Morphologies and Nonlinear Optical Properties of Fractal Ge

Sep 11, 2012 - the input irradiance (Ip) ranged from 0.58 to 1.65 GW/cm2. This nonlinear optical material may be tailor-made for a large number of app...
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Morphologies and Nonlinear Optical Properties of Fractal Ge Nanocrystals Embedded in Pd Matrix Lijun Wang,† Xiaojian Chen,‡ Chen Chen,† Yanyu Liu,† Zhiwen Chen,*,†,‡ Chan-Hung Shek,*,‡ C. M. Lawrence Wu,‡ and Joseph K. L. Lai‡ †

Shanghai Applied Radiation Institute, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444, People’s Republic of China ‡ Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

ABSTRACT: An integrated device or component for the semiconductor industry is highly desirable for versatile advanced applications. Group IV semiconductors such as germanium (Ge) and silicon (Si) are unique materials of widespread technological applications, particularly in the field of microelectronic devices and optoelectronic components. Herein, Pd/Ge bilayer films with interesting Ge clusters, which have noninteger dimensions and are called fractals, were successfully prepared by high-vacuum thermal evaporation techniques. It was found that Ge nanocrystals embedded in Pd matrix showed fascinating fractal morphologies with average size of fractal clusters at 680 nm and fractal dimension at 1.708 when the films were annealed at 350 °C for 30 min. The fractal clusters consisted of Ge nanocrystals with diameters ranging from 25 to 55 nm. Third-order optical nonlinearities of the annealed Pd/Ge bilayer films were investigated in detail by Z-scan techniques using a femtosecond laser. Experimental results indicated that the nonlinear absorption coefficient and refractive index of the fractal Ge nanocrystals embedded in Pd matrix were in the ranges from 3.4 to 4.3 × 10−7 cm/W and from 4.2 to 5.0 × 10−12 cm2/W, respectively, when the input irradiance (Ip) ranged from 0.58 to 1.65 GW/cm2. This nonlinear optical material may be tailor-made for a large number of applications such as high-speed microelectronics and infrared optical micro/nanodevices.

1. INTRODUCTION

extensive as that of Si and nebulous domains in our understanding of its precise technical functions still remain. In recent years, semiconductor Ge and composites have attracted much attention due to its broad applications in many fields such as microelectronic devices and optoelectronic components, one-dimensional quantum transistors, and lightemitting diodes, etc.10−12 It is known that Ge has an excitonic Bohr radius of 24.3 nm, which is much larger than that of silicon (4.9 nm).13 Thus, semiconductor Ge should exhibit more pronounced quantum size effects, which will be more prominent in Ge nanocrystals even for larger sizes of the crystallites. These electronic conditions lead to an expectation that it is much easier to change the electronic structures around the band gap of Ge nanocrystals, which results in strong

With the development and progress of science and technology, semiconductor materials encompass a burgeoning and fascinating area of materials research that has significant technological implications.1 In group IV semiconductors, germanium (Ge) and silicon (Si) belong to a class of unique materials with widespread technological applications because of their valuable semiconducting, mechanical, electrical, and optical properties in the fields of macro/mesoscopic materials and micro/nanodevices.2,3 These semiconductors are indispensable for many applications, particularly for the electronics and photovoltaic industry.4−6 Semiconductors such as Ge and Si micro/ nanoclusters are of fundamental importance to the development of smart and functional materials, devices, and systems.7−9 An integrated device or component for the semiconductor industry is highly desirable for versatile advanced applications. Notwithstanding the fact that semiconductor Ge has been applied to many areas, its use is not as © 2012 American Chemical Society

Received: July 31, 2012 Revised: September 5, 2012 Published: September 11, 2012 21012

