^{1,a)}and Christof P. Dietrich

^{1}

### Abstract

The photoluminescence from semiconductor alloys is inhomogeneously broadened due to alloy disorder. We present a model to explain the so-called “S-shape” temperature dependence of peak position, taking into account recombination of free excitons and excitons bound to impurities. We find the following effects to contribute with increasing temperature: exciton localization on impurities at low temperatures, exciton transfer between impurities, excitonionization from impurities, transfer of excitons between potential minima in the disorder potential, and shrinkage of band gap. We extend the common theory of ionization of excitons from impurities to take into account impurity ionization. We find this effect essential for our lineshape theory. The lineshape theory describes quantitatively the temperature dependent peak position in alloys.

We are grateful to H. Hochmuth for growth of the (Mg,Zn)O alloy samples and J. Lenzner for determination of the Mg content. This work has been supported by the Deutsche Forschungsgemeinschaft in the framework of SFB 762 (Functionality of Oxidic Interfaces) and the European Social Fund (ESF).

I. INTRODUCTION

II. EXCITON LOCALIZATION

A. Localization in the alloy disorder potential

B. Localization on shallow defects

III. EXPERIMENTAL

IV. LINESHAPE THEORY

A. Energy position

B. Spectral weight

C. Spectral width

V. INTERPRETATION OF ALLOY LUMINESCENCE

A. Exciton localization on impurities

B. Exciton transfer between impurities

C. Excitonionization from impurities

D. Transfer of excitons between potential minima

E. Discussion

VI. SUMMARY AND OUTLOOK

## Figures

Temperature dependence of the energy position of photoluminescence recombination peaks in alloys. The energy position is given relative to the maximum position of the low temperature recombination spectrum. For (a) and (b), recombination from donor-bound (down triangles) and free (up triangles) excitons can be observed spectrally separated. The solid and dashed lines are fitted with Eq. (9) using the same parameters. For (c), only a single recombination peak is observed. Solid line is guide to the eyes.

Temperature dependence of the energy position of photoluminescence recombination peaks in alloys. The energy position is given relative to the maximum position of the low temperature recombination spectrum. For (a) and (b), recombination from donor-bound (down triangles) and free (up triangles) excitons can be observed spectrally separated. The solid and dashed lines are fitted with Eq. (9) using the same parameters. For (c), only a single recombination peak is observed. Solid line is guide to the eyes.

Temperature dependence of the energy position of photoluminescence recombination peaks in alloys. The energy position is given relative to the maximum position of the low temperature recombination spectrum. Data for [(a) and (b)] taken from Ref. 35 for (c) from Ref. 36. Lines are guides to the eyes.

Temperature dependence of the energy position of photoluminescence recombination peaks in alloys. The energy position is given relative to the maximum position of the low temperature recombination spectrum. Data for [(a) and (b)] taken from Ref. 35 for (c) from Ref. 36. Lines are guides to the eyes.

Photoluminescence spectra (, scaled) of three alloys with , , and as labeled. The energy positions of and peaks are marked. The dashed line represents the peak energy of the line in ZnO [recombination channel ]. We note that for between and , there is a small shoulder due to [excitons bound to Zn interstitials acting as donors (Ref. 65)].

Photoluminescence spectra (, scaled) of three alloys with , , and as labeled. The energy positions of and peaks are marked. The dashed line represents the peak energy of the line in ZnO [recombination channel ]. We note that for between and , there is a small shoulder due to [excitons bound to Zn interstitials acting as donors (Ref. 65)].

Intensity of (down triangles) and (up triangles) recombination from a alloy. The solid line for is fitted with Eq. (21) using and . The solid line for is fitted with Eq. (22). The dashed line is fitted with Eq. (18) and . In (a) a linear -scale is used, and in (b) a logarithmic scale is used.

Intensity of (down triangles) and (up triangles) recombination from a alloy. The solid line for is fitted with Eq. (21) using and . The solid line for is fitted with Eq. (22). The dashed line is fitted with Eq. (18) and . In (a) a linear -scale is used, and in (b) a logarithmic scale is used.

Intensity of (down triangles) and (up triangles) recombination from a alloy. The solid line for is fitted with Eq. (21) using and . The dashed line is fitted with Eq. (18) and . The circle denotes the unphysical intersection of the fit using Eq. (18) with the free exciton intensity. The dash-dotted line has a slope of . Note the logarithmic -scale.

