METHODS AND SYSTEMS FOR PERFORMING

PHOTOLUMINESCENCE MEASUREMENTS WITH REDUCED

PHOTON REABSORPTION EFFECTS

5 Technical Field

The present invention relates generally to photoluminescence measurements and more particularly to photoluminescence minority carrier lifetime measurements performed on indirect bandgap semiconductor samples.

io Related Applications

The present application claims priority from Australian Provisional Patent Application No. 2006905288, which was filed on 25 September 2006. The entire contents of Australian Provisional Patent Application No. 2006905288 are incorporated herein by reference.

I ₅

Background

The effective minority carrier lifetime T is a significant characteristic quantity in indirect bandgap semiconductor materials and is often dominated by impurities in the material. Minority carriers generated in the material recombine, on average, at the end

20 of their lifetime T. Large minority carrier lifetimes are highly desirable in indirect bandgap semiconductor devices such as silicon solar cells and other photovoltaic devices.

In photoluminescence lifetime measurements, the effective minority carrier lifetime T may be determined by simultaneous measurement of the generation rate

2 ₅ G(t) and the spatially averaged excess carrier concentration δn(t) within the indirect bandgap semiconductor sample, according to the formula:

An(t)

T = dt

which, under quasi steady state (QSS) conditions, simplifies to:

τ = δn / G(t)

Determination of the minority carrier lifetime T thus requires determination of the generation rate G(t), which is a function of the incident light intensity, and of the spatially averaged excess carrier concentration δn(t), which may be determined from the measured photoluminescence signal. Lifetime measurements are generally performed at various light intensity levels to determine how the effective minority carrier lifetime T varies with average excess carrier concentration δn. The incident light intensity is typically swept to generate a graph of minority carrier lifetime T as a function of average excess carrier concentration δn. An example of such a graph is shown in Fig. 9, hereinafter. The graph is typically bell-shaped, thus exhibiting reduced minority carrier lifetime T at relatively lower and higher values of average excess carrier concentration δn.

Conversion of a measured (relative) photoluminescence signal into a spatially averaged absolute excess carrier concentration δn(t) requires determination and use of a calibration factor Aj. However, in cases where the relative carrier distribution varies significantly with illumination intensity, use of a single calibration factor Aj leads to errors in the interpretation of results. A cause of such errors is the reabsorption of photons that are spontaneously emitted as carriers (i.e., electrons and holes) recombine. Reabsorption occurs as the emitted photons travel to the surface of the indirect bandgap semiconductor sample and is generally manifested as a decrease in measured photoluminescence emission. As the fraction of reabsorbed photons varies with relative carrier distribution in the sample, the calibration factor Aj is different for each relative carrier distribution. However, adaptation of the calibration factor Aj for each relative carrier distribution is impractical.

A need thus exists for methods and systems that reduce the effects of photon reabsorption during photoluminescence measurements.

Summary Aspects of the present invention relate to methods and systems for performing photoluminescence measurements on indirect bandgap semiconductor samples with reduced photon reabsorption effects.

An aspect of the present invention provides a method for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects. The method comprises the steps of illuminating the indirect bandgap semiconductor sample with light suitable for inducing photoluminescence in the indirect bandgap semiconductor sample; long-pass filtering photoluminescence emitted from the indirect bandgap semiconductor sample to block luminescent photons having a wavelength shorter than a threshold value; and measuring the long-pass filtered photoluminescence emitted from the indirect bandgap semiconductor sample.

Another aspect of the present invention provides a system for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects. The system comprises a light source for illuminating the indirect bandgap semiconductor sample with light suitable for inducing photoluminescence in the indirect bandgap semiconductor sample; a photoluminescence measuring device oriented towards the indirect bandgap semiconductor sample for measuring photoluminescence induced in the indirect bandgap semiconductor sample by incident light; and a long-pass filter disposed between the photoluminescence measuring device and the indirect bandgap semiconductor sample, the long-pass filter adapted to block luminescent photons having a wavelength shorter than a threshold value.

Another aspect of the present invention provides a method for determining an injection level dependent minority carrier lifetime for an indirect bandgap semiconductor sample. The method comprises the steps of illuminating a surface of the indirect bandgap semiconductor sample with light of varying intensity suitable for

inducing photoluminescence in the indirect bandgap semiconductor sample; measuring photoluminescence emitted in response to the illumination from the illuminated surface and an opposite surface of the indirect bandgap semiconductor sample; determining an injection level dependent minority carrier lifetime for each of the illuminated and opposite surfaces based on the measured photoluminescence; and combining the injection level dependent minority carrier lifetimes to obtain a single injection level dependent minority carrier lifetime for the indirect bandgap semiconductor sample.

