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Thermoelectrical model for vertical cavity surface emitting lasers and arrays
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Image of FIG. 1.
FIG. 1.

Schematics of (a) etched-mesa VCSEL and (b) VCSEL array.

Image of FIG. 2.
FIG. 2.

Etched-mesa VCSEL and VCSEL array: schematics of electrical current flow (a) and of heat flow (b). is the thickness of the bottom DBR and is the effective radius of the device’s active region; arrows show the lines of current and heat flow, respectively.

Image of FIG. 3.
FIG. 3.

Correction factor for the spreading resistance of a DBR on a perfectly conducting substrate vs relative DBR thickness . Solid line: Obtained from Eq. (3) with ; filled circles: Calculated in Ref. 21 with at , (see Ref. 21 for parameters , , and ).

Image of FIG. 4.
FIG. 4.

Thermal resistance vs array size parameter : measured (squares), calculated from Eq. (3) (solid line), and calculated from an homogeneous semi-infinite substrate model (dashed line). Parameters are , , and .

Image of FIG. 5.
FIG. 5.

curves (left axis) and temperature rise (right axis) of VCSEL arrays of different sizes: measured (symbols) and calculated (curves).

Image of FIG. 6.
FIG. 6.

Active region, top and bottom DBR voltage drops in and arrays in the presence of self-heating (w.SH), as well as bottom DBR voltage drop calculated without the self-heating impact (w.o.SH).

Image of FIG. 7.
FIG. 7.

Slope of curves vs array size parameter : measured at temperature rise of (black squares) and (open squares); calculated from Eq. (11) with (solid line) and (dash line).


Generic image for table
Table I.

Parameters of the model of VCSEL arrays emitting at wavelength.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Thermoelectrical model for vertical cavity surface emitting lasers and arrays