Optics and Photonics Journal, 2011, 1, 216-220
doi:10.4236/opj.2011.14033 Published Online December 2011 (http://www.SciRP.org/journal/opj)
Copyright © 2011 SciRes. OPJ
On Negative Differential Mobility in Nanophotonic
Device Functionality
Emmanuel A. Anagnostakis
Hellenic Air Force Academy, Dekeleia, Greece
E-mail: emmanagn@oten et.gr
Received August 19, 2011; revised Sep t ember 17, 2011; acc e pt ed September 28, 2011
Abstract
A negative differential mobility (NDM) of the two-dimensional carrier-gas against some proper external
regulator allowing for gradual controlled modification of the nanointerfacial environment tends to occur as
interwoven with nanophotonic device functionality. In this work, several instances, in our two-decade prin-
cipal research, of both experimental observation and conceptual prediction concerning nanophotonics NDM
are reconsidered towards outlining a global potential for the appearance of the effect.
Keywords: Nanophotonics, Two-Dimensional Electron-Gas, Semiconductor-Device Nanointerface, Negative
Differential Mobility, Optoelectronics Nanotechnology
1. Introduction
Photonics is underlain by absorption, emission, genera-
tion, handling, and exploiting light, typically within the
electromagnetic radiation spectrum range between 100
nm of the ultraviolet and 1000 nm of the infrared—with
the human visual perception focused upon the 400 - 700
nm optical interval.
Nanophotonics, now, with its recently formulating dis-
ciplinary autonomy, traces, interprets, and envisions na-
notstructural spatial confinement-induced, often mysti-
fying, modifications in light propagation and light-matter
interaction. Nanophotonics, thus, is studying the essence
and manifestations of confined electron de Broglie waves
and confined light-wave photon flows. Interestingly, be-
tween 370 and 1600 nm there function nanophotonic de-
vices based on the GaN/GaAs, InAs/ GaAs and InAs/InP
materials-systems, nowadays adequately reaching the
middle infrared (mid-IR) regime.
Within the branch of electron-confinement Nanopho-
tonics, a crucial feature permeating semiconductor nan-
odevice photonic functionality is the appearance of a
negative differential mobility (NDM) of the two-dimen-
sional carrier-gas against some proper external regulator
(materialising as instantaneous cumulative photonic in-
take) allowing for gradual controlled modification of the
nanointerfacial environment.
In this work, several instances [1-20], in our two-de-
cade principal research, of both experimental observation
and conceptual prediction concerning NDM are recon-
sidered towards outlining a global potential for the ap-
pearance of the effect, the essence of which consists in
the variation of the nanointerfacial two-dimentional elec-
tron gas’s mobility becoming negative against further po-
sitive proper regulatory agent’s (bias’s, photonic dose’s)
change for some regulatory agent’s value-interval(s).
2. NDM Occurrence in Nanophotonics
Homodevices
In Figure 1, the energy band depth-profile of a generic-
homointerface nanophotonics device is presented: The
band bending occurs at the illuminated n-type upper
semiconductor-layer’s surface and within the nanodevice
interface extending between the equilibrium parts of this
epilayer and the relatively p-type-like lower semicon-
ductor-layer. The nanointerface (NIF) potential-energy
barrier eUb is equal to e(Ubi - Uph) , where Ubi is the NIF
diodic built-in voltage and Uph is the generated evolving
photovoltage [2-4,7]. The photocurrent density J through
the NIF consists of the space-charge-region photogenera-
tion-current density Jg, the current density Jp(x) at the
NIF upper-boundary locus x owing to hole diffusion
from the n-type epilayer downwards, and the current
density Jn(x + w) at the NIF lower-boundary locus x + w
owing to electron diffusion from the p-type sublayer up-
wards [1].
E. A. ANAGNOSTAKIS 217
Figure 1. Energy band depth-profile of a generic-homointerface nanophotonics device: The nanointerface (NIF) potential-
energy barrier eUb is equal to e(Ubi – Uph) , where Ubi is the NIF diodic built-in voltage and Uph is the generated evolving
photovoltage.