Another aspect of the present invention provides a system for determining an injection level dependent minority carrier lifetime for an indirect bandgap semiconductor sample. The system comprises a light source for illuminating a surface of the indirect bandgap semiconductor sample with light of varying intensity suitable for inducing photoluminescence in the indirect bandgap semiconductor sample; at least one photoluminescence measuring device for measuring photoluminescence emitted in response to the illumination from the illuminated surface and an opposing surface of the indirect bandgap semiconductor sample; and computational means for determining an injection level dependent minority carrier lifetime for each of the illuminated and opposite surfaces based on the measured photoluminescence, and combining the injection level dependent minority carrier lifetimes to obtain a single injection level dependent minority carrier lifetime for the indirect bandgap semiconductor sample.

The intensity of the light illuminating the indirect bandgap semiconductor sample in any of the aspects or embodiments of the present invention may be varied or swept to determine a minority carrier concentration dependent minority carrier lifetime for the indirect bandgap semiconductor sample.

Brief Description of the Drawings

A small number of embodiments are described hereinafter, by way of example only, with reference to the accompanying drawings in which:

Fig. 1 is a block diagram of a system for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects;

Fig. 2 is a schematic block diagram of another system for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects;

Fig. 3 is a spectral graph of light intensity as a function of wavelength for illustrating methods and systems described herein;

Fig. 4 is a cross-sectional side view of an indirect bandgap semiconductor sample for illustrating methods and systems described herein;

Fig. 5 is a block diagram of another system for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects;

Fig. 6a is a graph of photoluminescence as a function of effective minority carrier lifetime;

Fig. 6b is a graph of relative minority carrier lifetime as a function of bulk effective minority lifetime;

Fig. 6c is a graph of averaged relative minority lifetime as a function of bulk effective minority carrier lifetime; Fig. 7 is a flow diagram of another method for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects;

Fig. 8 is a flow diagram of a method for determining an injection level dependent minority carrier lifetime value for an indirect bandgap semiconductor sample with reduced photon reabsorption effects; and

Fig. 9 is a graph of minority carrier lifetime T as a function of average excess carrier concentration δn for an indirect bandgap semiconductor sample.

Detailed Description

Embodiments of methods and systems are described hereinafter for performing photoluminescence measurements on indirect bandgap semiconductor samples with reduced photon reabsorption effects. The methods and systems described hereinafter are useful for performing lifetime measurements on silicon samples and photovoltaic devices such as silicon solar cells. The open-circuit voltage and short circuit current and thereby the efficiency of a silicon solar cell is known to be directly related to the effective recombination lifetime of the substrate or sample. The recombination lifetime is dependent upon the concentration of excess carriers present in the sample. Varying lifetimes at low carrier concentrations typically result from impurities and/or defects in the substrate or sample.

Although the embodiments described hereinafter are useful for performing photoluminescence measurements on silicon samples and silicon photovoltaic devices as described above, it is not intended that the present invention be limited in this manner as the principles of the present invention have general applicability to other indirect bandgap semiconductor samples and devices, for example, Germanium samples.

Fig. 1 is a block diagram of a system 100 for performing photoluminescence measurements on indirect bandgap semiconductor samples.

Referring to Fig. 1, the system 100 comprises a light source 110, an optional short-pass filter unit 114 and a photoluminescence measuring device 130. The short- pass filter unit 114 may comprise one or more short pass filter/s. A short pass filter passes through the excitation light and absorbs or reflects an unwanted long wavelength emission(s). Examples of short pass filters include colored filters and dielectric interference filters. Alternatively, a dielectric mirror may be used (e.g. under 45 degrees) that reflects that part of the light that is to be used and transmits the unwanted long wavelength light. The short pass filter unit may also comprise a combination of short pass filters and dielectric mirrors. The system 100 may also comprise a collimator 112 and/or a homogenizer 116, which is a device for converting

a collimated beam of light that has non-uniform intensity into an approximately uniformly illuminated region of a plane approximately perpendicular to the collimated beam. Examples include cross cylindrical lens array(s) and a micro lens array. A collimator may be lenses of various sorts. hi the embodiment of Fig. 1, the elements of the system 100 are arranged as follows: a light source 110 facing the indirect bandgap semiconductor sample 140, the collimator 112, the short-pass filter unit 114, and the homogenizer 116 optically aligned in that sequence. In another embodiment, the ordering of the collimator 112 and the short-pass filter unit 114 may be reversed. A field lens (not shown) may be used between the homogenizer and the indirect bandgap semiconductor sample 140. The elements are spaced apart from the indirect bandgap semiconductor sample 140 so that a large area of the indirect bandgap semiconductor sample 140 can be illuminated. The light source 110 and, optionally, one or more of the collimator 112, the short-pass filter unit 114, field lens and the homogenizer 116 form an illumination sub-system 102.