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modification of its optical properties.14 Considerable effort has been focused on the synthesis of single component Ge nanoparticles, nanowires, nanorods, nanotubes, thin films (which have the zero, one, and two integer dimensions), and the exploration of their novel properties.15−17 It is expected that these integer dimensional nanostructures may constitute important building blocks for micro/nanodevices and offer exciting opportunities for both fundamental research and technological applications. However, fractal clusters with noninteger dimensions are also a class of unique materials with widespread technical applications. In our previous works, fractal micro/nanoclusters including Mn3O4 and SnO2 have been successfully prepared by chemical liquid homogeneous precipitation18 and pulsed laser deposition method,19 respectively. A variety of methods, such as thermal evaporation, magnetron sputtering, and chemical vapor deposition, are available for the preparation of the fractal clusters in metal/ semiconductor composite thin films.20 Since the properties of materials strongly depend on its micro/nanostructure, composition, atomic structure, local chemistry of interfaces and crystal defects, which all result from the fabrication processes, the influence of fractal clusters on material properties is especially remarkable. The development of materials with novel linear and nonlinear optical properties is the key to realizing the full potential of all types of optical computing and signal processing.21−23 Due to the fact that the porous Si was found to have efficient visible photoluminescence,24 semiconductor Ge and Si nanostructures have been extensively investigated because it will open up a new possibility for indirect gap semiconductors as novel materials for optoelectronic applications.25,26 In comparison with the electronic properties of Si, Ge has a larger dielectric constant and smaller effective mass for electrons and holes, and the energy difference (ΔE = E0 − Eg = 0.12 eV) between the indirect gap (Eg = 0.66 eV at 300 K, Γ′25 → L1) and the direct gap (E0 = 0.8 eV, Γ′25 → Γ′2) is smaller.26 To date, several preparation methods have been implemented to produce semiconductor nanocrystals with narrow and reproducible size distribution.27−29 Altering the average nanocrystal size allows a broad modification of their energy structure, particularly in the energy band gap. Moreover, three-dimensional quantum confinement results in discrete energy structures and atomic-like behavior for nanocrystal optical transitions. Strong and fast optical nonlinearities, and strong photo- and electroluminescence, have been observed in materials composed of semiconductor nanocrystals.30,31 However, the understanding of the nonlinear optical response in these materials is still not well established. In this article, we report an experimental investigation of third-order optical nonlinearities of fractal Ge nanocrystals embedded in Pd matrix using femtosecond laser pulses at 800 nm wavelength. New strategies of fractal assessment for Pd/Ge bilayer films after annealing are of fundamental importance in the development of micro/nanodevices. Pd/Ge bilayer films with interesting Ge clusters, which have noninteger dimensions and are called fractals, were successfully prepared by highvacuum thermal evaporation techniques. It was found that Ge nanocrystals embedded in Pd matrix showed fascinating fractal morphologies with average size of fractal clusters at 680 nm and fractal dimension at 1.708 when the films were annealed at 350 °C for 30 min. The fractal clusters consisted of Ge nanocrystals with diameters ranging from 25 to 55 nm. Third-order optical nonlinearities of the annealed Pd/Ge bilayer films were

investigated in detail by Z-scan techniques using a femtosecond laser. Experimental results indicated that the nonlinear absorption coefficient and refractive index of the fractal Ge nanocrystals embedded in Pd matrix were in the ranges from 3.4 to 4.3 × 10−7 cm/W and from 4.2 to 5.0 × 10−12 cm2/W, respectively, when the input irradiance (Ip) ranged from 0.58 to 1.65 GW/cm2. Our findings may enable this novel functional material with fractal Ge clusters to be tailor-made for a large number of applications such as high-speed microelectronics and infrared optical micro/nanodevices and provide new opportunities for future study of optical nonlinearities in semiconductor architectures.

2. EXPERIMENTAL SECTION Specimens were prepared by evaporation on a freshly cleaved NaCl (100) single crystal substrate at a pressure of 2.67 × 10−3 Pa at room temperature.32 We deposited Ge first and then Pd without breaking the vacuum (about 2.67 × 10−3 Pa) by evaporating high-purity germanium (99.9%) and palladium (99.9%) from two resistive-heated tungsten boats; viz., the bottom layer was amorphous Ge (a-Ge) and the top one was polycrystalline Pd (p-Pd). According to the evaporation equation t = m/4πr2ρ, where t is the thickness of the films, m is the mass of the Pd or Ge, ρ is the density of the Pd or Ge, and r is the distance from the specimen to the evaporation source, here r = 10 cm in present experiments. The thickness ratio of the p-Pd and a-Ge films was designed to be 25/50 nm. All as-deposited specimens were annealed in a vacuum of about 2.67 × 10−3 Pa at 350 °C for 30 min. After annealing, the specimens were floated on distilled water and then placed on copper meshes to be observed with a Philips CM20 transmission electron microscope at an acceleration voltage of 200 kV. By such annealing, self-similar fractal clusters may be formed in these annealed films. Since the annealing temperatures can effectively control the morphology of the fractal clusters, the density of the different fractal clusters formed at a given annealing temperature is also approximately uniform at different sites of the sample. The average value of the evaluated dimension, obtained from different regions can be approximately considered as the whole sample’s fractal dimension (D). The fractal dimension for the sample was calculated by measuring the fractal dimensions of these self-similar clusters using the conventional box-counting method.33,34 The linear optical absorption spectrum of the Pd/Ge bilayer films annealed at 350 °C for 30 min was measured by using a Hitachi U-3040 spectrophotometer at room temperature. The sensitive and reliable Z-scan techniques were used to determine the nonlinear absorption coefficient (β) and nonlinear refractive index (n2) values of the sample. In Z-scan experiments, the laser pulses were delivered by a mode-locked Ti:sapphire laser (Coherent MIRA 900-F) operating at a repetition rate of 76 MHz. The full width at half-maximum (fwhm) pulse duration was 120 fs (fs). All measurements were performed at a wavelength of 800 nm. 3. RESULTS AND DISCUSSION A typical bright-field image of transmission electron microscopy (TEM) and the corresponding selected area electron diffraction (SAED) patterns (the inset at the upper right-hand corner) of the morphology of the as-prepared Pd/Ge bilayer films is shown in Figure 1a. As seen in the TEM bright-field image, the 21013

