Full loss compensation in hybrid plasmonic waveguides under electrical pumping

0.62 MB·English

by  Dmitry A. Svintsov

Full loss compensation in hybrid plasmonic
5
1 waveguides under electrical pumping
0
2

n
a
J Dmitry A. Svintsov, Aleksey V. Arsenin, and Dmitry Yu. Fedyanin
∗
5
1

Laboratoryof NanoopticsandPlasmonics,MoscowInstituteofPhysicsand Technology,9
]
l
l
a InstitutskyLane, 141707Dolgoprudny,RussianFederation
h
-
s
e
E-mail: [email protected]
m
.
t
a
m
- Abstract
d
n
o Surface plasmon polaritons (SPPs) give an opportunity to break the diffraction limit and
c
[
design nanoscale optical components, however their practical implementation is hindered by

1
v highohmiclossesinametal. Here,weproposeanovelapproachforefficientSPPamplification
7
6
under electrical pumping in a deep-subwavelength metal-insulator-semiconductor waveguid-
6
3
ing geometry and numerically demonstrate full compensation for the SPP propagation losses
0
.
1 in the infrared at an exceptionally low pump current density of 0.8 kA/cm2. This value is an
0
5
orderofmagnitudelowerthaninthepreviousstudiesowingtothethininsulatorlayerbetween
1
:
v a metal and asemiconductor, which allows injection of minority carriers and blocks majority
i
X
carriersreducing theleakagecurrent tonearlyzero. Thepresented results provideinsight into
r
a
lossless SPP guiding and development of future high dense nanophotonic and optoelectronic
circuits.
Towhomcorrespondenceshouldbeaddressed
∗
1
Introduction
Surface plasmon polaritons (SPPs) being surface electromagnetic waves propagating along the
interfacebetweenametalandaninsulatorgiveauniqueopportunitytoovercometheconventional
diffractionlimitandthuscanbeusedforlightmanipulationatthenanoscale.1Thisgivesplasmonic
componentsa significantadvantageovertheirphotoniccounterpartsin theintegrationdensityand
strength of light-matter interaction. However, high mode confinement is paid off by a significant
localization of the SPP electromagnetic field in the metal and the resulting propagation length in
nanoscale plasmonic waveguides does not exceed a few tens of micrometers due to absorption in
themetal.1–3 Nevertheless,itispossibletoovercomethislimitationbycompensatingohmiclosses
withopticalgain intheadjacent dielectric. Full losscompensationwas successfullydemonstrated
by optical pumping,4–6 which is easily implemented in a laboratory, but is impractical due to its
very poor energy efficiency, stray illumination, and necessity of an external high power pump
lightsource. In thisregard, an efficient electrical pumpingschemeis stronglyneeded forpractical
realizationofSPP guidesand circuits.7–9
Inthispaper,weproposeanovelSPPamplificationschemebasedonminoritycarrierinjection
inmetal-insulator-semiconductor(MIS)structuresanddemonstratenumericallyfulllosscompen-
sation in an electrically pumped activehybrid plasmonicwaveguide. In contrast to the techniques
based on heterostructures and quantum wells,10 our approach gives a possibility to bring the ac-
tive gain medium to the metal surface at a distance of a few nanometers. At the same time, a
thin insulatorlayer can efficiently block the majority carrier current, which is quite high in metal-
semiconductor Schottky-barrier-diode SPP amplifiers.11 This guarantees high mode confinement
totheactiveregionand verylowthresholdcurrents.
Operating principle
Realization of an electrical pumping scheme for loss compensation in SPP waveguides and cavi-
ties is a significant challenge, since there are at least two limitations in the development of plas-
2
moniccomponents. Firstly, plasmonicsgives a possibilityto reduce the mode size well below the
diffraction limit, but, in order to use this opportunity, the component size should be comparable
with the mode size. Accordingly, one has to use the SPP supporting metal-dielectric or metal-
semiconductor interface as an electrical contact. Secondly, a limited choice of low-loss materials
with negative real part of permittivity poses a serious challenge for efficient carrier injection, be-
cause gold, silver and copper typically form Schottky contacts to direct bandgap semiconductors.
As a result, eitherthe modal gain is rather low for full loss compensation,or thethreshold current
densityisquitehigh,12 whichleadstosignificantpowerconsumptionandlowenergyefficiencyof
theamplificationscheme.
