Radiation- and convection-driven transient heat transfer during sublimation growth of silicon carbide single crystals

Klein, Olaf; Philip, Peter; Sprekels, Jürgen; Wilmanski, Krzysztof

doi:10.1016/s0022-0248(00)01009-5

Cited by 32 publications

(26 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the different alloys of steel are distributed smoothly in the domain, then a = a(x, y) should depend in a sufficiently smooth way on (x, y). Similarly, the heat conductivity depends on (x, y) in the growth of silicon carbide bulk single crystals, see Klein et al [23].…”

mentioning

confidence: 99%

First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations

Casas¹,

Tröltzsch²

2009

SIAM J. Control Optim.

View full text Add to dashboard Cite

Abstract. A class of optimal control problems for quasilinear elliptic equations is considered, where the coefficients of the elliptic differential operator depend on the state function. First-and second-order optimality conditions are discussed for an associated control-constrained optimal control problem. Main emphasis is laid on second-order sufficient optimality conditions. To this aim, the regularity of the solutions to the state equation and its linearization is studied in detail and the Pontryagin maximum principle is derived. One of the main difficulties is the non-monotone character of the state equation.

show abstract

mentioning

confidence: 99%

First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations

Casas¹,

Tröltzsch²

2009

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…Furthermore, it is assumed that the gas phase is made up solely of argon, which is a reasonable assumption for simulations of the temperature distribution [12,Section 5].…”

Section: Modeling and Numerical Methodsmentioning

confidence: 99%

“…The method used is described in Ref. [12,Section 4]. The discrete scheme was implemented as part of our software WIAS-HiTNIHS which is based on the program package pdelib [15].…”

Section: Article In Pressmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of temperature fields during the sublimation growth of SiC single crystals, using WIAS-HiTNIHS

Geiser

Klein

Philip

2007

Journal of Crystal Growth

Self Cite

View full text Add to dashboard Cite

We present numerical computations of the temperature fields in axisymmetric growth apparatus for sublimation growth of silicon carbide (SiC) bulk single crystals by physical vapor transport (PVT) (modified Lely method). The results are computed using our software WIAS-HiTNIHS, the WIAS High Temperature Numerical Induction Heating Simulator; pronunciation: $hit-nice, by solving the energy balance in the entire growth apparatus, taking into account the heat conduction in the solid parts as well as in gas cavities, and also accounting for the radiative heat transfer between the surfaces of the gas cavities. The insulation in a PVT growth apparatus usually consists of graphite felt, where the fibers are aligned in one particular direction, resulting in an anisotropic thermal conductivity. We show that neglecting this anisotropy can overestimate the SiC crystal's temperature by 70 K or underestimate the required heating power by 800 W. r

show abstract

“…The material data used for the following numerical experiments are precisely the data provided in the appendices of [11] and [12], respectively.…”

Section: Theorem 1 Assume (I)-(iv)mentioning

confidence: 99%

Modeling and simulation of sublimation growth of SiC bulk single crystals

Klein

Philip

Sprekels

2004

Interfaces Free Bound.

Self Cite

View full text Add to dashboard Cite

We present a transient mathematical model for the sublimation growth of silicon carbide (SiC) single crystals by the physical vapor transport (PVT) method. The model of the gas phase consists of balance equations for mass, momentum, and energy, as well as reaction-diffusion equations. Due to physical and chemical reactions, the gas phase is encompassed by free boundaries. Nonlinear heat transport equations are considered in the various solid components of the growth system. Discontinuous and nonlocal interface conditions are formulated to account for temperature steps between gas and solid as well as for diffuse-gray radiative heat transfer between cavity surfaces. An axisymmetric induction heating model is devised using a magnetic scalar potential. For a nonlinear evolution problem arising from the model, a finite volume scheme is stated, followed by a discrete existence and uniqueness result. We conclude by presenting and analyzing results of transient numerical experiments relevant to the physical growth process.

show abstract

Radiation- and convection-driven transient heat transfer during sublimation growth of silicon carbide single crystals

Cited by 32 publications

References 30 publications

First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations

First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations

Numerical simulation of temperature fields during the sublimation growth of SiC single crystals, using WIAS-HiTNIHS

Modeling and simulation of sublimation growth of SiC bulk single crystals

Contact Info

Product

Resources

About