Transistors: A Network Science-Based Historical Perspective
Alexandre Benatti, Henrique Ferraz de Arruda, Filipi Nascimento Silva, Luciano da Fontoura Costa
TTransistors: A Network Science-Based Historical Perspective
Alexandre Benatti, Henrique Ferraz de Arruda, Filipi Nascimento Silva, and Luciano da Fontoura Costa S˜ao Carlos Institute of Physics, University of S˜ao Paulo,PO Box 369, 13560-970, S˜ao Carlos, SP, Brazil Indiana University Network Science Institute, Bloomington, IN, USA. (Dated: August 19, 2020)The development of modern electronics was to a large extent related to the advent and popu-larization of bipolar junction technology. The present work applies science of science concepts andmethodologies in order to develop a relatively systematic, quantitative study of the developmentof electronics from a bipolar-junction-centered perspective. First, we searched the adopted dataset(Microsoft Academic Graph) for entries related to “bipolar junction transistor”. Community detec-tion was then applied in order to derive sub-areas, which were tentatively labeled into 10 overallgroups. This modular graph was then studied from several perspectives, including topological mea-surements and time evolution. A number of interesting results are reported, including a good levelof thematic coherence within each identified area, as well as the identification of distinct periodsalong the time evolution including the onset and coming of age of bipolater junction technologyand related areas. A particularly surprising result was the verification of stable interrelationshipbetween the identified areas along time.
I. INTRODUCTION
The influence of science and technology on society andthe economy has grown steadily along time. A great dealof this phenomenon relates to the autocatalytic potentialof scientific-technological developments, in the sense thatnew resources tend to increase the opportunity for furtherapplications and developments.To a good extent, the history of human modernity mir-rors the history of electronics, from the experiments withthe early transistors, based on germanium crystals tostate-of-the-art very large scale integrated circuits. De-spite its relatively short span of about 100 years, elec-tronics progressed all the way through varying materialsand paradigms. Then, in the 50’s, the transistor becamea reality, initiating the digital computer revolution. Fromthen on, we witnessed the appearance of satellite commu-nication, cell phone technology, the internet, the WWW,deep learning, and among others. Who can predict whatthe next step will be?Yet, despite its enormous influence on redefining howhumans live and interact, the history of electronics is rela-tively overlooked, at least at a more general level. Indeed,even the launching of the transistor received moderatemedia coverage (e.g. [1]). Although there are excellentworks on the history of electronics (e.g. [1–4]), the themeis relatively less explored in a more systematic, quanti-tative context.The present work aims at applying recently developedscience of science (e.g. [5]) concepts, and methods as themeans to try to understand, from real data, additionalaspects and relationships between the events in the his-tory of electronics from the specific perspective of BJT-related topics. This is interesting for several reasons.First, it provides an interesting case for science of sci-ence studies, given its multidisciplinarity, interrelation-ship between academics and industry [6], and the inter-play between scientific articles and patents [7]. Second, it has the potential for better understanding the chain ofevents, as well as the interrelationship of areas and con-cepts, that underlies what is probably among the mostimportant scientific-technological advances in recent hu-man history [8–10].The term ‘bipolar junction transistor’ (BJT) was usedas a reference from which a network of related works wasassembled. As a consequence, all results described anddiscussed in the present work are limited to this perspec-tive, and then only given the methodology and databaseentries considered. Other scientometric researches, fo-cusing on different emphases, methods or databases, arelikely to yield complementary and diversified results.We start this work by presenting an overall perspec-tive of electronics, developed in a chronological man-ner and centered (but not exclusively) on BJT relatedtopics, so as to provide reference and context for thediscussion of the obtained results. Then, we describethe adopted methodology, which involves modern net-work science concepts and methods. In particular, weconsidered the
