev.B
67, 085315 (2003).
an adjustable attenuator. During excitation the DC I-
[11] Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A.
V-characteristics were measured. The results for various Chao, Phys. Rev.Lett. 90, 046806 (2003).
excitation powers P are plotted in figure 4. The device
[12] P.G.Savvidis,B.Kolasa, G.Lee,and S.J.Allen,Phys.
shows a strong response towardsthe HF excitation. The Rev. Lett.92, 196802 (2004).
initiallyobservedNDCpeakiscompletelysuppressedfor [13] H. Kroemer, Top. Solid-State Quantum Electron. p. 20
large powers. A comparison with the semiclassically ex- (1972).
[14] E. S. Daniel, B. K. Gilbert, J. S. Scott, and S. J. Allen,
pected response [20], which is plotted in 2 dB steps as-
suming P ∼F2, shows qualitatively the same power de- IEEE Trans. Electron Devices 50, 2434 (2003).
ω [15] H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, K. W.
pendence as our data. The fact that the measurements West, and J. Spector, Appl.Phys. Lett.58, 726 (1991).
givesystematicallysmallercurrentvaluesthanthosepre-
[16] www.nextnano.de.
dicted by theory, is attributed to an increase in the ef- [17] Z. S. Gribnikov, N. Z. Vagidov, R. R. Bashirov, V. V.
fective electron temperature, as a result of the expected Mitin, and G. I.Haddad,J. Appl.Phys. 93, 330 (2003).
long inelastic scattering times. [18] T.Feil,R.A.Deutschmann,W.Wegscheider,M.Rother,
In summary we present the realization of a SL/shunt D. Schuh, M. Bichler, G. Abstreiter, B. Rieder, and
J. Keller, phys.stat. sol. (c) 1, 21112130 (2004).
system, which allowed us to study static and dynamic
[19] C. Minot, H.L. Person, J. F. Palmier, N.Sahri, F.Mol-
transport in surface SLs with a homogeneous electric lot,andR.Planel,Semicond.Sci.Technol.9,789(1994).
field distribution, completely avoiding domain forma- [20] S.Winnerl, E.Schomburg,J. Grenzer,H.-J. Regl,A.A.
tion. The samples reveal the long predicted stable I- Ignatov, A. D. Semenov, K. F. Renk, D. G. Pavel’ev,
V-characteristicofaSL.The largeregionofNDC due to Y.Koschurinov,B.Melzer,etal.,Phys.Rev.B56,10303
electrons performing Bloch oscillations is strikingly con- (1997).