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Sci-fi world "New Universe". Development.
Thread: Sci-fi world "New Universe". Development.
November 22, 2020, 02:32 AM #1
Moscow-City
Hello friends. As you know, i am russian sci-fi\fantasy writer (not only modder for TW). Here i`m working with my new incarnation of my sci-fi universe. Its about the saga of 2596 year AD, when galaxy turns to the period of Acheron war between Intergalactic Coalition and Achaeron League. This universe sometimes can remind you HALO, Mass Effect or Stargate, but its my unique work, so all ideas, which you`ll find there, are my own, and didn`t taken from other worlds.
Rise of the Acheronian League.
(or what triggered the beginning of the Acheronian War in the galaxy in general)
The League's ascension began with the Gathering of the Consistorium of the Great Races on the planet Acheron Prime, which belongs to the Unn-chor Empire. After the Draconian War, the hatred of many civilizations for the Elfurr state increased hundreds of times. If earlier the mysterious race of Elfurr was treated with great suspicion, but at the same time they preferred not to rant about its tyrannical foundations, then after the elimination of the Ser-Azzrai regime on Kroko, the situation changed. Elfurr raids on draconian planets and on the worlds of Kosatti have rocked the galaxy. Even when the dictatorship of Ser-Azzrai fell, most civilizations no longer regarded Elfurr as allies. At the end of 2592, a massive exit from the Coalition of entire interstellar states followed. The first to leave the Coalition of the Galaxy were Unn-Chor, led by the high priest Olmek R-Llandris. The second was followed by Ho-Nari, led by the high priest Fei Hoa. Sozidaus came third, making this final decision at the Council of Four. Some of the Aranguto states also followed the great races who did not trust the Coalition's pro-Elfurrian rule. Soon, at least 8 civilizations left the Coalition. The Khazaars, Kosatti and Ara-Nii had not previously been part of any associations. The Elfurr did not prevent many races from leaving, but they warned them that they were making an irreparable mistake. St-Finghi was the last to leave the galactic alliance. Following them, two human states, such as Neo-Liberon and Geranium, announced separation. The Elfurrian pharaoh Senuhsert called the act of these people unreasonable and warned about their difficult future without the Coalition.
A few months later, in 2593, civilizations and states that left the Coalition of the Galaxy began to cooperate with each other. Olmec R-Landdris has invited rulers of all races who are unfriendly towards Elfurr. On the planet Acheron Prime, the first meeting of the leaders of states that left the Coalition took place. The first meeting was named the Liberty Staircase. The Coalition was concerned about the gathering of large empires that were formerly part of the galactic association. Empress Farrukh Yuay Ang called this advice a dangerous undertaking. Many leaders of the Coalition expressed concern that the meetings organized by Olmec and calls for unification into a new alliance threaten a total split in the Galaxy. Fleet Admiral Zarina Menchfidel of the Elfurr Empire described Olmec's actions as an attempt to unleash an all-out galactic war. Olmec denied his participation in the anti-Elfurr association. He reported that the meetings held at Acheron Prime were not related to the discussion of the Elfurr aggression. But a month later, a new summit was held under the leadership of Olmec and his allies. The summit announced the creation of the Acheronian League in opposition to the Coalition of the Galaxy. Olmec R-Llandris officially announced the creation of a new association. He did not call his alliance Anti-Elfurr, but did mention that the League would be firmly opposed to any aggression. The Coalition Board called the Acheronian League "a dangerous organization of otherworldly people seeking power."
Closer to the standard April 2593 (in Earth reckoning), the Acheronian League first intervened in the affairs of another state. The anti-Elfurr sentiments instilled by Olmec and his comrades have spread to a good half of the galaxy. Because of this, massive protests began on thousands of planets. Demonstrations were usually suppressed by the Coalition's intelligence services, and the instigators were sent to prisons. But riots continued to erupt. In the Castambol Federation, a rebellion broke out against the local president who supported Elfurr. The people of Castambol took over the government quarter overnight, killing all the authorities. The rebels announced the joining of the federation to the Acheronian League. They called Elfurr the greatest threat in the universe. Olmec R-Landis willingly took the rebels under his wing, even though they were human. Since the annexation of Castambol, anti-Elfurr calls have been heard more and more frequently at League meetings. It all ended with the League's representatives closing all their consulates in the territories of the Coalition. There was a complete diplomatic rift between Acheron and the Coalition of the Galaxy. One of the prominent representatives of the Coalition's psi-special forces, Frederic Kartavin, called this step a declaration of war. The League also announced that it was not going to start a war with Elfurr, but at the same time it would not maintain any relationship with them. In the territories of Acheron, the Elfurric language was banned. All elfurr representatives have been expelled.
The last straw was a quarrel between the League leadership and the Earth Alliance closer to 2595. The last negotiations between the President of the Earth Joanna Kilich and the head of Acheron ended in a conflict situation. Joanna called Olmec "a power-hungry four-armed demon." Olmec told Kilich that "her pathetic planet Earth will be destroyed for such insults." The Farrukh office immediately sent a note of protest to the League leadership. Elfurr called such insults in the negotiations unacceptable. It all ended with the Acheronian flotilla hitting Earth's merchant ships in the disputed sector of Betelgeuse. The merchants called for reinforcements from the nearby Mirandolina space base. The help quickly destroyed the League's fleet in this system. Upon learning of the attack on his ships, Olmec ordered to send three combat armada to Betelgeuse. The Earthlings immediately requested help from Elfurr. The Elfurrian Allied Flotilla helped stop the League's advance. After the defeat of Acheron at Betelgeuse, Olmec convened a new summit, inviting all the allied leaders there. At the meeting, he formally declared war on the Elfurr Empire and the entire Galaxy Coalition. The war was supported by all representatives of the League, without exception.
War before the Achaeron War.
From "Donald Trump" to Cosatti Prime. Year 2590
In 2590, a full-scale war nearly broke out between the Earth Alliance and the Ho-Nari Empire. The confrontation between the High Priest of the Ho-Nari race (an arthropod race inhabiting the galactic east) Fay Hoa The Wisest and President Mitchell Pronin over the colonies on Procyon-12 could develop into a galactic conflict at any moment. It all started with the development of Procyon-12 by earthlings. The "Donald Trump" Expeditionary Mothership was the first to land on the planet, fully entering its crust. Fei Hoa immediately tracked down the colonists and sent a note of protest to President Pronin in connection with the "illegal expansion." As it turned out, there was a whole island on the planet, on which the ancient shrines of Kho-Nari stood for a long time. The Ho-Nari did not touch Procyon-12 due to its "sacredness". However, the planet was rich in minerals and was ideal for colonization. In addition, in 2585, there were serious tremors on Earth in the Yellowstone zone, which indicated the impending awakening of the supervolcano. Despite the fact that the Alliance has mastered enough exoplanets, new worlds with favorable conditions have become a tasty morsel for his government. As a result of negotiations between Ho-Nari and Earth, it was decided that colonization would take place only in the eastern hemisphere of Procyon-12. The West will remain with the Fei Hoa government. But things didn't go according to plan. In mid-2590, there was a brief conflict between the Alliance and the aquatic reptile race, Cosatti. Despot of Kosatti Ser'Chamurunkhi has ordered drone fleets to launch attacks on Earth colonies. One of these armadas attacked Procyon 12, and in particular the Donald Trump base. Since the Kosattians bombed everything that reminded them of structures, the Ho-Nari temple complex was also hit. Soon, the Earthlings repelled the attack using Trump's defensive systems and destroyed the drones. But Fei Hoa, upon learning of the attack on the shrines, immediately sent a new note of protest to Mitchell Pronin. He accused Pronin of violating the colonization treaties and of sacrilege. The Ho-Nari shrines were almost completely destroyed, which provoked outrage in the council of the Holies. The Ho-Nari Large Fleet originated in orbit with Procyon-12. President Pronin had to contact the Coalition Council and the Order of the Father to clarify the situation. The order sent envoys to the Ho-Nari Empire. As a result of new negotiations, it was decided that the earthlings are innocent, and they are not responsible for the destruction of the temple complex. The father of agent Ishken Derh, the Nicomedian count Onstant'Derh, took part in the negotiations. Fei Hoa listened to the delegates and ordered the armads to retreat from the Procyon sector. The threat of a full-scale war has passed the galaxy. Pronin also promised Fei Hoa to deal with the Kosattians. A month after the events, the Ho-Nari armada, supported by Elfurr, the Earth Alliance, and the N-Sai Union, entered the Kosatti systems. Ser'Chamurunha was ordered to stop military aggression. The Ho-Nari threatened to destroy Kosatti Prime with the Atmosphere Vaporizer (climate superweapon). However, the leader of the aquatic race agreed to pay a large contribution to Fei Hoa and help rebuild the temples. Moreover, he betrayed Kho-Nari the perpetrators of the destruction of the shrines, his two generals - Ser'Chargriman and Ser'Fakhatsian. At this, the interracial conflict was ended. The Kosattians were also forced to pay an indemnity to the Earth Alliance. As Ser'Chamurunhi himself later expressed, all this was done not out of repentance, but only for the sake of saving the Kosatti people. Procyon-12, in order to avoid new attacks, was fortified on all sides by the most powerful energy systems. "Donald Trump" has received a whole bunch of new technological improvements.
Regards A.K.Krokhmal
Author of the book "Legends of Moon Landscape"
also author of the book "Volcanorium" and other works too.
https://wiki.twcenter.net/index.php?...r:BagaturSasha
My Wiki page
Re: Sci-fi world "New Universe". Development.
Achaeron psyonic-sorcerer
Achaeron battleship in space
Achaeron battle cruiser "Ziqqurate" class.
Achaeron psy-ops soldiers
Frothy Goodness
Content Director Patrician Citizen
I'm intrigued by the mix of polite diplomatic protests, a collapsing Coalition and nations led by high priests.
New Town (Carthage AAR)
The reason is Elfurr Domination. Elfurr race is always like to control other nations and states. They have the most big army in the galaxy, the most powerful technologies (like Black Hole generators), the most strong space fleet. This race is the head of Coalition of the Galaxy. After the Draconid War, many races started to notice, that Elfurr power is increasing, and they are simply making genocide against all, who have disputes with them. Acheron League was founded by the Elfurr haters; creatures and alien species, who understood about the egocentrical power of Elfurr Empire.
Hello again friends. Need to talk. Today i get some messages from some people, who said me truth and i understand it fully. I need to really improve my artwork, especially modding realization and literature. For now my universe is almost everywhere, and as i see, i have more critic then positive opinion. These people said, that i need to improve my artwork, because things are getting worse for me. They said not only about Discord clubs, but abourt TWC too. I heard from them, that TWC are thinking that i am spreading a trashful work and my universe is really unfinished. I must say, i am improving it of course, and will improve till the "Gem" level. I don`t know, truth or not - it was information from these people. Maybe its just trolling , maybe its a truth.... don`t know. But fact is a fact. People said it (these 2 guys from Disc). My universe needs work, and a lot of work. So at first i must say you all sorry, if you are all dissapointed in my work. I will improve it as i said and promised.