Microsoft Academic Graph (MAG) [11]database, which incorporates scientific articles as well aspatents, etc.Several interesting results have been obtained. First,the identified areas were characterized by a good levelof coherence among the respectively obtained keywords,which allowed tentative labels to be assigned to each ofthose areas. The evolution of the identified areas alongtime presented several interesting features, including thecoming of age of several of the involved areas. Whenobserved in terms of networks, the evolution of the iden-tified areas presented striking conservation of interrela-tionships, in the sense that the patterns of interconnec-tivity between the main areas tended to remain nearlythe same.The rest of this paper is organized as follows. We startby presenting a summary panorama of electronics, in Sec-tion II, aimed at providing some context for readers from a r X i v : . [ c s . D L ] A ug other areas. In section III, we describe the methodologyemployed to obtain the citation network, as well as theadopted network measurements. Section IV, presents theobtained results. The conclusions and perspectives of fu-ture works are addressed in Section V. II. AN OVERALL PANORAMA OFELECTRONICS
One first important consideration when approachingthe history of electronics concerns its relationship anddistinction from the history of electricity. Generallyspeaking, electricity deals with (approximately) linearsystems such as power sources and passive devices suchas resistors, capacitors, and inductors. In this sense,the main differentiating aspect of electronics regards twopoints: (i) active devices, capable of amplifying the powerof signals (e.g. transistors); and (ii) non-linearities foundin most non-linear devices. Another important aspect isthat electronics can be subdivided into major areas, in-cluding but not being limited to: (a) linear; (b) digital;(c) power; and (d) high frequency.To a good extent, the history of electronics follows thedevelopment of a sequence of device technologies capableof rectification and, more importantly, power amplifica-tion. One of the first electronic devices was invented byK. F. Braun in 1874, named crystal detector [12]. Thisdevice consisted of a conductor, the cat whisker madeto touch the surface of a small galena rock. After sub-stantial efforts, this device was capable of unstable elec-tronic detection of rectification (i.e. directional currentconduction), being used in the first rudimentary radios.Another primitive rectifier was E. Branly’s coherer , in-vented in 1890 [13]. This device, basically of a tube filledwith iron powder, exhibited a rather limited ability forsignal rectification.An important subsequent event was the discovery ofthe diode vacuum tube, yet another rectifying device, byJ. A. Fleming in 1904 [14]. Basically, this device consistsof an incandescent lamp including an additional electrode(the plate, which acts as an anode). The filament cor-responds to the cathode. When positive potential (con-cerning the cathode) is applied to the plate, the electronsbeing emitted by the cathode are attracted to it, estab-lishing a respective current. However, no current is ob-served when the plate is biased negatively concerning thefilament. The vacuum diode allowed substantial improve-ments in electronic rectification, constituting perhaps thefirst mark in the history of electronics.Motivated by continuing demands of long-distancetelephony expansion, research efforts were invested intrying to develop a practical device capable of reinforc-ing the audio signal along the telephonic lines. The tri-ode, invented by L. de Forest in 1906 under the name of audion [15] was the first practical device capable of ef-fective amplification of the power of signals, being vastlyapplied not only in telephony, but paving the way for the unfolding of electronics into a variety of areas includingbut not being limited to telecommunications (the radio,and then television), space research, medical instrumen-tation, military (especially radar) and electronic comput-ing . As a consequence of the triode limited frequency re-sponse, more sophisticated vacuum tubes including moreelectrodes were developed.The early crystal detectors were improved as semi-conductor point-contact devices for military applicationsduring World War II, especially at Bell Labs, MIT, andPurdue [16]. Advances in quantum mechanics at the timefinally allowed some understanding of the rectifying ac-tion of the crystal diode.At about this same time, similar demands, allied tothe never-ceasing requirements from telephony and otherelectronics applications, motivated research aimed at ob-taining smaller and more energy-efficient amplifying de-vices based on semiconductor technology. The first tran-sistor was implemented and demonstrated at Bell Labsby J. Bardeen, W. Brattain, and W. Shockley, in 1947,a substantially important event that received moderatemedia coverage [1]. These first devices were based onpoint-contact technology, and further developments wererestricted by surface-charge phenomena. Ultimately, al-loy devices were obtained, followed by bipolar junc-tion transistors, which became the reference for severaldecades.After World War II, and also during it, great effortswere invested in achieving transistors capable of higherfrequency operation, for applications in telecommunica-tions. It also allowed the mass production of very smallradio sets. Also at that time, transistors started beingused as the basic