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The average size of fractal clusters was estimated by measuring the fractal regions. The measuring procedure was as follows: for each TEM image, we chose 10 fractal clusters at random to get an average value. The average size of the fractal clusters was obtained by averaging the values of TEM image with different orientations. The SAED patterns proved that, besides the Pd2Ge compound, the PdGe compound was also formed in the assigned annealing temperature. This indicated that the Pd2Ge compound can react completely with a-Ge and form the PdGe compound by solid-state reaction: Pd2Ge + Ge → 2PdGe. Figure 2a shows the corresponding size distribution of fractal Ge clusters in Figure 1b, where the solid line is a log-normal fit

Figure 1. (a) TEM bright-field image and SAED patterns (the inset at the upper right-hand corner) of the as-prepared Pd/Ge bilayer films. (b) TEM bright-field image and SAED patterns (the inset at the upper right-hand corner) of the Pd/Ge bilayer films annealed at 350 °C for 30 min.

Figure 2. (a) Size distribution of fractal Ge clusters in Figure 1b, where the solid line is a log-normal fit to the size distribution of fractal Ge clusters. The average size of fractal Ge clusters is 680 ± 0.1 nm. (b) Plot of ln(N) versus ln(1/L) of fractal Ge clusters in Figure 1b, where L is the box size and N is the number of boxes occupied by fractal Ge nanocrystals.

as-prepared bilayer films were homogeneous in morphology before annealing. The nanocrystals close to Bragg orientations were recognizable by their dark contrast. The SAED patterns of the as-prepared bilayer films confirmed that the films consisted of amorphous Ge (indicated by diffuse ring of a-Ge) and polycrystalline Pd (p-Pd). It can be seen that the Pd2Ge compound was formed in the as-prepared bilayer films during evaporation. This indicated that the formation process of the Pd2Ge compound is a solid state reaction between Pd and Ge atoms at room temperature: 2Pd + Ge → Pd2Ge. We found that the formation temperature (room temperature) of the Pd2Ge compound was lower than 150 °C, as reported in previous literature.35,36 Figure 1b shows a typical TEM brightfield image and SAED patterns (the inset at the upper righthand corner) of the Pd/Ge bilayer films annealed at 350 °C for 30 min. After annealing at 350 °C, the diffuse ring of a-Ge was replaced by crystalline Ge (c-Ge), as shown in the inset of Figure 1b. It can be seen that the films display fascinating white fractal clusters, which consisted of Ge nanocrystals with diameters ranging from 25 to 55 nm. These white fractal morphologies were composed of a few thick branches, and the fractal shape was a compact structure. The average size of fractal Ge clusters was calculated to be about 680 ± 0.1 nm.

to the size distribution of the fractal Ge clusters, which can be well described by a log-normal function with a geometric mean diameter of 680 nm and a dimensionless geometric standard deviation of 0.1 nm. It is found that the fractal Ge clusters are nearly uniformly distributed in the annealed films. Figure 2b shows the plot of ln(N) versus ln(1/L) of the fractal Ge regions in Figure 1b, where L is the box size and N is the number of boxes occupied by the fractal Ge nanocrystals. It can be seen that the plot shows a good linear relationship, which means that the morphologies of fractal Ge nanocrystals have scale invariance within these ranges. Thus, these Ge nanocrystals can be regarded as fractals. In order to obtain the fractal dimension (D), we fit a linear relationship for the function ln(N) versus ln(1/L). The results testify that the fractal dimension (D) is about 1.708, as shown in Figure 2b. At the early crystallization state of a-Ge, the crystallization energy and strain energy act together to make the Ge atoms crystallize and nucleate at some of the favorite sites at Pd/Ge and Pd2Ge/Ge interfaces. We believe that the interdiffusion behavior between Pd and Ge atoms may influence the fractal size and dimension. 21014

