Aspect Ratio and Quantum Confinement Tunable Giant Two-Photon Absorption from 1D CsPbI₃ Perovskite Nanorods

Abstract

Herein, we investigate the influence of aspect ratio and quantum confinement on the single-photon (σ₁) and two-photon absorption cross-section (σ₂) for perovskite CsPbI₃ nanorod (NR). Notably, experimentally measured data show extremely high σ₂ for CsPbI₃ NR (10.8 × 10⁷ GM) which is five orders of magnitude higher than organic chromophores, and two order of magnitude higher than CsPbBr₃ nanocrystals. Moreover, σ₂ for NRs can be enhanced by two-orders of magnitude by varying the aspect ratio and σ₁ enhances linearly with aspect ratios. Furthermore, experimental data show moderate quantum confinement effect on the volume-normalized σ₁ and σ₂ for nanorods.

Graphical Abstract:

1. Introduction

All-inorganic cesium lead halide perovskites, with general formula CsPbX₃ (X = Cl, Br, I) are becoming highly promising materials for linear and nonlinear light-emitting applications, due to tunable bandgap with large exciton binding energy properties^1–3. Two-photon absorption (2PA) from cesium lead halide perovskite is a third-order nonlinear optical effect which arises from the strong interaction between light electric fields with perovskite materials^3–8. Materials with large 2PA cross-section (σ₂) are required for modern quantum photonic technologies, nonlinear photonic devices for information, as well as for in vivo imaging, and photodynamic therapy^6–17. Since 2PA cross-sections for commonly used organic and polymeric materials are very low, alternatives are systematically explored by us and another groups^6–17. In the last decade, we and other groups have reported perovskite-based multiphoton absorption materials and shows they exhibit superior 2PA properties compared with traditional organic and polymeric materials^15–24. Since controllable synthesis of stable CsPbI₃ nanocrystals remains a challenge as compared to bromide perovskites, mostly reported 2PA study is based on CsPbBr₃ nanocrystals with different sizes and shapes^4–14. In the current manuscript, we have reported the design, microscopic and optical characterization as well as 2PA properties of one-dimensional (1D) CsPbI₃ nanorods (NRs) with different aspect ratios (AR = length/dimeter) (5.0, 15.0 and 20.0). We have investigated the influence of AR and quantum confinement (QC) on single-photon absorption (1PA) cross-section (σ₁) and σ₂ for perovskite CsPbI₃ nanorods. Experimental data shows σ₁ and σ₂ for nanorods can be enhanced by varying the AR and QC.

2. Experimental Section

Cs-oleate, PbI₃, 1-octadecene (ODE), oleyl amine (OLA), oleic acid (OA), NH₄I and different solvents were purchased from Sigma-Aldrich (St. Louis, MO, USA). The CsPbI₃ NRs with 5.0 AR were synthesized using solvothermal method¹⁷. In brief, for this purpose, 20 mL of Pb-I precursor and 1.8 mL of Cs-oleate precursor were heated at 180 °C using Teflon lined autoclave for 30 minutes. CsPbI₃ NRs with other AR (15.0 and 20.0) were synthesized by continuing the reaction for longer time (50, 110 min). At the end, the product was centrifuged at 8 000 rpm in hexane. Next, nanorods were characterized using tunneling electron microscopy (TEM), high resolution tunneling electron microscopy (HRTEM), scanning electron microscopy (SEM) for determining the size and morphology^12–14. The energy-dispersive X-ray (EDX) spectroscopy and inductively coupled plasma mass spectrometer (ICP-MS), were used to determine the ratio of Cs, Pb and I^12–14.

