Far Infrared Studies of Silicon using Terahertz Spectroscopy

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1 The Physics and Materials Challenges for Integrated Optics - A Step in the Future for Photonic Devices Organized by Animesh Jha, Andrew Bell, Nuggehalli M. Ravindra, and Andy R. Harvey Materials Science & Technology 2005 Far Infrared Studies of Silicon using Terahertz Spectroscopy Amartya Sengupta, Aparajita Bandyopadhyay, John F Federici and Nuggehalli M Ravindra Department of Physics, New Jersey Institute of Technology, Newark, NJ 07103, USA Keywords: Terahertz Spectroscopy, Electronic Materials, Characterization Abstract In this work, the optical properties of p- type silicon wafers, of various thicknesses, have been studied in the frequency range of THz. It is seen that, for low resistivity silicon, the optical properties are dominated by the presence of dopants. The analysis technique deployed in the present work explores a general iterative procedure to determine the real and imaginary parts of the complex dielectric constant without utilizing Kramers-Kronig relationships. This study not only holds scientific relevance in material science but also opens up rich avenues for novel applications of terahertz spectroscopy to semiconductors. Introduction In recent years, Terahertz (1 THz = cycles/sec and 300 µm in wavelength) spectroscopy has become a standard technique for non-contact, non-invasive, real-time characterization technique for the measurement of material parameters. Measurement of optical properties, in general, is important for studying energy band-structure, impurity levels, excitons, localized defects, lattice vibrations, and certain magnetic excitations. The far-infrared or the THz region of the electromagnetic spectrum is of critical importance in the spectroscopy of condensed matter systems as the optical and electronic properties of semiconductors and metals are greatly influenced by excitons and Cooper pairs whose energies are resonant with THz photons. The THz regime also coincides with certain inelastic processes like tunneling and quasi-particle scattering in solids. At the same time, THz time domain spectroscopy (THz-TDS) is a reliable tool for studying confinement energies in artificial dielectrics (ADs) such as artificially synthesized nanostructures and for non-contact estimation of interface traps in high dielectric constant (K) materials [1-3]. It has also been used to study the effects of grain size dependent scattering in various materials [4, 5]. Most recently, the possibility of interferometric imaging for security screening applications is also being considered using THz radiation [6, 7]. During the past several years, researchers have exploited the THz range of frequencies for material identification and characterization, which has been possible due to the availability of a variety of sources and detectors [8-10]. The allure of THz-TDS can be attributed to the facts that (a) coherent detection enhances the signal to noise ratio (SNR) of the measurement; (b) time resolved studies with sub picosecond time resolution is possible in the far-infrared component of the electromagnetic spectrum; and (c) compared to other methods such as millimeter wave spectroscopy, THz-TDS has more spatial resolution and it can record both the amplitude and phase of the THz waves simultaneously. In the field of material characterization, THz spectroscopy bears special significance as it can serve the purpose of an in situ, non contact measurement tool during device fabrication. This allows the 39

semiconductor device production line to achieve a dynamic control over the device properties even before the final quality control check of the packaged products.

and the low frequency limit of most practical lasers and other incoherent sources [12-14].

$In this work, a general method has been discussed to determine the complex index of refraction of semiconductors which could lead to estimation of other related parameters of the material such as$ Different types of silicon wafers have been used to validate the analysis which can be divided into three different classes on the following basis: resistivity, polishing and presence of oxide layer.

Different types of silicon wafers have been used to validate the analysis which can be divided into three different classes on the following basis: resistivity, polishing and presence of oxide layer.

