Study on photothermal vibration response of gold coating semiconducting microcantilevers

Abstract

The elastic vibration response of coat layered semiconducting microcantilevers, which were excited with a frequency-modulated pump laser and detected with another probe beam, was studied experimentally and theoretically in this paper. The photothermal vibration frequency spectra were measured and analyzed for a set of microcantilevers with different coating thickness at the region near the first resonant frequency. Also the vibrations of microcantilevers were calculated using coupled carrier dispersion, thermal wave and elastic wave equations. The results showed that the experimental results had a good agreement with the theoretical ones.

Keywords

Photothermal vibration coating microcantilevers

1. Introduction

The development of micro(nano)system technologies (surface and bulk micro-machining) resulted in the production and use of miniature sensors, actuators, resonators and electro-mechanical parts in large quantities. Cantilever, especially microcantilever, as one kind of highly sensitive sensor has received a great deal of attention in physical, chemical, biological and mechanical systems. This is primarily due to its high sensitivity, flexibility and reliability. These characterizations enable it can be used to detect small changes of properties. Usually resonant frequency and Q-factor are output parameters of this kind of sensors for dynamic mode measurement of micocantilever [1]. They are sensitive to external perturbations such as force, pressure, temperature or medium viscosity and density, etc. During the last ten years, many publications have been devoted to study the cantilever sensors experimentally and theoretically, especially for microscale cantilever sensors [2–8].

Single layered semiconducting micro-cantilever sensor have some limitations in practical application, such as liable to corrosion and oxidation, and with low light efficiency. Usually, some coatings, including Gold, Aluminum, Nickel and metal oxide, such as indium tin oxide, are integrated onto micromachined cantilevers. Deposited metal film elements on microcantilevers have important advantages, not only to eliminate limitation of single layer microcantilever, but also to reduce complexity and cost [9]. Gotoh [10] developed an innovative photothermal technique to obtain optical absorption spectra of thin film devices. Merced et al. [11] studied the response of VO₂: Cr-coated micro cantilevers in air and aqueous media. Kim et al. [12] investigated the high thermomechanical sensitivity of bi-material microcantilever using photothermal cantilever deflection spectroscopy (PSDS).

Many photoacousti (PA) and photothermal (PT) technologies are developed in investigation semiconductors and microelectronic structures due to the merits of non-contact and non-destructive. These methods are suitable to be used as detection ways of micro-electromechanical system (MEMS) and nanoelectromechanical system (NEMS), especially in situations where other techniques are not useful [13–20]. They can be applied to reveal surface and subsurface structure of samples and also to obtain the material properties such as thermal conductivity, thermal diffusivity, etc. A lot of excellent works have been done both in experiment [13–16] and theory [17–20]. The carrier diffusion generated by the absorbed intensity-modulated optical excitation, play dominant role in the PA and PT experiments for most semiconducting and microelectronics structures. Stearns and Kino [21] have experimentally demonstrated the electronic strain by measuring the phase of photoacoustically generated waves in silicon and developed a theory to predict the contribution of the electronic strain to the phototacoustic generation. Also depth-dependent thermal waves contribute to the generation of periodic heat vibrations in the sample [22–25]. So the theoretical analysis of the carrier and thermal effects in micromechanical structures consists in modeling a complex system by simultaneous analysis of carrier diffusion, thermal wave and elastic wave equations.

In this paper a nondestructive photothermal apparatus was used to detect the vibration of gold coating semiconducting microcantilevers under laser excitation. The photothermal response signal were obtained for microcantilevers with different coating thickness under different modulation frequencies. Also the deflection response of microcantilevers were given theoretically. The mesurement results were compared with that obtained by theoretical calculation and they showed a good agreement.