element, jointly with diodes, in digitalcomputing mainframes, replacing the previous vacuum-tube based machines with an impressive economy ofspace and energy, while also increasing reliability [16].Though semiconductor electronics initially reliedstrongly on Germanium, it gradually shifted to Silicon,which allowed improve thermal stability. Several newtransistor technologies followed, including FET, JFET,NMOS, CMOS, etc. These developments ultimately ledto the concept of integrated circuits, especially throughefforts of J. Kilby and R. Noyce, which would soon pro-vide the basis for the personal computer revolution alongwith the 70’s, 80’s and 90’s. Also impressive was the de-velopment of microcontrollers, which found immediateand wide applications in consumer electronics, amongother areas.In the analog world, the concept of the solid-state op-erational amplifier was progressively perfected roughlyalong this same period, often as a valuable resource inthe design and application of frequency and phase fil-ters. Also worth noticing was the development of hybridsolutions to analog problems, in which digital and ana-log approaches are integrated, placing a special demandon analog-to-digital and digital-to-analog converters, re-quired to provide the interface with an arguably analogreal-world. One particularly critical aspect here, as theresolution of these converters increases, concerns control-ling electromagnetic noise.Another aspect that has proven to be determinant inseveral electronics applications concerns the control ofelectromagnetic interference (EMI), both from the en-vironment into the circuit as well as vice-versa. An-other typical concern regards the effect of radiation (e.g.cosmic rays) on semiconductors, such as the possibilityof memory errors. Also important is the robustness ofsemiconductors to electric discharges induced by externalcharge accumulation. Yet another concern in electroniccircuits, especially in power electronics, regards the needto control the operating temperature of the devices. Eachof these problems has motivated its related research areaand set of respective approaches.
III. METHODOLOGY AND THE EMPLOYEDDATASET
In this section, we describe the employed dataset andthe methodology applied to create the network. Fur-thermore, we present network measurements used in ouranalyses.
A. Citation network
Many studies have been taking into account the organi-zation of papers in terms of citation networks [5, 17, 18].Here, we also consider this type of approach in or-der to obtain data regarding the transistor’s network.The employed dataset is the
Microsoft Academic Graph (MAG) [11], which contains data of millions of researchdocuments, including journal and conference papers,patents, books, and not assigned documents. Our datasetcontains data produced between 1926 and 2018. Thecomplete information of the dataset can be found inMAG’s web page [19].First, by considering the abstracts, we select an initialset of documents with the words bjt and bipolar junc-tion transistor . In order to obtain a respective network,each document is understood to represent a node, andthe edges denote the citations between the documents.First, this network is created, and the largest connectedcomponent is identified, which is henceforth called core (see Figure 1 (a)). In order to complement the connectiv-ity between nodes, we also consider the documents citedfrom the references listed in the initial set, green edgesas illustrated in Figure 1 (b). In the next step, we re-move among the blue nodes, those disconnected or withindegree one (leaf nodes), and we consider only the largerconnected component as result, as shown in Figure 1 (c).Finally, we insert the edges between the blue nodes (pur-ple edge), in Figure 1 (d)), if there is a citation betweenthem. It is important to recall that the direction of thenetwork edges is from the document that cites to thosecited.
Core (a)
Core (d)(b)
Core (c)
Core x FIG. 1. Diagram representing how the studied network iscreated. The region denoted by the dashed line represents thenetwork core. (a): the selected nodes (in red), obtained fromthe keyword search (”bjt” and ”bipolar junction transistor”)and the respective connections. (b): the cited documentsare included own in blue). (c): blue leaf nodes leading toentries not selected in the search are removed, and the largerconnected component is taken. (d): the edges between bluednodes are included.
We employed a keyword extraction method based onthe community structure of the network, as described in[18] to derive its main topics. This method starts bydetecting the network communities, which are defined asgroups of nodes more connected between themselves thanto others in the network [20]. Here, we considered thesame methodology variation proposed in [21], in which
Infomap [22] is employed to detect the community struc-ture of the network, a technique that has been used in re-lated applications of the science of science studies [23, 24].A visualization of the obtained citation network is shownin Figure 2.