2 semiconductor device production line to achieve a dynamic control over the device properties even before the final quality control check of the packaged products. Even though similar techniques exist at other wavelengths, THz-TDS offers a unique opportunity to estimate material parameters in the interval between the high frequency limit of modern electronics and the low frequency limit of most practical lasers and other incoherent sources [12-14]. Previous studies involving silicon have shown that it is an exceptional optical material in the infrared range of frequencies [15-19]. In this work, a general method has been discussed to determine the complex index of refraction of semiconductors which could lead to estimation of other related parameters of the material such as electrical conductivity. Different types of silicon wafers have been used to validate the analysis which can be divided into three different classes on the following basis: resistivity, polishing and presence of oxide layer. THz Set - up Experimental Arrangement The experimental arrangement consists of a Ti: Sapphire laser emitting 125 fs pulses at 800 nm, part of which pumps an Auston switch consisting of a semi insulating GaAs wafer with a gold transmission line structure microlithographically imprinted on it [20]. This acts as a coplanar stripline (CPS) antenna when an AC bias is applied to it and becomes the source of THz radiation with a center frequency of about 0.5 THz [21]. A schematic of the THz generator is shown in Fig 1. Figure 1: Configuration of the Auston switch used in the present set-up; A is the LTG-GaAs substrate, B is the transmission line structure, C is the pump laser beam, D is the source of ± 5 V bias at 12 KHz. The values of the switch are L = 1mm, b = 60 µm, d = 10 µm and w = 20 µm A silicon ball lens mounted above the antenna collects the emitted THz beam and guides it through a set of gold plated off axis parabolic mirrors to the detector. The detection scheme is just the reverse of the generation process, where the incoming THz electric field provides the bias for the antenna which is optically gated by the other part of the laser pulse. The sample being studied is placed at the focus of the THz beam between two parabolic mirrors. The experimental layout for THz TDS is shown in Fig. 2. Figure 2: Experimental arrangement of the THz Spectroscopy system 40

3 Samples Studied Table I summarizes the different types of wafers that were used in this study. All the wafers were of 4 diameter and were supplied by Virginia Semiconductors Inc and Silicon Sense Inc. Table I. Parameters of wafers that were used in the experiments Wafer Thickness Resistivity Polish Exposed Side p type Silicon 50 µm Ω-cm Double side <100> p type Silicon 250 µm Ω-cm Double side <100> p type Silicon 475 µm 1 2 kω-cm Single side <100> SiO 2 on Silicon SiO 2 : 0.5 µm Silicon: 700 µm Ω-cm Double side <100> Theoretical Analysis Time resolved THz spectroscopy measurements provide simultaneous information about the amplitude and phase of the samples under study. One reference waveform E ref (t) is measured without the sample or with a sample of known dielectric properties, and a second measurement E sample (t) is performed, in which the THz radiation interacts with the sample. The transmission spectrum is calculated using the Discrete Fourier Transform (DFT) of the sample and reference measurements: T exp Esample( ν ) ( ν ) = (1) E ( ν ) ref In the case of optically thin samples (the transit time of the THz pulse through the sample is comparable to the width of the pulse itself), the overlap between successive echoes limits the ability to break up the transmitted THz signal through the sample into individual echoes and hence we have to consider the effects of multiple reflections through the sample. The following conditions are assumed in the analysis: the electromagnetic response of all the media is linear; the sample is homogeneous with two optically flat and parallel sides; the sample and the overlayers are isotropic without surface charges or the presence of an interface. The transmitted electric field through the sample E sample (ν), is given by, E T P d R P d E ab, = m ab, = m 2 k sample( ν ) = ab m( ν, ) { ab m ( ν, )} ( ν) ab, = 1 k = 0 ab, = 1 a b a b (2) 41

4 The second term is the Fabry Perot term arising out of multiple reflections within the thin samples. In the above equation, E(ν) is the electric field of the emitted THz signal, R ab, T ab are the Fresnel reflection and transmission coefficients at the a-b interface [20], and P m is the propagation coefficient in medium m over a distance d and is given by, n aν d Pa ( ν, d) = exp i (3) c with n a ( ν ) = na( ν) + iκa( ν) being the complex refractive index of medium a. Hence the complex transmission coefficient T ( ν ) taking into account Fabry Perot effects is given by [17, 23], T( ν, n, l) = 4n 2 π( n 1) νl exp 2 i ( n + 1) c 2 n 1 4πν n l 1 exp i n + 1 c (4) T( ν, nl, ) = ρ ( ν, nl, ) ρ (,, )exp ( (,, ) (, FP ν nl iθ ν nl + θfp ν nl, )) single single (5) To evaluate the Fabry Perot contribution, the samples were assumed dispersionless and to have κ << 1, so that the total complex transmission coefficient can be expressed in terms of the following functions, n + κ 2πκνl ρsingle( ν, nl, ) = exp 2 2 ( n+ 1) + κ c 2 π( n 1) l 1 κ θ ( ν, nl, ) = + tan 2 c n( n 1) κ single ρfp ( ν, nl, ) = 2 n 1 4πν nl 21 cos n+ 1 c 2 n 1 4πν nl sin 1 n+ 1 c θfp ( ν, nl, ) = tan 2 n 1 4πν nl cos 1 n + 1 c (6) The transmission spectrum deconvolution obtained from the Fourier transform of the measured signals as shown in Eq. (1) is compared with the modeled transfer function of Eq. (6) using a minimization algorithm which evaluates the sum square error ε 2, defined as, where ( ) ( ) ε = ρ + θ (7) 42

