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Effect of Variable Thermal Conductivity during the Photothermal Diffusion Process of Semiconductor Medium

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Abstract

In this problem, we study the effect of variable thermal conductivity, which depend on temperature in the context of Photothermal diffusion (PTD). The PTD process is applied with thermoelasticity theory in chemical action. The model introduced describes the interaction between elastic-thermal-plasma waves, which based on the material properties of semiconductor elastic medium. The Laplace transform is used to solve the governing equations in one dimension of a thin circular plate. Some new constant will be appearing during the theoretical discussion. The mechanical forces and thermal loads are applied on the free surface of semiconductor to obtain the physical fields. The complete solutions in time domain are observed by using a numerical approximation method. The physical fields with some comparsions are presented analytically and graphically.

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Abbreviations

λ,μ :

Counterparts of Lame’s parameters,

N 0 :

Equilibrium carrier concentration at temperature T

δ n :

The difference of deformation potential of conduction and valence band, 𝜃 = T − T0 Thermodynamical temperature,

T :

Absolute temperature,

T 0 :

Temperature of the medium in its natural state assumed to be |T−T0T0| < 1

β 1 = (3λ + 2μ)α T :

The volume thermal expansion

σ ij :

Components of the stress tensor,

ρ :

Density of the medium,

α T :

The coefficient of linear thermal expansion,

e:

Cubical dilatation,

τ d :

The diffusion relaxation time,

C e :

Specific heat at constant strain of the solid plate,

ρ C e K 0 = 1 k :

The thermal viscosity,

D E :

The carrier diffusion coefficient,

τ :

The photogenerated carrier lifetime,

E g :

The energy gap of the semiconductor,

\(\kappa =\frac {\partial N_{0}} {\partial T}\frac {T}{\tau }\) :

The thermal activation coupling parameter,

c :

Measure the effect of thermoelastic diffusion,

D c :

The diffusion coefficient,

d n :

The coefficient of electronic deformation.

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  1. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Kh. Lotfy

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Lotfy, K. Effect of Variable Thermal Conductivity during the Photothermal Diffusion Process of Semiconductor Medium. Silicon 11, 1863–1873 (2019). https://doi.org/10.1007/s12633-018-0005-z

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