Advances in Historical Studies
2013. Vol.2, No.2, 19-31
Published Online June 2013 in SciRes (
Copyright © 2013 SciRes. 19
The Roots of the Theoretical Models of the Nanotechnoscience
in the Electric Circuit Theory
Vitaly Gorokhov1,2
1Institute of Philosophy, Russian Academy of Sciences, Moscow, Russia
2Institute of Technology Assessment and System Analysis, Karlsruhe Institute of Technology,
Karlsruhe, Germany
Received April 8th, 2013; revised May 12th, 2013; accepted May 20th, 2013
Copyright © 2013 Vitaly Gorokhov. This is an open access article distributed under the Creative Commons At-
tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
In the contemporary nanotechnoscience makes natural-scientific experimentation constitutive for design,
while research results are oriented equally on interpreting and predicting the course of natural processes,
and on designing devices. Nanoystems can be seen as nanoelectrical switches in a nanocircuit. In nano-
circuit structure, we find traditional electronic components at different levels, realized on the basis of
nanotechnology. In nanotechnoscience explanatory models of natural phenomena are proposed, and pre-
dictions of the course of certain natural events on the basis of mathematics and experimental data are
formulated, on the one hand, as in classical natural science; as in the engineering sciences, on the other
hand, not only experimental setups, but also structural plans for new nanosystems previously unknown in
nature and technology are devised. In nanotechnoscience different models (equivalent circuits with stan-
dard electronic components) of electric circuit theory are used for the analysis and synthesis of nanocir-
cuits, and a special nanocircuit theory is elaborated. So nanotechnology is, at the same time, a field of
scientific knowledge and a sphere of engineering activity—in other words, NanoTechnoScience, similar
to Systems Engineering as the analysis and design of complex micro- and nanosystems.
Keywords: History of Science; History of Engineering Science; Nanotechnoscience; Electric Circuits
Theory; Electronic Nanocircuit; Circuits Models of Nanosystems; Natural Science;
Engineering Science; Science and Engineering
Contemporary technoscience makes natural scientific expe-
rimentation inseparable from design, while research results are
equally oriented to interpret and predict the course of natural
processes and to design structures.
Engineering theory is oriented not toward interpreting and
predicting the course of natural processes but toward designing
engineering schemes. Natural scientific knowledge and laws
must be considerably specified and modified in engineering
theory to be applicable to practical engineering problems. To
adapt theoretical knowledge to the level of practical engineer-
ing recommendations, technical theory develops special rules
that establish a correspondence between the abstract objects of
engineering theory and the structural components of real engi-
neering systems and operations that transfer theoretical results
into engineering practice. Engineering sciences are specific be-
cause their engineering practice replaces experiments, as a rule.
It is engineering activity that checks the adequacy of theoretical
engineering conclusions and serves as a source of new empiri-
cal knowledge.
In the nanotechnoscience is equal important the explanation
and prognostication of the course natural processes (like in
natural science) and multiplying of structural schemes of nano-
systems (like in engineering science). Electron beam lithogra-
phy system is at the same time experimental investigation sys-
tem and is used for the nanofabrication as so-called “nano-
It is well-known that, in nanotechnoscience, constructs from
various scientific theories—classical and quantum physics,
classical and quantum chemistry, structural biology, etc.—are
used, whereas, in nanosystems, different physical, chemical and
biological processes take place. However one can also construct
the circuit on the basis of definite nanosructures, such as, e.g., a
super-heterodyne radio receiver on the nanolevel (see: Bhushan
2004: p. 240).
In the nanotechnoscience for analysis and synthesis of the
nanocircuits also are used the different models (equivalent cir-
cuits with standard electronics components) of the electric cir-
cuit theory and is elaborated a special nanocircuit theory. In the
structure of the nanocircuits we can find many different tradi-
tional electronic components (“molecular-scale electronics”)
realized on the nanolevel with the help of nanotechnology: first,
there are electronic elements, second, electronics blocks, and
third, large-scale nanosystems.
The Structure of NanoTechnoScience
In nanotechnoscience, on the one hand, explanatory models
of natural phenomena are drawn up and predictions of the
course of certain natural events on the basis of mathematics and
experimental data are formulated as in classical natural science,
and, as in the engineering sciences on the other hand, not only
experimental arrangements are constructed, but also structural
plans of new nanosystems previously unknown in nature and
technology (Figure 1).
Three main levels in the theoretical (ontological) schemes of
a nano scientific theory can be discerned, namely mathemati-
cally oriented functional schemes, “flow” schemes reflecting
natural processes going in the investigated or constructed sys-
tem, and structural schemes representing its structural parame-
ters and engineering analysis, i.e. systems structure.
The functional scheme is oriented on the mathematical de-
scription and fixes the general idea about the system (for exam-
ple, nanosystem), irrespective of the method of its realization.
The units of this scheme reflect only the functional properties
of the elements of the system for the sake of which they are
included in it to attain the general objective and reflect certain
mathematical relations. The blocks of this scheme reflect only
those functional properties of the systems elements, for which
they are incorporated and which contribute to achieving the
common purpose. The blocks express generalized mathematical
operations and their relations are particular mathematical de-
pendences. But they can be expressed as a simple decomposi-
tion of interrelated functions aimed at achieving the customer-
prescribed common purpose of system under investigation and/
or design. Such a functional scheme is used to construct a sys-
tem algorithm and determine a system configuration.
Flow schemes (for example, flow block diagram) describe
natural, for instance, physical processes taking place in the
technical system and connecting its elements into a single
whole. The units of such schemes reflect various operations
performed in the natural process by the elements of the techni-
cal system while it is functioning. These are based on natural-
scientific concepts first of all physical processes.
In the nanotechnology they present not only physical (elec-
trical, mechanical, hydraulic, etc.) processes, but also chemical
and biological ones, that is to say any natural processes in gen-
eral. The blocks of these schemes reflect various operations
performed by the elements of the nanotechnological system
during its function. In the extreme general terms, “flow”
schemes represent not only natural processes, but also any flow
of “substance” (matter, energy or information).
Structural schemes reflect the structural arrangement of ele-
ments and linkages in the given system and presuppose its pos-
sible realization. They are the theoretical drafts of the systems
structure to elaborate a project of the experimental situation
together with the experimental equipment. Hertz for example
developed structural schemes and a conceptual apparatus cor-
responding to them—such concepts as the dipole and vibrator.
