The Quasi-steady-state photoconductance (QSSPC) lifetime technique allows the measurement of the injection-dependent lifetime without making electrical contact to the silicon wafer [1]. This convenient, fast and non-destructive technique is very suitable for the characterisation of silicon wafers. A WCT-120 QSSPC lifetime tester from Sinton Instruments is used in this work.
During a QSSPC measurement, the silicon wafer is exposed to illumination by a flash. The conductance of the wafer and the intensity of the light are simultaneously measured, as functions of time. The conductance is measured by an inductive coil coupled to the sample, and the generation rate is determined by a calibrated reference cell. The excess conductance Δσ is converted into the average excess carrier density Δn by
∆𝑛 = ∆𝜎
𝑞(𝜇𝑒+ 𝜇ℎ)𝑊, (3.1)
where q is the electron charge, W is the sample thickness, and µe and µh are the electron
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𝐺 =𝐽𝑆𝐶∙ 𝑓𝑜𝑝𝑡𝑖𝑐𝑎𝑙
𝑞𝑊 , (3.2)
where JSC is the short circuit current of the reference cell, and foptical is the difference in
the absorption between the sample and the reference solar cell. Then, the recombination rate U can be obtained by the continuity equation
𝑑∆𝑛
𝑑𝑡 = 𝐺 − 𝑈, (3.3)
and the effective lifetime can be obtained by
𝜏𝑒𝑓𝑓 =
∆𝑛
𝑈 . (3.4)
Under QSS conditions, the sample is exposed to a long, slow-decaying pulse of light. The decay time constant of the light is much longer than the carrier lifetime, meaning that a quasi-steady state is achieved, so G=U. Under transient mode, a short pulse of light is used. The light decay time constant is much shorter than the carrier lifetime, so that G=0 once the illumination is terminated. Generally, the QSS mode is valid for lifetimes of approximately 200 µs or less, while the transient mode is valid for lifetimes greater than 100 µs. These threshold values are determined by the decay constant of the flash [2].
Applying the QSSPC lifetime measurements, we can use the changes in the measured injection-dependent lifetime before and after breaking metal-acceptor pairs to determine [Fei] and [Cri] in B-doped p-type silicon, as discussed in 2.2.2. Such techniques are well
established and often used in silicon solar cell research [3-5]. Another important application of such lifetime measurements is injection-dependent lifetime spectroscopy (IDLS) for deep-level defects in silicon. Here we give an introduction of this technique and focus on the aspects that are relevant to this work. A more systematic study of this technique can be found in Ref. [6].
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Due to the high sensitivity of the carrier lifetime to recombination-active defects, the injection-dependent lifetime can be analysed to identify impurities in silicon based on the Shockley-Read-Hall (SRH) model [7, 8]. Conversely, the defect parameters can be determined by fitting the injection-dependent lifetime of a known impurity with the SRH model. Substituting Eq. (2.15) into (2.14), and using k=σn/σp to replace σp, we have
𝜏𝑆𝑅𝐻 =
𝑘(𝑛0 + 𝑛1+ ∆𝑛) + (𝑝0+ 𝑝1+ ∆𝑛)
𝑁𝑡𝜎𝑛𝑣𝑡ℎ(𝑛0+𝑝0+ ∆𝑛) . (3.5) The doping level of the sample can be easily measured via dark conductance measurements. This gives both n0 and p0 in the equation. Then, the parameters to be
fitted are n1 (or p1, or Et), σn and σp (or k together with one of the capture cross section
ratios), and Nt. Generally it is not possible to separate σn and Nt if both are unknown, as
it is their product that appears in the SRH equation. For example, in the cases of the BO defect and the Al-O defect for which the absolute concentration is difficult to determine,
σn and Nt are usually not determined separately in lifetime spectroscopy studies [9, 10].
If Nt is known or can be measured using other techniques, then both σn and Nt can be
determined. Keeping this in mind, the three parameters to be fitted in the model can be regarded as Et, σnNt, and k.
Generally, fitting one set of injection-dependent lifetime data (usually measured at room temperature) does not allow all of the three parameters to be determined, as different combinations of the values of the parameters can result in the same lifetime value. To allow unambiguous determination of the defect parameters, one can measure the injection-dependent lifetime at different temperatures, which is termed Temperature- and Injection-Dependent Lifetime Spectroscopy (TIDLS) [6]. Another option is to simultaneously fit the injection-dependent lifetime measured on samples with different doping levels [11], which is the method we use to determine the defect parameters of Cri and CrB pairs in Chapter 5. Adding the temperature-dependence or the doping level-
dependence is essentially adding another condition (limit) in the fitting. A larger range of the temperature or the doping level helps to reduce the uncertainty ranges of the defect parameters.
An example of the doping level- and injection-dependent SRH lifetime of FeB pairs in p-type silicon is shown in Figure 3.1. The curves clearly show how the injection- dependence of the lifetime is changed by the doping level. It indicates that, when
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measuring recombination lifetime of a defect in differently doped samples, more information associated with the SRH lifetime is provided, which allows the unambiguous determination of the defect parameters. A study applying this principle to the determination of the capture cross sections of FeB pairs can be found in Ref. [12].
Figure 3.1 SRH lifetime of FeB pairs in p-type samples with different doping levels. The defect parameters are taken from Ref. [13]. The concentration of FeB in the model is 1×1013 cm-3.