In the past decades,Moore’s law drives the semiconductor industry to continuously shrink the critical size of transistors down to 7 nm.As transistors further downscaling to smaller sizes,the law reaches its limitatio...In the past decades,Moore’s law drives the semiconductor industry to continuously shrink the critical size of transistors down to 7 nm.As transistors further downscaling to smaller sizes,the law reaches its limitation,and the increase of transistors density on the chip decelerates.Up to now,extreme ultraviolet lithography has been used in some key steps,and it is facing alignment precision and high costs for high-volume manufacturing.Meanwhile,the introduction of new materials and 3D complex structures brings serious challenges for top-down methods.Thus,bottom-up schemes are believed to be necessary methods combined with the top-down processes.In this article,atomic level deposition methods are reviewed and categorized to extend Moore’s law and beyond.Firstly,the deposition brings lateral angstrom resolution to the vertical direction as well as top-down etching,such as double patterning,transfer of nanowires,deposition of nanotubes,and so on.Secondly,various template-assisted selective deposition methods including dielectric templates,inhibitors and correction steps have been utilized for the alignment of 3D complex structures.Higher resolution can be achieved by inherently selective deposition,and the underlying selective mechanism is discussed.Finally,the requirements for higher precision and efficiency manufacturing are also discussed,including the equipment,integration processes,scale-up issues,etc.The article reviews low dimensional manufacturing and integration of 3D complex structures for the extension of Moore’s law in semiconductor fields,and emerging fields including but not limited to energy,catalysis,sensor and biomedicals.展开更多
We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent bas...We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent basic elements, which makes a comparison with the generic elements of electronic integrated circuits more meaningful. The other is making a complex compo- nent equivalent to a series of basic elements of the same functionality, which is used to calculate the integration density for func- tional components realized with different structures. The results serve as a benchmark of the evolution of PICs and we can con- clude that the density of integration measured in this way roughly increases by a factor of 2 per year. The prospects for a continued increase of spatial integration density are discussed.展开更多
Chips are the carriers of ICs (integrated circuits). As a result of design, manufacturing, and packaging and testing processes, chips are typically wholly independent entities intended for immediate use. According to ...Chips are the carriers of ICs (integrated circuits). As a result of design, manufacturing, and packaging and testing processes, chips are typically wholly independent entities intended for immediate use. According to known data, one unit of chip output can drive up to ten units of output in the electronic information industry and 100 units of GDP (Gross Domestic Product). The Chip Information Industry is a strategic industry in most developed countries in Europe and North America. The development of the Chip Information Industry is related to national economies and personal livelihoods. Moore discovered a certain trend after analyzing data: in general, every newly produced chip has twice the capacity of the previous generation, and it takes 18 to 24 months for the next generation to be subsequently invented. This trend has come to be known as Moore’s Law. It applies not only to the development of memory chips but also to the evolutionary paths of processor capability and disk drive storage capacity. Moore’s Law has become the basis of performance prediction in several industries. However, since 2011, the size of silicon transistors has been approaching its physical limit at the atomic level. Due to the nature of silicon, additional breakthroughs in the running speed and performance of silicon transistors are severely limited. Elevated temperature and leakage are the two main sources that invalidate Moore’s Law. To counter these issues, This paper analyzes specific problems challenges in the Chip Information Industry, including the development of carbon nanotube chips and fierce competition in the international Chip Information Industry. In addition, this paper undertakes a critical analysis of the Chinese Chip Information Industry and countermeasures to Chinese Chip Information Industry development.展开更多
The matter about some far-going consequences commencing from the replacement of one of the basic principles of the traditional physics that is the principle of locality, with the recently put forward principle of boun...The matter about some far-going consequences commencing from the replacement of one of the basic principles of the traditional physics that is the principle of locality, with the recently put forward principle of boundedness is considered. It is proven that the thermodynamic theory which is explicitly grounded on the principle of locality, suffers inherent contradiction which roots lay down to the principle of locality. The way to overcome it goes via the replacement of the principle of locality with the recently put forward by the author principle of boundedness. In turn, the latter gives rise not only to a fundamentally novel notion for a number of ideas but also it yields replacement of the proportionality between the software and hardware components with a new non-extensive approach to the matter. It is proven that the famous Moore’s law stands in new reading both in its support and the way to overcome its limitations. Apart from its role for the technical applications, the present considerations stand also as a methodological example how the role of the basics of any theory affects practical rules such as the Moore’s law.展开更多