I wanna publish in this topic more stories and i wanna start from a simple LORE information (background). So, what its will be.... Its will be one or two small informations about the world in a week. I will publish it once or twice a week. For example, today i wanna publish the information about Armandov prophet, who foresaw the creation of Acheronian League even in the year 2582. He died soon, but said before the death about his vision. Nobody believed his vision, because in that time, Coalition was seemed as a powerful union of the galaxy states. Powerful and undivided. Later, i`ll start to post information about different races or heroes and their stories. And in parallel, i`ll continue my work with the biggest story.
So thank you, friends, for your support and sorry again for the not good things in past. I don`t know about the "TWC laughing at me" or "all my work is talentless" - but anyway, i`ll continue to improve it till the "Gem" level. Please believe in my forces. I wanna be best.
Flinn
Darth Yodarsconi
Patrician Citizen Content Emeritus Censor Gaming Director
Originally Posted by BagaturSasha
Hello again friends. Need to talk. Today i get some messages from some people, who said me truth and i understand it fully. I need to really improve my artwork, especially modding realization and literature. For now my universe is almost everywhere, and as i see, i have more critic then positive opinion. These people said, that i need to improve my artwork, because things are getting worse for me. They said not only about Discord clubs, but abourt TWC too. I heard from them, that TWC are thinking that i am spreading a trashful work and my universe is really unfinished.
can you provide a screen of this?
Under the patronage of Finlander, patron of Lugotorix & Lifthrasir & joerock22 & Socrates1984 & Kilo11 & Vladyvid & Dick Cheney & phazer & Jake Armitage & webba 84 of the Imperial House of Hader
To be honest, i would like to make a quotes not in this topic, but in PMs council. Because don`t want to make a "hot topic" infront of others here. Anyway, i was shocked when i get this kind of message. I don`t want to spam and didn`t do it. Maybe sometimes i wanted people "hey, i am working with universe, can you see this". But it was only once or twice. I prefer describe my universe with my friends. I have a lot of friends here and in Discord too. But i always thought, i can`t be annoying. Annoying people usually posting anytime , maybe 1 time a day, and next day too, and day after tomorrow too. But i prefer to work more, then make an advertisement campaigns.
About TWC-admins and Discord admins are against my universe - its completely not truth. I spoke with people, and many of them simply didn`t know about my universe things. So the information about i am as about the annoying advertiser-spammer - is nonsence absolutely.
Soon i`ll post here information about the Armandov prophet. And after that, maybe about the Hyperborean Times. Thanks all
Last edited by BagaturSasha; November 26, 2020 at 08:48 AM.
Prophecy Vision of the Andrey Armandov.
In 2582, Andrei Armandov, a member of the Earth Alliance Astrology Guild, reported to the Coalition Board information about an impending invasion of the Galaxy. He recommended that all governments immediately begin to strengthen the planets and star systems. He also called for the use of Elfurr technologies, since, according to him, they were able to deter the advance of an unknown enemy. In the Coalition, Armandov's forecasts were considered absurd and nonsense, which did not deserve attention. His letters to the management of the Board were constantly deleted. When the flow of messages became off scale, Armandov was arrested by the police at Reagan 2. He was taken to the Coalition security office, where they had many conversations with Andrei. He claimed that while on one of the transports between Mars and Reagan 2, he was subjected to a strange telepathic attack. According to Armandov, a whole stream of visions rushed into his mind. All of them displayed thousands and thousands of unknown diamond-shaped ships. In addition, he saw a split among the states of the Galaxy. Armandov said that part of the Coalition's interstellar empires could leave the alliance and form into a certain Acheronian League. He also mentioned a strange name , symbolizing "Darkness". When Andrei was asked about the reasons for the creation of the League, he replied that the mysterious evil coming from the depths of the universe, thus seeks to split the Galaxy into many warring factions, so that then they can destroy all at once. Armandov demanded a personal meeting with the leaders of the Coalition. He even managed to send a message to the Ho-Nari Empire to the Archpriest Fei Hoa. However, Ho-Nari considered his words for the delirium of a madman and advised the Coalition agents to send Armandov for a psychiatric examination. All Andrey's statements about a certain Acheronian league and about the mighty darkness from the depths of the universe were regarded as an insane stream of consciousness. A criminal case was opened against Armandov on attempts to introduce disinformation into the Coalition and on knowingly false predictions. Elfurr became seriously interested in the astrologer. The director of psi-intelligence, Totkhemris User-Kaf, recommended that Armandov be transferred to her department. But when Elfurr arrived to pick Andrei from the bullpen at Reagan 2, the astrologer died. According to doctors, he died of a heart attack. At that time he was already 87 years old. After that, the Armandov case was finally closed. Later, Ygraine, an elderly cleaning woman from the planet Una, spoke about a mysterious evil from distant worlds. But her words were not heard either.
Now about the states. Let me tell you about the most big states of my universe.
CGS (Coalition of the Galaxy States)
Coalition was announced in the middle of XXIII century by the Pact of Galaxy States. First president of Coalition was the elfurr pharaoh Amenemhet IV from the Menkaurr Dynastie. He added to his union many galaxy nations and human galaxy states. Main idea was to create a union of galaxy realms against the common threats. Under the leadership of the Elfurr race, many members of the galaxy had to work together and help each other. In the same period there was declared the Coalition United Government with the council of many races representatives. Council have 2 special organisations - Highest Council of United Galaxy Nations and Congress of the Galactic Safety. Coalition exists even now, in the 2596 AD. Nobody wanted to leave this organisation till the Draconids war in 2592 AD.
Achaeron League
League was declared by the alliance of some galaxy races, who are against of Elfurr domination. Its official creator is Olmec Rlandris, the leader of the Unn-chor race. Later, many other states and races of the galaxy joined him in the Achaeron-Prime planet. The League Representatives believes that the Elfurr are destroying the galaxy and are planning to exterminate all civilizations. The main goal of the League is the destruction of the "pro-elfurr" Coalition and the establishment of a new order in the universe. But many critics believe that the ancient Cult of Darkness, which has existed for millions of years, can operate under the banner of the Achaeron League. Its can be just a puppet organisation of the Cult.
November 28, 2020, 03:21 AM #10
Elfurr Empire.
Elfurr Empire is a mightiest and greatest state in the whole galaxy. This race consist of creatures with human-like form, but with spiky ears and high height. Many factions accepted Elfurr as the most beautiful race in the universe. Their women are so beautiful, hat often forced men from other civilizations to betray their race. Elfurr have egyptian-style culture. Its because all egyptian things, including Pyramides, were created by them. Information about this mysterious race appeared million years ago, so everyone can say, that Elfurr have a really long history. Elfurr have a great amount of technologies. They also have the most powerful in the universe space fleet and superweapons system. Elfurr don`t like to speak about their weapons, but they have a really destructive potential. They simply can destroy every galaxy state by the 1 click of button. Elfurr have in their secret techonology Generator of the Black Holes, which can make a singularity violation in every star system.
For now Elfurr are controlling the Coalition. Their pharaoh Amenemhet was initiator of this alliance. The present pharaoh Senuhsert The Greatest is also accepting his ancestors politics. But there is one biggest problem. Elfurr likes to control, and this is making their race as a highest race in the universe. Many other races dislike it and thinking about Elfurr, as about the egocentric and evil creatures with only one desire - to rule.
Earth Alliance
Earth Alliance was created in the beginning of XXII centyrt. Earth Global Crisis in 2098 pushed the earthlings to create united alliance. Situation was bad, and Earth was almost died in war. But decent leaders decided all problems and made an agreement between each other.
The global crisis in America (unemployment, poverty, economic failure, robbery) has led some of the American generals who disagree with President Jaime Glouchester settled in Antarctica and announced the creation of their own United States. The president immediately moved troops to punish the criminals, but the president of the Eurasian Alliance Alexander Kirsenko supported rebel generals, because counted actions of Glouchester for the manifestation of despotism. In the end, Eurasia, along with the rebels, striked North America. President Gloucester was supported by the another force - Pacific Rim Coalition. This almost led to a new world war, and subsequently to nuclear earth on the planet. But everything was decided by the successful operation of the rebels who destroyed the power of President Gloucester. Rebels took Washington in time. After this, the new president Andrzej Kilic (ancestor of modern Earth president Joanna Kilic) announced a general ceasefire. Kilich was supported by almost all world states and realms. Now it is believed that after the Crisis of 2098 that the heyday and rise of the United Earth Alliance has begun.
In 2114 AD Earth Alliance was borned completely. United expeditions came to the far space. And there also was the first official contact with alien races. New presidents of united nations started to keep the Union politics. Nations came to far history. Nations and tribes and other things.
"Donald Trump" colonial fleets.
"Donald Trump" fleet is the main colonial fleet of the Earth Alliance. It was created in 2123 AD by the will of the president Abraham Bikkerman. Now, in 2596 there are a lot of colonial fleets with the same name. Modern president Kilic split colonial expeditions to several groups. For example, "Donald Trump-1" was sent to the Ziabel star system. "Donald Trump - 33" was teleported to the Galaxy M-33. There already 100 colonial fleets under control of the Earth Alliance. All this colonial program was accepted by the Coalition Main Council. Main task of the fleets - to explore the whole galaxy and other galaxies too.
Colonial fleets consist of many vessels: battleships, transport ships and automatic ships (carriers).
- Transport colonists ship "Armstrong" class (biggest in the fleet)
- Line battleships "Pompeo" class
- Battle frigates "Conquest" class
- Automatic carriers "Jobs" class
- Allied Elfurr vessels "Nahar`kara" class
- Allied kinos vessels "In-Jraam" class
Cult of Cerberum
This cult appeared in the old times, maybe 22k years BC or earlier. The first cult appeared in the Hyperborean Empire. There are some chronicles about it. Cultists believed in the mysterious Cerberum (Si-Bad) god, which can transform to many different forms. They called himself as the Abrahsax or the God of Transformation. Chronicle authors described, that Cerberum fanatics were really mad and furious, they killed thousand victims and spreaded their alien religion in many planets. After the fall of Hyberborean empire, galaxy turned to Age of Darkness. After this age, the new civilization of humans appeared and borned from ashes. It was Our Civilization, nowadays humans community. But even now, in 2596 AD, there are some cults and sects, which are believing in strange gods. Origins of their religion is not explored. Coalition government prefer to not pay attention to these strange religions. Presiden of Earth Alliance Joanne Kilic called them "just strange guys", who are not dangerous for the whole galaxy. Terrorists group usually destroying by the special forces of Coalition.
But after the Achaeron League foundation, many experts started to think, that League and its council can be connected with strange cults. Cults started to be more active after the first summit of League. Coalition intelligence explored more cults in almost 20 planets of the known galaxy.
November 28, 2020, 05:38 PM #14
"Gortenzius" Rebellion
