Experimental Details of Lifetime Studies

In this thesis, mc-Si wafers with a cross sectional area of 15.6×15.6 cm² are cut by a laser into a sample size of 5×5 cm². As listed in Fig. 1.3, the saw damage of the Si samples is etched off by removing about 10 µm silicon on each side in a polishing etch consisting of HF (50%), CH3COOH (99.8%) and HNO₃ (65%) with the mixing ratio 1:2:15. This is followed by a cleaning sequence of 10 min hydrochloric acid of 3% (HCl) and hydrofluoric acid (2% HF) dipping. Then, POCl3 diffusions with different process parameters are applied in order to test their phosphorus diffusion gettering (PDG) behavior. For a detailed explanation of PDG see Sec.2.3.2. In addition, the influence of SiN_x:H layers deposited on both sides of the sample by an industrial-type plasma enhanced chemical vapor deposition (PECVD)¹is investigated. For this test vertically neighboring, so-calledsister samples, with comparable grain structure are divided into group A and B samples. After emitter removal (for group B additional removal of SiNx:H layers) and surface piranha cleaning² followed by a HF dip, samples are surface passivated. The applied surface passivation is hydrogen-rich amorphous silicon (a-Si:H) [32] deposited

1The deposition setup of this work involves a direct plasma.

2Piranha cleaning means the sample cleaning in a mixture of H₂O₂(30%) and H₂SO₄(95%) with the ratio 1:4 which is heated up to the temperatureT≈80^◦C.

(a)

Figure 1.4: Schematic view of the PL setup (a): Charge carriers are generated by the incident light of the LED panel underneath the sample and the resulting photoluminescence signal of the sample is detected spatially resolved by the Si-CCD camera.

The QSSPC setup in (b) uses a flash lamp illuminating the Si sample from the top while the change in photoconductance is measured by an induction coil underneath the sample. The declining flash light intensity is measured by a reference solar cell.

in a PECVD system from Oxford Instruments (Plasmalab 100). The a-Si:H passivation is activated by a 12 min annealing step at 250^◦C which is not explicitly shown in the process flow of Fig.1.3.

Two possible types of surface passivation are compared and discussed in Sec. 1.1.3. Finally, lifetime characterization is performed using the QSSPC and PL techniques.

Both setups of the QSSPC and PL methods are sketched in Fig.1.4. The applied QSSPC setup is the commercially available Sinton WCT-120 lifetime tester [33] whereas the PL setup has been constructed by Kiliani and Steuer [34–36]. PL images of this work are measured by a Si charge coupled device (Si CCD) camera at an incident photon flux ofΦPL=2.6×10¹⁷cm⁻²s⁻¹yielded by the light emitting diode (LED) panel underneath the sample as sketched in Fig. 1.4a. The operating principle of this setup is the spatially resolved measurement of the photons emitted by the charge carriers only recombining through the radiative band-band transition whereas sample regions allowing other recombination mecha-nisms such as SRH recombination will have a reduced PL signal. Hence, defect-rich regions will appear dark in PL imaging and regions of higher material quality will be brighter with a strong photolumines-cence signal. Since the measured photon flux of PL imaging is given in counts/s, images need to be lifetime-calibrated with the QSS lifetime at the above given generation flux [37]. The actual value of the photon generation flux within the a-Si:H passivated sample is smaller byR=37% which accounts for its reflection loss at the respective wavelengthλ =633 nm of the LED panel. The generation flux within the sample is thenG_PL=ΦPL(1−R) =1.7×10¹⁷cm⁻²s⁻¹. At this generation flux the sample’s lifetime measured by the QSSPC setup is used to calibrate its PL image. Note that the used techniques are separate setups in contrast to the combined system presented in [37]. It will be described in Sec.1.1.4 that a high injection level is needed to measure the interstitial iron concentration more accurately. This is yielded by an additional photon flux induced by a laser at a wavelength ofλ =808 nm applied to the upper sample surface as sketched in Fig. 1.4a. The resulting generation flux without reflection losses used for the OSSPC lifetime-calibration in this case isG_PL=4.8×10¹⁷cm⁻²s⁻¹.

