C. Cercignani, I.M. Gamba and C.L. Levermore, A High Field Approximation to a Boltzmann--Poisson System in Bounded Domains, Applied Math Letters, Vol (4), 111--118 (1997).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for m and more general stationary states can be easily obtained based on previous ideas. Realistic models include collisions, which usually determine a special class of stationary solutions (and the appropriate Lyapunov functional is then decreasing even for classical solutions) We refer to [37, 37, 6, 7, 17, 19] for more details on this subject. 7. Appendix: a convexity property of L functions. Let f be a nonnegative function in L ( Omega Gamma for some (not necessarily bounded) domain Omega , d 1. It is straightforward to check that oe(f) is also bounded in L 1( Omega Gamma if oe is a C ....

C. Cercignani, I.M. Gamba, and C.L. Levermore, A high field approximation to a Boltzmann -Poisson system in bounded domains, Applied Math Letters 4 (1997), pp. 111--118.

....for m and more general stationary states can be easily obtained using the previous ideas. Realistic models include collisions, which usually determine a special class of stationary solutions (and the appropriate Lyapunov functional is then decreasing even for classical solutions) We refer to [37, 37, 6, 7, 17, 19] for more details on this subject. 7. Appendix: a convexity property of L functions. Let f 0 be a nonnegative function in L ( Omega Gamma for some (not necessarily bounded) domain Omega , d 1. It is straightforward to check that oe(f 0 ) 2 L if oe is a C convex function on IR ....

C. Cercignani, I.M. Gamba, and C.L. Levermore, A high field approximation to a Boltzmann -Poisson system in bounded domains, Applied Math Letters 4 (1997), pp. 111--118.

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C. Cercignani, I.M. Gamba and C.L. Levermore, A High Field Approximation to a Boltzmann--Poisson System in Bounded Domains, Applied Math Letters, Vol (4), 111--118 (1997).

....Carlo Cercignani , Irene M. Gamba y , Joseph W. Jerome z , and Chi Wang Shu x Abstract A mesoscopic macroscopic model for self consistent charged transport under high field scaling conditions corresponding to drift collisions balance was derived by Cercignani, Gamba, and Levermore in [4]. The model was summarized in relationship to semiconductors in [2] In [3] a conceptual domain decomposition method was implemented, based upon use of the drift diffusion model in highly doped regions of the device, and use of the high field model in the channel, which represents a ....

....RI 02912. tel: 401) 863 2549, Fax: 401) 863 1355, email: shu cfm.brown.edu 1 1 Introduction In previous work [2] the authors introduced a conceptual domain decomposition approach, combining drift diffusion, kinetic, and high field regimes. The high field model had been introduced in [4]. The approach was implemented in preliminary form in [3] More precisely, the hydrodynamic model was used as a global calibrator (see also [9, 10] and used to define internal boundary conditions, separating drift diffusion from high field regions. In particular, it was found that this ....

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C. Cercignani, I. M. Gamba and C. D. Levermore. High field approximations to BoltzmannPoisson system boundary conditions in a semiconductor. Appl. Math. Lett., 10:111--117, 1997.

....means that the collisions continue to be dominant but the force field is higher and now the drift speed is of the order of the thermal speed. In this sense this scaling appears for higher potential drops than the LFS. The following equations are the corresponding ones to the DCBS as presented in [9, 10] for the lowest moments. The corresponding Augmented Drift di#usion Poisson (ADDP) system in its dimensionalized form reads # t # x (j hyp j vis ) 0 (2.13) j hyp = #E # e # o #( #E #) 2.14) j vis = # [#(# o 2 2 E 2 ) x #E(#E) x (2.15) E = # x , and # o # ....

C. Cercignani, I.M. Gamba and C.L. Levermore, A high field approximation to a Boltzmann--Poisson system in bounded domains, Applied Math. Letters, 4, 1997, pp.111--118.

....therein) Some recent numerical and analytical work on drift diffusion equations has been done by Golse and Klar[GK] and Klar [Kl] however they use different boundary conditions from those proposed here. Some of the results worked out here have been presented in a short communication (see [CGL]. For simplicity sake, we shall only consider electrons, since it is clear what modifications are needed when holes are to be taken into account. The semiclassical Boltzmann equation for the electron gas in a semiconductor, in the parabolic band approximation, i.e. one carrier transport model) ....

C. Cercignani, I.M. Gamba and C.L. Levermore, A High Field Approximation to a Boltzmann--Poisson System in Bounded Domains, Applied Math Letters, Vol (4), 111--118 (1997).

....collisions, electron electron short range interactions and so on. We refer to [26] for a complete list of scattering kernels. In the low density approximation and taking into account only collisions with background impurities, one can approximate Q(f) by a linear relaxation time operator [10, 11, 14, 20] given by Q(f) 1 (M (f) f) 1.4) where = x) or = E(t; x) constant in v, is an approximation for the relaxation time (x; v) M is the absolute Maxwellian at the temperature of the semiconductor given by M = 2 ) N=2 exp jvj 2 2 ; where = x) is the lattice ....

