^{1,a)}, Marc Rüdiger

^{1}, Wilhelm Warta

^{1}and Stefan W. Glunz

^{1}

### Abstract

Temperature-dependent lifetime spectroscopy allows for the determination of defect parameters (like ratio of the carrier capture cross sections and energy level) of pointlike defects in silicon. This necessitates reliable measurements of the low-level injection excess carrier lifetime. Photoluminescence-based measurement techniques have been shown to be ideal for this kind of measurements at room temperature, being immune to several measurement artifacts such as minority carrier trapping or depletion region modulation. In this article it will be shown how the effect of photon reabsorption influences the temperature-dependentphotoluminescencemeasurements and how this can be accounted for using a theoretical model based on the generalized Planck equation. An intentionally titanium-contaminated silicon sample is investigated by means of temperature-dependentphotoluminescence and injection-dependent photoconductance lifetime spectroscopy.Defect parameters of two independent recombination centers will be presented, which titanium introduces into the silicon band gap. One defect level at agrees very well with a level found via deep-level transient spectroscopymeasurements while another level at could be measured for the first time using the advanced lifetime spectroscopic approach presented here.

The authors thank T. Trupke and R. A. Bardos for providing the original photoluminescence measurement setup and for fruitful discussions. Also P. Würfel is gratefully acknowledged for helpful discussions. T. Roth thanks the German Federal Environmental Foundation (Deutsche Bundesstiftung Umwelt) and M. Rüdiger thanks the Evangelisches Studienwerk e.V. Villigst for their scholarships.

I. INTRODUCTION

II. PHOTOLUMINESCENCE THEORY

III. PHOTON REABSORPTION

IV. EXPERIMENTAL SETUP AND SAMPLE PREPARATION

V. MEASUREMENT RESULTS

VI. IN-DEPTH ANALYSIS

VII. CONCLUSION

### Key Topics

- Photons
- 21.0
- Photoluminescence
- 20.0
- Temperature measurement
- 16.0
- Carrier lifetimes
- 15.0
- Silicon
- 15.0

## Figures

Electron hole pairs, which are generated using an external light source, recombine radiatively, hence emitting photoluminescence light. Due to photon reabsorption the intensity and the spectrum changes the longer the optical path is within the sample.

Electron hole pairs, which are generated using an external light source, recombine radiatively, hence emitting photoluminescence light. Due to photon reabsorption the intensity and the spectrum changes the longer the optical path is within the sample.

Emitted photoluminescence spectra of a silicon sample at a temperature of 195 K. The spectra were simulated using the generalized Planck equation. Shown are the spectra that are emitted from a planar wafer surface for varying optical path lengths within the silicon sample. Nearly no differences are visible for the different path lengths.

Emitted photoluminescence spectra of a silicon sample at a temperature of 195 K. The spectra were simulated using the generalized Planck equation. Shown are the spectra that are emitted from a planar wafer surface for varying optical path lengths within the silicon sample. Nearly no differences are visible for the different path lengths.

Emitted photoluminescence spectra of a silicon sample at a temperature of 415 K. The spectra were simulated using the generalized Planck equation. Shown are the spectra that are emitted from a planar wafer surface for varying optical path lengths within the silicon sample. The overall shape of the spectra is broadened in the lower wavelength range due to multiphonon processes. The spectrum (and subsequently also the detectable intensity) changes significantly due to photon reabsorption, dependent on the path length of the photons within the sample.

Emitted photoluminescence spectra of a silicon sample at a temperature of 415 K. The spectra were simulated using the generalized Planck equation. Shown are the spectra that are emitted from a planar wafer surface for varying optical path lengths within the silicon sample. The overall shape of the spectra is broadened in the lower wavelength range due to multiphonon processes. The spectrum (and subsequently also the detectable intensity) changes significantly due to photon reabsorption, dependent on the path length of the photons within the sample.

Schematic of the temperature-dependent photoluminescence lifetime measurement setup. The LED light source illuminates the sample from the front and generates excess carriers within the sample. Some of these carriers recombine radiatively, hence emitting photoluminescence photons. These photons are detected from the rear of the sample using an appropriate photodetector. The sample is mounted within a liquid nitrogen cooled cryostat in order to access temperatures from 77 to 590 K. The generation rate is monitored independently using an external monitor cell.