The light source 110 generates light suitable for inducing photoluminescence in the indirect bandgap semiconductor sample 140. The total optical power of the generated light may exceed 1.0 Watt. Light sources of higher power are able to induce more intense photoluminescence in the indirect bandgap semiconductor sample 140. The light source 110 may generate monochromatic or substantially monochromatic light. The light source 110 may be at least one laser. For example, an 808 run diode laser may be used to generate monochromatic light. Two or more lasers with different principal wavelengths may also be practiced. Another light source 110 may comprise a broad spectrum light source (e.g., a flash lamp) combined with suitable filtering to provide partly filtered light. Still another light source 110 may be a high-powered light emitting diode (LED). Yet another light source 110 may comprise an array of light emitting diodes (LED). For example, such an LED array may comprise a large number (e.g. 60) LEDs in a compact array with heatsinking. Other high powered light sources may be practiced without departing from the scope and spirit of the invention.

The light from the light source 110 may be collimated into parallel beams by a collimator or collimator unit 112, which may comprise more than one element. This may be done using a short-pass filter unit 114 comprising one or more filter elements. Short-pass filtering the generated light reduces long-wavelength light above a specified emission peak. The short-pass filter 114 may reduce by a factor of about 10 or more the total photon flux in a long-wavelength tail of the generated light. The long-wavelength tail may begin at a wavelength that is about ten percent (10%) higher than a longest wavelength emission peak of the light source 110. For example, the filtering may remove unwanted spectrum components such as infra-red components with wavelengths in the range of 900 nm to 1800 nm or a sub-range of that range. Multiple short-pass filters may be used because one filter may not be sufficient itself to remove or reduce unwanted spectrum components. The short-pass filters may be implemented at numerous different positions in the overall combination of optical elements between the light source 110 and the indirect bandgap semiconductor sample 140. If more than one short pass filter is used, then one or more of the filters may be arranged so that they are tilted under some angle against the optical axis of the collimated beam to avoid multiple reflections of the reflected light. The short-pass filtered and collimated light may then be homogenized by an optional homogenizer 116 to homogeneously illuminate a large area of the indirect bandgap semiconductor sample 140. The homogenizer 116 may not be required for a broad spectrum light source or even when the light source is an LED array. Furthermore, it should be noted that the ordering of the steps may be altered. The illuminated area of the indirect bandgap semiconductor sample 140 may be greater than or equal to about 1.0 cm ² . The homogenizer 116 distributes the collimated beams evenly across the surface of the indirect bandgap semiconductor sample 140.

The illumination incident on the surface of the indirect bandgap semiconductor sample 140 is sufficient to induce photoluminescence in the indirect bandgap semiconductor sample 140. This photoluminescence is represented in Fig. 1 by arrows or rays emanating from a surface of the indirect bandgap semiconductor sample 140. The external photoluminescence quantum efficiency of silicon can be very low (of the order of < 10 ^"6 ). A photoluminescence measuring device 130 detects

and/or measures the level of photoluminescence induced in the indirect bandgap semiconductor sample 140. A long pass filter unit 118 is generally used in combination with the photoluminescence measuring device 130 to block reflected excitation light from contributing to the measured signal. Such a long pass filter unit typically exhibits a very sharp and deep cutoff, for example at around 850nm.

The incident light from the light source 110 may contain long wavelength light which is of a wavelength that is longer than the cut-off wavelength of the long pass filter unit 118. That light would be transmitted by the long pass filter unit 118. The short pass filter unit 114 blocks, or blocks to a significant degree, that incident long wavelength light and prevents it from being received by the photoluminescence measuring device 130. Light source tail radiation may be of the order of 10 ^"4 of a source peak, which can significantly exceed the photoluminescence efficiency of silicon (of the order of 10 ^"6 ) in contrast to that of direct bandgap semiconductors like AlGaAs (of the order of 10 ^"2 ). The long pass filter unit 118 normally has a cut-off wavelength that is longer than the wavelength of the incident light but shorter than shortest wavelength of photons that are present to a significant amount in the luminescence spectrum emitted by the sample. That way the measured signal is maximized because no luminescent photons are unnecessarily blocked. For silicon the cut-off wavelength would typically be in the range 850nm.

