Degree of Polarization (DoP)

In semiconductors, the polarisation of luminescence arises from the electric transition dipole moment of the electronic transition at its source, which itself results from the anisotropy of the material. The degree of polarization (DOP) of luminescence is defined as the normalized difference between the intensities of the emitted light polarized in two orthogonal directions, x and y, within the plane of the sample's surface.

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DOP= Ix-IyIx+Iy

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The DOP is a convenient way of highlighting variations in emitted light polarization. One particularly interesting use of DOP maps is that to a first-degree approximation, it is proportional to the strain anisotropy within the xy plane [1].

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DOP= -C*x-y

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For strain measurements, the rotated degree of polarization (ROP) is defined similarly using the intensities of the emitted light polarized in the x' and y' directions rotated by 45^o from x and y. The ROP is proportional to the shear strain within the xy plane.

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ROP= Ix'-Iy'Ix'+Iy'=C'*xy

The emission intensities polarised in the x and y directions can be measured simultaneously using a polarizing beam splitter and two detectors, such as in Figure 2. Another possibility is to measure them sequentially using a rotating polarizer alternating between 0 and 90 degrees. With the setups described above, the sample is usually positioned so that x and y are parallel to crystallographic directions. A second, more common, alternative is to measure the emission intensity in all directions of polarization using a fast-rotating beam spitter, optionally together with a modulated excitation [1].

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In the following example, DOP CL is used to measure the strain within a GaAs sample covered by a Si₃N₄ stripe (Figure 1a) [2]. In the CL intensity image (Figure 1b), electron and photon absorption attenuate the luminescence from under the Si₃N₄ stripe. DOP CL shows that the long stripe induces strain anisotropy (Figure 1c) but no shear strain (Figure 1d) in the underlying GaAs layer.

Such DOP CL measurements can be used to control the strain level within the quantum well of semiconductor laser diodes, within the gate of power transistors or in waveguides.