Intensity of (down triangles) and (up triangles) recombination from a alloy. The solid line for is fitted with Eq. (21) using and . The dashed line is fitted with Eq. (18) and . The circle denotes the unphysical intersection of the fit using Eq. (18) with the free exciton intensity. The dash-dotted line has a slope of . Note the logarithmic -scale.

Spectral width of (down triangles) and (up triangles) recombination from a alloy. The solid lines are fitted with Eq. (24) using the same phonon scattering parameters and , .

Spectral width of (down triangles) and (up triangles) recombination from a alloy. The solid lines are fitted with Eq. (24) using the same phonon scattering parameters and , .

Schematic representation of exciton recombination channels (dashed line arrows) and scattering processes (solid line arrows) in a semiconductor alloy. The wavy solid line represents the spatially varying exciton energy , and the short thick lines localized donor-bound exciton levels , shifted by from the local free exciton energy. On the right, the energy distributions for free and donor-bound excitons are sketched. (a) Recombination of free exciton, (b) recombination of donor-bound exciton, (c) capture of free exciton onto a donor, (d) transfer of exciton from donor to free exciton landscape (and subsequent capture (c) onto other donor), (e) transfer of exciton between donors, (f) ionization of exciton from donor, and (g) transfer of exciton within free exciton landscape.

Schematic representation of exciton recombination channels (dashed line arrows) and scattering processes (solid line arrows) in a semiconductor alloy. The wavy solid line represents the spatially varying exciton energy , and the short thick lines localized donor-bound exciton levels , shifted by from the local free exciton energy. On the right, the energy distributions for free and donor-bound excitons are sketched. (a) Recombination of free exciton, (b) recombination of donor-bound exciton, (c) capture of free exciton onto a donor, (d) transfer of exciton from donor to free exciton landscape (and subsequent capture (c) onto other donor), (e) transfer of exciton between donors, (f) ionization of exciton from donor, and (g) transfer of exciton within free exciton landscape.

(a) Temperature dependence of the energy position [squares, same data as in Fig. 1(c)] of the photoluminescence recombination peak in alloy. The energy position is given relative to the maximum position of the low temperature recombination spectrum. Thin solid lines are [Eqs. (7) and (8)], dashed lines including thermalization [Eqs. (10) and (11)]. The dash-dotted line represents . The thick solid line is lineshape fit to the peak position. (b) Intensity of recombination. The solid line is fitted with Eq. (21) for the and Eq. (22) for the component, i.e., of the lineshape fit. The dashed lines show these contributions individually. (c) Spectral width of recombination. The dashed lines are the individual widths of the and of the peak as labeled. The solid line is total width of lineshape fit. The dash-dotted line is the peak separation of and .

(a) Temperature dependence of the energy position [squares, same data as in Fig. 1(c)] of the photoluminescence recombination peak in alloy. The energy position is given relative to the maximum position of the low temperature recombination spectrum. Thin solid lines are [Eqs. (7) and (8)], dashed lines including thermalization [Eqs. (10) and (11)]. The dash-dotted line represents . The thick solid line is lineshape fit to the peak position. (b) Intensity of recombination. The solid line is fitted with Eq. (21) for the and Eq. (22) for the component, i.e., of the lineshape fit. The dashed lines show these contributions individually. (c) Spectral width of recombination. The dashed lines are the individual widths of the and of the peak as labeled. The solid line is total width of lineshape fit. The dash-dotted line is the peak separation of and .

Intensity of recombination from a alloy. The solid line is lineshape fit with Eq. (21) for the and Eq. (22) for the component. The dashed lines show these contributions individually. Note the logarithmic -scale.

Intensity of recombination from a alloy. The solid line is lineshape fit with Eq. (21) for the and Eq. (22) for the component. The dashed lines show these contributions individually. Note the logarithmic -scale.

Exciton localization energy (left scale) (squares) and inhomogeneous broadening of at low temperature (right scale), , (circles) for ZnO, and various alloys. The dashed line is . The solid line is theory of broadening for a RA according to Eq. (1). The dash-dotted line is theory with alloy clustering (25) assuming clusters .

Exciton localization energy (left scale) (squares) and inhomogeneous broadening of at low temperature (right scale), , (circles) for ZnO, and various alloys. The dashed line is . The solid line is theory of broadening for a RA according to Eq. (1). The dash-dotted line is theory with alloy clustering (25) assuming clusters .

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