Experimental findings for the mean electron-mobility
(μ) ( in 102 cm2/(V s) ) within the n-type (Si-ion implanta-
tion) epilayer of representative photonics NIF-devices
[1,9,12] vs. incoming instantaneous cumulative photon-
dose δ ( in photons/cm2 ) have been discussed in previ-
ous works of ours: The functional feature of negative
differential mobility (NDM) is being registered from the
mobility peak (at total photonic intake δpeak of around 1 ×
1011 photons/cm2 ) to the mobility valley (at cumulative
photon dose δvalley of around 4.64 × 1012 photons/cm2 ).
Each instantaneous value of the average mobility is de-
termined within the respective instantaneous extension of
the photo-widening flat-band portion of the epilayer
through the experimentally measured (mean) sheet elec-
tron conductivity (σd) and (mean) sheet electron concen-
tration (nd) of this flat-band epilayer extension by <μ> =
(σd)/(nd). The local mobility μ, furthermore, at the in-
stantaneous NIF-boundary locus x is interlplaying with
the mean mobility <μ> and the dose-rates u and v of evo-
lution of (σd) and (nd), respectively, according to the
causal correlation [1,9,10,12]:
v = [u/(e < μ >2)] [2 < μ > – μ],
with e being the absolute value of the electron charge.
3. NDM Occurrence in Nanophotonics Het-
erodevices
In Figure 2, the energy band depth-profile of a ge-
neric-heterointerface nanophotonics device is sketched:
The front, wider-bandgap, n-type semiconductor-layer is
succeeded by the lower, narrower-bandgap, relatively
p-type-like one. The NIF, now, hosts the ionized-donor
depletion zone, on the epilayer side, and the potential-
energy, approximately triangular, QW, formed within the
sublayer’s upper part. The photocurrent density J through
the NIF comprises the current density Jg produced by
photogeneration within both the ionized-donor deple-
tion-zone and the QW, the current density Jp(x) at the
NIF upper-boundary locus x owing to hole diffusion
from the n-type epilayer downwards, and the current
density Jn(x + w + L) at the NIF lower-boundary (deeper
by the consecutive extensions w and L of the depletion
zone and the QW) locus x + w + L owing to electron
diffusion from the p-type sublayer upwards [3,5,7,8].
The onset of the occupancy of the first excited QW-
subband (of bottom energy E1) occurs as soon as the
two-dimensional electron gas (2DEG) population already
confined within the NIF QW energy-wise span the inter-
val ΔE = Ζ0/ρ, from the QW fundamental-subband bot-
tom onwards, with Ζ0 constituting the capacity of the
fundamental subband and ρ being the parabolic-model
two-dimensional density of states (with respect to energy
graduation and QW-bottom cross-section interval). An
effective harmonic oscillator simulating the prime func-
tionality of the NIF QW leads to a simple, yet notionally
adequate and rather universal, NIF descriptor Γ = L ,
with being the simulative-oscillator strength, shown to
be expressible in terms of the carrier effective mass and
the entailed-nanoheterojunction conduction- band dis-
continuity as Γ = 2 (2 Φ/m*)1/2.
The reduced (over dark value μd) persistent photoen-
hancement (PPE) (Δμ/μd) in the 2DEG mobility μ has
been experimentally registered vs. relative (with respect
to a nanodevice-specific value δ*) total photonic intake
(δ/δ*), for representative nanophotonics (modulation-
doping) heterointerface-devices of previous studies of
ours [3,5,7,8,14,16,17] (based on a typical molecular-
beam epitaxy Si:Al0.3Ga0.7As/GaAs nanoheterodiode
Copyright © 2011 SciRes. OPJ
E. A. ANAGNOSTAKIS
218
Figure 2. Energy band depth-profile of a generic-heterointerface nanophotonics device: The NIF, now, hosts the ionized-donor de -
pletion zone, on the epilayer side, and the potential-energy, approximately trian gular, QW, formed within the subla yer’s upper part.