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(Z = 0) where it has the minimum transmittance for two or multiphoton absorption or maximum transmittance for saturation of absorption. Figure 4a and b show, respectively,

When the crystallization of a-Ge becomes easier after annealing, the a-Ge atoms near the grown crystal can easily coalesce other a-Ge before the Ge grain grows further, resulting in fine branches and smaller fractal dimension. During annealing, the a-Ge atoms nucleate at Pd/Ge or Pd2Ge/Ge interfaces, the surrounding Ge atoms diffuse along the interfaces and through the Pd layer to deposit on the nucleus, and the Pd atoms aggregate in the opposite direction. The heat released by crystallization leads to a local temperature rise in the surrounding area, and this temperature field can propagate quickly and stimulate new nuclei appearing randomly in nearby regions. The stimulated nuclei of the next generation can also cause a local temperature rise and repeat the above processes many times until fractal clusters are formed.37,38 This fractal cluster may lead to improvement in the design of semiconductor micro/nanodevices for microelectronic industry applications. It is known that the Ge is a unique indirect gap material in bulk form. When these semiconductors are prepared into lowdimensional nanoscale morphologies, the optical transitions across originally an indirect energy gap can be allowed in the first order of the perturbation theory due to confinementinduced mixing of states. For example, the calculations performed in Si nanocrystals show that the probability of these transitions remains low unless the nanocrystal size is smaller than 2−3 nm. Thus, it is not clear whether we can expect a large confinement-induced increase in absorption in the case of the relatively large fractal Ge nanoclusters. Figure 3

Figure 4. Normalized open-aperture (OA, Figure 4a) and closedaperture (CA, Figure 4b) Z-scan data of the Pd/Ge bilayer films annealed at 350 °C for 30 min. The solid circles are the experimental data. The solid curves are the theoretical fits.

the normalized open-aperture (OA) and closed-aperture (CA) Z-scan data of the Pd/Ge bilayer films annealed at 350 °C for 30 min obtained with linearly polarized 800 nm and 120 fs pulses. For each Z-position, the traces of the intensity collected by the OA and CA detectors can be acquired. It can be found that all the input irradiances are the peak irradiances at the focus within the sample. An exponential fit of these traces allowed us to produce the curves at different input irradiances. The curves obtained in this way, representing the single-pulse and cumulative effects, were used to estimate the values of nonlinear absorption coefficient (β) and nonlinear refractive index (n2).40 It is known that the total absorption coefficient can be written as α = α0 + βI, where I was the irradiance of the laser beam within the sample. Using the OA Z-scan theory,41 we calculated the normalized power transmittance as a function of the Z-position of the sample using β as a free parameter. The β value can be extracted from the best fitting curve. The solid line in Figure 4a shows the best fit to experimental Z-scan data at an irradiance of 0.98 GW/cm2, which yields β = 3.9 × 10−7 cm/W. We also conducted OA Z-scan measurements at input irradiances ranging from 0.58 to 1.65 GW/cm2; e.g., 0.58, 0.78, 0.98, 1.34, and 1.65 GW/cm2 correspond to β = 4.3, 3.5, 3.9, 4.0, and 3.4 × 10−7 cm/W, respectively. It was found that the measured β values were independent of the laser irradiance, as shown in Figure 5, which implied that the observed nonlinear absorption was a third-order process. Correspondingly, the total refractive index can be expressed as n = n0 + n2I, where n0 is the linear index of refraction. In Z-scan measurements with laser pulses at high repetition rate, it is known that the thermallens effect is important due to the strong linear absorption in the sample at 800 nm wavelength. The CA Z-scans are therefore sensitive to nonlinear refraction of either electronic or

Figure 3. Linear absorption spectrum of the Pd/Ge bilayer films annealed at 350 °C for 30 min.

shows a typical linear absorption spectrum for the annealed Pd/ Ge bilayer films with fractal Ge nanocrystals. Interestingly, it is found that the linear absorption spectrum shows two resonant absorption ramps at around 1.3 and 3.1 eV, respectively, which may correspond to the Γ′25 → Γ′2 (ΔE ∼ 0.8 eV) transitions and Γ′25 → Γ′15 (ΔE ∼ 2.7−3.6 eV) transitions in bulk Ge.39 The above experimental results indicated that the linear absorption is not negligible in the visible and near-infrared ranges when the fractal Ge nanocrystals formed in the annealed Pd/Ge bilayer films. It is common knowledge that the real part of the refractive index could be altered by cumulative sample heating in Z-scan measurements with high repetition rate lasers. The nonlinear absorption arises from either direct multiphoton absorption or saturation of single photon absorption. The Z-scan with no aperture is expected to be symmetric with respect to the focus 21015