3. Results and Discussions

TEM data as reported in Figure 1A indicates the AR of CsPbI₃ NRs is 5.0 ± 0.5 (average length 20 ± 5 nm and average diameters are 4 ± 0.5 nm), when the reaction has been performed for 30 minutes. Inserted HRTEM image shows the lattice fringes with interplanar spacing distance of ~0.31 nm, which is due to the (100) crystal plane. TEM image reported in Figure 1B indicates the AR of CsPbI₃ NRs is 15.0 ± 2.0 (average length 90.0 ± 10.0 nm and average diameters are 6.0 ± 2.0 nm), when the reaction has been performed for 50 minutes. TEM image reported in Figure 1C indicates the AR of CsPbI₃ NRs is 20.0 ± 2.0 (average length 240.0 ± 20.0 nm and average diameters are 12.0 ± 1.5 nm), when the reaction has been performed for 110 minutes.

Figure 1:

A) TEM image of CsPbI₃ NRs with aspect ratio (AR) 5.0 ± 0.2. Inserted HRTEM image shows the lattice fringes with interplanar spacing distance of ~0.31 nm, which is due to the (100) crystal plane. B) TEM image of CsPbI₃ NRs with AR 15.0 ± 2.0, C) SEM image of CsPbI₃ NRs with AR 20.0 ± 2.0, D) XRD analysis shows the presence of (100), (110), (200), (201), (202) and (024) indices. E) EDX spectra from nanorods show the presence of Cs, Pb and I. F) EDX mapping of Cs, Pb and I in nanorods. G) Single-photon absorption (1PA) spectra from CsPbI₃ nano rods with different aspect ratios. For this experiment we have used ~0.1 μM CsPbI₃ nano rods in hexane and optical path kept as 1 cm. H) Single-photon absorption (1PA) spectra from CsPbI₃ QDs. For this experiment we have used ~ 0.06 μM CsPbI₃ QDs in hexane and optical path kept as 1 cm. I) Single-photon absorption (1PA) and single-photon luminescence (1PL) spectra from CsPbI₃ NRs with aspect ratio (AR) 5.0 ± 0.2. J) Normalized single-photon absorption (1PA) spectra from CsPbI₃ nano rods with different aspect ratios. K) Single-photon luminescence (1PL) and single-photon luminescence (1PL) spectra from CsPbI₃ QDs. L) Time-resolved 1PL spectra from nano rods with different aspect ratios.

Figure 1D shows the XRD analysis from CsPbI₃ NRs, which indicates the presence of (100), (110), (200), (201), (202) and (024) indices, due to the cubic lattice (PDF#97-016-1481)^12–14,17. EDX spectroscopy and EDX mapping as reported in Figures 1E and 1F show the presence of Cs, Pb and I. Figure 1G and 1H shows the single photon absorption spectra for CsPbI₃ NRs with different aspect ratios and CsPbI₃ quantum dots (QDs). Figure 1I and 1J shows the single photon luminescence (1PL) spectra from CsPbI₃ NRs, which indicates aspect ratio dependent emission with λmax for luminescence from ~615 nm to ~640 nm. Figure 1K shows the 1PL spectra from CsPbI₃ quantum dots (QDs) which exhibits strong red emission with λmax at ~720 nm^{12–14,17–19}.

Comparing the spectra between 1J and 1K, one can clearly note that there is a 100 nm blue-shifted emission for NRs compared to QDs, which is due to the quantum confinement effect in NRs. As shown in Table 1, the extent of the blue shift of the emission depends on the diameter of CsPbI₃ NRs, which is also due to the quantum confinement effect^{4–11,17–19}. Since the Bohr radius for CsPbI₃ perovskite is ~ 6 nm^18–19, by changing the thickness from 4.0 nm to 12.0 nm in our experiment, we have developed strongly quantum-confined to weakly quantum-confined CsPbI₃ NRs and they have exhibited different amount blue-shifted emission^18–19.

Table 1:

Diameter, length, volume, aspect ratio (AR), QCP, λmax for luminescence, τ and PLQY for CsPbI₃ NRs.