The scrupulous description of test equipment designs (e.g., of
mirror material, shape and dimensions, etc.) was combined with
the general description of experimental measurement situations,
the latter being a prototype of future electric circuits of the
radio receiver and radio transmitter. In the nanotechnology can
be another realization as in the traditional electronics but the
structural scheme is similar. For example, the one of the main
elements of electric circuits—capacitor can receive in nan-
totechnology another construction as conventional Faraday ca-
pacitor but has the similar representation as two-terminal net-
work-capacitive resistance.
The structural scheme gives nodal points of “flows” (operat-
ing processes) which can be equipment items, parts of or even
entire complicated systems. The elements of the latter are re-
garded in them as having not only functional properties, but
also properties of the second order, i.e. those undesirable prop-
erties which are added by a definitely realized element, for
instance, non-linear distortions of the amplified signal in the
Figure 1.
The structure of NanoTecnoScience.
Copyright © 2013 SciRes.
amplifier. These schemes represent constructive-technical and
technological parameters, i.e. they reflect specific problems
cropping up in engineering practice. In modern man-machine
and nanobio hybrid systems, such a realization can be of di-
verse types and even be a non-engineering and non-physical
one. Therefore, the terms “technical parameters”, “construc-
tion” are not apt here. The case in point is the configuration of
systems, their general structure.
From the radio electronics point of view it makes no differ-
ence what kind of the realization has the circuit (also as nanos-
tructure). His blocs and elements can be represented in all cases
as the correspondent equivalent circuits with standard electron-
ics components.
Let us consider the specific features of the above-mentioned
theoretical schemes of engineering science, referring to the
electric circuit theory.
Even structural schemes of electric engineering are idealiza-
tions of real electric circuits. They omit many of particular
characteristics of an electrical device, such as its overall dimen-
sions, weight, assembly techniques, etc. (they are specified dur-
ing design work and manufacture, i.e. during engineering itself).
Such schemes give general structural and technical, and manu-
facturing parameters of standardized structural elements (resis-
tors, inductance coils, batteries, etc.), which will be used in
further analysis, namely, their types and dimensions taken from
catalogues, operating voltage, the best arrangements and con-
nection types, screening. In the electric circuit theory, such
schemes are initial ones. They are taken in the ready-to-use
form from other, more special electric engineering disciplines
are subjected to theoretical analysis.
One should differentiate between the structural theoretical
scheme and various types of real engineering schemes (e.g.,
wiring diagrams). Principal elements of the structural scheme
are a power source, load (electric power receiver) and idealized
structural elements, connecting them and represented by special
symbols. Numerous parameters of real structural elements are
The “flow” scheme of the electric circuit theory reflects an
electromagnetic process going in a functioning electric device
and the circuit itself is a set of elements and their relations
(connections), forming a current path. The latter has the fol-
lowing parameters: voltage, strength, power, amplitude, phase
and frequency (for sinusoidal current). In addition, there exist
various kinds of this process (and their respective modes of
circuit function): direct and alternating, periodical and non-
periodic, steady-state and transient currents, etc. Current trans-
formation is either the quantitative transformation of its para-
meters (for example, current strength and voltage) or the trans-
formation of the pattern of its variation in time (say, of direct
current into alternating current or vice versa). Resistance, in-
ductance, capacitance, which are further idealizations of the
corresponding structural elements of the electric circuit (the
resistor, inductor, capacitor), and ideal current and voltage
sources can be considered as “flow” scheme elements. This
“semiotic constructor” makes it possible to represent any struc-
tural element of the structural scheme.
To each element of the “flow” scheme there corresponds a
specific physical process whose detailed description is beyond
the scope of the electric circuit theory which takes it into ac-
count, however. (For example, resistance represents irrecover-
able losses of electric energy in the circuit, resulting from its
etc.) In the electric circuit theory, this process is expressed by a
definite relationship of physical parameters of an element, say,
voltage versus current strength or electric charge versus voltage,
and the number of appropriate units of measurement (ohm,
farad, hertz, etc.) Electric circuit elements form branches which
are joined by means of ideal electric connections (i.e. connec-
tions free of resistance, inductance, capacitance) to form nodes
and loops.
Similar i
transformation into other forms of energy-thermal, chemical,
n nanotechnology nanoinsulators and nanoconnec-
ameter is a
rs for optical nanocircuits may be considered to be complex
circuit elements, C1, C2 and L (see Figure 2): “it is possible to
characterize complex arrangements of (plasmonic and non-
plasmonic) optical nanocircuit elements using the circuit the-
ory” (Silveirinha, Alù, Li, & Engheta, 2007: p. 64).
Distributed-parameter circuits (“A distributed par
Figure 2.
ical nanocircuit formed by five nanomodules (four nanoca- (a) An opt
pacitors and one nanoinductor), mimicking the function of the circuit
shown in (b). Here a 2D configuration is considered. The value of the
permittivity for each nanomodule is shown in the color scale in (a). The
white region represents a material with a high permittivity (EVL). (c)
Two-dimensional (2D) finite element method (FEM) “quasi-static”
simulation of optical nanocircuit in (a). Here the color scheme shows
the optical potential distributions, and the arrows shows the direction
(not the amplitude) of displacement current in each nanomodule. We
note how high the value of optical potential reaches in some of the
nodes of this nanocircuit, due to the LC resonance (Silveirinha, Alù, Li,
& Engheta, 2007: p. 63).
Copyright © 2013 SciRes. 21
parameter which is spread throughout a structure and is not
confined to a lumped element such as a coil of wire” (Wilson,
2007), e.g., homogeneous lines, are theoretically presented for
engineering analysis as distributed-parameter circuits equiva1ent
to them under given operating conditions (e.g., in a particular
frequency band). The distributed-parameter circuit can be ana-
lyzed within the framework of the electric circuit theory and
with the use of the electromagnetic field theory. Moreover, the
flow scheme of substitution, derived within the framework of
the electric circuit theory can be represented by different func-
tional schemes (e.g., the potential diagram or two-ports). Simi-
lar in the nanotechnoscience can be described the geometry of
two-nanotube transmission line and his RF circuit model
(Burke, 2004: p. 3).