B. Network measurements
In this section we present the network measurementsemployed in the characterization of the obtained citationnetwork. Because our network is directed, we consideredthe directed version of degree [25]. More specifically, de-gree, k , is defined for each node as the number of edgesconnected to it. In this case, two definitions can be con-sidered, which refers to the counts of in and out edges.In terms of the citation networks, the measurements ofin and out degrees represent the number of times a doc- (a) Network
Nodes Sizes (b)
Reduced Network
FIG. 2. (a) Network visualization, where nodes and edges represent document citations, respectively. (b) The reduced versionof the network. More specifically, the nodes account for the communities, and the edges are weighted according to the number ofcitations between communities (edges with less than 7 citations are not shown). For both the visualizations, the node positionswere calculated from a force-directed algorithm described in [18]. ument is cited and cite others, respectively.Another considered measurement is clustering coeffi-cient [26]. For the sake of simplicity, we considered theundirected version of this measurement, which is definedas follows c i = λ ( i ) τ ( i ) , (1)where λ ( i ) and τ ( i ) are the number of triangles of edgesand triple connected, respectively. In the citation net-work, the high clustering coefficient is found for docu-ments that cite or are cited by others that also have edgesbetween them.Another measurement that is extensively used is thebetweenness centrality [27], which is calculated for eachnetwork node and can be computed as follows B k = (cid:88) ij σ kij σ ij , (2)where σ ij is the number of shortest paths that connects i and j , σ kij is the number of shortest paths connecting thenodes i and j that crosses k . Here, we consider directedpaths. This measurement has been employed in studiesconcerning the analysis of citation networks [28–30]. IV. RESULTS AND DISCUSSION
Table I lists the keywords obtained for each of the 10identified thematic areas, as well as their respective num-ber of nodes and average degree. The table is organizedin decreasing order of the number of nodes. It should beobserved that the labeling of each of these areas is onlyapproximate as an attempt to express the predominanttrend among the respectively obtained keywords. There-fore, the labels of the identified areas are mostly tentativeabbreviations of the respective topics.As could be expected, the major identified areas corre-spond more closely to BJT theory and modeling, whichwas considered as the focus of our research. 28 .
09% ofits nodes are part of the core, which is also the largestpercentage observed among all obtained areas. Interest-ingly, a substantial number of works were incorporatedinto this area, complementing the original core. The sizeof the other areas decreases progressively, reflecting notonly their intrinsic size but also how their developmentsrelate to BJTs. We observe expressive sizes for powerelectronics, field effect, and analog electronics. Anotherinteresting result in this table is the diversity of aver-age degree respective to each area, varying from 7 .
42 (foranti-statics) to 15 .
95 (for radiation control). These av-erage degree variations may indicate that the respectiveareas have specific levels of integration among its parts,as well as with other areas. For instance, area H seemsto be characterized by higher interconnection as far as itsaverage degree is concerned, while area C has about halfvalue for this measurement. Table II indicates the percentage of types of docu-ments — patent, journal, book, conference or other —obtained for each of the 9 identified groups. Interest-ingly, a substantial diversity can be observed regardingthese measurements, with areas G and I incorporatingmany patents, while area F presents a relatively highnumber of conference entries. Area H is mostly coveredin journals. These results provide further indication ofpossible heterogeneity between the specific ways in whicheach identified area has developed and been organized.Figure 2 depicts the overall network obtained from ourspecific approach, focusing on BJT and using the de-scribed data. One first interesting result is the diversityof interconnections observed for each of the identified ar-eas. For instance, the area I is highly compact, whileother areas such as D and G are more distributed. Ascould be expected, the BJT-related area A resulted asthe most central area in the obtained network, present-ing strong interfaces with many of the other obtainedareas.Areas G and I, as indicated in Table