It all started with the Earth Civil War in 2240. Then the Earth Alliance discovered a unique island on its main planet in the Pacific Ocean region. The island arose literally out of the water for inexplicable reasons. The President of the Earth Alliance, Orillano Fryazin, has given the order to investigate the mysterious artifact. The island turned out to be filled with traces of the oldest human civilization, whose age was 60,000 years, and this meant that the age of this civilization is much older than the Hyperborean era. Scientists have investigated mysterious structures in the form of stepped pyramids. They were confused by the giant statues of monsters, more reminiscent of all sorts of African gods. Orliano Fryazin and his researchers pulled out strange sources from the pyramids, which were then given to cybernetics. Deposits of minerals were also discovered that no one on Earth knew about. The so-called "Pan American Coalition" from the Alliance government immediately united against Fryazin. She advocated the destruction of the island and the cessation of its research due to the presence of a mysterious witchcraft power. The representatives of the African-Asian peoples in the government of the Earth, on the contrary, supported Orliano and his instincts. It ended with the fact that Fryazin was impeached. But Orliano responded by ordering the arrest of opposition leaders. This caused a storm of indignation throughout the Earth Alliance. Upon learning of the unrest on Earth, many of the Alliance colonies began to consider independence. Orillano continued to persist and arrest everyone who did not agree with his ideas. In 2241, a massive uprising took place on Mars, which was suppressed by the forces of Fryazin. And in 2242 the opposition attempted a military coup. But Orliano and his commandos repulsed the attacks of the rebels. Soon Fryazin declared his presidency for life, and then ordered the execution of all opposition leaders for treason.
The dictatorship of Orillano has caused outrage among the allies of the Earth Alliance and all alien powers. In 2243, Orliano Fryazin's regime collapsed. Most of the money went to cybernetic research and the extraction of minerals from the mysterious Pacific island. The island turned into a Forbidden Zone, where only military and scientists worked. Orillano was unable to hold on to the post of dictator due to economic reforms. Unemployment and crisis swept almost all territories of the Earth Alliance. The Defense Ministry launched a new military coup and overthrew Fryazin. Orliano died during the assault on the presidential palace. The militarists came to power in the Earth Alliance. The military continued to rule the power for a whole year under the strict supervision of the Elf'urr Empire. However, in 2245, Orillano's supporters again took power. The new coup was not long in coming. The former military scientist of Fryazin, William Gundahar, received the presidency. By his special order, special combat vehicles based on technologies from the forbidden Pacific island were brought to the streets of the Alliance cities. Elf'urr demanded information about cyber technologies from Gundahar, but the President of Earth refused to do so. Then the Elf'urr officially broke the alliance with the Earth Alliance. Gundahar announced his new Doctrine of the Unliving Warriors, as well as that in the near future not a single living person would die in battle. The doctrine was supported by most of the inhabitants of the Earth Alliance. Soon, however, the supporters of the old military dictatorship managed to hack into several factories for the production of military vehicles and gained control over the armies of robots.
The rebels sent an army of machines against President Gundahar. Other robotic armies, in favor of legitimate authority, rushed into the rebel forces. Fierce battles took place between robots in many territories of the Earth Alliance. President Gundahar, together with military scientists, decided to urgently rectify the situation by using a secret plan conceived by Orillano Fryazin. After the discovery of the mysterious island in the Pacific Ocean, many information sources were researched by scientists. This led to the creation of a powerful program, codenamed "Hortensius". Orillano and Gundahar planned in the future to transfer control of all war machines to this program, the mysterious Overmind. Gundahar and his scientists connected Hortensius to all combat robots on Earth, and at the same time gave him control of the Alliance's defensive systems. But to the dismay of the President of Earth, "Hortensius" did not defend the state from the rebels. He quickly reprogrammed all existing machines and brought them down on living beings. In just one day, the mutinous robots killed up to 80 thousand people. Escaped from the control of the government, "Hortensius" began a total seizure of the Earth and the surrounding planets, gaining control of the machine hordes. The Earth Alliance and many galactic states were on the brink of destruction. Upon learning of the AI uprising, the Elf'urr immediately reversed their differences with humans and re-formed an alliance with the Earth Alliance and President Gundahar. Alien allies helped the earthlings to cope with the machine hordes throughout the solar system. "Hortensius" continued to broadcast from a mysterious Pacific island. Gundahar urgently set up a special forces group and sent it to the island to eliminate the AI. As a result of the hardest battles, "Hortensius" was destroyed by a nuclear warhead, along with all the ruins of an unknown city. However, Gundahar also failed to survive. One of the drones managed to finish off the President of the Earth even before the liquidation of "Hortensius". Following the machine riot, the Earth Alliance imposed special restrictions on the use of robots. The new government has canceled research on all forbidden technologies. The project to study the Pacific Ocean for the detection of fragments of ancient civilizations was stopped. The newest organised Coalition Council assiduously assisted in the reign of peace and tranquility.
Last edited by BagaturSasha; November 28, 2020 at 05:41 PM.
It's interesting that Egyptian culture appears in different ways, in the Elfurr Empire and also in the ancient stepped pyramids discovered by the Earth Alliance on the unique island in 2240. It seems that this futuristic universe has connections far back into the Earth's past.
Earth have also the interesting story. Many of pyramides and ziqqurates, which were explored by scientists, are not the products of mankind. For example, Pyramides from Gyza were the monuments of Elfurr race. Its project was created near 10000 BC. Elfurr built it because of their respect to Earth people. Later, egyptian tribes created own civilization and borrowed many Elfurr things. Also Egyptian mythology and religion is also from Elfurr culture.
American pyramides weren`t created by Elfurr. But their creator was unknown. Maybe Lemurian arch-civilization. Maybe Athlantys Empire. But not Hyberborea.
Scientists also explored the 4 biggest and powerful civilizations of the humans race:
1. Lemuria (almost 70000 BC)
2. Hyperborea (almost 20000 BC)
3. Athlantys (almost 10000 BC)
4. New Civilization (modern humans, Anno Domini period)
Other scientists alienologists said, that humans can have 5 civilization periods. They thought that humans can be more ancient, what it seems. Human first civilization would appear in the period of Sovi-Lar Dominion, millions years ago. Sovi-Lar Dominion Era is the age of Sovi-lar race ascendancy. Sovi-Lars can be mysterious creators of the human race.
Kho-Nari Empire
Kho-Nari Empire is controlled by the Kho-Nari, intelligent insectoid race, which is very ancient in the universe. Outwardly, they resemble a cross between insects and arthropods. They have many limbs, eyes and strong chitinous armor. They haven`t got sex (male of female, because they are bi-genders. Kno-Nari can be the descendants of the extincted Zzhuz`hczch race, which controlled the galaxy 12 million years ago. They are connected with their relatives from Ara-Hnii Collective and Zenovians. But they prefer to have own states near the end of main galaxy. Kho-Nari are not agressive, and its wisely to call them, peaceful race. For now they are controlling by Archpriest Fei Hoa Tscholopaltzin Achikulantzoltle (he prefer to call himself as simply Fei Hoa). The helpers and advisors council is also exists, and have name of Sardurii Chamber. Every Sardurii is a highest Kho-Nari noble. Kho-Nari are very religious and believe in a Absolute Creator. They also have own technologies. Kho-Nari are peaceful, but can be a really dangerous in battle. They have a biggest space fleet with many kind of battleships. Their ships are always have form of giant black mantis. They are not racists, so in their army can serve every person from every race of galaxy.
For now Kho-Nari Empire is a part of the Achaeron League. In 2593 Archpriest Fei Hoa is officially made an alliance with League Consistorium. He is now the part of this council. Many experts are thinking that Kho-Nari Empire was forced by the League. Fei Hoa always was wise and peaceful, and his friendship with League can`t be the real and true.
Arthandir Galacticum Republic
Arthandir Republic is the descendant of the mighty Arthandir empire, which was reorganised near the 1940 AD. It always was the mighty and powerful realm with ancient dynasties in a high government. After the Crimson Revolution, Republicans came to power. Since then, Artandir began to lean not towards human domination, but towards alliances with other races. Over time, the power has become an international and interracial state. Now the Artandir Republic is not so much a human association as an association of many galactic civilizations. She is part of the Coalition of the Galaxy. It is now headed by 47 years old President Cedric, one of the most popular metal artists in the universe. His metal band "Cool Dudes of Cedric" is still considered the best of all musical groups. Artandir's army and navy are always at the service of the Coalition. The technologies of this republic are mixed. They use both the science of extinct civilizations and the technological knowledge of Elfurr.
Unn-Chorr Empire and Khazaar Ikhanate
Unn-Chor and Khazaars races are relatives. They are tall, grey-skinned and slim alien species with big and long heads, with some outgrowths and also fast-hearted organism-growing system. Their home is in Galaxy M33, but they have also lands in the Main Galaxy (Milky Way). Khazaars are having only 2 hands, Unn-Chor have 4, and also more eyes in the head. Both of these civilizations have a strong space fleets. Khazaars prefer to live in Tumens, space armadas, because of their nomadic past. Some thousand years ago Khazaars were space nomads, who lived by invasions to other worlds. Unn-Chor were always more peaceful. They always prefer to live in planets, instead of their relatives. Khazaars always had a strong absolute monarchy in government. Unn-Chor - not, because they were more democratic in it. Unn-Chorr usually had a Council government and sometimes teocratic power with a priest in the high stage.
Khazaars are living by the war and force. Thousand years they have a big number of warlords, who were extremely agressive to other nations. Also there was a time of a biggest war between Khazaars and Unn-Chorr. Its happened over 8000 BC, when Khazaar king Narayana Karama-Jaharana attacked Unn-Chor sector in the Galaxy M33. After this war, Khazaard and Unn-Chorr decided to save their "relatives politics" and stop all conflicts. After thousand years, in 2300, both of these races joined th Coalition.
For now Khazaars and Unn-Chorr states are parts of the Achaeron League. In 2593 these races left the Coalition and created the League Consistorium. First leader and high priest of League, Olmec Rllandris - is the representative of Unn-Chor race. Also the Khazaar king Zindropa III Karama-Nanjahara is also the member of League Consistorium. These races are always didn`t like the Elfurr Empire growing. And now they are in war with them.
Byzantian Empire
Byzantian Empire - is a big state of human-hybrides, allied a thousand years with Elfurr. To say honest, this realm is a country of hybrides, because every human there prefer to have relationship with Elfurr girls. So there are a lot of half-elfurrs in this empire. State is the part of Coalition. Now its controlling by the Emperor (dominus) Honorius Lentull Flavius Agricolanus, also known as Honorius The Builder. Empire is a really like Rome in the ancient Earth. Its have almost the same traditions and many elements. But the main government system there is a constitutional monarchy. Honorius is ruling with the help of Magnificum Sincletum (Senate). Sincletum helps the emperor to control on his state (its have 2 chambers - Patrician Councilium and Chamber of Commons). Byzantian empire have a capital in the planet Caesargrad in the Dominum sector. Its also have a good army and fleet. Byzantines are allies of Elfurr and Coalition. And they will never betray their mighty friends.
For now Byzantine empire is in war with Achaeron League, as other Coalition members. High patrician Eldran Siagrius is a part of the Coalition government. Pheotokius, great protostrator of Byzantines, is the high commander of Coalition diversion forces and safety service.
Last edited by BagaturSasha; December 01, 2020 at 06:24 PM.