Schematic of the temperature-dependent photoluminescence lifetime measurement setup. The LED light source illuminates the sample from the front and generates excess carriers within the sample. Some of these carriers recombine radiatively, hence emitting photoluminescence photons. These photons are detected from the rear of the sample using an appropriate photodetector. The sample is mounted within a liquid nitrogen cooled cryostat in order to access temperatures from 77 to 590 K. The generation rate is monitored independently using an external monitor cell.

Calculated temperature- and carrier lifetime-dependent correction factors for the thick titanium-contaminated silicon sample investigated here. For the calculations, the generalized Planck equation was used.

Calculated temperature- and carrier lifetime-dependent correction factors for the thick titanium-contaminated silicon sample investigated here. For the calculations, the generalized Planck equation was used.

Measured temperature-dependent LLI lifetime of the titanium-contaminated silicon sample. The data have been measured using the improved photoluminescence setup with the integrated cryostat. The triangles represent the original measurement data while the circles represent the data, which are corrected for the temperature- and lifetime-dependent photon reabsorption within the silicon. The lines represent the modeled data that have been obtained using a least square fit of a SRH-model featuring two independent defect levels.

Measured temperature-dependent LLI lifetime of the titanium-contaminated silicon sample. The data have been measured using the improved photoluminescence setup with the integrated cryostat. The triangles represent the original measurement data while the circles represent the data, which are corrected for the temperature- and lifetime-dependent photon reabsorption within the silicon. The lines represent the modeled data that have been obtained using a least square fit of a SRH-model featuring two independent defect levels.

Measured injection-dependent excess carrier lifetimes of the titanium-contaminated silicon sample. The data have been acquired using a standard QSSPC. Trapping influenced lifetimes have been measured below an injection density of approximately (blue triangles), which have been rejected for subsequent modeling. The lines represent the modeled data that have been obtained using a least square fit of a SRH model featuring two independent defect levels.

Measured injection-dependent excess carrier lifetimes of the titanium-contaminated silicon sample. The data have been acquired using a standard QSSPC. Trapping influenced lifetimes have been measured below an injection density of approximately (blue triangles), which have been rejected for subsequent modeling. The lines represent the modeled data that have been obtained using a least square fit of a SRH model featuring two independent defect levels.

DPSS analysis for the deep defect level. The energy depth and symmetry factor for the shallow level were set to fixed values for the analysis. A least square fit was carried out for the temperature-dependent and injection-dependent measurement data for a fixed but gradually varied defect energy depth , which results in corresponding values for the factor and the least square fit error . The results for the temperature-dependent data are depicted as solid lines while the results for the injection-dependent data are depicted as dashed lines. From the combination of both fits, the parameters for the deep defect level can be clearly identified as and .

DPSS analysis for the deep defect level. The energy depth and symmetry factor for the shallow level were set to fixed values for the analysis. A least square fit was carried out for the temperature-dependent and injection-dependent measurement data for a fixed but gradually varied defect energy depth , which results in corresponding values for the factor and the least square fit error . The results for the temperature-dependent data are depicted as solid lines while the results for the injection-dependent data are depicted as dashed lines. From the combination of both fits, the parameters for the deep defect level can be clearly identified as and .

DPSS analysis for the shallower defect level. The energy depth and symmetry factor for the deep level were set to fixed values for the analysis. A least square fit was carried out for the temperature-dependent and injection-dependent measurement data for a fixed but gradually varied defect energy depth , which results in corresponding values for the factor and the least square fit error . The results for the temperature-dependent data are depicted as solid lines while the results for the injection-dependent data are depicted as dashed lines. From the combination of both fits, the parameters for the deep defect level can be clearly identified as and .

DPSS analysis for the shallower defect level. The energy depth and symmetry factor for the deep level were set to fixed values for the analysis. A least square fit was carried out for the temperature-dependent and injection-dependent measurement data for a fixed but gradually varied defect energy depth , which results in corresponding values for the factor and the least square fit error . The results for the temperature-dependent data are depicted as solid lines while the results for the injection-dependent data are depicted as dashed lines. From the combination of both fits, the parameters for the deep defect level can be clearly identified as and .

## Tables

Reported energy levels for titanium in silicon. The data have been evaluated by means of DLTS or LS. While the DLTS technique is capable of measuring the majority carrier capture cross section, the LS techniques can determine the ratio of the carrier cross sections, known as symmetry factor .

Reported energy levels for titanium in silicon. The data have been evaluated by means of DLTS or LS. While the DLTS technique is capable of measuring the majority carrier capture cross section, the LS techniques can determine the ratio of the carrier cross sections, known as symmetry factor .

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