5 ρ = ρsingle ( ν) ρfp ( ν)~ T exp( ν) (8) θ = θ ν + θ ν ν { single ( ) FP( )} ~arg ( T exp( )) Minimization of the error gives a set of (n,κ, l) values for the sample which are the effective optical quantities of the assumed dispersionless medium. Using these values in the single pass model, i.e. without Fabry Perot effects, the actual optical quantities of the dispersive medium are obtained as functions of frequency as, ( Tsingle ν ) c n( ν) = 1 arg ( ) 2πν l 2 c ( n( ν ) + 1) κν ( ) = ln T single ( ν) 2πν l 4 n( ν ) (9) From the above set of n(ν) and κ(ν), the real and imaginary parts of the dielectric constant of the material are calculated as functions of frequency [24]. Demonstration of Reciprocity Principle Results The time domain transmission measurements and the corresponding frequency domain spectra, for all the double side polished (DSP) wafers under study of thickness 50 µm, 250 µm and 700 µm, demonstrate the reciprocity principle in the sense that the two opposite faces of the wafers yield identical transmission spectra under THz illumination. Figures 1 (a) and 1 (b) show the experimental time domain and corresponding frequency domain plot for the 250 µm thick silicon wafer. This is particularly interesting as it reflects the ability of THz radiation to characterize the substrate property even in the presence of native oxides on the surface. Corresponding plots obtained for other DSP wafers are not shown here. Figure 1 (c) shows the frequency domain plot for the single side polished 475 µm thick wafer. The difference in the spectra for two opposite faces suggests that, THz is sensitive to surface roughness and appropriate analysis of the measurement can lead to the determination of roughness. 43

Figure 1: Plots of the THz signal in (a) time domain and (b), (c) DFT of the same.

$imaginary parts of the complex refractive indices as a function of frequency are determined for the wafers from Eq.$ $refractive indices for the 250 µm thick DSP silicon wafer.$ indices has monotonic variation of about 10% over the frequency range of 0.2 to 1.2 THz.

indices has monotonic variation of about 10% over the frequency range of 0.2 to 1.2 THz.

The absorption is mainly due to the presence of the free carriers in the doped wafers.

$Thus the determination of refractive indices would be more precise which opens up the possibility of non contact$ $In previously published reports in the literature [15, 16, 23], the variations observed in the refractive indices$

6 Figure 1: Plots of the THz signal in (a) time domain and (b), (c) DFT of the same. Determination of Optical Parameters Using the analysis described in the previous section, both the real and the imaginary parts of the complex refractive indices as a function of frequency are determined for the wafers from Eq. (9). Figure 2 (a) shows a comparison of the experimentally obtained and numerically extracted frequency dependent refractive indices for the 250 µm thick DSP silicon wafer. The first one shows the characteristic Fabry Perot oscillations while the numerically corrected value of refractive indices has monotonic variation of about 10% over the frequency range of 0.2 to 1.2 THz. Figure 2 (b) shows the corresponding comparison of extinction coefficient for the same wafer. The absorption is mainly due to the presence of the free carriers in the doped wafers. In fact, for a very lightly doped wafer, or conversely, for a semiconductor of high resistivity, THz absorption would be almost negligible. Thus the determination of refractive indices would be more precise which opens up the possibility of non contact characterization of high resistivity semiconductors using THz radiation. In previously published reports in the literature [15, 16, 23], the variations observed in the refractive indices have been much larger compared to the results in the present study as shown in Figure 2 (c). The apparent discrepancies cannot be attributed to the difference in resistivity of the silicon wafers. Small variations in the optical parameters are anticipated in the THz regions as the dispersion becomes smaller 44

$Furthermore, the refractive index, by$ definition, does not depend on wafer

$Figure 2: Comparison of (a) refractive$ index, (b) extinction coefficients and (c)

$frequency dependent complex refractive$ complex dielectric constants are calculated.