Diameters	4.0 ± 0.5 nm	6.0 ± 1.0 nm	12.0 ± 1.5 nm
Length	20.0 ± 5.0 nm	± 10.0 nm	240.0 ± 20.0 nm
AR (L/D)	5.0 ± 0.5	15.0 ± 2.0	20.0 ± 2.0
Volume	251 nm3	2543 nm3	27146 nm3
QCP	0.33	0.50	1.0
λmax	615 nm	625 nm	640 nm
τ (ns)	18	27	39
PLQY (%)	30	38	48

The quantum confined parameter (QCP), can be expressed using Equation (1)^{3–7,18–19},

$$\text{QCP}=\frac{d}{2R_0}$$ (1)

Where d is the diameter of NRs and is R₀ is the Bohr radius. As shown in Table 1, QCP varies from 1 to 0.33 as the dimeter for NRs varies from 12 nm to 4 nm. Reported experimental data shows that the quantum confinement effects influence the energetic states of the exciton, which allow photoluminescence to be blue shifted, as shown in Figure 1J. For the determination of photoluminescence quantum yield (PLQY) for CsPbI₃ nanorods with different aspect ratios, we have used Equation (2).^3–10

$$\text{ PLQY }=\frac{N_{\mathit{\text{emit }}}}{N_{\mathit{\text{absorb }}}}$$ (2)

For this purpose, the number of emitted (N_emit) and absorbed (N_absorb) photons for CsPbI₃ nanorods were determined using an absolute PLQY spectrometer (Hamamatsu)^12–14. As reported in Table 1, the PLQY values for CsPbI₃ NRs with different ARs indicates that PLQY increases from 30% to 48% as we increase the AR. Figure 1L shows the time-resolved photo luminescence decay plots for CsPbI₃ NRs with different AR. The plot has been fitted with a single-exponential function and we have used the Equation (3) to calculate the lifetime τ^4–10.

$$\text{I}(\text{t})=\text{I}(0)e^{\text{t}/\tau }$$ (3)

In the above Equation, I(t) is the luminescence intensity at tine t, I (0) is the luminescence intensity when t = 0 and τ is the lifetime.

In Table 1, we report the τ for different AR of CsPbI₃ NRs calculated using Equation 3, which indicates τ values also depend on the AR for CsPbI₃ NRs. Next, we have determined the single-photon absorption cross-section for CsPbI₃ NRs with different ARs using elemental analysis. The linear absorption cross-section (σ₁) for CsPbI₃ NRs was calculated using Equation 4^7–15,

$${\sigma }_1={\epsilon }_{NPL}\frac{2303}{N_A}$$ (4)

Where ϵ_NPL is the molar absorption coefficient for CsPbI₃ NRs with different ARs and the N_A is Avogadro’s number. The concentration of CsPbI₃ NRs with different AR was calculated from the molar concentration of Pb ions and Cs ions, which was determined from inductively coupled plasma–mass spectrometer (ICP-MS) data and EDX data, as we and others have reported before^12–19. As reported in Table 2, the σ₁ for CsPbI₃ NRs with 20 AR is 58.0 × 10⁻¹⁴ cm². We also measured σ₁ using one-photon induced ground state bleaching (GSB) data^12–19 using femtosecond-transient absorption spectroscopy, as we and others have reported before^12–14.

Table 2:

AR, QCP, σ₁, σ₁ (VN), σ_2, σ₂ (VN) for CsPbI₃ NRs.

AR (L/D)	5.0 ± 0.5	15.0±2.0	20.0±2.0
QCP	0.33	0.50	1.0
σ1 (cm2)	20 ×10−14	42×10−14	58×10−14
σ1 (VN)	79 ×10−17	16.5×10−17	2.1×10−17
σ2 (GM)	1.4×106	11.6×106	10.8 × 107
σ2 (VN)	5.5×103	4.5 × 103	4.0 × 103

Using the transient absorption spectroscopy, we found that the σ₁ for CsPbI₃ NRs with 20.0 AR is 56.1 × 10⁻¹⁴ cm² at 440 nm, which matches very well with the measurement using molar extinction coefficients. Interestingly, as reported in Table 2 and Figure 2F, σ₁ increased around 3 times with the increases of AR. As reported in Figure 2F, σ₁ exhibits a linear relationship with the AR of NRs which is mainly due to volume factor.