Functional schemes of the electric circuit theory are diagrams,
graphical forms of the mathematical description of the electric
circuit state, To each functional element of this diagram there
corresponds a particular mathematical relationship, say, current
strength versus voltage in some circuit section, or a particular
mathematical operation (say, differentiation or integration). The
arrangement and characteristics of functional elements corre-
spond to the flow circuit scheme. Thus, in the circuit analysis,
say, with the aid of the graph theory, circuit flow scheme ele-
ments (inductances, capacitances, resistances, etc.) are substi-
tuted, in accordance with definite rules, by a special ideal func-
tional element—unistor, letting current to flow only in one di-
rection. The resultant homogeneous theoretical scheme can be
handled with the use of topological methods of circuit analysis
(Starzyk & Sliwa, 1984). Thus, the functional schematic circuit
diagram corresponds to a particular equation set and, at the
same time, it is equivalent to some flow scheme.
Nanosystem as Electronic Nanocircuit-Models
optical frequencies—nanoinductors, nano-capacitors, and nano-
resistors. “There is not that much difference between a battery
from the History of Science
The nanomachines can be regarded as nanoelectrical switches
the nanocircuit. In nanotechnology define a nanomachne also
as the nanocircuit. “Nanotechnological constructions are to re-
produce traditional electronic components (switches, diodes,
transistors, etc.) on a nanoscale. One main goal of this effort is
to open up new dimensions of data processing, namely through
the storage of large amounts of data in the smallest possible
space… Because of the intermediary position of the nanoscale,
it is also called ‘mesoworld’” (Schiemann, 2005).
In the nanocircuit structure we can find traditional electronic
components (“molecular-scale electronic components”) of the
different levels realized on the base of the nanotechnology:
1) First of all, such electronic elements as an electronic
switch (e.g. transistor), wires, inductors and capacitor or bat-
tery cell;
2) Second, electronic units (blocs) as antenna (“radiates
transmitted power in narrow beam for maximum ‘gain’ and
receives backscattered signal from targets”) or modulator (“to
‘trigger’ the transmitter operation at precise and regularly re-
curring instants of time”) (Barrett, 2000-2002: p. 23);
3) Third, complex nanosystems as a hole (e.g. nanocomputer).
anoinductors, Nano-Capacitors, and Nano-Resistors
(a) (b)
Figure 3.
(a) Geometry of a generic subwavelength nanocircuit element in the
form of A; (b) Equivalent
el for the nanowire depending on the electrical properties of
arged plates that are separated by
n insulating dielectric material. Instead of flat parallel plates,
such wave processes are investigated at the
al relative to a third, inde-
a nanowire with length l and cross-section T
circuit mod
the material (Silveirinha, 2007).
and a capacitor… Conventional Faraday capacitors store elec-
tric charge between parallel ch
capacitors that come in tubes use two metallic foils separated
by an electrolyte-impregnated paper in a “sandwich” that is
rolled up into the tube. For these devices, nanotube thin films
can increase the surface area of the conducting foil due to the
nanotubes’ very small size, orderly alignment and high conduc-
tivity. “Nanotubes provide a huge surface area on which to
store and release energy-that is what makes the difference…”
(Johnson, 2005).
Atomic-S ca l e T r an sistor and “E lectronic Tube”
In nanoscience,
level of the single electron, atom, or molecule, as well as of
cluster of atoms and molecules. And at the basis of this resear
r example, of the the wave function, a new nanosystem can
be constructed, which is in principle similar to radio equipment
or to those of its elements, such as the atomic-scale transistor
(see Figure 4), which “can be reversibly switched between a
quantized conducting on-state and an insulating off-state by
applying a control potential relative to a third, independent gate
electrode” (Xie, 2007), or “electronic tube” as two-dimensional
nanostructure. Electron transport in nanostructures on helium
films (Leider & Klier, 2008: p. 182). This is in principal similar
with the three-electrode radio tube in the traditional electronic
device. In engineering, schematic diagrams are more important
than in science, since the peculiarity of engineering thought is
operating with schemata and models. And these models adopt
today from the history of science.
The atomic-scale transistor “can be reversibly switched be-
tween a quantized conducting on-state and an insulating off-
state by applying a control potenti
ndent gate electrode. For this purpose, an atomic-scale point
contact is formed by electrochemical deposition of silver within
a nanoscale gap between two gold electrodes, which subse-
quently can be dissolved and re-deposited, thus allowing open
and close the gap”. Here is the effect of this electrochemical
cycling process and is discussed “the mechanisms of formation
In the Figure 3 you can see three basic circuit elements at
Copyright © 2013 SciRes.
Figure 4.
Illustration of the experimental setup. “Silver quantum point contacts
are electrochemically grown within a nanoscale gap between two elec
sited on a substrate. After repeated electrochemical deposi-
In recent study of the nanotechnoscience is constructed “a
rs by detecting the changes in intensity as a
Nanometer Scale
visib tic
radiation, one needsysical structure
trodes depo
tion/dissolution processes, a bistable contact configuration is formed,
and the reproducible switching of the contact between the two Au
working electrodes is achieved by means of an independent gate elec-
trode” (Xie, 2007: p. 115).
and operation of the atomic-scale quantum transistor” (Xie,
2007: p. 115).
molecular logic gate in a microfluidic system based on fluores-
cent chemosenso
sponse to various inputs (pH, metal ions)” (Berger, 2007) (see
Figure 5). In principle mode of functioning of this electronic
switch not differ from the coherer—an electrical component
formerly used to detect radio waves, consisting of a tube con-
taining loosely packed metal particles (filing in coherer of
Branly (see Figure 6) by Popov’s receiver or nickel powder (by
Marconi). The waves caused the particles to cohere, thereby
changing the current through the circuit (see Gorokhov, 2006:
pp. 21-22).
Miniaturized Antenna on the Micro- and
e can speak about for instance nanoantenna sensors in t
le and infrared regime: “In order to detect electromagne
two basic elements: 1) a ph
at efficiently couples to the radiation—the antenna; and 2) a
rectifying element that converts the high-frequency AC signal
to a low-frequency signal that can be detected by electronic
means. Antenna structures and rectifying diodes have long been
studied and applied for radio waves, television signals, cell
phones, and so on. Recent work has shown that miniaturized
antennas on the micro- and nanometer scale can be tuned to
infrared and visible radiation, and that these nanoantenna struc-
tures can be integrated with metal-oxide-metal (MOM) rectify-
ing diodes. The sensor consists of a MOM diode integrated
together with a dipole antenna” (Bernstein, 2006: pp. 133-138).