mounted upon a semi-insulating GaAs substrate): The
NIF 2DEG mobility PPE Δμ is icreasing up to a critical
relative cumulative photon-dose value (δ/δ*)crit of the
order of 4.79 × 102 and then it gets dropping, a NDM
([d(Δμ)/dδ] < 0) regime being marked, tantamount to the
process of occupancy of the first excited NIF QW sub-
band, following the saturation of the capacity Z0 = 1.01 ×
1012 electrons/cm2 (as determined through the experi-
mentally traced photon-dose-evolution of the 2DEG
sheet concentration ζ, observed at the above critical total
photonic intake) of the fundamental subband. The energy
separation ΔE, now, between the nominal bottoms of
these successive NIF QW subbands is (through the fun-
damental one’s capacity) deduced to be of 35.3 meV,
leading to a simulative harmonic oscillator’s strength
of 5.354 × 1013 s
-1 yielding (through the NIF descriptor
value Γ = 1.168 × 106 m/s valid for the pertinent QW-
electron effective mass and conduction-band discontinu-
ity) a 2DEG-QW effective spatial width L of 21.8 nm.
4. NDM Interweaving with Nanophotodevice
Operational Principle
In Figure 3., there appears the conduction-band depth-
profile of the nanophotonics launcher-receptor quantum
electron-device (LRD), proposed in 1994 [11] as a vertical-
transport optoelectronic nanodevice relying upon resonant
quantum-mechanical electron-tunnelling from a charge-
launcher element (CLE) into a charge-receptor pocket
(CRP) within an illuminated NIF semiconductor-heter-
ostructure. In a model visualization, the LRD comprises
an Al0.22Ga0.78. As epilayer hosting a narrow (of around 3
nm) δ-spike of high (especially with respect to back-
ground doping) sheet-density (on the order of 2.0 × 1012
Figure 3. Conduction-band depth-profile of the nano-
photonics launcher-receptor quantum electron-device (LRD),
proposed in 1994 as a vertical-transport optoelectronic na-
nodevice relying upon resonant quantumme-chanical elec-
tron-tunnelling from a charge-launcher element ( CLE ) int o a
charge-receptor pocket (CRP) within an illuminated NIF
semiconductor-heterostructure. Such an optoelectronic na-
noswitching functionality would, then, be permeated by
incidents of NDM owing to an appropriate timing for the
energising of different individual effective-mobility values
(via varying subband curvatures and scattering environments)
characterising conductively interplaying subbands.
donors/cm2) Si dopants as the photonic nanodevice CLE
and a non-intentionally doped GaAs underlayer contain-
ing a nanoheterointerfacial 2DEG-QW (of spatial width
on the order of 20 nm, adjacent to the ionized-back-
ground-donor depletion-zone of the epilayer side) as the
nanostructure CRP. A functionally strategic energy-ma-
tching between the CLE first excited sublevel ε1 and the
CRP fundamental sublevel E0 at around 50 meV below
the LRD Fermi level is attained, allowing for the possi-
bility of resonant quantum-mechanical tunnelling of part
of first-excited-subband CLE-electron population (present
there after the saturation of the local fundamental sub-
Copyright © 2011 SciRes. OPJ
E. A. ANAGNOSTAKIS 219
band’s capacity, at a critical cumulative photonic intake
during the persistent-photoenhancement experimental
procedure) into the fundamental CRP-QW subband. Such
an optoelectronic nanoswitching functionality would, then,
be permeated by incidents of NDM owing to an appro-
priate timing for the energising of different individual
effective-mobility values [5,11,16,17,19] (via varying sub-
band curvatures and scattering environments) character-
ising conductively interplaying subbands.