Figure 2:

A) Single photon luminescence (1PL) spectra from 20 AR CsPbI₃ NRs at different excitation power when we have used 440 nm excitation light. B) The variation of 1PL intensity with pulse energy for 440 nm excitation light. The linear plot indicates it is indeed a single-photon process. We have performed experiments five times and experimental errors are calculated as 4%, based on standard deviation formula. C) Two photon luminescence (TPL) spectra from 20 AR CsPbI₃ NRs excitation light intensity (pulse energy/cm²) for 880 nm excitation for several excitation laser power levels. D) The variation of 2PL intensity with the square of pulse energy for 880 nm excitation light. The linear plot indicates it is indeed a two-photon process. We have performed experiments five times and experimental errors are calculated as 8%, based on standard deviation formula. E) A comparative open-aperture Z-scan curve for 5 AR CsPbI₃ NRs and 15 AR CsPbI₃ NRs. F) Plot shows how σ₁ varies with aspect ratio (AR) for CsPbI₃ NRs. We have performed experiments five times and experimental errors are calculated as 4%, based on standard deviation formula. G) Plot shows how σ₁ (VN) varies with quantum confinement parameter (QCP) for CsPbI₃ NRs. We have performed experiments five times and experimental errors are calculated as 4%, based on standard deviation formula. H) Plot shows how σ₂ varies with AR for CsPbI₃ NRs. We have performed experiments five times and experimental errors are calculated as 8%, based on standard deviation formula. I) Plot shows how σ₂ (VN) varies with QCP for CsPbI₃ NRs. We have performed experiments five times and experimental errors are calculated as 8%, based on standard deviation formula.

Since PLQY and lifetime is higher for bigger volume NRs, in the presence of 440 nm light, the larger volume NR will be excited better. To understand the volume factor, we have also determined the volume normalized (VN) cross-section (σ₁/volume). As reported in Table 2, the volume independent σ_1, {σ₁ (VN)} for CsPbI₃ NRs varies with the diameter of NRs. As reported in Table 2 and Figure 2G, experimental data indicates higher σ₁ (VN) for lowest dimeter NRs which shows better quantum confinement effect on the σ₁ (VN) for NRs. To understand the influence of AR and QCP on 2PA properties for CsPbI₃ NRs, we have determined TPA properties using a Ti-sapphire laser with 880 nm as an excitation source, as we have reported before^12–14. The absolute σ₂, for CsPbI₃ NRs were calculated using fluorescein as the reference whose TPA cross-sections are known in literature^7–15. For the determination of TPA cross-section (σ_2P) we have used Equation 5^{4–15,22–28},

$${\mathbf{\sigma }}_{\mathbf{2}\mathbf{P}}=\left(\frac{{\mathbf{F}}_{\mathit{\text{CsPbl3 }}}}{{\mathbf{F}}_{\mathit{\text{fluorescein }}}}\right)\left(\frac{{\mathbf{\Phi }}_{\mathit{\text{fluarescein }}}}{{\mathbf{\Phi }}_{\mathit{\text{CsPbl3 }}}}\right)\left(\frac{{\mathbf{C}}_{\mathit{\text{fluarescali }}}}{{\mathbf{C}}_{\text{CsPbl3 }}}\right)$$ (5)

where F is the observed two-photon fluorescence intensity from CsPbI₃ NRs with different aspect ratios and fluorescein, Φ is the quantum yield for CsPbI₃ NR and fluorescein, C is the concentration for CsPbI₃ NR and fluorescein. To understand whether there is any morphological change for CsPbI₃ NRs during the measurement, we have performed XRD and absorption measurement before and after the 2PA cross-sections measurements. We have found out that the morphology change is negligible for our experimental intensity range for CsPbI₃ NRs.