text:
\section{Introduction}\label{Section:Introduction}
When mechanical load is applied, anisotropic change of conductivity is observed on the silicon structure. This effect can be employed for improvement of MOSFET performances. In this paper, behavioral description of MOSFET drain current, under low mechanical load, from linear piezoconductivity point of view will be considered. For this purpose, it is assumed that description of piezoconductivity for bulk layers is also valid for inversion layer in MOSFET channel. Based on this assumption general model of stressed MOSFET will be derived as well as possible simplifications will be considered.

\section{Preliminaries}
Piezoconductivity is an anisotropic phenomenon. Anisotropy can be described with the use of tensor calculus. In mathematical description of piezoconductivity, vector notation of tensors rank two (conductivity, stress) and matrix notation of tensors rank four (piezoconductivity) will be used in this article \cite{CSS58}, instead of tensor notation.

\subsection{Anisotropy of Ohm{\textquotesingle}s law}
\noindent In conductive layer the relation between density current $j={\left[j_1,j_2,j_3\right]}^T$ and electric field $E={\left[E_1,E_2,E_3\right]}^T$ can be described as follows \cite{CSS58} \cite{JFN57}:

\begin{equation}\label{Eq1}
\begin{bmatrix}
j_1 \\
j_2 \\
j_3 \end{bmatrix}
{=}
\begin{bmatrix}
\kappa_{11} & \kappa_{12} & \kappa_{13} \\
\kappa_{21} & \kappa_{22} & \kappa_{23} \\
\kappa_{31} & \kappa_{32} & \kappa_{33} \end{bmatrix}
\cdot \begin{bmatrix}
E_1 \\
E_2 \\
E_3 \end{bmatrix}.
\end{equation}

\noindent In (\ref{Eq1}) square matrix represents conductivity, which is second rank tensor with nine components \textit{$\kappa$${}_{ij}$}. This tensor (denoted as $K$) is symmetrical according to change of indexes \cite{CSS58} \cite{JFN57} \cite{Now95}. It means that $K$ has only six independent components:

\begin{equation}\label{Eq2}
K= \begin{bmatrix}
\kappa_{11} & \kappa_{12} & \kappa_{13} \\
\kappa_{21} & \kappa_{22} & \kappa_{23} \\
\kappa_{31} & \kappa_{32} & \kappa_{33} \end{bmatrix}=
\begin{bmatrix}
\kappa_{1} & \kappa_{6} & \kappa_{5} \\
\kappa_{6} & \kappa_{2} & \kappa_{4} \\
\kappa_{5} & \kappa_{4} & \kappa_{3} \end{bmatrix}.
\end{equation}

\noindent It can be represented as a vector with six components:

\begin{equation}\label{Eq3}
{K}{=}\begin{bmatrix}\kappa_{1},\kappa_{2},\kappa_{3},\kappa_{4},\kappa_{5},\kappa_{6}\end{bmatrix}^T.
\end{equation}

\noindent For isotropic case, both vectors \textit{E} and \textit{j} are parallel. From here, \textit{$\kappa$${}_{1}$=$\kappa$${}_{2}$=$\kappa$${}_{3}$}=\textit{$\kappa$} and \textit{$\kappa$${}_{4}$=$\kappa$${}_{5}$=$\kappa$${}_{6}$=0}. Hence, in vector notation isotropic conductivity is a vector as follows:
\begin{equation}\label{Eq4}
K=
\begin{bmatrix}
\kappa,\kappa,\kappa,0,0,0
\end{bmatrix}
^T.
\end{equation}

The state of stress in elastic body can be described as a second order symmetrical tensor, with only six independent components \cite{JFN57}. It can be represented also as a vector:

\begin{equation}\label{Eq5}
\sigma=
\begin{bmatrix}
\sigma _{1},\sigma _{2},\sigma _{3},\sigma _{4},\sigma _{5},\sigma _{6}
\end{bmatrix}^T.
\end{equation}
\noindent Components \textit{$\sigma$${}_{1}$, $\sigma$${}_{2}$, $\sigma$${}_{3}$ }represent normal stresses and components \textit{$\sigma$${}_{4}$, $\sigma$${}_{5}$, $\sigma$${}_{6}$} are shear stresses. Without stress, the conductivity of silicon crystal is isotropic. When the stress is applied, anisotropic change of conductivity is observed on the structure:
\begin{equation}\label{Eq6}
\Delta {K}{=}
\begin{bmatrix}
\Delta \kappa_{1},\Delta \kappa_{2},\Delta \kappa_{3},\Delta \kappa_{4},\Delta \kappa_{5},\Delta \kappa_{6}
\end{bmatrix}^T.
\end{equation}

\noindent In this case effective conductivity is a sum of isotropic conductivity (\ref{Eq4}) and anisotropic change of conductivity (\ref{Eq6}):
\begin{equation}\label{Eq7}
{K}{=}{{K}}_0{+}\Delta {K}.
\end{equation}
\noindent Relative change of conductivity can be described as follows:

\begin{equation}\label{Eq8}
\frac{\Delta K}{\kappa }{=}\frac{1}{\kappa}\cdot
 \begin{bmatrix}
{\Delta \kappa}_{1} \\
{\Delta \kappa}_{2} \\
{\Delta \kappa}_{3} \\
{\Delta \kappa}_{4} \\
{\Delta \kappa}_{5} \\
{\Delta \kappa}_{6} \end{bmatrix}
{=} \begin{bmatrix}
{\Pi }_{11} & {\Pi }_{12} & {\Pi }_{13} & {\Pi }_{14} & {\Pi }_{15} & {\Pi }_{16} \\
{\Pi }_{21} & {\Pi }_{22} & {\Pi }_{23} & {\Pi }_{24} & {\Pi }_{25} & {\Pi }_{26} \\
{\Pi }_{31} & {\Pi }_{32} & {\Pi }_{33} & {\Pi }_{34} & {\Pi }_{35} & {\Pi }_{36} \\
{\Pi }_{41} & {\Pi }_{42} & {\Pi }_{43} & {\Pi }_{44} & {\Pi }_{45} & {\Pi }_{46} \\
{\Pi }_{51} & {\Pi }_{52} & {\Pi }_{53} & {\Pi }_{54} & {\Pi }_{55} & {\Pi }_{56} \\
{\Pi }_{61} & {\Pi }_{62} & {\Pi }_{63} & {\Pi }_{64} & {\Pi }_{65} & {\Pi }_{66}
\end{bmatrix}
\cdot
\begin{bmatrix}
\sigma_{1} \\
\sigma_{2} \\
\sigma_{3} \\
\sigma_{4} \\
\sigma_{5} \\
\sigma_{6}
\end{bmatrix}
{=}\Pi \sigma.
\end{equation}

\noindent Matrix $\Pi$ in (\ref{Eq8}) represents piezoconductivity tensor. Between changes in resistivity and conductivity, there is a relation \cite{www}:
\begin{equation}\label{Eq9}
\frac{\Delta \rho}{\rho}{=-}\frac{\Delta {K}}{\kappa}.
\end{equation}
\noindent It means that there is equivalence between piezoconductivity and piezoresistivity matrices in a sense of opposition:
\begin{equation}\label{Eq10}
\Pi {=-}\pi.
\end{equation}
\subsection{Piezoconductivity on arbitrary coordinate system}
It is assumed that there is known piezoconductivity matrix in coordinate system that is conformable to elementary cell of silicon. For finding distribution of piezoconductance coefficients on arbitrary chosen coordinate system it is required square matrix $a$, of dimension $3\times3$ \cite{JFN57}, which describes transformation from old coordinate system to the new one:
\begin{equation}\label{Eq11}
a{=} \begin{bmatrix}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{32} & a_{33} \end{bmatrix}
\buildrel{def}\over= \begin{bmatrix}
l_{1} & m_{1} & n_{1} \\
l_{2} & m_{2} & n_{2} \\
l_{3} & m_{3} & n_{3} \end{bmatrix}.
\end{equation}
\noindent From here, matrix $\alpha $ can be calculated \cite{CSS58}:
\begin {equation}\label {Eq12}
\alpha {=} \begin {pmatrix}
l^ {2} _ {1} & m^ {2} _ {1} & n^ {2} _ {1} & {2} m_ {1} n_ {1} & {2} n_ {1} l_ {1} & {2} l_ {1} m_ {1} \\
l^ {2} _ {2} & m^ {2} _ {2} & n^ {2} _ {2} & {2} m_ {2} n_ {2} & {2} n_ {2} l_ {2} & {2} l_ {2} m_ {2} \\
l^ {2} _ {3} & m^ {2} _ {3} & n^ {2} _ {3} & {2} m_ {3} n_ {3} & {2} n_ {3} l_ {3} & {2} l_ {3} m_ {3} \\
l_ {2} l_ {3} & m_ {2} m_ {3} & n_ {2} n_ {3} & m_ {2} n_ {3} {+} n_ {2} m_ {3} & l_ {2} n_ {3} {+} n_ {2} l_ {3} & l_ {2} m_ {3} {+} m_ {2} l_ {3} \\
l_ {3} l_ {1} & m_ {3} m_ {1} & n_ {3} n_ {1} & m_ {1} n_ {3} {+} n_ {1} m_ {3} & l_ {1} n_ {3} {+} n_ {1} l_ {3} & l_ {1} m_ {3} {+} m_ {1} l_ {3} \\
l_ {1} l_ {2} & m_ {1} m_ {2} & n_ {1} n_ {2} & m_ {1} n_ {2} {+} n_ {1} m_ {2} & l_ {1} n_ {2} {+} n_ {1} l_ {2} & l_ {1} m_ {2} {+} m_ {1} l_ {2}
\end {pmatrix}
\end {equation}

\noindent This matrix is needed for piezoconductance coefficients $\Pi \textquotesingle$ calculation in a new coordinate system:
\begin{equation}\label{Eq13}
{\Pi }{{'}}{=}\alpha\Pi \alpha^{{-}{1}}{=-}\alpha\pi \alpha^{{-1}}.
\end{equation}

\noindent Results of transformation (\ref{Eq13}) can be presented in polar coordinate system \cite{Kan82} or in Cartesian coordinate system. This paper results will be presented with the use of Cartesian coordinate system only. For assumed planes $\{100\}$, $\{110\}$ and $\{111\}$, given in \cite{Gni05} method will be used for finding matrix (\ref{Eq11}).

\subsubsection{Transformation matrix on plane $\{100\}$}
Cartesian coordinate system conformed to crystallographic axes of silicon is considered. It is assumed that on plane $(001)$ current flows along $X$-axis. For investigation of piezoconductivity coefficients behavior on this plane, it is needed rotation of coordinate system located on $(001)$ around $Z$-axis by angle $\varphi$ (Fig. \ref{fig1}). Angles between coordinate system axes before rotation and after rotation are described in Table \ref{Tab1}. Therefore, specific matrix (\ref{Eq11}) which includes cosines of above-mentioned angles has a form \cite{JFN57}:
\begin{equation}\label{Eq14}
a{=}R(Z,\varphi){=}
\begin{bmatrix}
{\cos \varphi} & {\sin \varphi} & 0 \\
{-}{\sin \varphi\ } & {\cos \varphi\ } & 0 \\
0 & 0 & 1 \end{bmatrix}
\end{equation}

\noindent On plane $(001)$ range $0\leq\varphi\leq90^0$ of rotation angle is enough to describe behavior of piezoconductance coefficients, because of silicon cell symmetry. Based on formula (\ref{Eq13}), distribution of piezoconductance coefficients on plane $\{100\}$ can be received.

\begin{table}
\centering
\caption{Angles between axes of coordinate system before and after rotation}\label{Tab1}
\fontsize{10}{14}\selectfont{
\begin{tabular}{c|c|c|c|c} \hline
 \multicolumn{2}{c|}{\ } & \multicolumn{3}{|c}{$Axes {\ } before {\ } rotation$} \\ \cline{3-5}
\multicolumn{2}{c|}{\ } & $X$ & $Y$ & $Z$ \\ \hline \hline
$Axes$ & $X'$ & $\varphi$ & $90^0-\varphi$ & $90^0$ \\ \cline{2-5}
$after$ & $Y'$ & $90^0+\varphi$ & $\varphi$ & $90^0$ \\ \cline{2-5}
$rotation$ & $Z'$ & $90^0$ & $90^0$ & $0^0$ \\ \hline
\end{tabular}}
\end{table}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig1.png}
\caption{Piezoconductance on a plane $\{100\}$: a) the plane $(001)$; b) rotation of coordinate system around $Z$-axis.}\label{fig1}
\end{figure}

\subsubsection{Transformation matrix on plane $\{110\}$}
For obtaining piezoconductivity coefficients on plane $(-101)$ it is necessary to find transformation of $(001)$ to $(-101)$ plane. For this purpose, coordinate system on plane $(001)$ has to be rotated around $Y$-axis by angle $\theta=45^0$ (Fig. \ref{fig2}a). Rotation matrix has a form:

\begin{equation}\label{Eq15}
R(Y,\theta=45^0)=
\begin{bmatrix}
\cos 45^0 & 0 & \sin 45^0 \\
0 & 1 & 0 \\
-\sin 45^0 & 0 & \cos 45^0
\end{bmatrix}
\end{equation}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig2.png}
\caption{Piezoconductance on a plane $\{110\}$: a) construction of the plane $(-101)$; b) rotation of coordinate system around $Z'$-axis.}\label{fig2}
\end{figure}

\noindent For investigation of piezoconductivity coefficients behavior on the plane $(-101)$, in next step it is needed further rotation of coordinate system around the new one $Z\textquotesingle$-axis by angle $\varphi$ (Fig. \ref{fig2}b). Because of silicon cell symmetry, it is enough to change $\varphi$ in a range $0\leq\varphi\leq180^0$. Matrix of this rotation has a form:

\begin{equation}\label{Eq16}
R(Z',\varphi){=}
\begin{bmatrix}
{\cos \varphi} & {\sin \varphi} & 0 \\
{-}{\sin \varphi\ } & {\cos \varphi\ } & 0 \\
0 & 0 & 1 \end{bmatrix}
\end{equation}