The operating principle of the QSSPC is described as follows [25]: the flash lamp above the sample generates excess carriers within the Si sample that recombine according to the above described recombi-nation mechanisms. Hence, the sample’s photoconductanceσ deviates from its equilibrium value in the dark by∆σ(t)due to these generated excess carriers. This deviation∆σ(t)is measured by a induction

1.1 Minority Carrier Lifetime 7

coil located underneath the sample as sketched in Fig.1.4b. This circular coil with diameter≈1.7 cm is only sensitive in its vicinity centrally positioned underneath the 5×5 cm² sample [38,39]. The excess carrier density∆n(t)is determined from the measured photoconductance:

∆n(t) = ∆σ(t)

e(µn+µp)W (1.11)

µnandµpare the mobilities of electrons and holes that themselves depend on the carrier densitiesnand p. Therefore,∆n(t)must be determined iteratively.

The generation rateG(t)is determined independently of∆nby a reference solar cell. The reference cell measures the incident light intensityplight(t)given in sun equivalent units (sun=0.1 Wcm⁻²). To obtain the rate of generated electron-hole pairs this intensity is multiplied by the photon fluxN_phat the incident solar light of 1 sun. Additionally, it has to be considered that only a fraction fabsof the incident light is absorbed by the sample.

G(t) = p_light(t)Nphf_abs

W (1.12)

Note that both quantities∆n(t)andG(t)are averaged over the whole sample thicknessWwhile assuming them to be homogeneously distributed in depth.

The time scale of the declining flash light intensity p_light(t)is larger by several orders of magnitude than the one of the recombination mechanisms which equals the lifetime. This fact allows the determina-tion of lifetimes up to 200 µs in a quasi-steady-state mode [33]. The following equadetermina-tion is derived from the continuity equation for the excess carrier densities (see [22]).

τe f f = ∆n

G(t) (quasi-steady-state) (1.13)

If the lifetime is not significantly lower than the decay time of the flash light, the time dependence of∆n has to be considered.

τe f f =− ∆n d∆n(t)

dt

(transient) (1.14)

The difference between the transient mode and the quasi-steady-state (QSS) mode is the considerably shorter decay time of the flash light which results in a generation rate ofG(t) =0 during the actual measurement. Since the sample’s lifetime is not always significantly larger than the flash light decay time, it is calledquasi-transient. Comparable to the QSS mode not only one lifetime is measured that accounts for the whole light decay but rather several lifetimes versus∆nare determined. Hence, in both modes theτ(∆n)curve is extracted. In the following, this mode will simply be referred to astransient and the lifetime measured in transient mode astransient lifetime. The lifetime measured in QSS mode will be calledQSS lifetime.

There also exists a combination of equation 1.13and1.14which is called thegeneralized case[40].

This is not used in the present work since it is argued in [33] that the lifetime is determined most accu-rately if the proper mode is selected. This is discussed in more detail in the next section.

Trapping Artifact

A final note should be made for multicrystalline silicon: the measured bulk lifetime might be overesti-mated at low injection because of the so-calledtrappingof minority charge carriers. Due to that effect

Increased lifetime due to trapping

Filled traps

=> corrected lifetime

Figure 1.5: QSSPC measurement of a mc-Si sample in the as-grown state. Trapping is partly suppressed by applying a bias light.

a disturbance occurs in the excess carrier densities of electrons and holes. The relation∆p=∆nis not fulfilled any more but rather∆p=∆n+n_t with the trap densityn_t. This directly results in an apparent increase of the photoconductivity and hence lifetime. The Hornbeck and Haynes model clearly separates shallow trapsnt close to the minority carrier band (conduction band in p-type Si) from deep traps (SRH levelsN_t) [41]. Trapping mainly affects the lifetime measured by the QSSPC technique [18] whereas PL measurements are found to be affected not strongly or even not at all by trapping [19,42]. Fig. 1.5shows the QSS lifetime of a mc-Si sample, investigated in this work, that is affected by trapping. The sample is in the as-grown state and has been prepared for the lifetime measurement according to the process flow of group A samples depicted in Fig. 1.3without the processing steps associated with a POCl₃diffusion.

The trapping artifact might be reduced by applying an additional bias light which is also depicted in the figure. The bias light is aimed to be absorbed in order to fill all shallow traps which then do not affect the effective lifetime at low injection anymore. Of course, the density of traps determine the necessary light intensity to fill all traps. An evaluation of the proper illumination intensity is demonstrated by Macdonald et al [43]. They reported an optimum intensity that results in a complete filling of the traps.