II, mostly involvepatents. In particular, the densely interconnected area Iis mostly related to 6 patents [31–36] that are intensivelycited by other documents in this identified area. Areas B,C, and D present an interesting diversity of interconnec-tions, suggesting the existence of respective communitiesor modules.Figure 2(b) shows the network obtained by subsumingthe nodes in each of the identified areas as a single node.This representation provides a summarized representa-tion of the interconnection between the identified areas.The centrality of area A is again observed, also receivingmore connections than those that are sent to other areas,which is somehow surprising given the way in which thenetworks was built (see Section III A).Figure 3 presents the average of the measurementsobtained for all nodes of each of the identified areas,but considering them integrated into the overall net-work. The in-degree (Figure 3 (a)) and out-degree (Fig-ure 3 (b)) tend to be relatively homogeneous, except forarea H presenting larger in- and out-degree, and areas F,G, and J with small degrees. Also, the in-degrees distri-bution in (Figure 3 (a)) tends to be very similar to theout-degrees shown in (b). The betweenness centrality,which can be understood as a measurement of the in-formation flow in the network, is shown in Figure 3 (c).As expected, area A was found to be most central. Al-though F and H are relatively small communities, theyhave high values of Betweenness centrality, perhaps re-flecting their roles in telecommunications, one importantapplication of electronics that underwent an impressiveincrease along the last decades. Figure 3 (d) shows theclustering coefficient values obtained for each of the ar-eas, which resulted to be relatively small and uniform,indicating similar patterns for the most of the obtainedcommunities.Figure 4 depicts the relationship between the obtainedcommunities. Figure 4(a) represents the number of ci-
Detected key-words Tentative label No. of Nodes Core (%) (cid:104) k (cid:105) bipolar transistor, model, emitter, heterojunction bipolar, base A - Bipolar transistor 2270 (28.09%) 16.70 10.97power, h sic, high, h-sic, switch B - Power electronics 1407 (17,41%) 25.66 9.83soi, device, gate, lateral, channel C - Field Effect 848 (10.49%) 21.93 8.86circuit, filter, linear, analog, nonlinear D - Analog Electronics 769 (9.51%) 12.74 9.74reference, cmos, temperature, voltage, supply E - Reference voltage 644 (7.971%) 10.87 10.07noise, ghz, frequency, amplifier, db F - High frequency 629 (7.78%) 13.99 6.95form, region, layer, method, emitter G - Processing 601 (7.44%) 16.64 5.08radiation, irradiation, dose, damage, effect H - Radiation control 382 (4.73%) 30.89 15.95control, power, switch, converter, output I - Digital control 269 (3.33%) 7.06 11.08esd protection, electrostatic discharge, parasitic, device, discharge esd J - Anti-statics 263 (3.25%) 6.84 7.42TABLE I. Properties of the identified areas. The keywords, shown in the first column, were automatically obtained, and werethen employed to chose the labels of the second column. The average degrees were calculated by considering the undirectedversion of the network. Group Name Proportion of each document type (%)Patent Journal Book Conference None
A - Bipolar transistor 1.37 67.97 0.62 23.04 7.00B - Power electronics 2.99 59.28 0.71 30.70 6.33C - Field Effect 8.96 60.61 0.83 24.53 5.07D - Analog Electronics 1.43 59.69 1.69 22.50 14.69E - Reference voltage 19.10 38.82 0.78 33.23 8.07F - High frequency 2.23 43.72 1.43 43.72 8.90G - Processing 84.69 6.32 0 8.65 0.33H - Radiation control 0.26 77.75 1.05 13.09 7.85I - Digital control 62.83 18.22 0.74 15.61 2.60J - Anti-statics 14.83 36.88 1.52 41.44 5.32TABLE II. Proportions of types of documents in each of the identified areas, where
None represents the uncategorized docu-ments.
A B C D E F G H I J02468 A v e r a n g e D e g r ee ( I N ) (a) In-degree
A B C D E F G H I J02468 A v e r a n g e D e g r ee ( O U T ) (b) Out-degree
A B C D E F G H I J05001000 B e t w ee nn e ss C e n t r a li t y (c) Betweenness centrality
A B C D E F G H I J0.00.10.20.3 C l u s t e r i n g C o e ff i c i e n t (d) Clustering coefficient
FIG. 3. Each subfigure represents a network measurementcalculated for the entire network, in which bars denote theaverage values of each community. tations that a given community receives from the oth-ers. As a complement, we compute out-degree (see Fig-ure 4(b)), which accounts for the number of times a givencommunity cite others. We observe a high degree ofasymmetry between the connections, with area A receiv-ing many more citations than citing the other areas.