\noindent Resultant rotation of coordinate system can be described as a product of both mentioned above rotations (\ref{Eq15}) and (\ref{Eq16}) \cite{JFN57} \cite{Gni05}:

\begin{equation}\label{Eq17}
a=R(Z',\varphi)\cdot R(Y,45^0).
\end{equation}
\subsubsection{Transformation matrix on plane $\{111\}$}
\noindent Plane $(-101)$ can be formed from plane $(001)$ via rotation around $Y$-axis by angle $\theta=45^0$ (Fig. 3a). This rotation is described by matrix (\ref{Eq15}). Plane $(-111)$ can be obtained via rotation of above-mentioned plane $(-101)$ around $X\textquotesingle$-axis by angle $\phi$ (Fig. \ref{fig3}b). From geometrical consideration, it can be concluded that $\tan{\phi}=\sqrt{2}/3$. Thus, angle $\phi$ is equal to $35.26^0$. Therefore $cos{\phi}=\sqrt{2/3}$ and $sin{\phi}=\sqrt{3}/3$ . Suitable transformation matrix has a form:

\begin{equation}\label{Eq18}
R(X',\phi){=}
\begin{bmatrix}
1 & 0 & 0 \\
0 & {\cos \phi} & {\sin \phi} \\
0 & {-}{\sin \phi\ } & {\cos \phi\ }
\end{bmatrix}
\end{equation}
\noindent On Fig. \ref{fig3}b, the grey triangle is located on the new one $(-111)$ plane. Coordinate system on this plane is not marked on the picture, because of legibility. For investigation of piezoconductivity coefficients behavior on this plane, in next step it is needed further rotation of coordinate system around the new one $Z\textquotesingle\textquotesingle$-axis (not marked of Fig. \ref{fig3}) by angle $\varphi$. Because of silicon cell symmetry, it is enough to change angle $\varphi$ in range $0\leq\varphi\leq120^0$. Matrix of this rotation has a form:

\begin{equation}\label{Eq19}
R(Z'',\varphi){=}
\begin{bmatrix}
{\cos \varphi} & {\sin \varphi} & 0 \\
{-}{\sin \varphi\ } & {\cos \varphi\ } & 0 \\
0 & 0 & 1 \end{bmatrix}
\end{equation}

\noindent Resultant matrix of coordinate system rotation can be described as a product of mentioned above rotations (\ref{Eq15}) and (\ref{Eq18}) as well as (\ref{Eq19}) \cite{JFN57} \cite{Gni05}:

\begin{equation}\label{Eq20}
a=R(Z'',\varphi)\cdot R(X',\phi=35.26^0)\cdot R(Y,\theta=45^0)).
\end{equation}

\begin{figure}
\centering
\includegraphics[width=9cm]{fig3.png}
\caption{Piezoconductance on a plane $\{111\}$: a) the plane $(-101)$; b) construction of the plane $(-111)$ via rotation of coordinate system around $X\textquotesingle$-axis.}\label{fig3}
\end{figure}

\subsection{Distributions of piezoconductance coefficients}
For monocrystalline silicon, in coordinate system conformable to elementary silicon cell, piezoconductivity matrix has a form:

\begin{equation}\label{Eq21}
\Pi = -
\begin{bmatrix}
{\pi }_{11} & {\pi }_{12} & {\pi }_{12} & 0 & 0 & 0 \\
{\pi }_{12} & {\pi }_{11} & {\pi }_{12} & 0 & 0 & 0 \\
{\pi }_{12} & {\pi }_{12} & {\pi }_{11} & 0 & 0 & 0 \\
0 & 0 & 0 & {\pi }_{44} & 0 & 0 \\
0 & 0 & 0 & 0 & {\pi }_{44} & 0 \\
0 & 0 & 0 & 0 & 0 & {\pi }_{44}
\end{bmatrix}
\end{equation}

\noindent In engineering practice, the values of $\pi_{11}$, $\pi_{12}$ and $\pi_{44}$ should be extracted from the measurements, for bulk or inversion layers respectively. Theirs values for different types of conducting layers are given in literature \cite{CSS54} \cite{Can791} \cite{Col682} \cite{Mik811}. Using data from a variety of sources, different piezoconductivity coefficients will be obtained. Without loss of generality, coefficients $\pi_{11}$, $\pi_{12}$ and $\pi_{44}$ given by Smith \cite{CSS54} will be used for farther analysis (Table \ref{Tab2}). On Figures \ref{fig4}--\ref{fig9}, non-vanished piezoconductivity coefficients and specific sums on planes $\{100\}$, $\{110\}$ and $\{111\}$ are presented both for holes and for electrons. Analysis of distributions of piezoconductivity coefficients shows how to locate the MOSFET channel.

\begin{table}
\centering
\caption{Piezoresistance coefficients for silicon \cite{CSS54}.}\label{Tab2}
\fontsize{10}{14}\selectfont{
\begin{tabular}{c|c|c|c} \hline
 & $\pi_{11} [MPa^{-1}]$ & $\pi_{12} [MPa^{-1}]$ & $\pi_{44} [MPa^{-1}]$ \\ \hline \hline
P-Si & 66 & -11 & 1381 \\ \hline
N-Si & -1022 & 534 & -136 \\ \hline
\end{tabular}}
\end{table}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig4.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $ (001) $, $N$-type. The angles $0^0$ and $90^0$ are equivalent to crystallographic direction $<100>$. Angle $45^0$ is equivalent to crystallographic direction $ <110>$.}\label{fig4}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig5.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $(-101) $, $N$-type. The angles $0^0$, $35.26^0$, $90^0$, $144.74^0$ and $180^0$ are equivalent to crystallographic directions $[101]$, $[111]$, $[010]$, $[-11-1]$ and $[-10-1]$, respectively.}\label{fig5}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig6.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $\{111\}$, $N$-type. The angles $0^0$, $30^0$, $60^0$, $90^0$ and $120^0$ on these plots are equivalent to crystallographic directions $[101]$, $[112]$, $[011]$, $[-121]$ and $[-110]$, respectively.}\label{fig6}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig7.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $(001)$, $P$-type. The angles $0^0$ and $90^0$ are equivalent to crystallographic direction $<100>$. Angle $45^0$ is equivalent to crystallographic direction $<110>$.}\label{fig7}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig8.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $(-101)$, $P$-type. The angles $0^0$, $35.26^0$, $90^0$, $144.74^0$ and $180^0$ are equivalent to crystallographic directions $[101]$, $[111]$, $[010]$, $[-11-1]$ and $[-10-1]$, respectively.}\label{fig8}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig9.png}
\caption{Non-vanished piezoconductance coefficients versus angle of rotation around $Z$-axis. Plane $(-1-11)$, $P$-type. The angles $0^0$, $30^0$, $60^0$, $90^0$ and $120^0$ on these plots are equivalent to crystallographic directions $[101]$, $[112]$, $[011]$, $[-121]$ and $[-110]$, respectively.}\label{fig9}
\end{figure}

\subsubsection{The most promising MOSFET location}
From analysis of piezoconductance distributions (Figs. \ref{fig4}-\ref{fig9}) the most promising channel locations on different planes will be selected, for assumed uniaxial stress state:
\begin{enumerate}
\item $N$-channel on plane $\{100\}$: for direction $<100>$ ($0^0$ or $90^0$ on Fig. \ref{fig4}) maximum increment of conductivity can be obtained with positive uniaxial stress along channel – because of positive value of $\Pi_{11}$ maximum.

\item $N$-channel on plane $\{110\}$: for direction $<100>$ ($90^0$ on Fig. \ref{fig5}) desirable increment of conductivity can be obtained under uniaxial longitudinal positive stress, because of positive $\Pi_{11}$ maximum.

\item $N$-channel on plane $\{111\}$: for direction $<112>$ ($30^0$ on Fig. \ref{fig6}) occurs beneficial superposition of $\kappa_1$ and $\kappa_5$. Maximum increment of conductivity can be achieved under longitudinal positive (see values of $\Pi_{11}$ and $\Pi_{51}$) or transversal negative (see values of $\Pi_{12}$ and $\Pi_{52}$) stress.

\item $P$-channel on planes $\{100\}$: maximum increment of conductivity for $<110>$ direction ($45^0$ on Fig. \ref{fig7}) could be obtained for two cases of stress state:
\begin{enumerate}
\item For uniaxial negative (compressed) stress along $X$-axis (along channel) – because of negative minimum of $\Pi_{11}$.
\item For uniaxial positive (tensile) stress along $Y$-axis (in plane of channel, perpendicularly to channel length) – because of positive maximum of $\Pi_{12}$.
\end{enumerate}

\item $P$-channel on planes $\{110\}$: maximal increment of conductivity could be performed for $<111>$ direction ($35.26^0$ or $144.74^0$ on Fig. \ref{fig8}), under uniaxial longitudinal negative stress, because of $\Pi_{11}$ negative minimum.

\item P-channel on planes $\{111\}$: for $<112>$ direction ($90^0$ on Fig. \ref{fig9}) occurs beneficial superposition of $\kappa_1$ and $\kappa_5$. Drain current can be raised under longitudinal negative stress (coefficient $\Pi_{11}$ and $\Pi_{51}$) or under transversal positive stress (coefficient $\Pi_{12}$ and $\Pi_{52}$). The first one event is more profitable because of $|\Pi_{11}|>|\Pi_{12}|$.

\end{enumerate}
\noindent Summary results of these analyzes are presented in Table \ref{Tab3}.

\begin{table}
\centering
\caption{The most promising MOSTET location for the uniaxial state of stress.}\label{Tab3}
\fontsize{10}{14}\selectfont{
\begin{tabular}{c|c|c|c|c|c} \hline
Channel & Channel & \multirow{2}{*}{Angle} & \multirow{2}{*}{Reference} & Nonzero & \multirow{2}{*}{Cause} \\
 type & location & & & stress component & \\ \hline \hline
\multirow{4}{*}{N} & $[100]/(001)$ & $0^0$ or $90^0$ & Fig. \ref{fig4} & $\sigma_1>0$ & $\max\Pi_{11}$ \\ \cline{2-6}
 & $[010]/(-101)$ & $90^0$ & Fig. \ref{fig5} & $\sigma_1>0$ & $\max\Pi_{11}$ \\ \cline{2-6}
 & \multirow{2}{*}{$[112]/(-111)$} & \multirow{2}{*}{$30^0$} & \multirow{2}{*}{Fig. \ref{fig6}} & $\sigma_1>0$ & $\max\Pi_{51}$, $\Pi_{11}>0$ \\ \cline{5-6}
 & & & & $\sigma_2<0$ & $\min\Pi_{52}$, $\Pi_{12}<0$ \\ \hline
\multirow{6}{*}{P} & \multirow{2}{*}{$[110]/(001)$} & \multirow{2}{*}{$45^0$} & \multirow{2}{*}{Fig. \ref{fig7}} & $\sigma_1<0$ & $\min{\Pi_{11}}$ \\ \cline{5-6}
 & & & & $\sigma_2>0$ & $\max\Pi_{12}$ \\ \cline{2-6}
 & [111]/(-101) & $35.26^0$ & \multirow{2}{*}{Fig. \ref{fig8}} & \multirow{2}{*}{$\sigma_1<0$} & \multirow{2}{*}{$\min\Pi_{11}$} \\ \cline{2-3}
 & [-11-1]/(-101) & $144.74^0$ & & & \\ \cline{2-6}
 & \multirow{2}{*}{$[-121]/(-111)$} & \multirow{2}{*}{$90^0$} & \multirow{2}{*}{Fig. \ref{fig9}} & $\sigma_1<0$ & $\min\Pi_{51}$, $\Pi_{11}<0$ \\ \cline{5-6}
 & & & & $\sigma_2>0$ & $\max\Pi_{52}$, $\Pi_{12}>0$ \\ \hline
\end{tabular}}
\end{table}