However, the long pass filter unit 118 may be adapted to block luminescent photons emitted from the indirect bandgap semiconductor sample 140 that have a wavelength shorter than a threshold value. Alternatively, a separate long pass filter unit may be used in addition to the existing long pass filter unit 118 (i.e., in series with the existing long pass filter unit 118 in the optical path between the indirect bandgap semiconductor sample 140 and the photoluminescence measuring device 130) to block luminescent photons emitted from the indirect bandgap semiconductor sample 140 that have a wavelength shorter than a threshold value. For a silicon wafer (i.e., as the indirect bandgap semiconductor sample 140), the threshold value is typically in the range of lOOOnm to 1 lOOnm. For example the absorption coefficient of silicon at room temperature has a value of 30cm ^"1 at 1030nm wavelengths, which corresponds to an

absorption length of 300μm which is equivalent to the typical thickness of a silicon wafer, hi contrast, at 1140nm, the wavelength of maximum luminescent emission in crystalline silicon, the absorption length is lcm and reabsorption on an optical path equivalent to the thickness of a silicon sample (~300μm) is thus negligible. Accordingly, luminescent photons having an absorption length shorter than or similar to the thickness of the indirect bandgap semiconductor sample may be blocked. This removes or reduces a portion of the photoluminescence spectrum where the effect of photon reabsorption is generally most significant. hi another embodiment, a band-pass filter may be used in place of the long-pass filter 118. Such a band-pass filter requires a pass-band in the range of approximately 1050nm to 1200nm, depending on the thickness of the silicon sample.

A consequence of such a filtering arrangement is a reduction in photoluminescence measured by the measuring device 130, particularly if a silicon detector is used for detection of photoluminescence emitted by the silicon sample. However, use of smaller bandgap detectors such as Germanium or Indium-Gallium- Arsenide detectors result in relatively less reduction of detectable photoluminescence emitted by a silicon sample.

The photoluminescence measuring device 130 may comprise a light sensitive electronic element such as a single photo diode, for example, a Silicon, a Germanium or a Indium-Gallium-Arsenide photodiode. Alternatively, the photoluminescence measuring device 130 may comprise a focusing element 120 (e.g. one or more lenses) and a focal plane array 122 of light sensitive electronic elements, as shown in Fig. 1. hi this embodiment, the focal plane array 122 of light sensitive electronic elements may comprise an array of charge coupled devices (CCD). The focal plane array may be made of silicon and may be cooled. Cooling improves the signal-to-noise ratio of such a focal plane array. Alternatively, the focal plane array 122 of light sensitive electronic elements may be made from InGaAs. The photoluminescence measuring device 130 and long pass filter unit 118 form a photoluminescence measuring subsystem 104.

A general-purpose computer or another computational means can be used to acquire and/or process photoluminescence values measured by the photoluminescence measuring device 130 or photoluminescence measuring sub-system 104.

Fig. 2 is a block diagram of a system 200 for performing photoluminescence measurements on indirect bandgap semiconductor samples. The system 200 of Fig. 2 is similar to the system 100 of Fig. 1, save that the photoluminescence measuring device 130 and long pass filter unit 118 are positioned to detect and measure photoluminescence emitted from a surface of the indirect bandgap semiconductor sample 240 not directly illuminated by the light source 110. This photoluminescence is represented in Fig. 2 by arrows or rays emanating from the lower planar surface of the indirect bandgap semiconductor sample 240. In all other respects, the system 200 of Fig. 2 is equivalent or substantially similar to the system 100 of Fig. 1. Accordingly, like reference numerals used in both Figs. 1 and 2 indicate that the elements referenced by those numerals may be equivalent or substantially similar.

Fig. 3 is a spectral graph of light intensity as a function of wavelength. Referring to Fig. 3, spectrum 350 represents essentially monochromatic light generated by an 808 nm diode laser for inducing photoluminescence in a silicon sample. The spectrum 360, centred at a wavelength of approximately 1140nm, represents the photoluminescence induced in the silicon sample.

