Quantum Transport in a Silicon Nanowire FET Transistor: Hot Electrons and Local Power Dissipation

A review and perspective is presented of the classical, semi-classical and fully quantum routes to the simulation of electro-thermal phenomena in ultra-scaled silicon nanowire field-effect transistors. It is shown that the physics of ultra-scaled devices requires at least a coupled electron quantum transport semi-classical heat equation model outlined here. The importance of the local density of states (LDOS) is discussed from classical to fully quantum versions. It is shown that the minimal quantum approach requires self-consistency with the Poisson equation and that the electronic LDOS must be determined within at least the self-consistent Born approximation. To bring in this description and to provide the energy resolved local carrier distributions it is necessary to adopt the non-equilibrium Green function (NEGF) formalism, briefly surveyed here. The NEGF approach describes quantum coherent and dissipative transport, Pauli exclusion and non-equilibrium conditions inside the device. There are two extremes of NEGF used in the community. The most fundamental is based on coupled equations for the Green functions electrons and phonons that are computed at the atomically resolved level within the nanowire channel and into the surrounding device structure using a tight binding Hamiltonian. It has the advantage of treating both the non-equilibrium heat flow within the electron and phonon systems even when the phonon energy distributions are not described by a temperature model. The disadvantage is the grand challenge level of computational complexity. The second approach, that we focus on here, is more useful for fast multiple simulations of devices important for TCAD (Technology Computer Aided Design). It retains the fundamental quantum transport model for the electrons but subsumes the description of the energy distribution of the local phonon sub-system statistics into a semi-classical Fourier heat equation that is sourced by the local heat dissipation from the electron system. It is shown that this self-consistent approach retains the salient features of the full-scale approach. For focus, we outline our electro-thermal simulations for a typical narrow Si nanowire gate all-around field-effect transistor. The self-consistent Born approximation is used to describe electron-phonon scattering as the source of heat dissipation to the lattice. We calculated the effect of the device self-heating on the current voltage characteristics. Our fast and simpler methodology closely reproduces the results of a more fundamental compute-intensive calculations in which the phonon system is treated on the same footing as the electron system. We computed the local power dissipation and “local lattice temperature” profiles. We compared the self-heating using hot electron heating and the Joule heating, i.e., assuming the electron system was in local equilibrium with the potential. Our simulations show that at low bias the source region of the device has a tendency to cool down for the case of the hot electron heating but not for the case of Joule heating. Our methodology opens the possibility of studying thermoelectricity at nano-scales in an accurate and computationally efficient way. At nano-scales, coherence and hot electrons play a major role. It was found that the overall behaviour of the electron system is dominated by the local density of states and the scattering rate. Electrons leaving the simulated drain region were found to be far from equilibrium

Isomorphism Theorems on Quasi Module

A quasimodel is an algebraic axiomatisation of the hyperspace structure based on a module. We initiated this structure in our paper [2]. It is a generalisation of the module structure in the sense that every module can be embedded into a quasi module and every quasi module contains a module. The structure a quasimodel is a conglomeration of a commutative semigroup with an external ring multiplication and a compatible partial order. In the entire structure partial order has an intrinsic effect and plays a key role in any development of the theory of quasi module. In the present paper we have discussed order-morphism which is a morphism like concept. Also with the help of the quotient structure of a quasi module by means of a suitable compatible congruence, we have proved order-isomorphism theorem

Gaining insights into the codon usage patterns of TP53 gene across eight mammalian species.

TP53 gene is known as the "guardian of the genome" as it plays a vital role in regulating cell cycle, cell proliferation, DNA damage repair, initiation of programmed cell death and suppressing tumor growth. Non uniform usage of synonymous codons for a specific amino acid during translation of protein known as codon usage bias (CUB) is a unique property of the genome and shows species specific deviation. Analysis of codon usage bias with compositional dynamics of coding sequences has contributed to the better understanding of the molecular mechanism and the evolution of a particular gene. In this study, the complete nucleotide coding sequences of TP53 gene from eight different mammalian species were used for CUB analysis. Our results showed that the codon usage patterns in TP53 gene across different mammalian species has been influenced by GC bias particularly GC3 and a moderate bias exists in the codon usage of TP53 gene. Moreover, we observed that nature has highly favored the most over represented codon CTG for leucine amino acid but selected against the ATA codon for isoleucine in TP53 gene across all mammalian species during the course of evolution