\section{General model of stressed MOSFET}
Switched on MOSFET is investigated. MOSFET channel is located on arbitrary chosen crystallographic plane. Cartesian coordinate system associated with the MOSFET will be further considered. Transistor channel can be treated as a conducting layer located along $X$-axis of this coordinate system. $Y$-axis is located horizontally in a plane of channel. It is transversal to the channel length. $Z$-axis is vertical to the plane created by length and width of the MOS transistor (Fig. 10). In the channel, there exists a vector of electric field $E$ and density current $j$, because of transistor polarization. Such a coordinate system gives adequate signs of specific components of electric field and current density. In normal polarization, in $n$-type MOSFET this components are positive and in $p$-type – negative.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig10.png}
\caption{Schematic diagram of MOSFET.}\label{fig10}
\end{figure}

Component $E_1$ of electric field is parallel to $X$-axis. Vertical component $E_3$ is parallel to $Z$-axis. In plane of channel, component $E_2$ parallel to $Y$-axis can be also respected. In MOS transistor channel, density current $j_1$ parallel to $X$-axis is considered. This component is dependent on all nonzero components of electric field. Based on formulas (\ref{Eq1}) and (\ref{Eq2}) it can be expressed:

\begin{equation}\label{Eq22}
j_1=\kappa_1E_1+\kappa_6E_2+\kappa_5E_3.
\end{equation}

\noindent Only three components $\kappa_1$, $\kappa_5$ and $\kappa_6$ of conductivity (\ref{Eq2}) are inherent in this equation. From (\ref{Eq4}), (\ref{Eq6}) and (\ref{Eq7}), these components can be expressed as follows:

\begin{equation}\label{Eq23}
\begin{cases}
\kappa_1=\kappa+\Delta\kappa_1 \\
\kappa_5=\Delta\kappa_5 \\
\kappa_6=\Delta\kappa_6
\end{cases}
\end{equation}

\noindent Using (\ref{Eq23}), density current (\ref{Eq22}) can be articulated as:
\begin{equation}\label{Eq24}
j_1=\kappa{E_1}+\Delta\kappa_1E_1+\Delta\kappa_6E_2+\Delta\kappa_5E_3.
\end{equation}
\noindent Whole drain current can be obtained from integration of density component $j_1$ over transistor channel cross-section $S$ \cite{Sah05}:

\begin{equation}\label{Eq25}
I_D=\int\limits_{S}j_1dS=\int\limits_{S}(\kappa{E_1}+\Delta\kappa_1E_1+\Delta\kappa_6E_2+\Delta\kappa_5E_3)dS.
\end{equation}

\noindent It can be noticed that $\kappa$ is an effective conductivity of unstressed MOSFET. On the other hand, relative change of conductivity is dependent on stress in MOSFET channel. According to (\ref{Eq8}), changes of conductivity components $\Delta\kappa_1$, $\Delta\kappa_5$ and $\Delta\kappa_6$ can be expressed as follows:

\begin{equation}\label{Eq26}
\begin{cases}
\Delta\kappa_1=\kappa\sum\limits_{j=1}^6\Pi_{1j}\sigma_j \\
\Delta\kappa_5=\kappa\sum\limits_{j=1}^6\Pi_{5j}\sigma_j \\
\Delta\kappa_6=\kappa\sum\limits_{j=1}^6\Pi_{6j}\sigma_j
\end{cases}
\end{equation}

Substituting (\ref{Eq26}) to (\ref{Eq25}), general model of drain current has a form:

\begin{equation}\label{Eq27}
I_D=\int\limits_{S}{\left(
\kappa{E_1}
+\kappa E_{1}\sum^6_{j=1}{\Pi_{1j}\sigma_j}
+\kappa E_{2}\sum^6_{j=1}{\Pi_{6j}\kappa_j}
+\kappa E_{3}\sum^6_{j=1}{\Pi_{5j}\kappa_j}
\right)dS}.
\end{equation}

\noindent If no stress is assumed, then components $\Delta\kappa_1$, $\Delta\kappa_5$ and $\Delta\kappa_6$ are vanishing and model (\ref{Eq27}) has no anisotropic components. It describes (denoted as $I_{D0}$) MOSFET drain current without stress in the channel:

\begin{equation}\label{Eq28}
I_{D0}=\int\limits_{S}{j_1dS}=\int\limits_{S}{\kappa{E_1}dS}.
\end{equation}

\noindent All this means that drain current (\ref{Eq27}) can be described as a superposition of two components. The first one $I_{D0}$ is not dependent on stress. The second one denoted as ${\Delta}I_D$ is an anisotropic component dependent on stress:

\begin{equation}\label{Eq29}
{\Delta}I_D=\int\limits_{S}{\left(
\kappa E_{1}\sum^6_{j=1}{\Pi_{1j}\sigma_j}
+\kappa E_{2}\sum^6_{j=1}{\Pi_{6j}\sigma_j}
+\kappa E_{3}\sum^6_{j=1}{\Pi_{5j}\sigma_j}
\right)dS}.
\end{equation}

\noindent This way, whole drain current can be expressed as a sum of these two components:
\begin{equation}\label{Eq30}
I_D=I_{D0}+{\Delta}I_D.
\end{equation}

For modeling drain current without stress, only $I_{D0}$ can be used. In practical application, this component can be substituted by any of numerical or analytical correct model, if necessary. Model of $I_{D0}$ should take into consideration all complicated physical aspects inherent in MOSFET: saturation region, short channel, mobility vs. velocity, etc. For instance, in analytical mode it can be modeled with the use of any SPICE like model. Component ${\Delta}I_D$ allow incorporating of stress, in any of $I_{D0}$ model without stress effect.

For increment of current efficiency, in formula (\ref{Eq29}) positive increment of conductivity (\ref{Eq26}) is necessary. This increment will be positive if signs of stress components will be the same like signs of specific piezoconductivity coefficients.

\section{Model simplification}
Specific properties of considered structure allows simplify component (\ref{Eq29}). Simplifications resulted from stress state in transistor channel, MOS structure symmetry as well as analytical approach will be taken into consideration in further analysis.

\subsection{Specific stress state in MOSFET channel}
In formula (\ref{Eq29}), there are components of piezoconductance coefficients $\Pi_{ij}$ with first index $i$ equal to $1$, $5$ or $6$. Selection of second index $j$ is determined by nonzero $\sigma_j$ stress components inherent in the channel. In general case of stress state, indexes $j$ can have all possible values from $1$ to $6$. For further analysis, some specific cases of stress state in plane of MOSFET channel \cite{Mai071}, against a general case of stress state will be considered:

\begin{itemize}
\item Isotropic stress induced by hydrostatic pressure $p$ $–-$ indexes $j$ are equal to $1$, $2$ and $3$.
\item Isotropic stress in a plane of channel $–-$ indexes $j$ are equal to $1$ and $2$.
\item Uniaxial stress along channel $–-$ index $j$ is equal to $1$.
\item Uniaxial stress across channel $–-$ index $j$ is equal to $2$.
\item General case of flat stress in a plane of channel $–-$ indexes $j$ are equal to $1$, $2$ and $6$.
\end{itemize}

\noindent Changes of conductivity component $\Delta\kappa_i$ versus specific stress state are presented in Table \ref{Tab4}. From here, it can be concluded which of piezoconductance coefficients are indispensable for modeling of stress influence on MOSFET drain current. These coefficients should be taken into consideration in MOS transistor drain current modeling.

\begin{table}
\centering
\caption{Change of i-th conductivity component as a function of stress state.}\label{Tab4}
\fontsize{10}{14}\selectfont{
\begin{tabular}{c|c|c} \hline
Stress state & Stress in vector notation & Change of conductivity \\ \hline \hline
General case & $\sigma=\left[\sigma_1,\sigma_2,\sigma_3,\sigma_4,\sigma_5,\sigma_6\right]^T $ & $\Delta\kappa_i=\kappa\sum\limits_{j=1}^{6}{\Pi_{ij}\sigma_j} $ \\ \hline
Hydrostatic & \multirow{2}{*}{$\sigma=\left[-p,-p,-p,0,0,0\right]^T $} & \multirow{2}{*}{$\Delta\kappa_i=-\kappa{p} \sum\limits_{j=1}^{3}{\Pi_{ij}} $} \\
 pressure $p$ & & \\ \hline
Isotropic stress & \multirow{2}{*}{$\sigma=\left[\sigma_0,\sigma_0,0,0,0,0\right]^T $} & \multirow{2}{*}{$\Delta\kappa_i=\kappa\sigma_0 \left(\Pi_{i1}+\Pi_{i2} \right) $} \\
in plane of channel & & \\ \hline
 Uniaxial stress & \multirow{2}{*}{$\sigma=\left[\sigma_1,0,0,0,0,0\right]^T$} & \multirow{2}{*}{$ \Delta\kappa_i=\kappa\sigma_1\Pi_{i1}$} \\
 along channel & & \\ \hline
Uniaxial stress & \multirow{2}{*}{$\sigma=\left[0,\sigma_2,0,0,0,0\right]^T $} & \multirow{2}{*}{$\Delta\kappa_i=\kappa\sigma_2\Pi_{i2}$} \\
across channel & & \\ \hline
General case & \multirow{3}{*}{$\sigma=\left[\sigma_1,\sigma_2,0,0,0,\sigma_6\right]^T $} & \multirow{3}{*}{$\Delta\kappa_i=\kappa\left(\Pi_{i1}\sigma_1+\Pi_{i2}\sigma_2+\Pi_{i6}\sigma_6\right) $} \\
of flat stress & & \\
in plane of channel & & \\ \hline
\end{tabular}}
\end{table}

\subsection{Symmetry of MOSFET structure}
Classical MOSFET is symmetric relatively to $XZ$ plane. Assumption about symmetry of MOS transistor structure implies supposition about symmetry of distributions of theirs parameters. In particular, distributions of piezoconductance coefficients and stress components are also symmetric. It means that these quantities are even functions of variable $Y$. On the other hand, component $E_2$ of electric field along $Y$-axis has opposite signs near opposite edges and it is vanished in the middle of the structure. It can be supposed that it is an odd function of variable $Y$ with average value equal to zero. If such assumptions are reliable then suitable component in (\ref{Eq27}) can be vanished:

\begin{equation}\label{Eq31}
\int\limits_{S}{\left(
\kappa E_{2}\sum^6_{j=1}{\Pi_{6j}\sigma_j}
\right)dS}=0.
\end{equation}

\noindent This way model (\ref{Eq27}) can be simplified to the form without piezoconductance coefficients with first index equal to $6$:

\begin{equation}\label{Eq32}
I_D=I_{D0}+\Delta{I_D}=
\int\limits_{S}{\left(
\kappa E_1
+\kappa E_{1}\sum^6_{j=1}{\Pi_{1j}\sigma_j}
+\kappa E_{3}\sum^6_{j=1}{\Pi_{5j}\sigma_j}
\right)dS}.
\end{equation}

\noindent Three-dimensional ($3-D$) model of $\Delta{I_D} $ vs. electric field is reduced to a two-dimensional ($2-D$) problem. This result is conformable with principle of $2-D$ compact model \cite{Sah05}.

\subsection{Analytical approach}
Model (\ref{Eq32}) gives possibility to take into consideration the influence of the stress to the MOSFET current. This model has a general capacity. On the other hand, analytical compact model is necessary in circuit simulator \cite{Sah05}. Special problem is adequate transformation of (\ref{Eq32}) to analytical form. Analytical model contains semi-empirical and empirical parameters, which must be extracted. In general, it contains two types of parameters: process parameters and electrical parameters. Process parameters must be taken from process characterization. Electrical parameters must be determined from measured electrical data \cite{Fot99}. Additionally, model that takes into consideration influence of stress should contain information about stress and piezoconductivity coefficients. In general, both of these parameters can be non-homogeneous in the channel. In compact analytical modeling, non-uniform distributions of parameters must be substituted by representative constant values. For modeling of bulk piezoresistive devices average stress and extracted effective piezoresistivity (piezoconductivity) coefficients are used \cite{Gni06}. The same procedure can be employed for this paper approximation. If real stress and piezoconductance coefficients distributions are substituted by theirs effective values (it means values that are not a function of integrated area), then suitable sums of products $\Pi_{ij}\sigma_j$ can be drawing out before integrals.