A B C D E F G H I J050010001500 D e g r ee ( I N ) (a) Degree of groups (in)
A B C D E F G H I J0200400600800 D e g r ee ( O U T ) (b) Degree of groups (out)
FIG. 4. Each subfigure represents a measurement calculatedamong the obtained communities, in which bars denote theaverage values of each community.
It is also interesting to consider the changes in thenumber of works in each identified area along time, whichis shown in Figures 5(a-b). For simplicity’s sake, we brokethese time series according to two subsequent periods:from 1926 to 1970 and from 1971 to 2015. Observe thedifferent scales of the y-axes in these two figures.The time series in the earlier group are, as could be ex-pected, more sparse, corresponding to the onset of severalof the identified areas. The main area A, more directlyrelated to bipolar transistors, has a peak around 1990, de-creasing gradually thereafter. This could be interpretedas an indication of the come of age of bipolar technologyaround that time. A similar trend can be seen in thecase of area D, which reaches a peak around 2000. Also (a) 1926 - 1970 (b) 1971- 2015
FIG. 5. Temporal evolution of papers published along subsequent years for each of the identified areas. Note that we dividethe temporal series into two plots given their different scales. interesting is the increase, followed by a relative stabiliza-tion, observed for area B. The above discussed temporaltrends can be complemented by taking into account thechanges in the topology of the respective overall networkover time, which is illustrated in Figure 6 (a-h).In order to better understand the possible reasons be-hind the peak observed in Figure 5, we performed thefollowing additional experiment. We considered the en-tries and respective interconnections along the time pe-riod from 1985 to 1995, and obtained the respective par-tial network, which is depicted in Figure 7 superimposedonto the more complete network, the latter being shownin diluted colors.This figure indicates that some areas, such as analogelectronics as well as reference voltage areas (in red),seem to be particularly dense when compared to the otherareas. Table III provide the total and relative numberof nodes and connections accounted by the partial net-work (i.e. extending from 1985 to 1995). We have fromFigure 7 and Table III that the following identified ar-eas are particularly pronounced, considering the adopteddatabase, along the period from 1985 to 1995: (i) ana-log electronic; (ii)voltage regulation; (iii) processing; and(iv) radiation controlTherefore, we hypothesize that the peak in the identi-fied BJT area seems to be related to the coming of age ofits relationship with analog electronics and other neigh-boring areas.The steady growth and consolidation of area A canagain be noticed along the period extending from 1950to 1990. The other areas tend to follow the developmentof area A, though relatively few citations can be observedin the networks corresponding to these periods (many iso-lated nodes). A steady increase in connectivity betweenthese areas can be appreciated after 1990. Remarkably,the relative distribution of the identified areas remainedalmost unaltered over the years, indicating that the in-terrelationship between those areas tended to preserve its pattern.The identified area I, which is mostly constituted bypatents (62.83%) resulted particularly dense in connec-tivity, which was found to be related to the fact that sixentries in that community receive citations for many ofthe other entries in that area. In striking contrast, theother identified area incorporating many patents, namelycommunity G, is particularly sparse.Additional information about the interrelationship be-tween the identified areas can be provided by the meanand standard deviation of the shortest path in the respec-tive network, as depicted in Figure 8. The mean short-est path can be observed to grow steadily from 1960 to1990, stabilizing thereafter, corroborating the previousdiscussion. We also observe an increase of shortest pathlength deviation around 1990, implying that at this timethe network is not only particularly intensely connected,but these connections also exhibit an elevated degree ofheterogeneity, as expressed by the respective standarddeviation of the node degree.The noticeable stabilization of the network in Figure 8from around 2000 suggests that most of the possible ap-plications of electronics were by this time well covered.
V. CONCLUSIONS
The modern world is has been, to a considerable ex-tent, influenced, or even shaped by electronics. The es-tablishment of modern electronics was largely driven bythe development of bipolar junction technology, whichleads to widespread commercial applications of the re-spectively developed transistor. In the present work, weapplied concepts and methods from network science, aswell as science of science, to derive a tentative analysis ofhow several related areas started and evolved along time.Several interesting results have been reported and dis-cussed, which need to be understood in the context of the (a) (cid:104) k (cid:105) = 0 .
