Effect of Dopant Compensation on the Behavior of Dissolved Iron and Iron-Boron Related Complexes in Silicon

Low-cost silicon feedstock for photovoltaic (PV) industry contains dopant species and metal impurities, in most cases boron (B), phosphorous (P), and iron (Fe) [1–3]. In some cases, a significant dopant compensation also exists, which affects the properties of the silicon substrate and reduces the efficiency of the solar cells [4, 5]. One of the unresolved issues of compensated B-doped silicon is the influence of compensation on the behavior and properties of dissolved iron and of iron-boron pairs (FeB). The stable configuration of FeB is that an interstitial Fe atom (Fei) occupies a tetrahedral (T) interstitial site close to a substitutional B atom (Bs) whereby the positively charged Fe atom is attracted by the negatively charged B atom [6, 7]. In any B-doped p-type silicon wafer, even when it is strongly compensated, Fei is always positively charged and will therefore form pairs with the negatively charged acceptor atoms [8]. As the B atoms are quasi immobile in the relevant temperature range and the pairing reaction itself is very fast, the formation kinetics of FeB are determined only by Fei + diffusion [9, 10] which is little or not affected by the presence of compensating dopants [8]. The migration energy of Fei , which is close to the formation energy of FeB, has been reported to be in the range of 0.58 to 0.81 eV [7]. For compensated silicon, Istratov et al. [7] reported that the effect of P on Fei + migration energy can be ignored.The equilibrium concentration of Fei + (N(Fei+)) depends on the binding energy (Eb) of FeB, the temperature, and the B concentration [11], whereby N(Fei+) can be monitored by the variation of carrier lifetime before and after the association of FeB [11]. E

Low-cost silicon feedstock for photovoltaic (PV) industry contains dopant species and metal impurities, in most cases boron (B), phosphorous (P), and iron (Fe) [1][2][3].In some cases, a significant dopant compensation also exists, which affects the properties of the silicon substrate and reduces the efficiency of the solar cells [4,5].One of the unresolved issues of compensated B-doped silicon is the influence of compensation on the behavior and properties of dissolved iron and of iron-boron pairs (FeB).The stable configuration of FeB is that an interstitial Fe atom (Fe i ) occupies a tetrahedral () interstitial site close to a substitutional B atom (B s ) whereby the positively charged Fe atom is attracted by the negatively charged B atom [6,7].In any B-doped p-type silicon wafer, even when it is strongly compensated, Fe i is always positively charged and will therefore form pairs with the negatively charged acceptor atoms [8].As the B atoms are quasi immobile in the relevant temperature range and the pairing reaction itself is very fast, the formation kinetics of FeB are determined only by Fe i + diffusion [9,10] which is little or not affected by the presence of compensating dopants [8].The migration energy of Fe i + , which is close to the formation energy of FeB, has been reported to be in the range of 0.58 to 0.81 eV [7].For compensated silicon, Istratov et al. [7] reported that the effect of P on Fe i + migration energy can be ignored.The equilibrium concentration of Fe i + (N(Fe i + )) depends on the binding energy (  ) of FeB, the temperature, and the B concentration [11], whereby N(Fe i + ) can be monitored by the variation of carrier lifetime before and after the association of FeB [11].  is in the range of 0.45 to 0.65 eV as reported in a previous study [7,12].For compensated silicon, first-principles calculations show that there is a binding energy of 0.82 eV when B s pairs with substitutional P (P s ) located at its second-neighbor sites [13].This pairing of B and P, which can occur during crystallization from a melt, will also lead to a different binding energy of Fe with the B-P pair due to the fact that also the apparent thermodynamic properties of FeB (in fact of the carrier recombination centers associated with the FeB-P and FeB complexes), as determined from lifetime measurements, will be different in compensated material.Comparing the Fe behavior in compensated silicon with that in uncompensated silicon will therefore yield information on   of iron-boron-phosphorus (FeB-P) related complexes in compensated material.