The proposed technique based on an electrically pumped MIS structure (Figure 1) is remark-
ablydifferentfromtheestablishedapproaches.10,11,13,14 First,SPPpropagationlossesarereduced
byplacingaverythinlayerofalowrefractiveindexinsulatorbetweenthemetalandsemiconduc-
tor. In this case, the SPP electromagnetic field is pushed into the insulator reducing the portion
of the SPP mode in the metal, which, however, does not impair the mode confinement.3 Second,
and more important, a thin insulator layer can play a dual role: it is semi-transparent for elec-
trons moving from the metal to semiconductor, which ensures favourable conditions for efficient
minority carrier injection, and blocks the hole current. Such a unique feature gives a possibility
tosuppresshighleakagecurrents,15 whichareunavoidableinmetal-semiconductorSchottkycon-
tacts,13 and not to form an ohmic contact to the semiconductor at the SPP supporting interface,
as opposed to double-heterostructure and quantum-well SPP amplifiers.12 At the same time, the
proposed scheme provides high density of non-equilibrium carriers right near the metal surface,
at the distance equal to the thickness of the insulator layer. At a high bias voltage, it becomes
possibletocreateasufficientlyhighelectronconcentrationinthesemiconductorandtosatisfythe
condition for population inversion,16 which provides gain for the plasmonicmode propagating in
theMISwaveguide.
3
Figure1: SPP amplificationschemesbased onaSchottkybarrier diode11 and tunnelMIScontact.
Top panels: Energy band diagrams for the Schottky contact between gold and indium arsenide
in equilibrium (a) and at high forward bias (b). The Schottky barrier height for electrons j
Bn
at the Au/InAs contact is negative owing to the large density of surface states and, under high
forward bias, electrons (minority carriers in p-type InAs) are freely injected in the bulk of the
semiconductor. However, majority carriers (holes) also pass across the Au/InAs contact without
any resistance, which results in a high leakage current. Bottom panels: Energy band diagrams
for the tunnel Au/HfO /InAs MIS structure in equilibrium (c) and at high forward bias (d). If
2
the barrier height for holes c is substantially greater than that for electrons (j ), the insulator
VI MI
layer can efficiently block majority carriers (holes), but be semi-transparent for minority carriers
(electrons)escapingfrom themetal.
Previously, an attempt to describe the carrier transport in an electrically pumped hybrid plas-
monicwaveguidewasmadeinRef.17 However,theauthorsassumedthatbothelectronsand holes
passfreelythroughtheinsulatinglayerandusedthethermionicemissionboundaryconditions(lit-
erally the same as in the Schottky junction theory9,18). This is erroneous in the presence of the
insulating barrier and contradicts the well-established theory of current transfer through thin in-
sulatingfilms.19,20 In fact, theinsulatingbarrier stronglysuppresses thethermioniccurrent, while
4
themaincurrent componentis duetotunneling.
The electron and hole tunnel injection currents J and J across the MIS contact can be
t,cb t,vb
calculated by integrating the flux of carriers incident on the contact timed by the transparency of
the insulating barrier (see Methods). According to the energy band diagram shown in Figure 1
c,d, theratio oftheelectron tunnelingprobabilityD to theholetunnelingprobabilityD can be
cb vb
easilyestimatedas
D m1/2d
cb =exp 23/2 i i c 1/2 j 1/2 , (1)
D h¯ VI − MI
vb " #
(cid:16) (cid:17)
where c is the valence band offset between the insulator and semiconductor, and j is the
VI MI
barrierheightforelectronsatthemetal-insulatorinterface. Asevidentfromthissimpleexpression,
in order to block only one type of carriers, the effective barrier height for holes (c ) must be
VI
substantially greater than that for electrons (j ) or vice versa. Hafnium oxide appears to be a
MI
very promising material for electron injection into the p-type III-V materials thanks to the low
tunneling mass m = 0.1m 21 and large valence band and small conduction band offsets. Both
i 0
theoretical22 and experimental23 studiesreport c =2.4eV and c =3.2eV fortheHfO /InAs
CI VI 2
interface. At the same time, j = 2.6 eV for the gold contact,22 and the ratio D /D equals
MI cb vb
five,which ishighenoughforpractical applications.