2. Experiments

2.1. Experimental setup

Figure 1 gave a block diagram of the experimental setup. This nondestructive apparatus mainly include excitation laser (doubled Nd:YAG laser, wavelength = 532 nm), detection laser (HeNe laser, wavelength = 632 nm), AOM (acousto-optic modulator), lock-in amplifier (the detection range is 1 KHz ∼ 1 MHz), photoelectric transducer and network analyzer. This setup was installed on an anti-vibration table. The intensity of excitation laser beam was 200 milliwatts and the probe beam was 3 milliwatts. So the vibration of microcantilever was considered induced only by excitation beam. Due to the interference of probe laser beam and the reflected one, the small vibration of the samples induced by the heating of excitation laser could be recorded as the resulting PT signals. These signals were sent to the lock-in amplifier and the magnitude and phase of displacement of microcantilever were extracted at each modulation frequency. The sample was excited by probe laser, which was uniform at the back side of cantilever, and detect by detection laser, which was focused at the front side of microcantilever. The samples were glued on the specific holders and put on the 2-axis translation table. The maximum signal could be obtained by accurately adjust two axis of this table. The measurement results used in this paper were the mean values of at least three measurements at the same excitation and detection position. The results showed that the measurement has good reproducibility.

Fig. 1.

Experimental apparatus.

Fig. 2.

SEM image of Microcantilevers D, E, F with 50 nm gold film.

2.2. Samples

The vibration responses of several sets of gold coating silicon cantilevers (NSC12Tipless AFM probe) with different length were measured. The SEM image of three microcantilevers were shown in Fig. 2. The dimension and characteristic of the Si cantilevers used in the measurements were shown in Table 1. The samples were cleaned in chemical solution first to obtained the totally silicon microcantilever and measured the resonance frequenies. And then deposit 50 nm gold coating on silicon cantilever and measure again. After that, the 50 nm gold coating microcantilever were deposited 50 nm gold coating again to obtain 100 nm gold coating microcantilever and measured the response of the samples again.

Table 1
The dimensions and characteristics of the Si cantilevers were used in this work

No. Of Length Width Thickness Resonance frequency

CLs (μm) (μm) (μm) Thickness of gold film h₁ = 50 nm Thickness of gold film h₁ = 100 nm

Expt. Calc. Relative Expt. Calc. Relative

(Hz) (Hz) error % (Hz) (Hz) error %

A 97.93 33.45 2 228540 238590 4.21% 214628 228538 6.09%

B 79.96 32.09 2 345366 357881 3.50% 324694 342805 5.28%

C 114.45 33.05 2 165656 174684 5.17% 155148 167325 7.28%

D 278.54 33.60 2 29290 29492 0.68% 27538 28250 2.52%

E 327.31 33.46 2 21360 21358 0.01% 20084 20458 1.83%

F 226.19 32.90 2 44150 44724 1.28% 41424 42840 3.31%

No. Of	Length	Width	Thickness	Resonance frequency
A	97.93	33.45	2	228540	238590	4.21%	214628	228538	6.09%
B	79.96	32.09	2	345366	357881	3.50%	324694	342805	5.28%
C	114.45	33.05	2	165656	174684	5.17%	155148	167325	7.28%
D	278.54	33.60	2	29290	29492	0.68%	27538	28250	2.52%
E	327.31	33.46	2	21360	21358	0.01%	20084	20458	1.83%
F	226.19	32.90	2	44150	44724	1.28%	41424	42840	3.31%

3. Theoretical models

Generally, theoretical analysis of transport process in semicondutor consist of consideration coupled carrier diffusion, thermal wave and elastic waves simultaneously. The carrier density N(r, t), temperature distribution T(r, t) and elastic displacement u(r, t) are the main quantities.