As described hereinbefore with reference to Fig. 1, a long pass filter unit having a very sharp and deep cutoff at around 850nm (e.g., represented by vertical line 320 in Fig. 3) may be used to block reflected or transmitted incident light generated by the laser diode from contributing to the measured photoluminescence. Alternatively, or additionally, a long pass filter unit may be provided to block luminescent photons emitted from the indirect bandgap semiconductor sample that have a wavelength shorter than a threshold value. For a silicon sample (wafer), the threshold value is typically in the range of lOOOnm to 1 lOOnm and is represented by the vertical line 330 in Fig. 3. Accordingly, the part of the photoluminescence spectrum where the effects of photon reabsorption is most significant, is removed or reduced by filtering.

Fig. 4 is a cross-sectional side view of an indirect bandgap semiconductor sample 400. A photon 410, which is spontaneously emitted as a result of carrier recombination, is depicted at a distance d} from the upper planar surface 402 of the sample 400 and a distance d ₂ from the lower planar surface 404 of the sample 400. The sum of the optical paths that the photon 410 can travel to be liberated from the sample 400, either via the upper planar surface 402 or lower planar surface 404, of the sample 400, is equal to the thickness of the sample 400 (i.e., di + d ₂ = d). By combining (e.g., averaging, or summing and scaling) the photoluminescence emitted from the upper 402 and lower 404 planar surfaces of the sample 400, a representative photoluminescence value may be obtained for which the total probability of reabsorption is exactly the same for all photons spontaneously emitted at any given position within the sample 400. The combined value of photoluminescence emitted from the upper 402 and lower 404 planar surfaces of the sample 400 (a relative value) may be converted into an absolute, spatially averaged value of excess carrier concentration δn(t), for example, by means of a calibration method and factor. Injection level dependent minority carrier lifetime may be determined as a function of excess carrier concentration δn(t) and generation rate G(t) in the sample 400. Thus, the effect or influence of photon reabsorption on the value of minority carrier lifetime may be eliminated or at least substantially reduced.

In an alternative embodiment, the photoluminescence measured from the upper 402 and lower 404 planar surfaces are separately converted into absolute, spatially averaged excess carrier concentrations. Injection level dependent minority carrier lifetimes are determined from each of the spatially averaged excess carrier concentrations (i.e., as a function of a respective excess carrier concentration and the generation rate of excess minority carriers in the sample 400). The injection level dependent minority carrier lifetimes are then combined (e.g., averaged or summed and scaled) to produce a single injection level dependent minority carrier lifetime for the sample 400.

Fig. 5 is a block diagram of a system 500 for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects.

Referring to Fig. 5, the system 500 comprises an illumination sub-system 502 and two photoluminescence measuring sub-systems 504 and 506. The illumination sub-system 502 is equivalent or substantially similar to the illumination sub-system 102 of Fig. 1, as described hereinbefore, and the photoluminescence measuring subsystems 504 and 506 are equivalent or substantially similar to the photoluminescence measuring sub-system 104 of Fig. 1, as described hereinbefore. Accordingly, like reference numerals used in both Figs. 1 and 5 indicate that the elements referenced by those numerals may be equivalent or substantially similar.

Referring to Fig. 5, the photoluminescence measuring sub-systems 504 and 506 are disposed to measure photoluminescence emitted from opposite surfaces of the indirect bandgap semiconductor sample 540 while one of the surfaces is directly illuminated by the illumination sub-system 502. The photoluminescence is represented in Fig. 5 by arrows or rays emanating from both opposing planar surfaces of the indirect bandgap semiconductor sample 540.

The long pass filter units 118 in the photoluminescence measuring sub-systems 504 and 506 may optionally be adapted to block luminescent photons emitted from the indirect bandgap semiconductor sample 540 that have a wavelength shorter than a threshold value, as described hereinbefore in relation to Fig. 1. Ideally, the long pass filter units 118 in the photoluminescence measuring sub-systems 504 and 506 should be substantially identical.

Those skilled in the art will appreciate that other embodiments and/or arrangements may be practiced to achieve a similar purpose. For example, a single photoluminescence measuring sub-system may be physically relocated to separately detect and measure photoluminescence emitted from both opposite surfaces of the indirect bandgap semiconductor sample 540.

The values of photoluminescence measured from the illuminated and opposite surfaces may each be converted into a spatially averaged absolute excess carrier concentration δn using one of a number of methods.

For example, a calibration factor Aj may be determined using a "self-consistent calibration" method developed by the present inventors and another, which is described in a paper entitled "Self-consistent calibration of photoluminescence and photoconductance lifetime measurements ^' " and published in Applied Physics Letters 87, 184102 (2005). The contents of this document are incorporated herein in their entirety by reference thereto.