International Journal of Photoenergy
At temperatures below 100 ∘ C, the formation of FeB is the dominant process in uncompensated material, while a recovery of Fe i species and a reduction in the concentration of FeB are observed at temperatures between 100 and 200 ∘ C [7].At temperatures above 200 ∘ C, acceptors can no longer provide stable traps for iron and iron will diffuse towards more stable sinks such as dislocations, precipitates, or even the sample surface [7,14].Zeng et al. [14] reported that iron forms small precipitates from 300 to 700 ∘ C in as-received Czochralski (CZ) silicon and that Fe precipitation is a diffusion-limited process that follows closely Ham's law [15].Krain et al. [16] reported that the precipitation activation energy is close to the Fe i migration energy.To limit the influence of Fe precipitation,   is determined at temperatures below 200 ∘ C in our experiment.To completely dissociate FeB for B concentrations above 10 16 cm −3 , however, the temperature must be higher than 300 ∘ C in uncompensated Si [17].The total iron concentration can be determined before and after the light induced dissociation of FeB (or Fe-B related complexes) both in compensated and in uncompensated silicon [8].
In this letter, the effect of dopant compensation in silicon on the behavior and properties of Fe is investigated at temperatures between 50 and 270 ∘ C. The concentration of single positively charged interstitial iron atoms N(Fe i + ) in B and P codoped silicon has been compared with that in uncompensated silicon in this temperature range.
1 × 1 cm 2 p-type ⟨100⟩ crystalline silicon samples are prepared.One set of samples (labeled CZ-1) is only B-doped, with a B concentration ( B ) of 1.1 × 10 16 cm −3 .The second set of samples (labeled CZ-2) is B and P codoped, with  B of 4.10 ± 0.04 × 10 16 cm −3 and P concentration ( P ) of 1.20 ± 0.01 × 10 16 cm −3 , as determined by secondary ion mass spectroscopy (SIMS).The interstitial oxygen concentration in all the samples is about 10 18 cm −3 , as determined by Fourier transform infrared spectroscopy (FTIR) using the 3.14 × 10 17 cm −2 calibration factor.After dipping in 0.1 mol/L ferric nitric acid (Fe(NO 3 ) 3 ) solution, Fe was diffused into the samples by annealing in an argon ambient at 800 ∘ C for 2 h, followed by quenching in air.Fe concentration that can be introduced into the samples at that temperature is of the order of 10 12 cm −3 according to the solubility of iron in silicon [7].After that, the samples were subjected to chemical polishing and surface-passivation with SiN  :H films by plasma-enhanced chemical vapor deposition (PECVD) technique.Then, the samples were kept in the dark for more than 24 h to allow the dissolved iron atoms to diffuse and form complexes with dopant atoms until an equilibrium is established at room temperature.Subsequently, the samples were annealed at different temperatures in the range between 50 and 270 ∘ C until equilibrium was reached at each temperature, followed by cooling in water.The applied anneal times were at 50 ∘ C/2 h, at 100 ∘ C/1 h, at 120 ∘ C/40 min, at 140 ∘ C/30 min, at 160 ∘ C/25 min, at 180 ∘ C/17 min, and above 200 ∘ C/10 min.After 200 ∘ C/10 min anneal, the annealing times (<200 ∘ C) were determined when the carrier lifetimes reached the equilibrium state at each temperature.Note that the effects of the B-O complexes were eliminated after 200 ∘ C/10 min anneal, since the B-O complexes were dissociated.The evolution of carrier lifetime with the anneal temperature is measured by the microwave-detected photoconductance decay (MW-PCD) technique using Semilab WT2000 instrument.In all experiments the change of the carrier density after FeB dissociation is less than 6%.