Today we witness the exponential growth of scientific research. This fast growth is possible thanks to the rapid development of computing systems since its first days in 1947 and the invention of transistor till the p...Today we witness the exponential growth of scientific research. This fast growth is possible thanks to the rapid development of computing systems since its first days in 1947 and the invention of transistor till the present days with high performance and scalable distributed computing systems. This fast growth of computing systems was first observed by Gordon E. Moore in 1965 and postulated as Moore’s Law. For the development of the scalable distributed computing systems, the year 2000 was a very special year. The first GHz speed processor, GB size memory and GB/s data transmission through network were achieved. Interestingly, in the same year the usable Grid computing systems emerged, which gave a strong impulse to a rapid development of distributed computing systems. This paper recognizes these facts that occurred in the year 2000, as the G-phenomena, a millennium cornerstone for the rapid development of scalable distributed systems evolved around the Grid and Cloud computing paradigms.展开更多
The author presents a new approach which is used to solve an important Diophantine problem. An elementary argument is used to furnish another fully transparent proof of Fermat’s Last Theorem. This was first stated by...The author presents a new approach which is used to solve an important Diophantine problem. An elementary argument is used to furnish another fully transparent proof of Fermat’s Last Theorem. This was first stated by Pierre de Fermat in the seventeenth century. It is widely regarded that no elementary proof of this theorem exists. The author provides evidence to dispel this belief.展开更多
Using the same method that we used in [1] to prove Fermat’s Last Theorem in a simpler and truly marvellous way, we demonstrate that Beal’s Conjecture yields—in the simplest imaginable manner, to our effort to prove...Using the same method that we used in [1] to prove Fermat’s Last Theorem in a simpler and truly marvellous way, we demonstrate that Beal’s Conjecture yields—in the simplest imaginable manner, to our effort to prove it.展开更多
This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of...This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of the twentieth century. For this reason it can be easily understood by any mathematician or by anyone who knows basic mathematics. The important thing is that the above “theorem” is generalized. Thus, this generalization is essentially a new theorem in the field of number theory.展开更多
If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） ...If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） are blocked. In these standard accounts （Godel＇s own paper and the exposition in Boolos＇ Computability and Logic are treated as exemplars）, it is assumed that certain formulas （notably so called ＂Godel sentences＂） containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term ＂provable＂ （and indeed ＂unprovable＂） favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.展开更多
Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly...Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.展开更多
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo...This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.展开更多
基金the National Natural Science Foundation of China(51835005,51702106,51911540476,and 51575217)HUST state key lab project(DMETKF2019003)。
文摘In the past decades,Moore’s law drives the semiconductor industry to continuously shrink the critical size of transistors down to 7 nm.As transistors further downscaling to smaller sizes,the law reaches its limitation,and the increase of transistors density on the chip decelerates.Up to now,extreme ultraviolet lithography has been used in some key steps,and it is facing alignment precision and high costs for high-volume manufacturing.Meanwhile,the introduction of new materials and 3D complex structures brings serious challenges for top-down methods.Thus,bottom-up schemes are believed to be necessary methods combined with the top-down processes.In this article,atomic level deposition methods are reviewed and categorized to extend Moore’s law and beyond.Firstly,the deposition brings lateral angstrom resolution to the vertical direction as well as top-down etching,such as double patterning,transfer of nanowires,deposition of nanotubes,and so on.Secondly,various template-assisted selective deposition methods including dielectric templates,inhibitors and correction steps have been utilized for the alignment of 3D complex structures.Higher resolution can be achieved by inherently selective deposition,and the underlying selective mechanism is discussed.Finally,the requirements for higher precision and efficiency manufacturing are also discussed,including the equipment,integration processes,scale-up issues,etc.The article reviews low dimensional manufacturing and integration of 3D complex structures for the extension of Moore’s law in semiconductor fields,and emerging fields including but not limited to energy,catalysis,sensor and biomedicals.
文摘We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent basic elements, which makes a comparison with the generic elements of electronic integrated circuits more meaningful. The other is making a complex compo- nent equivalent to a series of basic elements of the same functionality, which is used to calculate the integration density for func- tional components realized with different structures. The results serve as a benchmark of the evolution of PICs and we can con- clude that the density of integration measured in this way roughly increases by a factor of 2 per year. The prospects for a continued increase of spatial integration density are discussed.
