Effect of orientation and size of silicon single crystal to Electro-Ultrasonic Spectroscopy

Transcription

1 Effet of orientation and size of silion single rystal to Eletro-Ultrasoni Spetrosopy Mingu KANG 1, Byeong-Eog JUN 1, Young H. KIM 1 1 Korea Siene Aademy of KAIST, Korea Phone: , Fax: ; yhkim67@kaist.a.kr, bejun@pknu.a.kr, iordia@naver.om Abstrat Reently, a novel nondestrutive method so-alled Eletro-Ultrasoni Spetrosopy (EUS) has been reported. In this tehnique, the intermodulation signals between mehanial and eletrial exitation is measured, so that it offers high signal to noise ratio due to the different frequeny range from those of exitation signals. EUS is the method under developing, so that the proedure of EUS should be established. In the present work, the size and orientation effet of the speimen were analyzed. Firstly, peak frequeny of transduer is measured. Wave veloity in eah orientation is alulated from Crystoffel s equation, and appropriate length of speimen was seleted. The atual vibration of speimen and transduer was measured by laser Doppler vibrometer. Results onfirm that the size of speimen should be determined by onsidering the wave veloity. Keywords: Eletro-Ultrasoni Spetrosopy, Speimen size effet, Crystal orientation 1. Introdution Eletro-Ultrasoni Spetrosopy (EUS) is reently reported non-destrutive method whih ould obtain high signal to noise ratio by measuring intermodulation signal of interation between mehanial and eletrial vibration. EUS has been applied to evaluation of miroraks in onduting materials [1] and thik film resistors []. Single rystals of silion and admium telluride were also investigated by EUS [3]. Sine EUS is method under developing, proedure of EUS should be established. For effetive EUS experiment, mehanial vibration with large amplitude is essential. In previous work standing wave modes were employed for suh purpose. The size of speimen should be determined by onsidering exitation frequeny and wave veloities of the speimen. Until now, EUS researhes mostly do not onern about size and orientation of speimen. However, aording to reent study with anistropi speimen, number of intermodulation harmonis and relation between power of ultrasoni osillation and amplitude of intermodulation signal are measured differently aording to orientation of speimen [4]. These results imply that size ould affet to EUS analysis. In the anisotropi rystal, natural frequeny is deided by size and diretion of speimen. Therefore, to maximize amplitude of mehanial vibration, standardization of size and diretion of speimen is neessary. In the present work, resonane frequeny of transduer is analyzed. One of peak frequeny is seleted and resonane size and diretion of silion anisotropi rystal is deided by Crystoffel's equation. Finally, vibration amplitude of speimen aording to size and diretion is analyzed.

2 . Theoretial Bakground Wave veloity in rystal is determined by Crystoffel s equation whih is basially ombination of Newton s law and Hooke s law, and given by λ ρ λ λ λ1 λ ρ λ3 det = 0 λ λ λ ρ Where λ im = iklmnk nl, iklm is rystal onstant, n i is diretion osine, is wave veloity, and ρ is rystal density [5]. In silion single rystal, there are three rystal onstants whih are = = 33 = Pa, 1 = 1 = 31 = 13 = 3 = 3 = Pa, and 44 = 11 = = Pa [6]. Crystal density is 39 kg/m 3. In the present work, [110] and [11] rystal diretion is estimated, and there diretion osine is given by 1/, 0 in [110] and / 6, 1/ 6 in [11]. By solving Crystoffel s equation, three wave veloities are obtained in [110], [11] rystal orientation, and listed in the table 1. The wave mode of in [11] is not lear. Wave veloity of in [11] diretion is similar to that of onventional value of longitudinal wave in silion; however wave vetor is perpendiular to the displaement of partiles. Table 1. Wave Veloity in silion single rystal [110] 1 3 Wave veloity (m/s) Wave type Longitudinal wave Transverse wave Transverse wave [11] 1 3 Wave veloity (m/s) Wave type Transverse wave Transverse wave 3. Experimental Proedure Fig. 1 shows the photograph of overall experimental setup. Bolt-lamped Langevin Type (BLT) transduer was exited by power amplifier and funtion generator. The settings of instruments were fixed during whole experiment. The vibration veloity of transduer surfae was measured by Laser Doppler Vibrometer (LDV) with varying frequeny to determine resonant frequeny. Retangular bars were made from silion wafer of 150 mm diameter and mm thikness. The dimension of bar was deided by onsidering the resonant frequeny of BLT transduer and wave veloity in silion rystal. Distribution of the vibration veloity of silion bars, whih is attahed on the BLT transduer, was measured by LDV.