Figure 2A shows the single photon luminescence (1PL) spectra from 50 AR CsPbI₃ NRs at different excitation power at 440 nm excitation light. Figure 2B shows how PL intensity varies with 440 nm laser power. The experimental plot clearly shows the linear plot, which indicates it is indeed a one-photon process. Figure 2C shows the two-photon luminescence (2PL) spectra from 50 AR CsPbI₃ NRs at different excitation powers when we have used 880 nm excitation light. Figure 2D shows how 2PL intensity varies with square of the 880 nm laser power. The experimental plot clearly shows the linear plot, which indicates it is indeed a two-photon process. As shown in Figures 2A and 2C, the 1PL and 2PL spectra from CsPbI₃ NRs are very identical. The experimentally observed identical 1PL and 2PL spectra indicates that when CsPbI₃ NRs are excited by either 440 nm for single-photon absorption or 880 nm for two-photon absorption it will relax to the same lowest excited state. Using fluorescein as a reference, whose σ₂ is well documented in the literature (σ₂ ~ 4.8 GM, where 1 GM = 10⁻⁵⁰ cm⁴ s photon⁻¹)^4–10, and Equation 5, we have determined the σ₂ for 20 AR CsPbI₃ NRs to be 10.4 × 10⁷ GM or 104 × 10⁻⁴⁴ cm⁴ S photon⁻¹ at 880 nm excitation. Experimentally σ₂ for 20 AR CsPbI₃ NRs are several orders of magnitude higher than the two-photon absorption cross-sections reported for organic chromophores (>100 GM) or semiconductor colloidal nanocrystals (>10⁴ GM)^4–12. The reported two-photon absorption cross-section is also more than one to two-orders of magnitude higher than reported CsPBr₃ NRs and CsPb(Cl_0.2Br_0.8)₃ nanorod or CsPb(I_0.15Br_0.85)₃ nanorod reported in literature, as shown in Table 3^{10–14, 21–24}. To validate our finding, we have also determined the two-photon absorption for CsPbI₃ NRs with different AR using the Z-scan technique^{5–15, 25–28} as shown in Figures 2E. For the Z-scans measurement, as we have reported before, Ti-sapphire femtosecond pulsed laser (Coherent, Chameleon) with 100 fs pulse width and 80 MHz repetition rate has been used as an excitation source^12–14.

Table 3:

Two-photon absorption cross-section for perovskite nanorods, nanoplatelets and nanowires reported in the literature and in this manuscript.

Perovskites	σ2 (GM)	AR	Ref.
CsPb(Cl0.2Br0.8)3 nanorod	1.2 × 106 (800 nm)	5.6	10
CsPbBr3 nanorod	1.5 × 106 (800 nm)	5.27	10
PEG coated CsPbBr3 nanorod	2.3 × 105 (800 nm)	15.0	10
CsPb(l0.15Br0.85)3 nanorod	2.4 × 106 (800 nm)	5.28	10
CsPbl3 nanorod	1.4 × 106 (880 nm)	5.0	This work
CsPbl3 nanorod	1.16 × 107 (880 nm)	15.0	This work
CsPbl3 nanoplatelets	2.1 × 107 (760 nm)	2.2	24
CsPbl3 nanoplatelets	2.3 × 106 (800 nm)	0.13	23
CsPbBr3 nanowire	1.7 × 106 (800 nm)	19.0	23
CsPb0.2Cd0.8Br3 nanorod	1.4 × 104 (780 nm)	3.0	22

The normalized transmittance for Z scan measurement for two photon absorptions ΔT (2PA) can be expressed by Equation 6^{5–15, 22–28}.

$$\Delta \text{T}(2\text{PA})=\frac{1}{\left\{1+{\alpha }_2\left[\frac{1-e^{-\alpha 0L}}{{\alpha }_0}\right]\left[\frac{I_0}{1+{\left(\frac{Z}{Zr}\right)}^2}\right]\right\}}$$ (6)

where α₂ is the nonlinear optical coefficient, z is the position of CsPbI₃ NRs in the light path during the measurement, α_o is the linear absorption for CsPbI₃ NRs, I₀ is the laser peak intensity at focal point when Z = 0, Z_r is the Rayleigh length and L is the thickness of the sample^7–15. Using experimental data and Equation 6 we have determined σ₂ for 20 AR CsPbI₃ NRs to be 10.8 × 10⁷ GM at 880 nm excitation, which matches very well with two-photon luminescence measurement.