文摘Chips are the carriers of ICs (integrated circuits). As a result of design, manufacturing, and packaging and testing processes, chips are typically wholly independent entities intended for immediate use. According to known data, one unit of chip output can drive up to ten units of output in the electronic information industry and 100 units of GDP (Gross Domestic Product). The Chip Information Industry is a strategic industry in most developed countries in Europe and North America. The development of the Chip Information Industry is related to national economies and personal livelihoods. Moore discovered a certain trend after analyzing data: in general, every newly produced chip has twice the capacity of the previous generation, and it takes 18 to 24 months for the next generation to be subsequently invented. This trend has come to be known as Moore’s Law. It applies not only to the development of memory chips but also to the evolutionary paths of processor capability and disk drive storage capacity. Moore’s Law has become the basis of performance prediction in several industries. However, since 2011, the size of silicon transistors has been approaching its physical limit at the atomic level. Due to the nature of silicon, additional breakthroughs in the running speed and performance of silicon transistors are severely limited. Elevated temperature and leakage are the two main sources that invalidate Moore’s Law. To counter these issues, This paper analyzes specific problems challenges in the Chip Information Industry, including the development of carbon nanotube chips and fierce competition in the international Chip Information Industry. In addition, this paper undertakes a critical analysis of the Chinese Chip Information Industry and countermeasures to Chinese Chip Information Industry development.
文摘The matter about some far-going consequences commencing from the replacement of one of the basic principles of the traditional physics that is the principle of locality, with the recently put forward principle of boundedness is considered. It is proven that the thermodynamic theory which is explicitly grounded on the principle of locality, suffers inherent contradiction which roots lay down to the principle of locality. The way to overcome it goes via the replacement of the principle of locality with the recently put forward by the author principle of boundedness. In turn, the latter gives rise not only to a fundamentally novel notion for a number of ideas but also it yields replacement of the proportionality between the software and hardware components with a new non-extensive approach to the matter. It is proven that the famous Moore’s law stands in new reading both in its support and the way to overcome its limitations. Apart from its role for the technical applications, the present considerations stand also as a methodological example how the role of the basics of any theory affects practical rules such as the Moore’s law.
基金in part,supported by the European Commission through the EU FP7 SEE GRID SCI and SCI BUS projectsby the Grant 098-0982562-2567 awarded by the Ministry of Science,Education and Sports of the Republic of Croatia.
文摘Today we witness the exponential growth of scientific research. This fast growth is possible thanks to the rapid development of computing systems since its first days in 1947 and the invention of transistor till the present days with high performance and scalable distributed computing systems. This fast growth of computing systems was first observed by Gordon E. Moore in 1965 and postulated as Moore’s Law. For the development of the scalable distributed computing systems, the year 2000 was a very special year. The first GHz speed processor, GB size memory and GB/s data transmission through network were achieved. Interestingly, in the same year the usable Grid computing systems emerged, which gave a strong impulse to a rapid development of distributed computing systems. This paper recognizes these facts that occurred in the year 2000, as the G-phenomena, a millennium cornerstone for the rapid development of scalable distributed systems evolved around the Grid and Cloud computing paradigms.
文摘The author presents a new approach which is used to solve an important Diophantine problem. An elementary argument is used to furnish another fully transparent proof of Fermat’s Last Theorem. This was first stated by Pierre de Fermat in the seventeenth century. It is widely regarded that no elementary proof of this theorem exists. The author provides evidence to dispel this belief.
文摘Using the same method that we used in [1] to prove Fermat’s Last Theorem in a simpler and truly marvellous way, we demonstrate that Beal’s Conjecture yields—in the simplest imaginable manner, to our effort to prove it.
文摘This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of the twentieth century. For this reason it can be easily understood by any mathematician or by anyone who knows basic mathematics. The important thing is that the above “theorem” is generalized. Thus, this generalization is essentially a new theorem in the field of number theory.
文摘If the concept of proof （including arithmetic proof） is syntactically restricted to closed sentences （or their Godel numbers）, then the standard accounts of Godel＇s Incompleteness Theorems （and Lob＇s Theorem） are blocked. In these standard accounts （Godel＇s own paper and the exposition in Boolos＇ Computability and Logic are treated as exemplars）, it is assumed that certain formulas （notably so called ＂Godel sentences＂） containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term ＂provable＂ （and indeed ＂unprovable＂） favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.
文摘Goldbach’s Conjecture (“Every even positive integer strictly larger than 4 is the sum of two primes”) has remained unproven since 1742. This paper contains the proof that every positive composite integer n strictly larger than 3, is located at the middle of the distance between two primes, which implicitly proves Goldbach’s Conjecture for 2n as well.
基金by Dr Kemp from National Mathematics and Science College.
文摘This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.