....semiconductor given by M = 2 ) N=2 exp jvj 2 2 ; where = x) is the lattice temperature ( kB T m with the Boltzmann constant kB , and T is the lattice temperature in Kelvin) A drift collision balance scaling for the system (1.1) 1.2) with Q given by (1. 4) was studied in [10, 11]. In this paper we are going to consider another possibility to model the lattice collision operator Q(f ) The hydrodynamical semiconductor models describe the 2 motion of the electrons as a uid, while kinetic Boltzmann type semiconductor equations treat the scattering process in a very ....

[Article contains additional citation context not shown here]

C. Cercignani, I.M. Gamba, C.L. Levermore, A High Field Approximation to a Boltzmann{Poisson System in Bounded Domains, Applied Math Letters, 4, 111-118, 1997.

....means that the collisions continue to be dominant but the force field is higher and now the drift speed is of the order of the thermal speed. In this sense this scaling appears for higher potential drops than the LFS. The following equations are the corresponding ones to the DCBS as presented in [9, 10] for the lowest moments. The corresponding Augmented Drift diffusion Poisson (ADDP) system in its dimensionalized form reads ae t x (j hyp j vis ) 0 (2.13) j hyp = GammaaeE e o ae( GammaaeE ) 2.14) j vis = Gamma [ae( Theta o 2 2 E 2 ) x E(aeE) x (2.15) E ....

C. Cercignani, I.M. Gamba and C.L. Levermore, A high field approximation to a Boltzmann--Poisson system in bounded domains, Applied Math. Letters, 4, 1997, pp.111--118.

....collisions, electron electron short range interactions and so on. We refer to [26] for a complete list of scattering kernels. In the low density approximation and taking into account only collisions with background impurities, one can approximate Q(f) by a linear relaxation time operator [10, 11, 14, 20] given by Q(f) 1 (M Theta ae(f ) Gamma f) 1.4) where = x) or = E(t; x) constant in v, is an approximation for the relaxation time (x; v) M Theta is the absolute Maxwellian at the temperature of the semiconductor given by M Theta = 2 Theta) GammaN=2 exp Gamma jvj ....

.... GammaN=2 exp Gamma jvj 2 2 Theta ; where Theta = Theta(x) is the lattice temperature ( Theta = kB T m with the Boltzmann constant kB , and T is the lattice temperature in Kelvin) A drift collision balance scaling for the system (1.1) 1.2) with Q given by (1. 4) was studied in [10, 11]. In this paper we are going to consider another possibility to model the lattice collision operator Q(f ) The hydrodynamical semiconductor models describe the motion of the electrons as a fluid, while kinetic Boltzmann type semiconductor equations treat the scattering process in a very ....

[Article contains additional citation context not shown here]

C. Cercignani, I.M. Gamba, C.D. Levermore, A High field Approximation to a Boltzmann-Poisson System in Bounded Domains, preprint 1998.

....collisions, electron electron short range interactions and so on. We refer to [26] for a complete list of scattering kernels. In the low density approximation and taking into account only collisions with background impurities, one can approximate Q(f) by a linear relaxation time operator [10, 11, 14, 20] given by Q(f) 1 (M Theta ae(f ) Gamma f) 1.4) where = x) or = E(t; x) constant in v, is an approximation for the relaxation time (x; v) M Theta is the absolute Maxwellian at the temperature of the semiconductor given by M Theta = 2 Theta) GammaN=2 exp Gamma jvj ....

.... GammaN=2 exp Gamma jvj 2 2 Theta ; where Theta = Theta(x) is the lattice temperature ( Theta = kB T m with the Boltzmann constant kB , and T is the lattice temperature in Kelvin) A drift collision balance scaling for the system (1.1) 1.2) with Q given by (1. 4) was studied in [10, 11]. In this paper we are going to consider another possibility to model the lattice collision operator Q(f ) The hydrodynamical semiconductor models describe the motion of the electrons as a fluid, while kinetic Boltzmann type semiconductor equations treat the scattering process in a very ....

[Article contains additional citation context not shown here]

C. Cercignani, I.M. Gamba, C.L. Levermore, A High Field Approximation to a Boltzmann--Poisson System in Bounded Domains, Applied Math Letters, 4, 111--118, 1997.

....macroscopic states. Reference scalings are defined by the background doping levels and distinct, experimentally measured mobility expressions, as well as locally determined ranges for the electric fields. The mobilities reflect a coarse substitute for reference scales of scattering mechanisms. See [9] for elaboration. The high field approximation is a formally derived modification of the augmented drift diffusion model originally introduced by Thornber some fifteen years ago [25] We are able to compare our approach with the earlier kinetic approach of Baranger and Wilkins [5] and the ....

.... the work initiated by [14] and [22] on strong forcing scaling for external fields, where the dominant term in the scaled BTE equation (1) is given by the balance of the forcedrift e m E(x; t)r v F and the collision terms, the following 3 scale dimensionless formulation has been formulated in [9] in Euclidean dimensions: jF t v Delta r x F j r x OE Delta r v F = 1 f F M Gamma Fg ; 4OE = fl 1 j F GammaN d (x) 2) where = 1=2 L is the scaled mean free path for a length scale L and relaxation time , and is the reference scale of the ....

[Article contains additional citation context not shown here]

C. Cercignani, I. M. Gamba and C. D. Levermore. High field approximations to BoltzmannPoisson system boundary conditions in a semiconductor. Appl. Math. Lett., to appear.

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