It is well known that association and dissociation of FeB in silicon are reversible, which can be expressed by [9]: Similarly, the formation of FeB-P complexes maybe expressed by where the positively charged P atom is assumed to be located close to the negatively charged B atom.Since Fe i + and FeB have different recombination properties [7], Fe i + concentration can be determined by lifetime measurements on uncompensated samples, using the following equation [18]: where the prefactor  is 3.4 × 10 13 s⋅cm −3 for the WT2000 instruments as determined from the recombination parameters of Fe i + and FeB,  0 is the carrier lifetime when all the Fe i atoms have paired with B, and   is the carrier lifetime after the sample is annealed at temperature  as shown in Figure 1(a).In first-order approximation, the same prefactor  is also used for FeB and FeB-P complexes in compensated silicon since the electronic properties of both defects are not significantly different [19,20].The total concentration of Fe, N(tot), is determined by measuring the lifetime before and after thermal treatment at 200 ∘ C for 10 min [7].This method can only be used when  B is smaller than 10 16 cm −3 [17].N(Fe i ) after thermal treatment at 200 ∘ C for 10 min is (6.1 ± 0.1) × 10 12 cm −3 and (6.2 ± 0.1) × 10 12 cm −3 for compensated and uncompensated silicon, respectively, as shown in Figure 1(b), illustrating that the iron solubility is the same in both materials.The samples are quenched by cooling in water immediately after thermal treatment to reduce the diffusion of iron and thus the complex formation with dopant atoms or iron precipitation.N(Fe i ) increases with temperature even above 200 ∘ C for both samples.This illustrates that not all iron-dopant complexes or small iron silicide clusters dissociated, even at 270 ∘ C. N(tot), can however still be determined by the lifetime measurement before and after illumination.The estimated values of N(tot) are (1.9 ± 0.2) × 10 13 cm −3 and (1.4 ± 0.1) × 10 13 cm −3 for compensated and uncompensated silicon, respectively.Both values are somewhat higher than the estimated solubility which is due to the prefactor  that varies with B (and/or P) concentration [20] while it is assumed constant for the WT2000.In the following, we focus on the ratio of N(Fe i + ) over N(tot) to eliminate the effect of the prefactor .
Figure 2 shows the ratio of N(Fe i + ) to N(tot) at temperatures between 50 and 200 ∘ C for the compensated and uncompensated samples.Note that Fe i concentration is equal to N(Fe i + ) as the Fermi level is below the defect level  V + 0.39 eV of Fe 0/+ , for all temperatures studied [7].It can be seen from Figure 2 that the value of N(Fe i + )/N(tot) increases with increasing temperature for both samples.But the increase rate of N(Fe i + )/N(tot) for the uncompensated material is larger than that for the compensated one if temperature is above 100 ∘ C.
In uncompensated material and assuming there are only two carrier recombination centers, that is, Fe i + and FeB, the equilibrium concentration of Fe i + at a given temperature is given by [21]: where  is the number of possible orientations of the pair with the same symmetry around one B atom (four for the tetrahedral interstitial site),  Si is the lattice site density in silicon (5 × 10 22 cm −3 ),  B is the Boltzmann constant, and  is the absolute temperature.Note that (3) is only valid when iron precipitation can be neglected.In such case the equilibrium FeB concentration, N(FeB), is equal to (N(tot) − N(Fe i + )) [11].Since, at temperatures above 200 ∘ C, the B atoms can no longer provide stable traps for iron, it diffuses towards more stable sinks where it agglomerates [7].Fitting the experimental data by (3), as shown in Figure 2, one obtains   = (0.53 ± 0.02) eV for uncompensated silicon, which is well in the range of 0.45 to 0.65 eV as previously published [7,10] and is close to the electrostatic binding energy of 0.52 eV based on the model of ionic type binding of FeB pair [7].The preexponential factor is (3 ± 1) × 10 −6 which is close to the theoretical value of 0.9 × 10 −6 for ( B / Si ) since  B is 1.1 × 10 16 cm −3 .As shown in Figure 2, when using the same equation ( 3) (meaning that one assumes again that there are two carrier recombination centers, i.e., Fe i + and an iron-dopant complex) for compensated silicon, the best fit yields an effective binding energy of (0.25 ± 0.03) eV, which is 0.28 eV lower than   of FeB in uncompensated silicon.And the preexponential factor is (4 ± 3) × 10 −3 which is three orders of magnitude larger than the value of ( B / Si ), 3.3 × 10 −6 , since  B is 4.10 × 10 16 cm −3 .It illustrates that P codoping with B leads to the creation of different carrier recombination centers, probably besides FeB also FeB-P related complexes.Iron might indeed also form complexes with B-P pairs with a different binding energy than that with B, leading to the observed lower effective binding energy which would be a combination of the binding of FeB and of FeB-P.Substitutional P + close to B − will indeed impact the electrostatic interaction between Fe i + and B s − .On the basis of photoluminescence (PL) measurements, Tajima et al. [22] suggested that P and B impurities in solar grade silicon are separated from each other by about 1.9 to 3.3 nm, which is smaller than the capture radius of B s − for Fe i + , which is about 5-6 nm [7,12].Therefore P s + will lead to a lower binding energy of Fe i + in (Fe i + B s − -P s + ).