A higher intensity hampers the measurement of the corrected lifetime without trapping and leads to a distorted lifetime value. The sample is illuminated with a bias light to measure the corrected lifetime which is also shown in Fig. 1.5. The physical origin of the shallow traps in mc-Si has not been completely understood up to now. Macdonald and Cuevas, however, revealed a correlation between dislocation density and trap density [44]. Further work on this issue has been published by Gundel et al., for example [45].

Quasi-steady-state versus Transient Mode in mc-Si

For accurate lifetime measurements it is important to decide between the two modes as pointed out in the manual of the Sinton tool used in this work [33]. It is suggested that lifetimes below 200 µs shall be measured in QSS mode and above this value in transient mode. In case of multicrystalline material, a further aspect needs to be considered which originates from its strongly non-uniform lifetime distribution. Cuevas published a detailed analysis addressing this issue in [46]. Lifetime measurements in QSS mode are found to reflect the arithmetical mean lifetime of the measured sample region. In transient mode, however, the higher lifetimes are emphasized while the contribution of low-lifetime regions to

1.1 Minority Carrier Lifetime 9

Figure 1.6: Gettered mc-Si sample, passivated with a-Si:H, is shifted towards all four different positions with respect to the QSSPC coil. Lifetime determination is performed in QSS mode.

the photoconductance vanishes quickly. Due to these opposing aspects concerning high lifetimes above 200 µs, it is necessary to measure the lifetime in both modes. The fact that a mc-Si sample may contain grains of exceptionally high lifetime next to grains of very low lifetime is likely to result in a considerably overestimated transient lifetime. Before the comparison of two lifetime curves measured in the different modes will be addressed, the influence of the inhomogeneous grain structure on the QSS lifetime of a mc-Si sample is demontrated.

QSS measurements of a mc-Si sample shifted towards all four directions up to 1.5 cm away from its centered position are shown in Fig.1.6. This shift is very large compared with the typical inaccuracy during sample positioning of±2 mm. The sample is surface passivated with hydrogenated amorphous silicon (a-Si:H). It reveals, as an example, the influence of the inhomogeneous lifetime distribution on the QSS lifetime of a mc-Si sample. Note that the sample is shifted in such a manner that the sample’s edges do still cover the coil area. The standard deviation of all lifetime curves of the shifted positions is converted into relative deviation which is also depicted versus excess carrier density and linked to the right y-axis. The relative deviation at∆n=1×10¹⁵cm⁻³is 11% due to inaccurate sample orientation.

Note that this deviation gives only a hint for the deviations of other mc-Si samples because of the specific grain structure present in each different sample. It still helps to estimate the deviation originating from wrong sample positioning, in particular, due to the extended shift significantly beyond the inaccuracy of

±2 mm. The value of 11% is close to the error of 10% which is often assumed to be the experimental error of the QSSPC technique applied in QSS mode [22,47].

In another experiment two gettered samples are measured in QSS as well as in transient mode and compared with each other. Again the applied surface passivation is a-Si:H. In Fig.1.7a the transient lifetime is higher than the QSS lifetime except at the quite high injection∆nof 1×10¹⁶cm⁻³. Hence, for sample 1 the QSS mode leads to a more representative mean lifetime value, even though its life-time is slightly higher than 200 µs. It indicates the overestimation of the lifelife-time by the transient mode since grains of higher material quality are weighted more strongly in this mode. The absolute lifetime discrepancy of sample 1 measured in the two different modes is 151 µs (at∆n=1×10¹⁵cm⁻³) which corresponds to a relative deviation of even 59% related to the more accurate QSS lifetime. This stresses the need to select the correct mode. In Fig.1.7bthe transient lifetime of≈600 µs is significantly lower than the QSS lifetime. The approximation of a quasi-steady state injection induced by the declining flash light does not apply for the high lifetime of sample 2. Thus, the transient mode is more reliable despite the fact that grains of higher material quality are weighted more strongly.

(a) (b)

Figure 1.7: Comparison of the QSS mode with the transient mode is shown for two different mc-Si samples 1 and 2.

It should be mentioned that the transient lifetime curve diverges at high injection. This is an experi-mental artifact originating from the fact that the lifetime extraction starts too early. The flash light is not completely switched off at that point in time. Hence, the generation rate is not zero as required for the validity of equation 1.14. As a consequence,∆nis still slightly increasing until it reaches the maximum of the∆nversus time curve. The lifetime is extracted at and close to the maximum where the derivative d∆n/dt is zero. According to equation1.14, this results in a divergent transient lifetime. Beyond the maximum of the curve,∆nstarts to decrease and the lifetime extraction becomes reasonable.