The minority carrier lifetime T may then be determined according to the formula:

An(t)

T = dAn(t)

G(O- dt where:

δn(t) is the spatially averaged excess minority carrier concentration, and

G(t) is the generation rate of excess minority carriers in the indirect bandgap semiconductor sample.

Variations in the measured photoluminescence due to geometric considerations (e.g., differences in positioning of the photoluminescence measuring sub-systems 504 and 506 relative to the indirect bandgap semiconductor sample 540) may be compensated for by using separate calibration factors Aj ₁ and Aj ₂ that correspond to the illuminated and opposite surfaces of the indirect bandgap semiconductor sample 540, respectively. The calibration factors Aj ₁ and Aj ₂ are not constant, but vary as a function of the minority carrier concentration profile throughout the indirect bandgap semiconductor sample 540, which is a function of the minority carrier lifetime. This may be illustrated by considering that the light illuminating the indirect bandgap semiconductor sample 540 is absorbed quite close to the illuminated surface. The minority carriers (electrons or holes) produced by absorption move away from the illuminated surface by diffusion. For short lifetimes, the minority carriers do not get very far before recombining, so the minority carrier profile decays sharply as a function of depth from the illuminated surface. In contrast, at high minority carrier

lifetimes, the minority carriers that are generated near the illuminated surface can diffuse deeper into the bulk of the sample and are thus, on average, further away from the illuminated surface and closer to the opposite (i.e., non-illuminated) surface. The resulting variation in the relative minority carrier profile results in variations in the influence of reabsorption on the measured luminescence signal from the illuminated and opposite surfaces, respectively. If detection is performed in relation to the illuminated surface, the influence of reabsorption is minimal for short lifetimes and maximal for long lifetimes. On the other hand, if detection is performed in relation to the non-illuminated surface, the influence of reabsorption is maximal for short lifetimes and minimal for long lifetimes.

The effect of reabsorption on the fractions of photons detected from the illuminated and opposite (i.e., non-illuminated) surfaces, respectively, may be seen in Fig. 6a, which is a graph of photoluminescence (measured) as a function of the effective minority carrier lifetime. The graph shows the calculated fractions of photons detected over the total number of emitted photons, assuming a silicon sensor and a 3mm lOOOnm Schott glass long pass filter located between the sample and the sensor. The curve 610 represents the fraction of photons detected from the illuminated surface and the curve 620 represents the fraction of photons detected from the opposite (i.e., non-illuminated) surface. For high minority carrier lifetimes the excess carrier distribution within the sample is homogeneous and the fractions of photons detected from the opposite surfaces are therefore identical and are about 0.085. The fact that these values (fractions) are less than one can be taken into account by the calibration factors A ₁₁ and A ₁₂ , respectively. However, variation of the fractions cannot be accounted for by single calibration factors. The scale on the right-hand side of Fig. 6a shows relative injection level dependent lifetime based on single calibration factors A ₁₁ and A ₁₂ for separate measurements from the illuminated or opposite (i.e., non-illuminated) surfaces, respectively, assuming that both measurements are calibrated separately (i.e., using calibration factors A ₁₁ and A ₁₂ ) at high minority carrier lifetimes. The graph of Fig. 6a shows that a reduced probability of reabsorption at low minority carrier lifetimes leads

to an up-to-25% overestimation in the minority carrier lifetime at low lifetime values for detection from the illuminated side and that an enhanced photon reabsorption probability leads to a corresponding underestimation of the minority carrier lifetime for detection from the opposite (non-illuminated) surface. Curve 630 in Fig. 6a represents the injection level dependent minority carrier lifetime that is obtained by averaging the injection level dependent lifetime curves 610 and 620, which are obtained from separate detection measurements performed on the illuminated and opposite (i.e., non-illuminated) surfaces, respectively. The variation in the resulting injection level dependent lifetime curve 630, τ _av (δn), is notably less than 2.5% across the entire range of minority carrier lifetimes. This demonstrates that averaging the injection level dependent lifetime curves 610 and 620, obtained from photoluminescence data measured from the illuminated and opposite (i.e., non- illuminated) surfaces, respectively, leads to a significant reduction of the artificial influence of reabsorption in the sample.