3 Figure 1. Experimental Setup for measuring resonant frequeny of transduer 4. Results and Disussion 4.1 Charateristis of BLT transduer Typial waveform of funtion generator signal, LDV signal, and urrent and voltage aross the transduer are shown in Fig. Amplitude of vibration veloity signal in mv is onverted to m/s. Fig 3 shows vibration veloity as a funtion of frequeny from 0 khz to 10 khz in 0.5 khz steps. As a result, it was found that the resonant peak frequeny is 94.5 khz. Figure. Typial spetrum of signals observed by osillosope. Eah one is Laser Doppler Vibrometer signal, funtion generator signal, and voltage and urrent signal aross the transduer (highest to lowest).

4 Vibratinon Veloity Signal(m/s) 0,14 0,1 0,1 0,08 0,06 0,04 0, Vibration frequeny (khz) 4. Size of Speimen Figure 3. Vibration veloity signal amplitude versus vibration frequeny The exat information on the rystal orientation of wafer was not learly known and should have been founded. The silion wafer was broken by hammer and angle between two frature lines was 60 degree. From this hexagonal symmetry, antiipated diretion of silion wafer is [111], and antiipated diretion of eah edge is [110]. To onfirm the diretion of silion wafer, XRD is used to larify diretion of ross setion. Compared with standard silion XRD results, 6 th peak at θ =88 degree, whih indiates [11] diretion, is appeared in XRD results of ross setion. This result onfirms expetation sine [11] diretion is proportional to both [110] and [111] diretion. Figure 4. Expeted diretion of silion wafer Figure 5. XRD result of ross setion of silion wafer

5 Resonane lengths of speimens are alulated from wave veloity. The relationship is L = where f = 94.5 khz is resonant frequeny of transduer. Beause vibration diretion is perpendiular to wave diretion in our experiment, transverse wave veloity was used. Speifially, m/s in [110], m/s and 4873 m/s in [11] were seleted. Three resonane lengths are shown in table. v f Table. Resonane length of speimen in eah wave veloity Wave veloity (m/s) Resonane length (m) Resonane orientation [110] [11] [11] Seven speimens are prepared. First, to analyze size effet,.57 m,.89 m, 3.09 m, 3.4 m speimen in [110] diretion is sawed. Seond, to analyze orientation effet,.57 m,.89 m, 3.09 m speimen in [11] diretion is sawed and ompared with [110] diretion speimens. Speimen is sawed with the width of 5 mm and thikness of mm. 4.3 Vibration energy of speimen Vibration veloity of speimen is measured from one end to the other end with the interval of 1mm. After obtain amplitude of vibration veloity signal at eah point, vibration energy per unit length is alulated by E = 0.1 v / L where v is veloity of vibration veloity signal, and L is length of speimen. Table 3. Variation of vibration energy per length versus speimen length [110] L (m) E (m/s^) Vibration of transduer is highly transported to speimen only in 3.09 m speimen, whih is resonant in transduer frequeny. Comparing with.89 m speimen, 3.09 m speimen has 40 times higher vibration energy though their length differs only 6%. This result implies that size of speimen affets mehanial vibration hugely and should be onerned in EUS analysis. Table 4. Variation of vibration energy per length versus speimen orientation L( m ) [110] E (m/s^) [11] E (m/s^)

6 At the same length, higher vibration energy is obtained in resonane speimens. In 3.09 m, [110] oriented speimen has higher energy than [11] oriented speimen. In.89 m and.57 m, [11] oriented speimen has higher energy. This implies orientation of speimen also should be onerned in EUS analysis. However, differene in vibration energy aording to hange of orientation is smaller ompared to differene in energy aording to hange of size. 5. Conlusions Size and orientation effet of speimen to vibration veloity is analyzed. It was found that vibration veloity and vibration energy per unit length of speimen are signifiantly affeted by size and orientation of speimen. This implies that size and orientation of speimen should be onsidered for the quantitative and reliable analysis of EUS results. Referenes 1. K Hajek, J Sikula, The improved system for eletro-ultrasoni nonlinear spetrosopy, 4th NDT in Progress, pp , 007. V Sedlakova, J Sikula, P Tofel, J Majzner, Eletro-ultrasoni spetrosopy of polymer-based thik film layers, Miroeletron. Reliab. Vol 48, , P Tofel, J Sikula, V Sedlakova, NDT of single rystal CdTe and Si by eletroultrasoni spetrosopy, 5th NDT in Progress, Y H Kim, M Han, V Sedláková, J Šikula, Feasible study on eletro-ultrasoni spetrosopy of silion single rystal, Pro Symp Ultrasoni Eletronis, pp , H F Pollard, Sound waves in solids, pp. 8-30, Pion ltd, London, M A Hoproft, 'What is the Young s modulus of silion?', J Miroeletromehanial System, Vol 19, No, pp 9-38, April 010.