5. NDM Tractability via Nanophotonics
Wavefunction-Engineering
In Figure 4, furthermore, the wavefunction-engineering
of a THz-LASER nanophotonics device proposed in
2010 [18] is outlined: The optically pumped dual-reso-
nant-tunnelling LASER-action unipolar-charge transport
mechanism is simulatively energized for an indicative
generic semiconductor nanoheterostructure based on the
conventional AlxGa1-x As/GaAs material system.
In particular, two asymmetric in the spatial width and
in the energetic barrier height, communicating through
an intervening barrier layer, approximately rectangular
quantum wells, both formulated within (different por-
tions of) the GaAs semiconductor are employed: The
front QW [F] of spatial width of 96˚A and energy barrier
height of 221 meV, contained between a surface Al0.3
Ga0.7 As slab and the inter-QW communication barrier
layer, and the back QW [B] of growth axis extension
162˚A and energy confinement hill of 204 meV, span-
ning the region between the inter-QW communication
barrier layer and a botton Al 0.33 Ga0.67 As slab. The in-
tervening, inter-QW communication barrier layer may
non-exclusively be regarded as the succession (either
abrupt or graded) of two rather equithick sublayers of
Al0.3 GA0.7 As and Al0.33 Ga0.67 As. It is, then, algo-
Figure 4. Wavefunction-engineering of a THz-LASER nano-
photonics device proposed in 2010: The optically pumped
dual-resonant-tunnelling LASER-action unipolar-charge-
transport mechanism is simulatively energised for an in-
dicative generic semiconductor nanoheterostructure based
on the conventional AlxGa1-x As/GaAs material system.
rithmically determined (through Quantum-Well Tridi-
agonal Algorithm [20]) that the partially localised con-
ductivity electron eignestates accommodated by the cou-
ple of communicating QWs in the model application
under study correspond to the energy eigenvalues (mea-
sured within each QW from its energetic bottom up-
wards): E (If>) = 32 meV, E (If ’>) = 136 meV, for the
front QW fundamental and first excited bound state, re-
spectively, and E (Ib>) = 14 meV, E (Ib’>) = 55 meV,
and E (Ib’’>) = 121 meV—for the back QW fundamen-
tal, first excited, and second excited bound state, respec-
tively.
Notably, against this predicted energy eigenvalue con-
figuration, the fundamental back QW eigenstate Ib>
elevated by 14 meV over the back QW energetic botton
finds itself well aligned with the conjugate fundamental
eigenstate If> of the front QW raised above its QW en-
ergetic botton by an amount corresponding to the inter -
QW energetic bottom discrepancy plus, about, the former
fundamental eigenstate Ib> height over its local QW
bottom. In an analogous manner, the uppermost bound
eigenstates of the two communicating QW, emerge ali-
gned, as the difference in the height of each over its local
QW bottom almost cancels the energetic height asym-
metry of the two QW bottoms.
The determinable intersubband transition (ISBT) effe-
ctive dipole lengths, furthermore, demonstrate the oscil-
lator strengths supporting the different ISBT events,
whereas the LASER action population inversion pre-
dicted would lead to the device stimulated optical gain.
The notional and functional framework, furthermore,
of the principle of operation of such an intersubband THz-
LASER nanophotonics device provides fruitful ground
[5,14-16] for the prediction, monitoring, and registration
of NDM features marking incidents of local transition
and resonant-tunnelling vertical transport, the essence of
the innovation of a nanophotonics launcher-receptor quan-
tum electron-device (LRD) [11] getting recapitulated and
modellingly advanced and generalised.
6. Conclusions
Several instances, in our two-decade principal research,
of both experimental observation and conceptual predic-
tion concerning nanophotonics NDM have been recon-
sidered, the technological importance of the NDM cru-
cial feature having been envisaged to be emerging.
There derives worth mentioning that a global potential
for the manifestation of NDM would be the nanopho-
tonic device’s capacity for simultaneously supporting
subsets of the interfacial conductivity-carrier ensemble
through distinctly mobility-valued mechanisms.
Copyright © 2011 SciRes. OPJ
E. A. ANAGNOSTAKIS
Copyright © 2011 SciRes. OPJ
220
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