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Application of network identification by deconvolution method to the thermal analysis of the pump-probe transient thermoreflectance signal
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10.1063/1.3176463
/content/aip/journal/rsi/80/7/10.1063/1.3176463
http://aip.metastore.ingenta.com/content/aip/journal/rsi/80/7/10.1063/1.3176463

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of the RC one-port circuit of one layer (a) and the full structure (b).

Image of FIG. 2.
FIG. 2.

Schematic diagram of the sample structures with a finite size silicon substrate [case (a)] and a semi-infinite silicon substrate [case (b)].

Image of FIG. 3.
FIG. 3.

(a) Calculated 1 W normalized temperature transient rise over a time range of 660 ns with a time resolution of 10 ps after an application of a step power function to the top free surface of the two structures, with SiGe alloy (solid line) and Si/SiGe SL (dashed line), deposited on a finite size substrate. is assumed to be zero at the interface metal transducer/SC layer. (b) Calculated temperature decay over the same time range with the same time resolution after application of a delta power function of amplitude of to the top free surface of the same two structures.

Image of FIG. 4.
FIG. 4.

TCS of the two structures with finite thickness substrate for both step and delta functions excitations over a time range of 660 ns with 10 ps time resolution and starting at 10 ps. Log-lin representation (a) and log-log representation (b).

Image of FIG. 5.
FIG. 5.

Cumulative structure functions of the two structures with finite thickness substrate for both step and delta functions excitations over a time range of 660 ns with 10 ps time resolution and starting at 10 ps.

Image of FIG. 6.
FIG. 6.

Differential structure functions of the two structures with finite thickness substrate for both step and delta functions excitations over a time range of 660 ns with 10 ps time resolution and starting at 10 ps.

Image of FIG. 7.
FIG. 7.

TCS in the log-log representation of the structure with Si/SiGe SL layer on a finite size substrate for both step (a) and delta (b) functions excitations over different time ranges: 660 ns (solid line), 500 ns (solid-dashed line), 100 ns (dashed line), 50 ns (short-dashed line), and 13 ns (dotted line) with 10 ps time resolution and starting at 10 ps.

Image of FIG. 8.
FIG. 8.

Differential structure functions of the structure with Si/SiGe SL layer on a finite size substrate for both step function excitation (a) and delta function excitation (b) over a time range of 660 ns with 10 ps time resolution and starting at different times of 10 ps (solid line), 100 ps (solid-dashed line), and 500 ps (dashed line).

Image of FIG. 9.
FIG. 9.

Comparison between the analytically calculated input transient temperature rise after application of a step excitation (a), the integrated (b) and the raw (c) analytically calculated input transient temperature decay after application of a delta excitation, with the reconstructed new transient temperature rise [(a) and (b)] and decay (c) signal based on NID results for the studied structure with Si/SiGe SL layer on a finite size substrate over a time range of 660 ns with 10 ps time resolution and starting at different times of 10 ps (open circles), 100 ps (open squares), and 500 ps (open triangles). In each figure, represents the number of the RC one-ports used for the discretization of the corresponding TCS.

Image of FIG. 10.
FIG. 10.

Differential structure functions of the structure with Si/SiGe SL layer on a semi-infinite substrate for both step function excitation (a) and delta function excitation (b) over different time ranges: 500 ns (solid line), 100 ns (solid-dashed line), 50 ns (dashed line), and 13 ns (short-dashed line) with 10 ps time resolution and starting at 10 ps.

Image of FIG. 11.
FIG. 11.

TCS of the structure with Si/SiGe SL layer on both finite and semi-infinite substrates with and . A delta function excitation is applied over two time ranges, 500 ns (a) and 13 ns (b), with 10 ps time resolution and all starting at 10 ps.

Image of FIG. 12.
FIG. 12.

Cumulative structure functions of the structure with Si/SiGe SL layer on both finite and semi-infinite substrates with and . A delta function excitation is applied over two time ranges, 500 ns (a) and 13 ns (b), with 10 ps time resolution and all starting at 10 ps.

Image of FIG. 13.
FIG. 13.

Cumulative structure functions of the structure with Si/SiGe SL layer on both finite and semi-infinite substrates with [(a) and (b)] and [(c) and (d)] for raw and normalized delta function excitation signals over two time ranges, 500 ns [(a) and (c)] and 13 ns [(b) and (d)], with 10 ps time resolution and all starting at 10 ps. (e) Comparison between the cumulative structure functions of normalized signals for and .

Image of FIG. 14.
FIG. 14.

Cumulative structure functions of the structure with Si/SiGe SL layer on a semi-infinite substrate with for a delta function excitation over different time ranges, (solid line), (solid-dashed line), (dashed line), (short-dashed line), and (dotted line) with 1 ps time resolution and all starting at 1 ps. (a) 150 nm thick and 10 W/m/K thermal conductivity SL. (b) 150 nm thick and 15 W/m/K thermal conductivity SL. (c) 100 nm thick and 15 W/m/K thermal conductivity SL.

Image of FIG. 15.
FIG. 15.

(a) Temperature decays at the top free surface of the structure with an 80 nm thick Si/SiGe SL layer deposited on a semi-infinite silicon substrate and covered by a 30 nm thick Al film with (solid line), (solid-dashed line), and (dashed line) after excitation with a delta laser pulse function of energy of . Cumulative structure functions (b) and differential structure functions (c) corresponding to the temperature decays in (a).

Tables

Generic image for table
Table I.

Geometrical and thermal properties as well as the calculated thermal resistances and capacitances of the different layers in the structures under study [case (a)].

Generic image for table
Table II.

Extracted thermal resistances and capacitances based on NID results for the case of a finite size silicon substrate [case (a)].

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/content/aip/journal/rsi/80/7/10.1063/1.3176463
2009-07-20
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Application of network identification by deconvolution method to the thermal analysis of the pump-probe transient thermoreflectance signal
http://aip.metastore.ingenta.com/content/aip/journal/rsi/80/7/10.1063/1.3176463
10.1063/1.3176463
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