00 and n = 14) (b) (cid:104) k (cid:105) = 2 .
00 and n = 62) (c) (cid:104) k (cid:105) = 2 .
92 and n = 234) (d) (cid:104) k (cid:105) = 3 .
21 and n = 570) (e) (cid:104) k (cid:105) = 4 .
68 and n = 1682)) (f) (cid:104) k (cid:105) = 7 .
68 and n = 4337)) (g) (cid:104) k (cid:105) = 8 .
65 and n = 6892)) (h) (cid:104) k (cid:105) = 9 .
74 and n = 8082) FIG. 6. The citation network visualized along time. The average degree ( (cid:104) k (cid:105) ) was calculated by considering the undirectedversion of the networks, and n is the number of nodes. Group name Size Averange degreeEntire network From 1985 to 1995 proportion (%) Entire network From 1985 to 1995
A - Bipolar transistor 2270 923 44.66 10.97 11.62B - Power electronics 1407 211 15.00 9.82 8.94C - Field Effect 848 202 23.82 8.86 8.96D - Analog Electronics 769 184 23.93 9.73 10.70E - Reference voltage 644 91 14.13 10.07 10.89F - High frequency 629 128 20.35 6.95 7.39G - Processing 601 178 29.62 5.07 4.93H - Radiation control 382 92 24.08 15.94 19.29I - Digital control 269 36 13.38 11.08 7.83J - Anti-statics 263 55 20.91 7.42 8.32
TABLE III. Absolute and relative number of nodes in the partial (from 1985 to 1995) and complete networks.
FIG. 7. In order to try to better understand the peak of citations of the BJT area occurring around 1990, we obtained apartial network considering the nodes and interconnections along the period from 1985 to 1995, which is shown in darker colors,overlain onto the complete network (diluted colors). Observe that the identified areas of analog electronics, voltage regulation,processing, and radiation control are resulted markedly pronounced in the partial network. This visualization is complementedby absolute and relative indications of the number of nodes and interconnections provided in Table III. adopted dataset and methodology, as well as parametricconfigurations. In this restricted and tentative context,we observed a good thematic coherence between the en-tries obtained in each of the 10 identified areas, whichwere assigned respective tentative labels. These commu-nities were then characterized in terms of several topolog-ical measurements including in- and out-degree, between-ness centrality, and clustering coefficient. We observed asurprising homogeneity in in- and out-degree obtainedfor each of the 10 communities. A more heterogeneousdistribution was observed for the betweenness centrality,suggesting distinct patterns of interconnectivity amongthe communities.The study of the identified areas along time revealedthe onset and coming of age of the several identified areas,with the communities related to high frequency and dig- ital control presenting a more recent pattern of growth.A peak of publications was observed around 1990 for thereference area of bipolar junction technology. The timeevolution of the areas was also considered from the per-spective of graph visualization along with different timeinstants, revealing surprising stability of the pattern ofinterconnections among the identified areas.Several future developments are possible, including theextension of the analysis to other areas of electronics (e.g.integrated circuits, personal computers, telecommunica-tions), or even other fields such as the Internet, artificialintelligence, among many other possibilities.0 A v g . S h o r t e s t P a t h L e n g t h FIG. 8. Mean shortest path lengths, obtained for the undi-rected version of the network. The vertical bars represent thestandard deviations.
ACKNOWLEDGMENTS
Alexandre Benatti thanks Coordenao de Aperfeioa-mento de Pessoal de N´ıvel Superior - Brasil (CAPES)- Finance Code 001. Henrique F. de Arruda acknowl-edges FAPESP for sponsorship (grant no. 2018/10489-0and no. 2019/16223-5). Luciano da F. Costa thanksCNPq (grant no. 307085/2018-0) and NAP-PRP-USPfor sponsorship. This work has been supported also byFAPESP grants 2015/22308-2. Research carried out us-ing the computational resources of the Center for Math-ematical Sciences Applied to Industry (CeMEAI) fundedby FAPESP (grant 2013/07375-0). [1] M. Riordan and L. Hoddeson, “Cristal fire. the inventionof the transistor and the birth of the informational age,”1997.[2] E. Braun and S. MacDonald,
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