In an embodiment of the invention, one side or surface of a sample or wafer is illuminated with light suitable for causing emission of photoluminescence from the sample. A first injection level dependent minority carrier lifetime value is determined from a first photoluminescence measurement taken from one side of the sample or wafer using a calibration factor An. The calibration factor An may be determined using the "self-consistent calibration" method incorporated hereinbefore by reference or by comparison with another lifetime measurement method (e.g., a quasi-steady- state photoconductance measurement). Calibration of the first photoluminescence lifetime measurement is carried out at a specific carrier injection level An _02I , which is associated with a specific lifetime. A second injection level dependent minority carrier lifetime value is then determined from a second photoluminescence measurement taken from the other side of the sample using a calibration factor Aj ₂ . The calibration factor Aj ₂ may be determined by comparison with the injection level dependent lifetime value obtained from the first photoluminescence measurement or by using the "self-consistent calibration" method incorporated hereinbefore by reference, or by comparison with another lifetime measurement method. The correct value of the

calibration factor Aj ₂ is found when the lifetime from the second photoluminescence measurement is equal to the lifetime from the first photoluminescence measurement at the specific carrier injection level δri _ca i (i.e., when T^δri _ca i) = 7 ₂ (δn _cal )).

The calibrated injection level dependent lifetime values determined from the first and second luminescence measurements may be averaged to yield an average injection level dependent lifetime value τ _av (δn) = (T ₁ (An) + T ₂ (δn))/2, with reduced influence of photon reabsorption.

The first and second photoluminescence measurements can be performed simultaneously or separately. Fig. 6b is a graph of relative minority carrier lifetime as a function of bulk effective minority lifetime, to illustrate the implications of using different injection levels for calibration. Referring to Fig. 6b, curves 612 and 614 relate to detection from the illuminated side where calibration occurred at injection levels corresponding to high and low minority carrier lifetimes respectively. Curve 612 shows that calibration at an injection level corresponding to a high minority carrier lifetime results in an overestimation of the relative minority carrier lifetime at lower effective minority carrier lifetimes. Curve 614 shows that calibration of the same data at an injection level corresponding to a low minority carrier lifetime results in an underestimation of the relative minority carrier lifetime at high effective minority carrier lifetimes. Curves 622 and 624 relate to detection from the non-illuminated side where calibration occurred at injection levels corresponding to high and low minority carrier lifetimes respectively. Curve 622 shows that calibration at an injection level corresponding to a high minority carrier lifetime results in an underestimation of the relative minority carrier lifetime at lower effective minority carrier lifetimes. Curve 624 shows that calibration of the same data at an injection level corresponding to a low minority carrier lifetime results in an overestimation of the relative minority carrier lifetime at high effective minority carrier lifetimes.

Fig. 6c is a graph of average relative minority carrier lifetime as a function of bulk effective minority carrier lifetime, which illustrates the importance of calibrating Aj ₁ and Aj ₂ at injection levels corresponding to similar lifetimes. Preferably, calibration should occur at the same injection level, i.e. under identical illumination

conditions. Curve 636 relates to the relative averaged minority carrier lifetime when both photoluminescence measurements are calibrated at the same injection level. Curve 616 relates to the relative averaged minority carrier lifetime if the photoluminescence measurement for the illuminated side is calibrated at a high minority carrier lifetime value and the photoluminescence measurement for the non- illuminated side is calibrated at a low minority carrier lifetime value. Curve 626 relates to the relative averaged minority carrier lifetime if the photoluminescence measurement for the illuminated side is calibrated at a low minority carrier lifetime value and the photoluminescence measurement for the non-illuminated side is calibrated at a high minority carrier lifetime value.

Averaging reduces the distortion of the injection level dependent lifetime curve, independently from the injection level at which the two curves are calibrated. Calibration at different injection levels however leads to an error by a constant factor. Calibration of both photoluminescence measurements at the same or similar injection levels is thus important for accurate absolute values.

In an embodiment of the invention, calibration of the first photoluminescence measurement is performed at a given injection level. The second photoluminescence measurement is taken under near identical illumination conditions as the first photoluminescence measurement. Calibration of the second photoluminescence measurement then comprises selection of the calibration factor Aj ₂ so that the minority carrier lifetime from the second photoluminescence measurement agrees with the lifetime from the first photoluminescence measurement at the injection level at which the first photoluminescence measurement was calibrated.

Fig. 7 is a flow diagram of a method for performing photoluminescence measurements on an indirect bandgap semiconductor sample with reduced photon reabsorption effects.

At step 710, the indirect bandgap semiconductor sample is illuminated with light suitable for inducing photoluminescence in the indirect bandgap semiconductor

sample. The light may additionally be short-pass filtered to reduce light of wavelength above a threshold wavelength and collimated.

