Estudo do ponto invariante com a temperatura (ZTC) em transistores nanofolhas com porta ao redor (GAA-Nanosheet)
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2021-04-13
Autores
Coelho, Carlos Henrique Santos
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Universidade Estadual Paulista (Unesp)
Resumo
Neste trabalho, foram avaliados os parâmetros básicos de transistores de nanofolhas de silício de porta ao redor (GAA-nanosheet) a fim de entender melhor o funcionamento do dispositivo e alimentar o modelo Camilo-Martino (CM) para avaliar se o mesmo pode ser utilizado como ferramenta para auxiliar os projetistas de circuitos integrados na polarização dos circuitos uma vez que é desejável a estabilidade dos circuitos com a temperatura. O modelo Camilo-Martino (CM) calcula o ponto invariante com a temperatura (VZTC), ou seja, o ponto de polarização de porta que resulta em uma corrente de dreno (ID) constante (IZTC), com a variação de temperatura. Os parâmetros analisados, que estão diretamente relacionados com o modelo Camilo-Martino (CM), são: a tensão de limiar (VT), inclinação sublimiar (SS), mobilidade dos portadores (µ) e transcondutância (gm). Também foi necessário efetuar a análise da variação de VT e de gm com a temperatura, para que desta forma fosse possível avaliar o comportamento do modelo Camilo-Martino (CM) para esta tecnologia. Os resultados para ambos os tipos de canal (P e N) mostraram um bom ajuste na região linear de operação, ficando o erro inferior a 7% do valor de VZTC. Foi mostrado também que para os dispositivos de comprimento de canal de 28nm o erro apresentado ficou ligeiramente maior que para os transistores de comprimento de canal de 70nm e 200nm devido ao início da influência do efeito de canal curto e da forte influência da resistência série. Quando avaliados em saturação, estes dois efeitos indesejados passam a ter maior influência no comportamento do transistor e uma vez que o modelo adotado não os considera, o erro aumentou razoavelmente para os transistores mais curtos. No entanto, sabendo-se que usualmente falamos de saturação para aplicações analógicas e que neste campo nunca utilizamos o comprimento de canal mais curto permitido pelo nó tecnológico devido à degradação de sua performance analógica, quando avaliados os comprimentos de canal de 70nm e 200nm, o modelo apresentou valores mais próximos dos extraídos experimentalmente apresentando um erro médio de 17,23% para canal N e 20% para canal P. Porém considerando a simplicidade do modelo e a pequena variação em corrente causada por este erro consideramos o modelo como uma boa ferramenta para estimar o ponto de polarização invariante com a temperatura. O modelo Camilo-Martino (CM) apresentou alta sensibilidade aos parâmetros, ΔVT/ΔT e fator c, principalmente em saturação uma vez que para esta tecnologia esses parâmetros tornaram-se muito pequenos, fazendo com que em pequenas mudanças nos valores destes fatores, o modelo sofra grande variação. Além do modelo, a partir dos dados experimentais foi mostrado que os transistores fabricados em nanofolhas de silício possuem um altíssimo controle das cargas no canal, resultando em uma pequena influência dos efeitos de canal curto, mas em contrapartida apresentaram uma forte influência da resistência série, que se torna mais importante para os dispositivos mais curtos.