Similarly, if $\kappa$ is an effective conductivity of unstressed MOSFET then it can be drawing out before integrals too. This way, integrals of electric field components over cross-section $S$ can be substituted by products of $S$ and average values of electric field components in mentioned cross-section. From here, equation (\ref{Eq32}) can be still simplified to compact analytical form:

\begin{equation}\label{Eq33}
I_D=I_{D0}{\left(
1+\sum^6_{j=1}{\Pi_{1j}\sigma_j}
\right)}
+S\kappa{E_3}\sum^6_{j=1}{\Pi_{5j}\sigma_j}.
\end{equation}
\subsection{Models of drain current on selected planes}
For assumed symmetry of MOSFET and assumed planes of structure location as well as stress distribution, model (\ref{Eq33}) can be further simplified. For this purpose, we assume that MOSFET channel can be located on typical planes: $\{100\}$, $\{110\}$ and $\{111\}$. For that reason, distribution of piezoconductance coefficients should be considered on these planes. In our approach, only piezoconductance coefficients with first indexes $1$ and $5$ will be examined, because of assumed structure symmetry. Second indexes are determined by assumptions about stress state in the channel.

From Table \ref{Tab4} it follows, that for assumed flat stress state in the channel, only coefficients with second indexes equal to $1$, $2$ and $6$ are important. Moreover, sums $(\Pi_{11}+\Pi_{12}+\Pi_{13})$ and $(\Pi_{51}+\Pi_{52}+\Pi_{53})$ have to be investigated, for hydrostatic pressure. Additionally, sums $(\Pi_{11}+\Pi_{12})$ and $(\Pi_{51}+\Pi_{52})$ are significant for isotropic stress state in a plane of channel. Analysis of distribution of specific coefficients on different planes can show which directions of transistor channel location are desirable for improvement of MOSFET performances. For assumed specific stress state model of drain current (\ref{Eq33}) can be simplified to the forms presented in Table \ref{Tab5}.

\begin{table}
\centering
\caption{Analytical models of MOSFET current.}\label{Tab5}
\fontsize{10}{14}\selectfont{
\begin{tabular}{c|c|c|c} \hline
 \multirow{2}{*}{No.} & \multirow{2}{*}{State of stress} & \multirow{2}{*}{Form of equation (\ref{Eq33})} & Plane \\
 & & & of channel \\ \hline \hline
 \multirow{2}{*}{(M1)} & Hydrostatic & \multirow{2}{*}{$I_D=I_{D0}\left(1-p\left(\Pi_{11}+\Pi_{12}+\Pi_{13}\right)\right)$} &
 \multirow{2}{*}{All} \\
 & pressure $p$ & & \\ \hline
\multirow{2}{*}{(M2)} & Isotropic stress & $I_D=I_{D0} \left(1+\sigma_0\left(\Pi_{11}+\Pi_{12} \right)\right)$ & $\{100\}, \{110\}$ \\ \cline{3-4}
 & in plane of channel & $I_D=I_{D0} \left(1+\sigma_0\left(\Pi_{11}+\Pi_{12}+\Pi_{13}\right)\right)$ & $\{111\}$ \\ \hline
 \multirow{2}{*}{(M3)} & Uniaxial stress & $I=I_{D0}\left(1+\Pi_{11}\sigma_1\right) $ & $\{100\}, \{110\}$ \\\cline{3-4}
 & along channel & $I=I_{D0}\left(1+\Pi_{11}\sigma_1\right)+S\kappa{E_3}\Pi_{51}\sigma_1 $ & $\{111\}$ \\ \hline
\multirow{2}{*}{(M4)}
& Uniaxial stress & $I=I_{D0} \left(1+\Pi_{12}\sigma_2 \right) $ & $\{100\}, \{110\}$ \\ \cline{3-4}
& across channel & $I=I_{D0} \left(1+\Pi_{12}\sigma_2 \right)+S\kappa{E_3}\Pi_{52}\sigma_2 $ & $\{111\}$ \\ \hline
\multirow{2}{*}{(M5)}
 & Flat stress state &
 $I=I_{D0}\left(1+\Pi_{11}\sigma_1+\Pi_{12}\sigma_2+\Pi_{16}\sigma_6 \right) $ & $\{100\}, \{110\}$ \\ \cline{3-4}
 & in plane of channel &
 $I=I_{D0}\left(1+\Pi_{11}\sigma_1+\Pi_{12}\sigma_2+\Pi_{16}\sigma_6 \right) $ & \multirow{2}{*}{$\{111\}$}\\
 & $-$general case &
 $+S\kappa{E_3}\left(\Pi_{51}\sigma_1+\Pi_{52}\sigma_2+\Pi_{56}\sigma_6 \right) $ & \\\hline
\end{tabular}
}
\end{table}
\section{Examples}
As an example, analytical approach will be presented based on the formulas $(M2)$ and $(M3)$ in Table \ref{Tab5}. For this purpose, uniaxial stress with a value of $200MPa$ will be considered in transistor channel. For calculation of drain current under stress, it is necessary to know specific piezoconductance coefficients and drain current $I_{D0}$. Additionally, on plane $\{111\}$ effective conductivity κ in MOSFET channel as well as vertical component of electric field $E_3$ should be known. Conductivity $\kappa$ will be calculated as normalized output conductance $G_{DS}$:

\begin{equation}\label{Eq34}
\kappa=G_{DS}\cdot\frac{L}{S}=\frac{\partial{I_{D0}}}{\partial{V_{DS}}}\cdot\frac{L}{S}.
\end{equation}

In plane $\{111\}$ two types of the stress impact on the MOSFET drain current are observed. The first type is associated with the impact of stress on the conductivity component $\kappa_1$, through coefficients $\Pi_{11}$ or $\Pi_{12}$ (respectively for longitudinal or transverse stress). The second one is associated with the impact of the stress on the conductivity component $\kappa_5$, through coefficients $\Pi_{51}$ or $\Pi_{52}$ (respectively for longitudinal or transverse stress). Conductivity component $\kappa_1$ combines current density $j_1$ with electric field component $E_1$. Conductivity component $\kappa_5$ combines current density $j_1$ with vertical electric field component $E_3$. It would be interesting to examine the nature and scope of these two interactions.

\subsection{N-channel MOSFET under stress}
For calculation influence of stress, classical n-channel MOSFET was modeled in $2-D$ mode, with the use of Minimos $6.1$ Win simulator \cite{Minimos}. For calculation it was assumed oxide thickness $T_{OX}=15nm$, channel width $W=1\mu{m} $, channel length $L=0.85\mu{m} $. Calculated characteristics are shown on Fig. \ref{fig11}.

For proposed methodology, stress influence under $UG=2V$ was considered. Results of calculation was used for approximation of effective values of conductivity, vertical component of electric field $E_3$ and drain current $I_{D0}$. Thickness of inversion layer was assumed $x_d=0.15\mu{m} $. Area of transistor cross-section was approximated as $S=x_d\cdot{W}=0.15\mu{m} ^2$. Vertical electric field was assumed $E_z=0.23V/\mu{m} $. Calculated conductance $G_{DS}$ under $U_G=2V$ is presented on Fig. \ref{fig12}.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig11.png}
\caption{N-MOSFET drain current without stress.}\label{fig11}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=10cm]{fig12.png}
\caption{Conductance $G_{DS}$ under $U_G=2V$.}\label{fig12}
\end{figure}

From analysis of piezoconductance distributions (Figs. \ref{fig4}, \ref{fig6} and \ref{fig8}) for $N$-channel MOSFET, on specific planes $\{100\}$, $\{110\}$ and $\{111\}$ the most promising channel locations are along $<100>$, $<100>$ and $<121>$ directions respectively (see Table \ref{Tab3}). With these assumptions, the drain current under stress was calculated and presented in Figure \ref{Eq13}. The best results are obtained for channel located on $(001)$ along $[100]$ under tensile longitudinal stress. The same results are obtained for channel location on $(-101)$ plane along $[010]$ direction, also for tensile longitudinal stress. The results on the plane $\{111\}$, for both of tensile longitudinal stress and compressive transversal stress are nearly identical, with a slight predominance of the former.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig13.png}
\caption{Influence of $200 MPa$ uniaxial stress on $N$-MOSFET characteristics: a) $U_G=2V$, no stress; b) channel $[100]/(001)$ or $[010]/(-101)$, tensile longitudinal stress; c) channel $[112]/(-111)$, tensile longitudinal stress; d) channel $[112]/(-111)$, compressive transversal stress.}\label{fig13}
\end{figure}

N-MOSFET current change associated with the change of the conductivity components under stress were examined on plane $\{111\}$ (Fig. \ref{fig14}). It was found that the change in conductivity $\kappa_1$ increases the MOSFET current by about six percent. Meanwhile, the change of MOSFET current caused by a change of conductivity $\kappa_5$ is non-linear. In the linear part of the MOSFET characteristics, change of current is more than twelve percent. When the MOSFET current comes into saturation region, these changes are disappearing.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig14.png}
\caption{The impact of the stress on the growth of current for $N$-MOSFET in channel $[112]/(-111)$: a) impact of tensile longitudinal stress via conductance $\kappa_1$; b) impact of compressive transversal stress via conductance $\kappa_1$; c) impact of tensile longitudinal stress via conductance $\kappa_5$ or impact of compressive transversal stress via conductance $\kappa_5$.}\label{fig14}
\end{figure}

\subsection{P-channel MOSFET under stress - thought experiment}
To compare the effects of stress on the characteristics of $p$-channel MOSFET, a thought experiment will be tested, assuming the same current efficiency as previously analyzed $N$-MOSFET. In addition, it is assumed $U_G=-2V$, area of transistor cross-section $S=0.15\mu{m} ^2$ and vertical electric field $E_z=0.23V/\mu{m} $.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig15.png}
\caption{Influence of 200 MPa uniaxial stress on P-MOSFET characteristics: a) UG=2V, no stress; b) channel [110]/(001), compressive longitudinal stress; c) channel [110]/(001), tensile transversal stress; d) channel [111]/(-101) or [-11-1]/(-101), tensile longitudinal stress; e) channel [-121]/(-111), compressive longitudinal stress; f) channel [-121]/(-111), tensile transversal stress.}\label{fig15}
\end{figure}

From analysis of piezoconductance distributions for p-channel MOSFET (Figs. \ref{fig5}, \ref{fig7} and \ref{fig9}), on specific planes $\{100\}$, $\{110\}$ and $\{111\}$ the most promising channel locations are along $<110>$, $<111>$ and $<121>$ directions, respectively.

\begin{figure}
\centering
\includegraphics[width=10cm]{fig16.png}
\caption{The impact of the stress on the growth of current for $P$-MOSFET in channel $[-112]/(-111)$: a) impact of compressive longitudinal stress via conductance $\kappa_1$; b) impact of tensile transversal stress via conductance $\kappa_1$; c) impact of tensile transversal stress via conductance $\kappa_5$ or impact of compressive longitudinal stress via conductance $\kappa_5$.}\label{fig16}
\end{figure}

Obtained results are presented in Fig. \ref{fig15}. The best results are achieved for channel located on $\{110\}$ along $<111>$, under tensile longitudinal stress. On plane $\{100\}$, results obtained for compressive longitudinal stress are slightly better than results for tensile transversal stress. On plane $\{111\}$, results achieved for compressive longitudinal stress are better than results for tensile transversal stress.