We next explore the carrier transport in the semiconductor. It is important to note that the
electric potential is abruptly screened near the interface between the insulator and heavily doped
semiconductor,whichdirectlyfollowsfromthesolutionofPoisson’sequation. Atadopingdensity
of N = 1018 cm 3, the estimated screening length is equal to 2 nm, while the electron mean
A −
free path limited by impurity scattering equals l = 10 nm. This implies that electrons move
fp
ballistically through the screening region. Out of the screening region, the driving electric field is
weak and the electron transport is governed by diffusion. Accordingly, the density distribution of
theinjectedelectrons isgivenby
J t z
0,n R
n(z) exp +n , (2)
0
≈ e D −L
n D
r (cid:18) (cid:19)
5
where J is the current density at the insulator-semiconductorinterface, L =√t D is the dif-
0,n D R n
fusion length, and n is the equilibrium electron density. L is the most critical parameter deter-
0 D
mining the distribution of carrier density in InAs, and, consequently, the material gain profile. It
dependsontheelectronmobilitythroughtheelectrondiffusioncoefficientD andontherecombi-
n
nationratethroughtheelectronlifetimet . Equation(2)showsthat,inordertocompensateforthe
R
SPP propagation losses efficiently, L should be comparable with the half of the SPP penetration
D
depth in InAs (500 nm at l =3.22 m m) or greater than the latter. The electron mobilityin p-type
InAs is mainly limited by charged impurity scattering and is about m = 2 103 cm2V 1s 1 at
n − −
×
77 K at a doping levelof N =1018 cm 3.24 The main contributionsto the carrier recombination
A −
in InAs at 77 K come from the nonradiativeAuger process R =(C n+C p)(np n p ) and ra-
A n p 0 0
−
diativerecombinationduetospontaneousemissionR =B (np n p ),wheren and p arethe
sp sp 0 0 0 0
−
equilibrium electron and hole densities,C =C =10 27 cm6/s are the Auger coefficients,25 and
n p −
B istheradiativerecombinationcoefficient calculatedto be4 10 10 cm3s 1. Sincein ap-type
sp − −
×
semiconductor the density of electrons is much smaller than that of holes even at high injection
levels, t = [C N2 +B N ] 1 = 700 ps, which corresponds to a diffusion length of L = 950
R p A sp A − D
nm ensuring an excellent overlap between the distributions of the material gain (that is nearly
proportionalto thecarrierconcentration)andtheSPP field.
TheelectroncurrentJ atthesemiconductor-insulatorjunctionismainlydeterminedbyquan-
0,n
tummechanicaltunnelingthroughtheinsulatinglayer. Inthecaseofanidealinterface,J issim-
0,n
ply equal to the tunnelcurrent J . However,thepresence of intrinsicand extrinsicsurface states
t,cb
atthesemiconductor-insulatorinterfacehasasignificantimpactonthecharacteristicsofthetunnel
MIScontact(seeMethods). First,surfacestatesactaschargestoragecentersandaffectthevoltage
drop across the insulator layer and band bending in the semiconductor. Second, these states are
recombinationcenters25 andreducetheefficiencyofelectroninjection. Theelectroncurrentatthe
insulator-semiconductorinterfaceJ issmallerthanthetunnelinjectioncurrent J bythevalue
0,n t,cb
ofthesurfacerecombinationcurrentJ . Third,directtunnelingfromthemetaltosemiconductor
sr,n
throughthesurfacestatesisalsopossible.26,27 Thisprocesscontributesonlytothemajoritycarrier
6
current and reduces the energy efficiency of the SPP amplification scheme. Fortunately, intrinsic
surfacestatesinInAshaveamoderatedensityr 3 1012 cm 2eV 1.28 Depositionofmetal29
ss − −
≃ ×
orinsulator30 layers producesadditionaldefects andr can beincreased upto1014 cm 2eV 1 at
ss − −
HfO /InAs interfaces.31 Nevertheless, both intrinsic and extrinsicstates can be treated by surface
2
passivation before HfO deposition. The reported values of r at the trimethylaluminum-treated
2 ss
HfO /InAs interface is about 1013 cm 2eV 1,32 while advanced oxygen-termination and surface
2 − −
reconstruction techniques give a possibility to reduce r down to 2 1011 cm 2eV 1,33 which
ss − −
×
eliminatestheinfluenceofsurface statesoncarrier transportin highqualitysamples.
Active hybrid plasmonic waveguide in the passive regime
In order to achieve strong SPP mode localization and efficiently inject both electrons and holes
into the active semiconductor region, a modified T-shaped plasmonic waveguide approach11 has
been implemented [Figure 2 (a)]. InAs rib with an acceptor concentration of 1018 cm 3 on InAs
−
substrateiscoveredbyathinHfO layerandsurroundedbyalowrefractiveindexdielectric(SiO )
2 2
to confine optical modes in the lateral direction. Finally, a metal layer is placed on top of the
semiconductor-insulator structure to form an SPP supporting interface and a tunnel MIS contact
for electron injection, while the substrate plays a role of the ohmic contact for majority carrier
(hole)injection.