As reported in Table 3, σ₂ for CsPbI₃ NRs with 15 AR is much higher than CsPbBr₃ NRs, CsPb(Cl_0.2Br_0.8)₃ nanorod or CsPb(I_0.15Br_0.85)₃ nanorod reported in literature. To understand whether the Kerr effect (thermal lens) can overestimate the values of the two-photon absorption cross-section through open aperture Z-scan technique, we have also measured σ₂ for CsPbBr₃ QDs with 10 nm size using and using Z-scan technique and two photon emission technique, whose σ₂ values are well reported in literature^{17,23, 24–28}. We have determined σ₂ for CsPbBr₃ QDs are 1.6 × 10⁵ GM using Z-scan technique and 2.3 × 10⁵ GM using two photon emission technique, which match very well with the literature reported values 1.8 × 10⁵ GM^17,23.

As reported in Table 2 and Figure 2H, σ₂ for CsPbI₃ NRs varies from 1.4 × 10⁶ GM to 10.8 × 10⁷ GM, as the AR increases from 5 to 20. Experimentally measured data clearly shows σ₂ for NRs can be enhanced around two-orders of magnitude by varying the aspect ratios. As reported in Table 2, it is interesting to note that σ₂ can be enhanced two orders of magnitude for CsPbI₃ NRs by changing the AR from 5 to 20, whereas σ₁ enhancement only 3 times for CsPbI₃ NRs by changing the AR from 5 to 20.

Recently Chou and co-workers reported²⁰ theoretical modeling for two-photon excitation properties for quantum dots and they found that σ₂ enhances very sharply with size of the quantum dots, where σ₂ ∝ (diameter)³. On the other hand, theoretical modeling indicates σ₁ enhances slowly, and enhancement factor is proportional with (diameter)¹. Our experimental data also indicates σ₂ enhancement efficiency with aspect ratio is much higher for CsPbI₃ NRs in comparison to the σ₁ enhancement efficiency with aspect ratio. The observed two-orders of magnitude higher TPA properties can be due to the enhanced volume, as reported in Table 2. To understand the volume factor, we have also determined the volume normalized (VN) two-photon absorption cross-sections (σ₂/volume). As reported in Table 2, the volume independence σ₂ {σ₂ (VN)} for CsPbI₃ NRs is dependent on the diameter of NRs. As reported in Table 2 and Figure 2I, experimental data indicates higher σ₂ (VN) for lowest dimeter NRs which shows prominent quantum confinement effect on the σ₂ (VN) for NRs. All the reported results indicate that aspect ratio and quantum confinement are important parameters for developing NLO materials for possible device applications. Since in case of nanorod, as AR decreases the QCP increases, one can enhance the QCP by decreasing the AR.

4. CONCLUSION

In conclusion, experimental data indicates giant two-photon absorption cross-sections from 1D CsPbI₃ NRs which is five-orders of magnitude higher than reported organic chromophores and two-orders of magnitude higher than other cesium bromide nanocrystals. Our findings reveal a prominent aspect ratio effect on the σ₁ and σ₂, properties for 1D CsPbI₃ NRs, which mainly due to the volume effect. Experimental data shows the volume effect for σ₂ is stronger than that of σ_1. Reported data show a moderate quantum confinement effect on the σ₁ (VN) and σ₂ (VN) properties for 1D CsPbI₃ NRs. We have demonstrated aspect ratio and quantum confinement are important parameters to design excellent nonlinear optical nanomaterial for possible applications in quantum computing, light-emitting diodes, non-linear bioimaging and other applications.

Highlights.

• Very high two-photon absorption properties (σ₂) have been observed for CsPbI₃ nanorods.

• σ₂ enhanced around two orders of magnitude with the variation of aspect ratios of nanorods.

• Single-photon absorption cross-section (σ₁) enhances linearly with aspect ratios.

• Volume-normalized σ₁ and σ₂ enhanced moderately with quantum confinement effect.