Analogy between an early Hertzian antenna to operate at mi-
crowave frequencies and the nanodimer antenna see in Figure
7. “The pioneering work of Hertz at the end of the nineteenth
ntury is at the foundation of the modern antenna science and
engineering, and therefore of an important part of current wire-
Figure 5.
“Illustration of an electronic switch made of a conducting molecule
bonded at each end to gold electrodes. Initially it is nonconducting
hen the voltage is sufficient to add an electron from the gold
however, w
electrode to the molecule, it becomes conducting. A further increase
makes it nonconducting again with addition of a second electron” (Pool
& Owens, 2003: p. 351).
Figure 6.
Coherer of branly (Gorokhov, 2006: p. 48).
Figure 7.
Analogy between two dimr antennas: (a) An ear
Hertzian antenna to operate at microwave frequen-
he plasmonic nanodimer antenna in the
cies; (b) T
form of two closely spaced spherical nanoparticles
(Alù, 2008: 195111-1).
Copyright © 2013 SciRes. 23
less tec
distribut … has
In radio electronics and radiolocation, modulation is the pro-
ely to be largely
f View of the Electrical Circuits—Historical
Transfer of the Method olo g y for the Research of the
ic elements of any
hnology. His intuition of driving oscillating charges
ed over two closely spaced spherical capacitors
successful for generatinproven g the first class of working ra-
diators, and it has paved the way to myriads of wireless appli-
cations in the current technology... Currently, the theory and
practice of RF antenna design is well established, and the old
geometry of Hertz’s first antennas… would definitely look
outdated, compared with the myriad of different antenna de-
signs currently available for numerous different purposes and
applications… However, for different reasons the optical na-
noantenna science is still in its early stage, and the recent ex-
periments on optical nanoantennas may be well compared with
the first attempts performed by Hertz… In this context, we have
recently proposed a general theory that may bring and utilize
the concepts of input impedance, radiation resistance, antenna
loading, and matching of optical nanoantennas in order to trans-
late the well-known and established concepts of RF antenna
design into the visible regime” (Alù, 2008: 195111-1). This is
right for nanocircuits at all.
Micrometer-Scale Silicon Electro-Optic Modulator
cess of varying one or more properties of a high frequen
waveform to receive a modulating signal with help of
modulator. “Because of the high rate of switching (many hun-
dreds of pulses per second) and the very short time intervals
being used (a few microseconds at the most for the pulse dura-
tion) the transmitter operation cannot be controlled by normal
switches or relays. The circuit which does this switching, and
also supplies the input power required by the oscillator, is the
modulator. It is an electronic circuit which is ‘triggered’ by the
output from the master timing unit and which produces a d.c.
pulse whose duration is determined by the circuitry of the
modulator. This d.c. pulse of controlled pulse duration, recur-
ring at the precise instants of time determined by the master
timing unit, is used to switch the oscillator on and off (Barrett,
2000-2002: p. 16). The same nanoblock as modulator we can
see in the nanotechnology. “Much of our electronics could soon
be replaced by photonics, in which beams of light flitting
through microscopic channels on a silicon chip replace elec-
trons in wires. Photonic chips would carry more data, use less
power and work smoothly with fiber-optic communications
systems. The trick is to get electronics and photonics to talk to
each other… Now Cornell University researchers have taken a
major step forward in bridging this communication gap by de-
veloping a silicon device that allows an electrical signal to mo-
dulate a beam of light on a micrometer scale… Their modulator
uses a ring resonator—a circular waveguide coupled to a straight
waveguide carrying the beam of light to be modulated. Light
traveling along the straight waveguide loops many times around
the circle before proceeding… The ring is surrounded by an
outer ring of negatively doped silicon, and the region inside the
ring is positively doped, making the waveguide itself the intrin-
sic region of a positive-intrinsic-negative (PIN) diode. When a
voltage is applied across the junction, electrons and holes are
injected into the waveguide, changing its refractive index and
its resonant frequency so that it no longer passes light at the
same wavelength. As a result, turning the voltage on switches
the light beam off… The PIN structure has been used previ-
ously to modulate light in silicon using straight waveguides.
But because the change in refractive index that can be caused in
silicon is quite small, a very long straight waveguide is needed.
Since light travels many times around the ring resonator, the
small change has a large effect, making it possible to build a
very small device. Tests using a pulse-modulated electrical
signal produced an output with a very similar waveform to the
input at up to 1.5 gigabits per second” (Steele, 2005).
Nanotechnology-Complex Electronic Circuitry with
Multiple Junctions and Interconnects
An important area for development within molecular manu
facturing is systems design of the extremely complex molecula
systems. “Although the design issues are lik
parable at a subsystems level, the amount of computation
required for design and validation is likely to be quite substan-
tial. Performing checks on engineering constraints, such as
defect tolerance, physical integrity, and chemical stability, will
be required as well” (Arnall, 2003: p. 37). “Because the switches
are so tiny, they operate in the realm of quantum physics, which
opens the possibility of using the switch to make a multi-bit
memory device… The researchers also used the switches to
form the basic binary logic gates required to make computer
processor chips. They made an AND gate using two switches
formed from a single silver sulfide wire and two platinum wires
combined with a resistor that restricts electric currents to spe-
cific voltages. An AND gate produces a 1 only if both inputs
are 1. They made an OR gate using two switches formed from
two silver sulfide wires and a single platinum wire combined
with a resistor. An OR gate produces a 0 only if both inputs are
0. They made a NOT gate using one switch combined with two
resistors and a capacitor, which briefly stores electric charge. A
NOT gate turns an input of 1 into 0 and vice versa” (Smalley,
Analysis a nd Synthesis o f the Nanocircuits from the
Point o
New Types of the Technical Systems
Following the paradigm of the electric circuit theory nano
circuits may be considered in different frequency regimes a
complex circuits consists of the three bas
ear circuit, R, L, and C. For example, pass-band optical nan-
ofilter can be described as parallel RLC resonance (see Figure
8) and stop-band optical nanofilter als series LC resonance.