The ratio of N(Fe i + ) to N(tot) above 200 ∘ C for 10 min has also been measured, as shown in Figure 3.The experimental points are always below the simulated data based on (3) and the difference increases with increasing temperature.This behavior illustrates that some of the dissociated Fe atoms have reassociated with the dopant or have agglomerated into iron precipitates in the bulk or at the wafer surface.Zeng et al. [14] International Journal of Photoenergy found that the Fe precipitation at 300-700 ∘ C is a diffusionlimited process, just like for the association of FeB.Krain et al. [16] obtained an activation energy close to Fe i + migration energy of 0.67 eV [7].Therefore, we fit the line with (4), taking into account the dissociation of FeB and the decrease of the iron concentration due to a diffusion-limited reaction: where  is a preexponential factor to be fitted and   is the iron diffusion energy which is fixed at 0.67 eV.A best fit is obtained for  = (6.8± 0.5) × 10 4 and   is fixed at value of (0.53 ± 0.01) eV with  2 = 0.9997.This result confirms that some of iron has precipitated or reassociated whereby both processes are controlled by iron diffusion.However, the situation is different in compensated silicon, as shown in Figure 4.In that case, the experimental result for N(Fe i + )/N(tot) is greater than the simulated values based on (3), which is in contrast to uncompensated silicon as shown in Figure 3.This is probably due to the formation of FeB-P complexes.Macdonald et al. [8] reported that the diffusion barrier of Fe i + is not affected by the presence of compensating dopants.As mentioned, P s + will however affect the electronic interaction between B s − and Fe i + .Based on (1a) and (1b), where  is the fraction of iron that forms pairs with boron,  2 is the binding energy between Fe and the BP pair in the FeB-P complex, and   is fixed at value of 0.53 eV.The best fit yields  2 = (0.45 ± 0.17) eV and  = (0.74 ± 0.05) with  2 = 0.995, as shown in Figure 4.The value of  suggests that 26% of the iron has formed FeB-P complexes which is in good agreement with the ratio of  P over  B (1.1 × 10 16 cm −3 /4.10 × 10 16 cm −3 ).This illustrates once more that, besides the recombination centers related to FeB and Fe i + , also the FeB-P complex is an effective recombination center in compensated silicon.The reduced binding energy of FeB in the FeB-P complexes results in 0.28 eV decrease of the apparent binding energy in compensated silicon.
For further support of the above mentioned model, the binding energy of FeB and FeB-P complexes has been calculated using the density-functional theory (DFT).All calculations were performed with the Vienna ab initio simulation package (VASP) [23].A 216-atom supercell, Brillouinzone sampling with 2 × 2 × 2 Monkhorst-Pack -point

3 2 1 CZ- 1 :CZ- 1 :Figure 1 :
Figure 1: (a) The carrier lifetime as a function of temperature for CZ-1 and CZ-2.(b) The concentration of Fe i as a function of temperature for CZ-1 and CZ-2.Black squares and red circles refer to the CZ-1 and CZ-2 samples, respectively.

Figure 2 :
Figure 2: The ratio of N(Fe i + )/N(tot) as a function of temperature for CZ-1 and CZ-2.Black squares and red circles refer to the CZ-1 and CZ-2 samples, respectively.The solid lines represent the best fits based on (3).

Figure 3 :
Figure 3: The ratio of N(Fe i + )/N(tot) as a function of temperature for CZ-1.Black squares refer to the experimental data, the blue solid line represents a best fit, and the red dash line is a simulated line based on the function of N(Fe i + )/N(tot) = 1/(1 + 2.7 × 10 −6 exp(0.53eV/ B )).