7
Figure 2: Schematic of a T-shaped hybridplasmonicwaveguidebased on the Au/HfO /InAs MIS
2
structure, w is the waveguide width, d is the thickness of the low refractive index insulator layer
i
between the metal and semiconductor, and H is the waveguide height. (b) Distribution of the
normalized energy density per unit length of the waveguide for the fundamental TM mode at l
00
=3.22 m m, H =2.5 m m, w=400 nmand d =3 nm. Thedielectricfunctionsofthematerialsare
i
as follows: e =2.00,34 e =3.84,35 e =12.3836 and e = 545+38i.11
SiO HfO InAs Au
2 2 −
Two-dimensionaleigenmodesimulationsusingthefiniteelementmethodrevealthatthewaveg-
uide depicted in Figure 2(a) supports a deep-subwavelength TM SPP mode [Figure 2(b)]. For
00
the chosen waveguide dimensions, at a free space wavelength of 3.22 m m, which appears to be
optimal for SPP amplification (see Section 4 for details), the effective index of the TM mode
00
is equal to 2.799 and the propagation length in the passive regime assuming the semiconductor
to be lossless is about 66 m m corresponding to a modal loss of 2Imb = 152 cm 1. The other
psv −
modessupportedbytheT-shapedwaveguidearevery leakyphotonicmodes. Inspiteofpoorfield
confinement to thelossy metal,propagationlengths ofthephotonicTM , TE , and TE modes
10 00 10
are5.8m m,12.8m mand2.7m m,respectively,whicharemuchshorterthanthatoftheTM mode
00
8
duetoleakageintothehighrefractiveindexsubstrate. TheribheightofH =2.5m misclosetothe
optimum, since, as H decreases, the radiation loss of the plasmonic mode becomes substantially
greater than the absorptionin themetal and theSPP propagationlengthdecreases downto 39 m m
at H = 2 m m. On the other hand, greater rib heights do not provide a significant loss reduction,
whilehigh-aspect-ratio structures are difficult in fabrication. For theselected optimal geometrical
parameters, the SPP mode demonstrates an exceptionally high level of confinement37 within the
InAs regionofmorethan 95%providedbythesmallmodewidthandhigh groupindex.
Full loss compensation in a deep-subwavelength waveguide
Applying a negative voltage to the top Au electrode of the active plasmonic waveguide shown in
Figure 2a, one injects electrons into the p-type InAs region. This creates a high density of non-
equilibrium electrons in the semiconductor rib, which reduces absorption in InAs.16 As the bias
voltage increases, the quasi-Fermi level for electrons shifts upward towards the conduction band.
Whentheenergydifferencebetweenquasi-Fermilevelsforelectronsandholesexceedstheenergy
h¯w of the SPP quantum, InAs starts to compensate for the SPP propagation losses. The modal
gain G is given by the overlap integral of the material gain profile g(y,z) and the electric field
distributionoftheSPP mode:
+w/2 H
ce n dy dzg(y,z) E(y,z) 2
0 InAs
| |
G= −+wR/¥ 2 +dRi¥ −2Imb psv. (3)
2 dy dzP(y,z)
z
¥ ¥
−R −R
Here, E(y,z) and P(y,z) are the complex amplitudes of the electric field and the local power den-
z
sityoftheSPPmode,respectively,and2Imb isattributedtotheSPPradiationandohmiclosses
psv
(seeSection3). Inturn,thematerialgaincoefficientg(y,z)isrelatedtothecarrierquasi-Fermilev-
elsF (y,z)and F (y,z)bytheintegralovertransitionsbetweentheenergy levelsintheconduction
n p
and valence bands separated by the energy h¯w (see Methods). In heavily doped semiconductors,
9
thematerialgainstronglydependsontheimpurityconcentration,38 soaretheelectrical properties
(L , m , and t ). The optimal acceptor concentration is found to be 1018 cm 3. As the doping
D n R −
concentration increases, the Auger recombination rate and the impurity scattering rate rapidly in-
creasegreatlyreducingtheelectrondiffusionlength. Ontheotherhand,atlowerdopinglevels,the
numberoffreeelectronstatesinthevalencebandisinsufficienttoprovideapronouncedgainupon
electrical injection. At the given impurity concentration and a reasonably high density of injected
electrons of 2 1016 cm 3 (which corresponds to F E =k T), the material gain spectrum ex-
− n c B
× −
hibitsamaximumof310cm 1 ath¯w =0.385eV(l =3.22m m),sufficientlyhighforthenetSPP
−
amplification.
Figure 3 shows the simulated gain-current characteristic of the plasmonic TM mode in the
00
active hybrid plasmonic waveguide for the HfO /InAs interfaces of different quality. All curves
2
exhibit the same trend. At zero bias, the concentration of holes in the semiconductor is many
orders of magnitude greater than that of electrons, InAs strongly absorbs the SPP propagating in
the waveguide and the modal loss is two-and-a-half times greater than in the case of the lossless
(e.g. wide bandgap) semiconductor. As the bias voltage increases, electrons are injected in the
InAs rib (Figure 4a), which reduces absorption in the semiconductor near the MIS contact, but
still, InAs strongly absorbs at a distance greater than L /2 (Figure 4b). Nevertheless, the SPP
D
modal loss steadily decreases with the injection current (this region is shown in blue in Figure 3).
At some point (green curve in Figure 4b), the overlap between the distributions of the material
gain and the SPP field is zero and, at higher bias voltages, the gain in InAs produced by injected
electrons partiallycompensatesfor theSPP propagationlosses.
10