fabricating nanofilters in optical lumped nanocircuit devices…
The importance of transplanting the classical circuit concepts
into optical frequencies is based on the possibility of squeezing
circuit functionalities (e.g., filtering, waveguiding, multiplex-
ing…) in subwave length regions of space, and on correspond-
ingly increasing the operating frequency with several orders of
magnitude. Moreover, nowadays the interest in combining op-
tical guiding devices, as optical interconnects, with micro- and
nanoelectronic circuits is high…, since it is “Following the
nanocircuit theory, we show how it is possible to design such
complex frequency responses by simple rules, similar to RF
circuit design, and we compare the frequency response of these
optical nanofilters with classic filters in RF circuits. These re-
sults may provide a theoretical foundation for not still possible
to perform all the classic circuit operations in the optical do-
main. Introducing new paradigms and feasible methods to bring
more circuit functionalities into the optical domain would rep-
Copyright © 2013 SciRes.
Figure 8.
Transfer function (amplitude and phase) and electric field distribution
at the resonance for an optical pass-band nanofilter formed by tw
uxtaposed in parallel in a waveguide, one made of silicon
eveloping a novel paradigm for optical nanocircuits, with the
similar since the synthesis of a new technical system involves
theory function is by “shuttle” iteration.
transformed into a
pecifically, its ideal model, theoretical
r the functional
nanorods j
and the other made of silver (Alù, Youngy, & Engheta, 2008: 144107-4).
resent an important advance in nanoelectronics technology…
we have introduced and discussed the fundamental concepts for
aim to extend classic circuit concepts, commonly available at
RF and lower frequencies, to higher frequencies and in particu-
lar to the optical domain. Specifically, we have discussed…
how a proper combination of plasmonic and non-plasmonic
nanoparticles may constitute a complex nanocircuit at infrared
and optical frequencies, for which the conventional lumped
circuit elements are not available in a conventional way. After
introducing the nanocircuit concepts for isolated nanocircuit
elements…, and after having applied them to model infinite
stacks of nanoelements to design nanotransmission lines and
nanomaterials…, we have been interested in analyzing in de-
tails how the connections and interactions among the individual
nanoelements may be modeled and designed in a complex op-
tical nanocircuit board with functionalities corresponding to
those of a classic microwave circuit” (Alù, Youngy, & Engheta,
2008: 144107-1).
In principle, the both procedures analysis and synthesis are
the analysis of the existing similar devices.
The engineering
rst, an engineering problem consisting in construction of
some technical system is formulated. Then it is represented as
an ideal structural scheme which is then
tural process scheme showing technical system function. To
analyze and mathematically model this process, a functional
scheme representing particular mathematical relationships is
constructed. The engineering problem is thereby reformulated
into a scientific problem, and then into deductively solved ma-
thematical problems. This upward way is termed the ana1ysis
of schemes.
The reverse way—the synthesis of schemes—makes it possi-
ble to use the available structural elements, more specifically
the corresponding abstract objects, to synthesize a new techni-
cal systems (more s
heme) in accordance with definite rules of deductive trans-
formation, calculate basic parameters of the object and simulate
its function. The solution obtained at the ideal model level is
gradually transformed to the engineering level where such en-
gineering parameters as overall dimensions and weight of parts,
types of connections, connection and part screenings from side
electromagnetic effects, the best structural arrangements, etc.,
considered to be secondary parameters from the ideal model
viewpoint, are taken into account and additional theory-cor-
recting computations are performed. Thus, the lower level of
engineering-theory abstract objects (structural schemes) di-
rectly involves empirical (structural & technical and manufac-
turing) knowledge, and is intended for utilization in engineering.
It is this last fact that largely determines the specific feature of
design-oriented engineering theory: to its abstract objects there
must correspond a class of hypothetical technical systems
which have not been created yet. Therefore, both analysis and
synthesis of theoretical schemes of technical systems are im-
portant in engineering theory (see Figure 1).
In the analysis of an electric circuit in the electric circuit the-
ory, the initial scheme is a structural diagram of an electric
device. In conformity with the problem being solved, it is sub-
stituted by an equivalent flow scheme valid fo
ode of the device, the substitution being done in accordance
with special rules. Further transformations of the latter scheme
are aimed at obtaining simpler schemes which will be more
suitable for computations. With this aim in view, special theo-
rems are proved, definite scheme transformation rules formu-
lated and standard design methods described. The synthesis of
schemes consists in finding electric circuit elements which can
ensure the required functional mode meeting the conditions
specified in the form of a certain mathematical relationship. To
simplify synthesis, use is made of standard schemes, tables of
standard circuits and corresponding mathematical relationships.
In engineering practice, pure synthesis is extremely rare; certain
parameters of a technical system and its elements are generally
specified as early as in the problem statement and synthesis is
often reduced to mere updating of an earlier device. Moreover,
engineering practice always uses traditional empirical structural
schemes, usually ready-to-use ones. Therefore, synthesis is re-
duced to analysis and what is to be determined is a few para-
meters of the newly designed circuit. At this stage the engi-
neer often resorts to iteration methods, based on successive
approximation; he approaches to the solution step by step, re-
turning to the initial problem more than once. In mature engi-
neering practice associated with mass and series production,
Copyright © 2013 SciRes. 25
technical systems are constructed of standard elements. There-
fore, in theory, synthesis also involves the combination of
standard idealized elements in accordance with standard rules
of theoretical scheme transformation. Analysis is also reduced
to the same procedure.
It is possible to extend the classic circuit concepts, com-
monly available at microwave and lower frequencies, to higher
frequencies and in particular to the optical domain (Figure 9).
“We have developed accurate circuit models at optical wave-
ngths to characterize the equivalent impedance of the envi-
sioned nanocapacitors and nanoinductors. It has also been
shown that the induced displacement current may leak out of
the subwavelength nanocircuit elements, causing strong cou-
pling between the nanoelements and the neighboring region. To
circumvent this problem, we have introduced the concept of
optical nanoinsulators for the displacement current… We have
confirmed, both analytically and numerically, that nanocircuit
elements… may be accurately characterized using standard cir-
cuit theory concepts at optical frequencies, and in particular
they may indeed be characterized by an equivalent impedance
for nanocircuit elements. We have further explained how to
apply the proposed circuit concepts in a scenario with realistic
optical voltage sources. We have also studied how to ensure a
good connection between the envisioned lumped nanoele-
ments… This has led us to consider unit nanomodules for
lumped nanocircuit elements, which may be regarded as build-
ing blocks for more complex nanocircuits at optical wave-
lengths” (Silveirinha, Alù, Li, & Engheta, 2007: p. 64).