The change of P-MOSFET current, associated with the change of the conductivity components under stress, were examined on plane $\{111\}$ (Fig. \ref{fig16}). The change in conductivity $\kappa_1$ under compressive longitudinal stress increases the MOSFET current by about $14\%$. On the other hand, the change in conductivity $\kappa_1$ under compressive transversal stress increases the current by about $4\%$. The change of MOSFET current caused by a change of conductivity $\kappa_5$ is non-linear. In the linear part of the MOSFET characteristics, change of current is more than ten percent. In saturation region, these changes are disappearing.

\section{Discussion}
In this paper, behavioral description of MOSFET drain current, under low mechanical load, from linear piezoconductivity point of view was considered. The approach proposed above, implies several other problems that should be more precisely explained.

\subsection{Symmetry reduction}
The proposed method does not take into account the reduction of symmetry \cite{SymRed2010}. It was assumed that description of piezoconductivity for bulk layers is also valid for inversion layer in MOSFET channel. Under this assumption, for monocrystalline bulk silicon, in coordinate system conformable to elementary silicon cell, matrix of piezoconductivity has a form:
\begin{equation}\label{Eq35}
\Pi_B =
\begin{bmatrix}
{\Pi }_{11} & {\Pi }_{12} & {\Pi }_{12} & 0 & 0 & 0 \\
{\Pi }_{12} & {\Pi }_{11} & {\Pi }_{12} & 0 & 0 & 0 \\
{\Pi }_{12} & {\Pi }_{12} & {\Pi }_{11} & 0 & 0 & 0 \\
0 & 0 & 0 & {\Pi }_{44} & 0 & 0 \\
0 & 0 & 0 & 0 & {\Pi }_{44} & 0 \\
0 & 0 & 0 & 0 & 0 & {\Pi }_{44}
\end{bmatrix}
\end{equation}
On the other hand in $<100>/(001)$ MOSFET, because of symmetry reduction, the number of independent piezoconductance coefficients increases to six. In such case, in coordinate system conformable to elementary silicon cell, piezoconductivity matrix takes the form \cite{SymRed2010}:

\begin{equation}\label{Eq36}
\Pi =
\begin{bmatrix}
{\Pi }_{11} & {\Pi }_{12} & {\Pi }_{13} & 0 & 0 & 0 \\
{\Pi }_{12} & {\Pi }_{11} & {\Pi }_{13} & 0 & 0 & 0 \\
{\Pi }_{13} & {\Pi }_{13} & {\Pi }_{33} & 0 & 0 & 0 \\
0 & 0 & 0 & {\Pi }_{44} & 0 & 0 \\
0 & 0 & 0 & 0 & {\Pi }_{44} & 0 \\
0 & 0 & 0 & 0 & 0 & {\Pi }_{66}
\end{bmatrix}
\end{equation}
Reduction of symmetry introduces disturbance in the description of the piezoconductivity. It means that piezoconductivity in MOSFET can be described as a superposition of the matter tensor and the field tensor. For that reason, both effects can be considered independently. Matrix (2) can be expressed as the sum of two matrices:
\begin{equation}\label{Eq37}
\Pi=\Pi_B+\Delta\Pi
\end{equation}
The first one is the matrix (\ref{Eq35}) that represents tensor of matter in coordinate system of elementary silicon cell. The second one is a matrix, which represents disturbance associated with reduction of the symmetry. It may be interpreted as a field tensor. The change of coordinate system changes tensor components. It is assumed, that optimal direction of the transistor channel is searched on the plane $(001)$. The matrix (\ref{Eq36}) should be rotated around the $Z$-axis, in accordance with equation (\ref{Eq13}):
\begin{equation}\label{Eq38}
\Pi^{\textquotesingle}=\alpha\Pi\alpha^{-1}=\alpha\left(\Pi_B+\Delta\Pi\right)\alpha^{-1}=\alpha\Pi_{B}\alpha^{-1}+\alpha\Delta\Pi\alpha^{-1}.
\end{equation}
There is a problem, how to take into account the reduction of symmetry on other planes? To solve this problem, first it is necessary to find matter tensor $\Pi_B$ on the given plane. For the plane $\{110\}$, the formula (\ref{Eq15}) should be used. Similarly, formulas (\ref{Eq18}) and (\ref{Eq19}) should be used, for the plane $\{111\}$. In turn, for finding the optimal direction of transistor channel, for the given field tensor $\Delta\Pi$ (in the same coordinate system), formula (\ref{Eq14}) should be used.

Because the piezoconductivity in MOSFET can be described as a superposition of material tensor and field tensor, both effects can be considered independently. Therefore, the proposed method can easily be expanded into a form that will take into account the reduction of symmetry.

\subsection{Other problems}
The approach proposed above, implies several other problems that should be more precisely explained.

First problem is a model simplification. General model (\ref{Eq27}) can be simplified for practical use.
First simplifications results from reduction of some stress components in the channel or from vanishing of a certain piezoconductance components in specific crystallographic planes.
Next simplification results from omission of electric field component $E_2$, because of symmetry of MOSFET structure assumption. If this component is omitted, then conductivity component $\kappa_{12}$ (denoted as $\kappa_6$ in vector notation) and piezoconductance coefficients with first index equal to six are omitted too. This way, $3-D$ model of $I_D$ is reduced to a $2-D$ model, in electric field space.
Last simplification is based on substitution of real distributions of stress, piezoconductance coefficients, conductivity and electric field by theirs effective values, which should be extracted (piezoconductivity coefficients) or calculated (stress components, specific electric field component, conductivity $\kappa$). These gives an analytical approach and it is desirable from point of view of circuit simulator model.
On the other hand, it can be stated that these simplifications are not obligatory. If model is not simplified then for exact calculation of drain current numerical methods have to be used.

The second problem is a model obligation in a context of MOSFET modes of operation. Proposed model of current increment $\Delta{I_D}$ is obliging in all modes of MOSFET operation in the same degree as chosen model $I_{D0}$ (model of current without stress). On the other hand, current sensitivity on stress is dependent on mode of MOSFET operation. Significant factor in formula of current increment (\ref{Eq29}) is conductivity $\kappa$. The value of $\kappa$ (which is normalized output conductance $G_{DS}={\partial{I_{D0}}}/{\partial{V_{DS}}}$) in saturation region is small. It means current sensitivity on stress is smaller in saturation region than in linear region.

As a third problem there appears model universality. Described model of stress influence on MOSFET drain current was established with assumption that there is a transistor structure with a silicon channel. Matrix $\Pi$ (\ref{Eq21}) is used for description of piezoconductivity of silicon (which has diamond cubic crystal structure) in coordinate system conformable with elementary silicon crystal cell. On the other hand, instead of silicon the other material can be considered for transistor channel forming. For instance, it can be SiC (silicon carbide), which has zincblende (cubic) or hexagonal crystal structure \cite{Gut2009}. In this case, the shape of matrix $\Pi$ should be adjusted to actual crystal structure.

At the end, the weakness of the model should also be considered. This limitation is a nonlinearity of piezoconductivity coefficients versus stress level. Up to $100$MPa, assumption about linearity of the piezoconductivity phenomenon can be used. For stresses up to $200$MPa, non-linearity ranges from several to tens of percent \cite{Matsud1993}. Since magnitude of stress in MOSFETS is on $1$GPa range of level, assumption about linear piezoconductance cannot be applied.

\section{Conclusions}

In this paper piezoconductivity phenomenon in MOSFET channel was discussed and model of drain current with possibility of stress consideration was proposed. General model which is obliging in all modes of MOSFET operation was simplified for practical use.

The analysis of proposed model combined with examination of stress components inherent in the channel as well as distributions of specific piezoconductance coefficients on a plane of channel showed which directions of transistor channel are desirable for improvement of MOSFET performances. This model gives possibility to predict optimum orientation of transistor channel, for the given stress state.

Described model was established with assumption that there is a transistor structure with a silicon channel. On the other hand, instead of silicon the other material can be considered for transistor channel forming. For instance, it can be SiC (silicon carbide), which has zinc blende (cubic) or hexagonal crystal structure. In this case, the shape of piezoconductivity matrix should be adjusted to actual crystal structure. By this means, in this paper general approach to modeling of stressed MOSFET is proposed.

redpajama_set_name: RedPajamaArXiv


A little over a week ago, we welcomed the first of April 2019 as we always do–on high alert of incoming April Fools Day pranks.
As per usual, brands of all sorts–from McDonald's to Tinder–participated in prank day (check out our favorite pranks here). And also as per usual, some pranks were brilliant while others failed to hit the mark. For the most part, April 1st was a day of good-hearted fun on the Internet yet still one question remains.
Why in the world do brands spend money on pranks?
To answer that question, we'll take a walk back into history beginning in 1983, where BMW kicked off a new tradition of April Fools Day pranks through print advertising and thus became pioneers of brand pranks. The first prank was an advertisement promising the world's first "rain-deflecting open-top car". Nearly a decade of pranks followed including the road warming lasers prank of 1989.
Despite BMW's "success" with April Fools Day pranks, the European car company was in a company of few when it came to brand pranks pre-social media and YouTube days. For years, April Fools Day pranks were the purview to local radio stations and newspapers.
Fast forward to 2008, when YouTube and social media kicked off their heydays. In what was perhaps one of the greatest April Fools Day pranks of modern times, YouTube quite literally rickrolled the world by redirecting all video links to the music video for Rick Astley's famous 80's hit, Never Gonna Give You Up. The video platform's competition that year included Nestle, who unveiled a "shorter, more contemporary" new name for their delicious Butterfinger candy bars–The Finger–and, of course, BMW who revealed their new "Canine Repellant Alloy Protection", a product that would keep dogs from peeing on your car.
From 2008 onward, April Fools Day has become an unspoken invitation for even the most serious brands to expose their silly side. At least, that's how the rest of us see it. The truth is, even April Fools pranks are a part of every participating brand's marketing strategy and though it is an opportunity for brands to have a good laugh, most pranks are planned with an ulterior motive.
The most common reasons behind brand pranks are low-level product testing and low-cost advertising. Product testing, you ask? Indeed, some of our favorite April Fools Day pranks of yesteryears were actually visions of a future still to come.
In 2007, BMW's prank was centered around instant messaging in your car powered by technology that allowed you to use your voice to "type" messages from your vehicle. Today, nearly all new cars have this very feature. While we're pretty sure this particular prank wasn't actually a product test, pranks like Burger King's 2019 Impossible Burger are a different story. In BK's case, the Impossible Burger, an all plant-based burger is in the works.
Burger King's Impossible Whopper is now being tested in St. Louis, MO locations.
Some brands like ThinkGeek turn their April Fools Day pranks into limited quantity products consumers can actually buy while other brands simply use the day as a good reason for cheap advertising by showing their fun side. In the end, all brands who participate in prank day have one ultimate goal in mind–to turn consumers into brand customers.
ThinkGeek's Roomby: Kirby Robot Vacuum was a hilarious April Fools prank..but now you can buy it on their website for a cool $299.99!
Want to know if April Fools Day 2020 should be part of your future marketing goals? We have the answer. Request a consultation with Momentum Consulting today to find out how we can help you create a dynamic, profitable marketing strategy for your business.


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Once Adobe Premiere files are encrypted, they can be opened only when a authorized T-Safe Dongle is attached. Even if someone copies the files, they will remain encrypted, hence of no use.
once the launcher is opened, i.e., encryptor is on, every Premiere file you open, even if it is normal starts getting encrypted.
Select "Adobe Premiere Pro" in "Select Program".
Protected Extensions for Adobe Premiere is prproj.
Select the Source folder(folder containing Adobe Premiere files to be encrypted) and destination folder, click on "Start Encryption", wait till the files are encrypted, close the window.
Select "Adobe Premiere Pro" from "Select Program", Enter the details, select "Installer Type" depending on the software configuration at the End User.
User should choose the same folder in which Adobe Premiere is already Installed.