In this work, the basic parameters of the gate all around nanosheet silicon transistors (GAA-nanosheet) were evaluated in order to better understand the functioning of the device and feed the Camilo-Martino (CM) model to assess whether it can be used as a tool for assist designers of integrated circuits in polarizing the circuits since the stability of the circuits with temperature is desirable. The Camilo-Martino (CM) model calculates the Zero Temperature Coefficient (VZTC), that is, the gate bias point that results in a constant drain current (ID) (IZTC), with temperature variation. The parameters analyzed, which are directly related to the Camilo-Martino (CM) model, are: the threshold voltage (VT), subthreshold slope (SS), carrier mobility (µ) and transconductance (gm). It was also necessary to perform the analysis of the variation of VT and gm with the temperature, so that in this way it was possible to evaluate the behavior of the Camilo-Martino (CM) model for this technology (gate all around nanosheet devices). The results for both types of channel (p and n) showed a good agreement in the linear region of operation, with the error being less than 7% of the VZTC value. It was also shown that for the 28nm channel length devices the error presented was slightly higher than for the 70nm and 200nm channel length transistors due to the beginning of the influence of the short channel effect and the strong influence of the series resistance. When evaluated in saturation, these two unwanted effects have a greater influence on the behavior of the transistor and since the assumed model doesn’t consider them, the error increased reasonably for the shorter transistors. However, knowing that we usually talk about saturation for analog applications and that in this field we never use the shortest channel length allowed by the technological node due to the degradation of its analog performance, when evalueted the channel lengths of 70nm and 200nm, the model presented values closer to those extracted experimentally showing an average error of 17.23% for channel n and 20% for channel p. Although considering the simplicity of the model and the small variation in current caused by this error, we consider the model as a good tool to estimate the zero temperature coefficient bias point. The Camilo-Martino (CM) model showed high sensitivity to the parameters, ΔVT / ΔT and c factor, mainly in saturation, since for this technology these parameters became very small, causing small changes in the values of these factors, the model suffers great variation. In addition to the model, from the experimental data it showed that the made of silicon nanosheets transistors have a very high control of the charges in the channel, resulting in a small influence of the short channel effects, but in compesation they showed a strong influence of the series resistance, which becomes more important for shorter devices.
In this work, the basic parameters of the gate all around nanosheet silicon transistors (GAA-nanosheet) were evaluated in order to better understand the functioning of the device and feed the Camilo-Martino (CM) model to assess whether it can be used as a tool for assist designers of integrated circuits in polarizing the circuits since the stability of the circuits with temperature is desirable. The Camilo-Martino (CM) model calculates the Zero Temperature Coefficient (VZTC), that is, the gate bias point that results in a constant drain current (ID) (IZTC), with temperature variation. The parameters analyzed, which are directly related to the Camilo-Martino (CM) model, are: the threshold voltage (VT), subthreshold slope (SS), carrier mobility (µ) and transconductance (gm). It was also necessary to perform the analysis of the variation of VT and gm with the temperature, so that in this way it was possible to evaluate the behavior of the Camilo-Martino (CM) model for this technology (gate all around nanosheet devices). The results for both types of channel (p and n) showed a good agreement in the linear region of operation, with the error being less than 7% of the VZTC value. It was also shown that for the 28nm channel length devices the error presented was slightly higher than for the 70nm and 200nm channel length transistors due to the beginning of the influence of the short channel effect and the strong influence of the series resistance. When evaluated in saturation, these two unwanted effects have a greater influence on the behavior of the transistor and since the assumed model doesn’t consider them, the error increased reasonably for the shorter transistors. However, knowing that we usually talk about saturation for analog applications and that in this field we never use the shortest channel length allowed by the technological node due to the degradation of its analog performance, when evalueted the channel lengths of 70nm and 200nm, the model presented values closer to those extracted experimentally showing an average error of 17.23% for channel n and 20% for channel p. Although considering the simplicity of the model and the small variation in current caused by this error, we consider the model as a good tool to estimate the zero temperature coefficient bias point. The Camilo-Martino (CM) model showed high sensitivity to the parameters, ΔVT / ΔT and c factor, mainly in saturation, since for this technology these parameters became very small, causing small changes in the values of these factors, the model suffers great variation. In addition to the model, from the experimental data it showed that the made of silicon nanosheets transistors have a very high control of the charges in the channel, resulting in a small influence of the short channel effects, but in compesation they showed a strong influence of the series resistance, which becomes more important for shorter devices.
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Engenharia elétrica, Semicondutores, Sistemas eletrônicos, Transistores