Analytical quasi-static circuit models (“modeled theoreti-
cally”) for the coupling among small nanoparticles excited by
an optical electric field in the framework of the optical lumped
nanocircuit theory in Figure 10 are of importance in the
anding of complex optical nanocircuits at infrared and optical
Figure 9.
(Color online) A nanoparticle illuminated by a uni-
form optical electric field E0 (black arrows) may be
viewed in terms of the circuit analogy presented…
mpedance nano Z excited by the im-
as a lumped i
pressed current generator imp I and loaded with the
fringe capacitance associated with its fringe dipolar
fields (red arrows) (Alù, Salandrino, & Engheta,
Figure 10.
A basic nanocircuit in the optical regime, using the interaction of an
optical wave with an individual nanosphere. (left column) A non-
plasmonic sphere with ε > 0, which provides a nano-capacitor and a
nano-resistor; (right column) A plasmonic sphere with ε < 0, which
-inductor and a nanoresistor. Solid arrows show the inci- gives a nano
dent electric field, and the thinner field lines represent the fringe dipolar
field from the nanosphere (Engheta, Salandrino, & Aiu, 2004: p. 12).
Figure 11.
Nanocircuit synthesis. (Top left) Conceptual nanocircuit formed by
rectangular blocks of plasmonic and non-plasmonic segments; (bottom
left) Its equivalent circuit; (right) A closed “nano-loop” (Enghet
Salandrino, & Aiu, 2004: p. 13).
Figure 11.
Synthesizing nanocircuit elements in the optical domain us-
ing plasmonic and non-plasmonic nanoparticles from three
basic circuit elements, i.e., nanoinductors, nano-capacitors, and
ano-resistors see for example inn
“All these concepts are important steps towards the possibil-
ity of synthesizing a complex optical nanocircuit board with
the functionalities analogous to a classic microwave circuit (e.g.,
filtering, waveguiding, multiplexing…)”. Such approach “would
allow one to quantitatively design and synthesize desired nano-
circuits (such as nanofilters, nanotransmission line, parallel and
series combination of nanoelements, etc.) at optical frequencies
using properly designed collections of nanoparticles acting as
“lumped” nanocircuit elements. This concept may open doors
to design of more complex nanocircuits and nanosystems in the
optical domains” (Alù, Youngy, & Engheta, 2008).
This methodology is typical for the engineering sciences at
all and was developed already in the theory of mechanisms in
the end of the 19th century. For example Fr. Reuleaux defines
in his “Kinematics of Machinery. Outlines of a Theory of Ma-
chines” (Reuleaux, 1875) kinematic analysis and synthesis as
follows: Kinematic analysis consisted in decomposing the ex-
isting machines into their component mechanisms, chains, links
and pairs of elements, i.e., in determining the kinematic com-
position of the machine involved. The final result of that analy-
sis was the choice of kinematic pairs, links, chains and mecha-
nisms to be used to assemble a machine for carrying out the
required motions. Reuleaux differentiated between direct and
Copyright © 2013 SciRes.
indirect synthesis. The former concerned the compositions of
mechanisms which could effect particular changes of the body
worked. This was possible when the mechanism was reduced to
a kinematic pair. In that situation, the solution was the choice of
a proper design for the elements of that pair. According to
Reuleaux, the main method of theoretical synthesis of new
mechanisms was indirect synthesis, i.e., the preliminary solu-
tion of all problems of a particular type, among which the
method sought could be found. Such synthesis was possible
because the number of realizable mechanisms was limited. First,
all possible simple chains were investigated, which could be
used to obtain a number of mechanisms by changing the ratio
of various links to that chain, transforming some links of that
chain into a fixed member, replacing some mechanism pair by
another one, etc.
The operation of nanotheory is realized also as in the engi-
neering theory by the iteration method. At first a special engi-
neering problem is formulated. Then it is represented in the
form of the structural scheme of the nanosystem which is
transformed into the idea about the natural process reflecting its
procedures, type analyses which are suitable in various, more
special (scientific and es and engineering
practice. The creation os of this kind, the ela-
for which a ready-to-use
& technical and manufacturing knowledge.
p of a correspondence between the technical sys-
ons (the formation of substitu-
rformance. To calculate and mathematically model this proc-
ess a functional scheme is constructed. Consequently, the engi-
neering problem is reformulated into a scientific one and then
into a mathematical problem solved by the deductive method.
This path from the bottom to the top represents the analysis of
schemes (the bottom up approach). For instance, this can be the
investigation of “the possibility of connecting nanoparticles in
series and in parallel configurations, acting as nanocircuit ele-
ments” (Salandrino, 2007). The way in the opposite direction—
the synthesis of schemes (the top down approach)—makes it
possible to synthesize the ideal model of a new nanosystem
from idealized structural elements according to the appropriate
rules of deductive transformation, to calculate basic parameters
of the nanosystem and simulate its function. Nanocircuit syn-
thesis can be, for example, a synthesizing nanocircuit elements
in the optical domain using plasmonic and non-plasmonic na-
noparticles (Engheta, Salandrino, & Aiu, 2004).