7 at longer wavelengths. Furthermore, the refractive index, by definition, does not depend on wafer thickness and it is observed in this study for wafers of different thickness. Figure 2: Comparison of (a) refractive index, (b) extinction coefficients and (c) data from Ref [16]. Calculation of the Complex Dielectric Constant and AC Conductivity Using the frequency dependent complex refractive index, real and imaginary parts of the complex dielectric constants are calculated. The results of these calculations are plotted in Figures 3 (a) and 3 (b) respectively for the 250 µm thick DSP silicon wafer. 45

Figure 3: Plots of (a) the real part and (b) the imaginary part of the dielectric constant The imaginary

The frequency dependent conductivity of the sample is shown in Figure 4.

2 THz gives a fair estimation of the DC conductivity, which is equivalent to a resistivity of 2 cm.

real-time characterization technique for semiconductors using THz- TDS has been introduced.

$index of refraction by minimizing the errors between the calculated and the theoretical values from the$ constant and conductivity of semiconductors.

constant and conductivity of semiconductors.

8 Figure 3: Plots of (a) the real part and (b) the imaginary part of the dielectric constant The imaginary part of the complex dielectric constant is directly related to the AC conductivity [24]. The frequency dependent conductivity of the sample is shown in Figure 4. The value of the conductivity at the lowest frequency, that is, at 0.2 THz gives a fair estimation of the DC conductivity, which is equivalent to a resistivity of 2 cm. This value of the resistivity is in good agreement with an independent four probe measurement on the same wafer which yielded 4.5 cm. Figure 4: Conductivity as a function of frequency Conclusions A non-contact, non-destructive and real-time characterization technique for semiconductors using THz- TDS has been introduced. By measuring the optical transmission spectrum, the analysis yields optical parameters such as complex index of refraction by minimizing the errors between the calculated and the theoretical values from the time domain experimental data and extends it to determine the electrical parameters like the dielectric constant and conductivity of semiconductors. Also, since the effect of multiple reflections has been included in the model, it opens up new vistas for non invasive material characterization techniques for both optically thin and thick materials. Efforts to determine the mobility, density of free carriers and the effect of sample roughness on the THz transmission spectra are currently 46

9 ongoing. The future scope of expanding this study will include materials having multiple interfaces such as the presence of overlayers on the substrate. Acknowledgements We acknowledge the assistance of Vishal R. Mehta in performing the four probe resistivity measurements. References 1. J.F. Federici and H. Grebel, Characteristics of nano-scale composites at THz and IR spectral regions in Terahertz Sensing Technology, Vol 2, D. L. Woolard, W.R. Loerop and M. S. Shur, eds. (World Scientific, New York, 2003). 2. Amartya Sengupta, Hakan Altan, Aparajita Bandyopadhyay, J.F. Federici, H. Grebel and D. Pham, Investigation of Defect States of HfO 2 and SiO 2 on p-type Silicon using THz Spectroscopy, (paper to be presented at OSA Annual Meeting, Frontiers In Optics, 19 October 2005). 3. Hakan Altan, Amartya Sengupta, J.F. Federici, H. Grebel and D. Pham, Estimation of Defect Characteristics of HfO 2 and SiO 2 on p-type Silicon wafers, submitted to Phys. Rev. B. 4. Amartya Sengupta, Aparajita Bandyopadhyay, J.F. Federici and R.B. Barat, Study of Morphological Effects on THz Spectra using Ammonium Nitrate, (paper presented at OSA Topical Meeting, Optical THz Science and Technology, Orlando, Florida, 14 March 2005). 5. Amartya Sengupta, Aparajita Bandyopadhyay, J.F. Federici, D.E. Gary and R.B. Barat, Estimation of grain size dependent scattering on THz Absorption Spectra, submitted to Appl. Phys. Lett. 6. Aparajita Bandyopadhyay, Amartya Sengupta, R.B. Barat, D.E. Gary, Z. Michalopoulou and J.F. Federici, Application of THz Imaging in Security Screening (paper to be presented at OSA Annual Meeting, Frontiers In Optics, 19 October 2005). 7. Aparajita Bandyopadhyay, Amartya Sengupta, R.B. Barat, D.E. Gary, Z. Michalopoulou and J.F. Federici, Interferometric terahertz imaging for detection of lethal agents using Artificial Neural Network Analysis (paper to be submitted to Appl. Phys. Lett.). 8. D. Grischkowski, Time domain far-infrared spectroscopy, in Proceedings of the Fourth International Conference on Infrared Physics, R. Kesselring and F.K. Kneubuhl eds. (ETH, Zurich, 1988). 9. K.P. Cheung and D.H. Auston, A novel technique for measuring far infrared absorption and dispersion, Infrared Phys., 26 (1986), Ch. Fattinger and D. Grischkowski, Point source terahertz optics, Appl. Phys. Lett., 53 (1988),