Codon Usage Bias Prefers AT Bases in Coding Sequences Among the Essential Genes of <i>Haemophilus influenzae</i>

The base composition at three different codon positions in relation to codon usagebias and gene expressivity was studied in a sample of twenty five essential genes from Haemophilus influenzae. ENC, CBI and Fop were used to quantify the variation in codon usage bias for the cds. CAI is used to estimate the level of gene expression of the cds selected in the present study. To find out the relationship between the extent of codon bias and nucleotide composition the values of A, T, G, C and GC they were compared with the A3, T3, G3, C3 and GC3 values, respectively. The results showed relatively weak codon usage bias among the coding sequences (cds) of Haemophilus influenzae. This in turn, implies that the essential genes prefer to use a set of restricted codons. However, the base compositional analysis of essential genes in Haemophilus influenzae revealed preference of AT to GC bases within their coding sequences and this preference might affect gene expression as indicated by the relatively high CAI values ofthe coding sequences

Codon Usage Bias Prefers AT Bases in Coding Sequences Among the Essential Genes of <i>Haemophilus influenzae</i>

The base composition at three different codon positions in relation to codon usagebias and gene expressivity was studied in a sample of twenty five essential genes from <i style='mso-bidi-font style:normal'>Haemophilus influenzae. </i>ENC, CBI and Fop were used to quantify the variation in codon usage bias for the cds. CAI is used to estimate the level of gene expression of the cds selected in the present study. To find out the relationship between the extent of codon bias and nucleotide composition the values of A, T, G, C and GC they were compared with the A3, T3, G3, C3 and GC3 values, respectively. The results showed relatively weak codon usage bias among the coding sequences (cds) of <i style='mso-bidi-font-style:normal'>Haemophilus influenzae</i>. This in turn, implies that the essential genes prefer to use a set of restricted codons. However, the base compositional analysis of essential genes in <i style='mso-bidi-font-style:normal'>Haemophilus influenzae</i> revealed preference of AT to GC bases within their coding sequences and this preference might affect gene expression as indicated by the relatively high CAI values ofthe coding sequences

Distribution of RCBS for <i>TP53</i> gene across eight mammalian species.

<p>Distribution of RCBS for <i>TP53</i> gene across eight mammalian species.</p

Overall relative synonymous codon usage patterns (RSCU) for <i>TP53</i> gene among eight mammalian species.

<p>^a mean values of RSCU based on the synonymous codon usage frequencies of <i>TP53</i> gene, N: Total number of preferred codons,</p><p>*RSCU>1.</p><p>Overall relative synonymous codon usage patterns (RSCU) for <i>TP53</i> gene among eight mammalian species.</p

Codon usage bias indices for <i>TP53</i> gene across mammalian species.

<p>RCBS-Relative codon usage bias, ENC-Effective number of codons, GC_3s-GC contents at third positions of codon, FOP-Frequency of optimal codons, RSCU-Relative synonymous codon usage.</p><p>Codon usage bias indices for <i>TP53</i> gene across mammalian species.</p

Phylogenetic analysis of the Kimura 2- parameter (K2P) distances of the selected coding sequences among <i>TP53</i> genes of different mammalian species.

<p>The percentage of replicate trees in which the associated taxa clustered together in the bootstrap test (1000 replicates) is shown next to the branches. The tree is drawn to scale, with branch lengths in the same units as those of the evolutionary distances used to infer the phylogenetic tree. The evolutionary distances were computed using the Kimura 2-parameter method and are in the units of the number of base substitutions per site. The analysis involved 8 cds sequences. All positions containing gaps and missing data were eliminated. There were a total of 1200 positions in the final dataset. Evolutionary analyses were performed in MEGA6.</p

Overall frequency of optimal and non optimal codon used in <i>TP53</i> genes among mammals.

<p>Red color coding represents optimal used codons with corresponding amino acid.</p