Thus, the engineering theory function consists in solving par-
ticular engineering problems with the aid of
engineering) studi
f new procedure
ration of rules and proofs of theorems concerning the ade-
quacy of equivalent transformations and allowable approxima-
tions, the construction of new standard theoretical schemes per-
tains to the engineering theory advance on the frontiers of the
theoretical research in engineering sciences, and its findings,
are stated in primary publications (first of all, in articles) where-
as textbooks and monographs provide examples of the engi-
neering theory function, theoretically classify and systematize
proven methods of engineering problem solution, demonstrate
their compatibility with the general system of theoretical know-
ledge of the engineering discipline involved. In the natural sci-
entific theory primary importance are flow schemes, but not
structural schemes. Both the mathematical apparatus and ex-
periments are for natural scientist just a means of prediction and
explanation of the natural processes. For example, Hertz in
principle worked as an engineer, when designing new experi-
mental equipment. But he did not mean to find some technical
application for his experimental devices. One of the major pro-
blems of the well-developed engineering theory function in
“copying” of type structural schemes for various engineering
requirements and conditions. Then the solution of any engi-
neering problems, the construction of any new systems will be
theoretical supported. This is the essence of the constructive
function of engineering theory (theory in engineering science),
its lead of engineering praxis. His solution result is cast into
practical-methodical recommendations (for designer, inventor,
production engineer, etc.). To its abstract objects there must
correspond a class of hypothetical technical systems which
have not been crated yet. Therefore, in the engineering theory is
important not only analysis, but first of all synthesis of theo-
retical schemes of technical systems. So nanotechnology is at
the same time a field of scientific knowledge and a sphere of
engineering activity, in other words—NanoTechnoScience—
similar with Systems Engineering as the analysis and design of
complex man/machine systems but now as large-scale micro-
and nanosystems. That is why is very important to investigate
the historical sources of the nanotechnological methods in the
history of science and technology.
The engineering theory function is aimed at approximation of
the theoretical image of an technical system, its equivalent
transformation into some new, simpler scheme which will be
more suitable for computations, at the reduction of complex
cases to simpler and standard ones
lution exists, Therefore, the major attention of the engineer-
ing theorist is directed at evolving standard solutions of engi-
neering problems, standard design-simplifying methods. It also
largely determines the nature of engineering theory supporting
the validity of such equivalent transformations and approxima-
tions. No matter whether the analysis, synthesis of schemes or
mere engineering computations are done, the following general
“algorithm” of engineering theory function can be formulated
(see Figure 12).
1) In the starting point of the process of the theoretical solu-
tion of a new engineering problem, the initial conditions of this
problem, engineering requirements and limitations and possible
analogies with previously solved problems are formulated in
terms of structural
his procedure can be termed the engineering problem concep-
2) The empirical description shall be theoretically formulated
in concepts and notions which are standard for the engineering
theory involved. This procedure can be termed the identifica-
tion of the engineering problem with a scientific problem, i.e.
the setting-u
m under design and investigation and a particular theoretical
scheme of the engineering theory involved. The result is a
structural scheme constructed of idealized elements taken from
a standard elements catalogue.
3) The so constructed structural scheme is transformed into a
simpler type scheme by the first-order approximation. The
transformation is accompanied by singling out technical system
parameters which are the most important in the problem in-
volved. Equivalent transformati
n schemes) are used to form flow schemes for various modes
of technical system function, specified in the problem statement.
If a complex flow scheme cannot be approximated, in one or
several steps, to the simplest type diagram for which there ex-
ists a standard theory—evolved solution (if even these manipu-
lations are not required, the solution is found directly from table
Copyright © 2013 SciRes. 27
1. Engineering problem
Initial conditions
Soci al demands
fication of engin
catalogue problem with scientific one
3.First-order approximation
4.Second-order approximati on
5.Standardization and solution of
mathematical problem (deductive inference)
6. Formulation of scientific
problem solution resu lts
7. Additional computations
and correcting
8. Formulation of engineer in
problem solution results
Functional schemes subst itut i on (for each flow scheme)
Flow schemes (for different functional modes)
Stru ct ural schem e
Stru ct ural schem e
Functional schemes (computed data)
Flow schemes
Practical methodological rec ommendations
Figure 12.
General algorithm of engineering theory function.
formulas), it is substituted by an equivalent functional scheme
in accordance with definite rules of correspondence.
ctional scheme constructed with the aid of the sec-
te an equation set
be solved by special mathematical methods (e.g., by matrix
ample, a
ce with definite rules of substitution. Thus, in the
t in engineering
new nanosystem
ductor (L), resistor (R) and capa-
resistors, capacitors, and
4) A fun
ond—order approximation is used to formula
ones). These equations are obtained on the basis of physical
(Ohm’s, Kirchhoff’s and other) laws setting up, for ex
lationship between circuit current parameters and circuit ele-
ment parameters. Their concrete numerical values known from
the problem statement make it possible to determine unknown
current and circuit element parameters through solving the
5) The functional scheme is used to solve the mathematical
problem using a standard computational procedure and standard
problem solution methods based on previously proved theorems.
To this end, the functional scheme is reduced to a standard one
in accordan
ectric circuit theory, mixed connections are transformed into
simpler, series and parallel ones, multiloop circuits are turned
into single—loop ones, etc. In the electric circuit theory, such
simplifying transformations are based on specially proved equi-
valence of some type schemes (e.g., of a “delta” and “star” and
vice versa) and relevant theorems (say, the equivalent current
and voltage source theorem) which give more computationally
suitable schemes. This makes it possible to substitute certain
circuit sections by other, equivalent and scheme—simplifying
ones. The problem solution result obtained, by mathematical
methods is translated to the flow scheme level by reverse equi-
valent transformation. Scientific problem solution results are
formulated. Several flow schemes (for various functional modes)
are then synthesized into an engineer object structural model.
7) Then the solution is adapted to a specific case and partly
modified, i.e. additional computations are done and structural
and engineering amendments introduced. It is necessitated by
the fact that both the analysis and synthesis of schemes are in-
variably based on a compromise, trade—off between the com
exity and accuracy of computations, on approximate methods
and standard artificial techniques. The findings of theoretical
computations must be corrected to take account of various en-
gineering, social, economical, ecological and other require-
ments. It may call for the incorporation of new elements satis-
fying these requirements into theoretical schemes; these ele-
ments may be considered as connotations (additional, accom-
panying attributes) of these schemes. Framing a system of con-
notations which are incorporated into engineering-theory theo-
retical schemes as special elements may make it necessary to
multiply return to previous stages (the iteration procedure) in
order to construct new flow and structural schemes (corrected
for these connotations), perform new approximations, equiva-
lent transformations and computations. One of the major prob-
lems of well-developed engineering theory function is “copy-
ing” of type structural schemes for various engineering re-
quirements and conditions. Then the solution of any engineer-
ing problems, the construction of any new engineering systems
of a given type will be theoretically supported. This is the es-
sence of the constructive function of engineering theory, its
lead of engineering practice. Otherwise its function will amount
only to solving routine engineering problems.