At step 720, the photoluminescence emitted from the indirect bandgap semiconductor sample is long-pass filtered to block luminescent photons having a wavelength shorter than a threshold value. The threshold value may be in the range lOOOnm to HOOnm for silicon samples. Accordingly, luminescent photons having an absorption length shorter than the thickness of the indirect bandgap semiconductor sample may be blocked.

At step 730, the long-pass filtered photoluminescence emitted from the indirect bandgap semiconductor sample is measured.

An average excess minority carrier concentration for the indirect bandgap semiconductor sample may be determined as a function of the photoluminescence measured in step 730. An injection level dependent minority carrier lifetime for the indirect bandgap semiconductor sample may be determined as a function of the average excess minority carrier concentration and the generation rate of excess minority carriers in the indirect bandgap semiconductor sample. The method of Fig. 7 may, for example, be performed using the systems described hereinbefore with reference to Fig. 1 and Fig. 2.

Fig. 8 is a flow diagram of a method for determining an injection level dependent minority carrier lifetime for an indirect bandgap semiconductor sample.

At step 810, a surface of the indirect bandgap semiconductor sample is illuminated with light of varying intensity suitable for inducing photoluminescence in the indirect bandgap semiconductor sample. At step 820, photoluminescence emitted in response to the illumination is measured from the illuminated surface and an opposite surface of the indirect bandgap semiconductor sample.

At step 830, an injection level dependent minority carrier lifetime is determined for each of the illuminated and opposite surfaces based on the respective values of photoluminescence.

The average excess carrier concentrations may each be determined from a respective measured photoluminescence and the injection level dependent minority carrier lifetimes may be determined from the respective average excess carrier concentrations and from the generation rate G(t), which is determined from the measured incident light intensity. The average excess carrier concentrations may each be determined from a respective measured photoluminescence using a different calibration factor. The injection level dependent minority carrier lifetimes are preferably calibrated at substantially the same excess carrier concentration in the indirect bandgap semiconductor sample. At step 840, the injection level dependent minority carrier lifetimes that are determined in step 830 from the photoluminescence measurements carried out in step 820 are combined to obtain a single injection level dependent minority carrier lifetime value for the indirect bandgap semiconductor sample. The injection level dependent minority carrier lifetimes may be combined by averaging the minority carrier lifetime values relating to the illuminated and opposite surfaces.

The method of Fig. 8 may further comprise the steps of measuring the intensity of the light used to illuminate a surface of the indirect bandgap semiconductor sample and determining the excess carrier generation rate as a function of the measured light intensity. The intensity of the light illuminating the indirect bandgap semiconductor sample may be varied to determine a minority carrier concentration dependent minority carrier lifetime for the indirect bandgap semiconductor sample.

The method of Fig. 8 may be performed using the system described hereinbefore with reference to Fig. 5.

Advantageously, the effect of combining (e.g., averaging, or scaling and summing) injection level dependent minority carrier lifetimes is that errors due to photon reabsorption in the injection level dependent lifetime measurements are reduced. Errors due to photon reabsorption are generally most pronounced if the minority carrier lifetime varies as a function of minority carrier concentration within a range of about lμs to lOOμs, because it is in this lifetime range that the carrier profile

changes from being strongly localized near the illuminated surface (i.e., short lifetime) to substantially homogeneous throughout the sample (i.e., long lifetime). Within this lifetime range, errors due to reabsorption are more substantial when the lifetime differs from the lifetime at which the calibration was performed. That is, the maximum error due to reabsorption occurs at high lifetimes if calibration is/was performed at carrier concentrations corresponding to a low lifetime, and vice versa.

The foregoing description provides exemplary embodiments only, and is not intended to limit the scope, applicability or configurations of the present invention. Rather, the description of the exemplary embodiments provides those skilled in the art with enabling descriptions for implementing an embodiment of the invention. Various changes may be made in the function and arrangement of elements without departing from the spirit and scope of the invention as set forth in the claims hereinafter.

Where specific features, elements and steps referred to herein have known equivalents in the art to which the invention relates, such known equivalents are deemed to be incorporated herein as if individually set forth. Furthermore, features, elements and steps referred to in respect of particular embodiments may optionally form part of any of the other embodiments unless stated to the contrary.

The term "comprising", as used herein, is intended to have an open-ended, nonexclusive meaning. For example, the term is intended to mean: "including principally, but not necessarily solely" and not to mean "consisting essentially of or "consisting only of. Variations of the term "comprising", such as "comprise", "comprises" and "is comprised of, have corresponding meanings.