10 11. M.C. Nuss and J. Orenstein, Terahertz time-domain spectroscopy in Millimeter and Submillimeter Wave Spectroscopy of Solids, G. Gruner, ed. (Springer Verlag, Germany, 1998) and references therein. 12. L. Hui, F. Zhongyu and Y. Jianqi, Infrared imaging solar spectrograph at Purple Mountain Observatory, Sol. Phys., 185, (1999), K. Sato, T. Tato, H. Sone and T. Takagi, Development of a high speed time resolved spectroscope and its application to analysis of time varying optical spectra, IEEE Trans. Instrum. Meas., IM- 36, (1987), R. E. Burge, X. C. Yuan, J. N. Knauer, M. T. Browne and P. Charalambous, Scanning soft X ray imaging at 10 nm resolution, Ultramicroscopy, 69, (1997), D. Grischowski, Soren Keiding, Martin van Exter and Ch. Fattinger, Far infrared time domain spectroscopy with terahertz beams of dielectrics and semiconductors, J. Opt. Soc. Am. B, 7, (1990), Martin van Exter and D. Grischowski, Carrier dynamics of electrons and holes in moderately doped silicon, Phys. Rev. B, 41, (1990), Timothy D. Dorney, Richard G. Baraniuk and Daniel M. Mittleman, Material parameter estimation with terahertz time domain spectroscopy, J. Opt. Soc. Am. A, 18, (2001), S. Abedrabbo, J.C. Hensel, A.T.Fiory and N.M.Ravindra, Evidence from Spectral Emissometry for Conduction intraband transitions in the intrinsic regime for Silicon, J. Elec. Mater., 28, (1999), N.M. Ravindra, S. Abedrabbo, W. Chen, F.M.Tong, A.K.Nanda and A.C.Speranza, Temperature Dependent Emissivity of Silicon-related materials and Structures, IEEE T. Semicon. Manufac., 11, (1998), P. Smith, D. Auston and M. Nuss, Subpicosecond Photoconducting Dipole Antennas, IEEE J. Quant. Elec., 24, (1988), D. Dragoman and M. Dragoman, Terahertz Fields and Applications, Prog. Quantum. Elect., 28, (2004 ), M. Born and E. Wolf, Principles of Optics (London UK: Cambridge University Press 1999). 23. L. Duvillaret, F. Garet and J-L. Coutaz, Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy, Appl. Opt., 38 (1999), Mark Fox, Optical Properties of Solids (New York NY: Oxford University Press Inc. 2001). 48

Simple strategy for enhancing terahertz emission from coherent longitudinal optical phonons using undoped GaAs/n-type GaAs epitaxial layer structures

Presented at ISCS21 June 4, 21 Session # FrP3 Simple strategy for enhancing terahertz emission from coherent longitudinal optical phonons using undoped GaAs/n-type GaAs epitaxial layer structures Hideo