8) The final procedure of engineering theory function is that
the solution result is cast into practical methodological recom-
mendations (for the designer, inventor, etc.).
The constructive application of nanoscience as technoscience
is expressed in its guidance of developmen
actice. In nanotechnoscience, therefore, a prediction of the
flow of natural processes on the nanolevel is just as important
as the replication of the structural diagram of a
or example, a spintronic component, such as the “spin valve”).
The superconductivity re-entrant phenomenon opens genuine
prospects for building a very rapidly operating device, the “su-
perconducting spin valve” for superconducting spintronics.
Graphene electronics could even manipulate electrons as quan-
tum-mechanical waves (similar to light waves made up of pho-
tons) rather than as particles.
It is very important to differentiate real fabricated “large
scale MEMS” or “large-scale carbon nanotube devices” as three
dimensional nanostructures from equivalent circuit modelled
their components. Figures 13(a) and (b) show “scanning ion
microscope (SIM) image of in
tor (C) in a parallel circuit structures with free space nano-
wiring” (Bhushan, 2004: p. 187).
The “electrical engineering” schematic diagrams reflect
physical processes which take place within the elements and
units of radio engineering devices. Such diagrams deal with the
calculation of parameters and the mapping of electric currents
in standard electrical elements such as
ductors. Of course, these devices can be called electrical cir-
cuit only with reservations. Use is made of electronics theory to
describe the physical processes in the new radio engineering
elements such as, for example, electron tubes or semiconductor
devices. But to calculate of the parameters of these devices in
which they are included use is, as a rule, made of traditional
equivalent circuit (resistors, capacitors and inductors). As the
Copyright © 2013 SciRes.
Copyright © 2013 SciRes. 29
processes take place. One can, however, also con-
y is used to analyze complex circuits, the parameters of
physical processes in elements of radiolocation devices (kly-
strons, magnetrons, cathode ray tubes, antennas, etc.) operating
in new radio engineering regimes are different, it was necessary
to modify the former methods of their calculation and repre-
sentation or to develop new ones, as well as to develop new
mathematical resources. The process was also stimulated by the
need to investigate and develop methods of internal noise sup-
pression in elements of radiolocation equipment (for example,
the schrot effect in electron tubes). Similar is in the nanotech-
It is well-known that, in nanotechnoscience, constructs from
various scientific theories—classical and quantum physics,
classical and quantum chemistry, structural biology, etc.—are
used, whereas, in nanosystems, different physical, chemical and
press the nature of the function or scheme under approximation
as accurately as possible, and be as simple as possible, in order
to simplify the mathematical solutions of engineering problems.
Any approximation calls for a special substantiation of solution
adequacy, one type of approximation being preferable for one
functional mode and other types being preferable for other-
The two-port concept is introduced to facilitate the transition
to mathematical relationships, making it possible to apply Kir-
chhoff’s laws, which describe the natural process of current
flow in the two-port circuit, and the corresponding equations in
the matrix form. The coefficients of these equations are called
two-port parameters, because they are determined solely by the
two-port’s properties. By solving these equations with the aid
of the matrix theory, one can determine the structural parame-
ters of two-ports sought—input resistance, input and output
ruct a circuit on the basis of definite nanosructures, such as,
e.g., a super-heterodyne radio receiver on the nanolevel (Figure
One of the important methods in the engineering sciences
and also nanotechnscience is an approximation. The imple-
mentation of engineering theory involves a sequence of so-
called approximations. For example, in electronics, the two-port
L, C, R Circuit Structure
hich are difficult to determine, owing to the awkwardness of
the computations. Approximation is the substitution of some
mathematical functions or designs by other, very similar, sim-
pler functions or designs, which are equivalent in the desired
aspect and for which known solutions exist, or can easily be
obtained. In engineering sciences, this is a method for solving
engineering problems on the basis of theoretical models and
with the aid of a series of equivalent substitutions and trans-
formations. The method of approximation is essentially a com-
promise between the accuracy and the complexity of designs.
Accurate approximation usually involves complex mathemati-
cal relationships and computations. An oversimplified equiva-
lent scheme of a technical system affects the accuracy of com-
putations. The approximating expression or scheme must ex-
(a) (b)
Figure 13.
Scanning ion microscope (SIM) micrograph of inductor (L), resistor (R)
and capacitor (C) structures: (a) equivalent circuit modelled (b) three
dimensional nanostructure (Bhushan, 2004: p. 186).
Figure 14.
Schematic of a super-heterodyne radio architecture (VCO = voltage-controlled oscillators, radio frequency (RF) and intermediate frequency (IF),
SAM = self-assembled monolayer, PLL = phase-locked loop, LNA = low-noise amplifier) (Bhushan, 2004: p. 240).
power, insertion loss, etc. A number of theorems (the reversi-
bility theorem, equivalent oscillator theorem, etc.) are proved in
two-port theory. Its use makes it possible not only to simplify
the computations, but also to synthesize new models by deduc-
tive equivalent transformation of two-ports. Such a transforma-
tion gives the most economical and effective engineering solu-
tions. It indicates natural restrictions on these transformations,
the main types of two-ports and the types of their connections.
It should be noted that, in analyzing complex circuits, these are
preliminarily transformed into a combination of simpler two-
ports, the parameters of which are taken from special tables.
Matrices for each of them are then used to carry out mathe-
matical operations (addition, multiplication, etc.), depending on
their connection type.
Several types of mathematical methods correspond to the
same engineering theory. This is due to the fact that ideal ob-
jects are investigated at different levels. We have just consid-
ered the two-port theory and its mathematical apparatus. How-
ever, electric circuit analysis also involves the concept of a
one-port making up larger structural “building-blocks”, or units.
(The one-port is a two-pole circuit section to which a difference
is applied and which carries current.) Any ampli-
of potentials
fier, oscillator, filter, etc. can be considered to be a sum of ca-
acitors, inductors, resistors, current and voltage sources. The p
latter are also idealizations, i.e., circuit theory deals with a com-
paratively small number of ideal elements and their combina-
tions, representing these ideal elements at the theoretical level,
and not with a great variety of radio-device structural elements
differing in their characteristics, principles of operation, designs,
etc. To apply the mathematical apparatus, further idealization is
required; each of the above elements can be considered to be an
active or passive one-port.
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