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nonlinearities of the annealed Pd/Ge bilayer films were investigated in detail by Z-scan techniques using a femtosecond laser. Experimental results showed that the nonlinear absorption coefficient and nonlinear refractive index of the fractal Ge nanocrystals embedded in Pd matrix were in the ranges from 3.4 to 4.3 × 10−7 cm/W and from 4.2 to 5.0 × 10−12 cm2/W, respectively, when the input irradiance (Ip) ranged from 0.58 to 1.65 GW/cm2. Our finings may enable this novel functional material with fractal Ge clusters to be tailormade for a large number of applications such as high-speed microelectronics and infrared optical micro/nanodevices and provide new opportunities for future study of optical nonlinearities in semiconductor architectures, with the goal of optimizing photoelectronic functional material properties for specific applications.

Figure 5. Measured nonlinear absorption coefficient (β) and nonlinear refractive index (n2) values versus the input irradiance (Ip) of the Pd/ Ge bilayer films annealed at 350 °C for 30 min.

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thermal origin, and to nonlinear absorption. By using the calculation method of previous reports,23,26 the normalized transmitted power for CA Z-scans can be written as 1 T= ⎡ 1 − exp(−αL) ⎤ 2 1 + βI 0 ⎣ ⎦ /(1 + ξ ) α ⎤ ⎡ C1z C2z ×⎢ + − 1 ⎥ ⎦ ⎣ (1 + ξ 2)2 (1 + ξ 2)

AUTHOR INFORMATION

Corresponding Author

*Phone: +86 21 66137503. Fax: +86 21 66137787. E-mail: [email protected] (Z.C.); [email protected] (C.-H.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work described in this article was financially supported by the Shanghai Pujiang Program (Project Number: 10PJ1404100), China, Key Innovation Fund of Shanghai Municipal Education Commission (Project Number: 10ZZ64), National Natural Science Foundation of China (Project Number: 11074161), Science and Technology Commission of Shanghai Municipality (Project Number: 10JC1405400), and Shanghai Leading Academic Discipline Project (Project Number: S30109). This work was also supported by strategic research grant (Project Number: 7008184) from the City University of Hong Kong and a General Research Fund (Project Number: CityU 119212) from the Research Grants Council, Hong Kong.

(1)

where C1 = (2LI0n2)/(n02ω02), C2 = (LPincKT)/(πn02ω02), ζ = z/z0, z0 = πω02/λ, I0 is the peak irradiance at the focal plane, Pinc is the beam average power on the sample, L is the sample thickness, ω0 is the Gaussian beam radius, and KT is a constant related to the thermo-optic coefficient and thermal conductivity of the films. It is worth noting that n2 in eq 1 is the electronic contribution to the nonlinear refractive index, excluding the thermal contribution. C1 and C2 denote the electronic and thermal contribution to nonlinear phase shift, respectively. The different Z dependence of the two terms with C1 and C2 inside the bracket of eq 1 comes about because the electronic contribution to the refractive nonlinearity is proportional to the peak irradiance, whereas the thermal contribution is proportional to the laser average power. Using eq 1, the n2 and KT values can be extracted from the best fit curves to experimental CA Z-scan data at five different input irradiances. The obtained values were n2 = 4.95, 4.2, 4.45, 5.0, and 4.38 × 10−12 cm2/W, as shown in Figure 5, which were independent of the different input irradiances at 0.58, 0.78, 0.98, 1.34, and 1.65 GW/cm2, respectively, implying that the observed nonlinear refraction is of Kerr nonlinearity. This indicates that the fractal Ge nanocrystals give rise to the observed nonlinearities in the annealed Pd/Ge bilayer films. This nonlinear optical film with fractal Ge nanocrystals may be tailor-made for a large number of applications such as high-speed microelectronics and infrared optical micro/nanodevices.

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4. CONCLUSIONS In summary, the Pd/Ge bilayer films with interesting Ge clusters, which have noninteger dimension and are called fractals, were successfully prepared by high-vacuum thermal evaporation techniques. It was found that Ge nanocrystals embedded in Pd matrix showed fascinating fractal morphologies with average size of fractal clusters at 680 nm and fractal dimension 1.708 when the films were annealed at 350 °C for 30 min. The fractal clusters consisted of Ge nanocrystals with diameters ranging from 25 to 55 nm. Third-order optical 21016

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