For a medium with isotropic and homogeneous propertie, the partically coupled plasma, thermal and elastic transport equations can be given below as a vector for [18–20] $\begin{eqnarray}\displaystyle \frac{\partial N(\mathbf{r},t)}{\partial t} & = & \displaystyle D_{E}{\nabla}^{2}N(\mathbf{r},t)-\frac{N(\mathbf{r},t)-N_{o}}{{\tau}}+\frac{\partial N_{0}}{\partial t}\frac{T(\mathbf{r},t)-T_{0}}{{\tau}}+Q(\mathbf{r},t),\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle {\rho}C_{p}\frac{\partial T(\mathbf{r},t)}{\partial t} & = & \displaystyle k{\nabla}^{2}T(\mathbf{r},t)+\frac{E_{\text{g}}}{{\tau}}(N(\mathbf{r},t)-N_{o})+{\beta}_{u}{\rho}C_{p}{\nabla}^{2}\frac{\partial \mathbf{u}(\mathbf{r},t)}{\partial t}+G(\mathbf{r},t),\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle {\rho}\frac{\partial ^{2}\mathbf{u}(\mathbf{r},t)}{\partial t^{2}} & = & \displaystyle {\mu}{\nabla}^{2}\mathbf{u}(\mathbf{r},t)+({\lambda}+{\mu}){\nabla}[{\nabla}\times \mathbf{u}(\mathbf{r},t)]-{\beta}_{T}{\nabla}T(\mathbf{r},t)-{\delta}_{n}{\nabla}N(\mathbf{r},t),\end{eqnarray}$ (3) where r is the position vector, t is time variable, D _E is the carrier diffusion coefficient, τ is the lifetime of photogenerated charge carriers, the so-called Auger recombination time and N _o is the equilibrium carrier concentration, T ₀ is the ambient temperature and Q is the incident modulated laser source, G (r, t) is the carrier photogeneration source term, 𝜌, C _p, k, 𝛽_u are density, thermal conductivity, specific heat and thermoelastic coupling parameter, respectively; 𝜆 and 𝜇 are Lam’s constant; 𝛽_T = (3𝜆 +2𝜇)𝛼_T and 𝛼_T is coefficient of linear thermal expansion, δ_n = (3𝜆 +2𝜇)d _n and d _n is coefficient of electronic elastic deformation.

From Eqs (1)–(3), we can see that the field quantities, i.e., carrier density, temperature and displacement are coupled and the problems are three dimensional and nonlinear. Due to the excitation laser is uniform on the front surface of microcantilever, so this problem can be simplified to a one-dimensional problem and the solution process was shown in references [22–24]. The deflection for microcantilever in frequency domain can be given analytically as below $\begin{eqnarray}w(L,{\omega})=w_{s}(L,{\omega})G({\omega}),\end{eqnarray}$ in which $\begin{eqnarray}\displaystyle w_{s}(L,{\omega})\text{} & =\text{} & \displaystyle -\frac{L^{2}}{2}(\bar{m}_{T}+\bar{m}_{n}),\quad G({\omega})=\frac{2\sin {\eta}\sinh {\eta}}{{\eta}^{2}(1+\cos {\eta}\cosh {\eta})},\nonumber\\ \displaystyle \bar{m}_{T}\text{} & =\text{} & \displaystyle bF{\alpha}_{T}m_{T}/B,\quad m_{T}=\int _{0}^{h}zT(x,z,{\omega})dz,\nonumber\\ \displaystyle \bar{m}_{n}\text{} & =\text{} & \displaystyle bFd_{n}m_{n}/B,\quad m_{n}=\int _{0}^{h}zN(x,z,{\omega})dz,\nonumber\\ \displaystyle B\text{} & =\text{} & \displaystyle FI,\quad F=E_{y}/(1-{\nu}^{2}),\quad I=bh^{3}/12,\quad {\eta}=kL,\quad k=(1+i)({\omega}/2D_{T})^{1/2}\nonumber\end{eqnarray}$ in which L, b, h are length, width and thickness of sample. E _y, 𝜈, D _T are Young’s modulus, Poisson’s ratio and thermal diffusivity. x, z are coordinates of mocrocantileve length and thickness, and ω is frequency. i is imagnery unit. w is the deflection of microcantilever.

4. Results and discussion

Figure 3 gave the results of experimental measurements amplitude for microcantilever A withoutgold coating in the frequency range 1 kHz ∼1 MHz. In the measurements the pump laser heating sources were uniform at the whole back surface of cantilevers and probe lasers focused on the free end of front surface. Obvious peak can be observed in this figure. It respresents the first resoance frequency of microcantilever. From this figure it can be seen that near first frequency the response signal are much lager than the background noise. So using this experimental setup can obtain good results.

Fig. 3.

Measurement results for Microcantilevers A without gold coating.

Fig. 4.

Measurement results for Microcantilevers A.

Figure 4 showed the results of experimental measurements for amplitude and phase of microcantilevers A near first resonance frequencies with different thickness of gold coating. In these measurements the pump laser heating sources were uniform at the whole surface of cantilevers and probe lasers focused on the free end. Each experiment was repeated at least three times and the resonance frequencies were stable in the different measurements. This denoted that the mechanical properties of the cantilever were stable. The two figures showed a typical frequency dependence of the PT signal. Due to high detection frequency and relatively high excitation power the experiment results showed that the background noise and vibration of the environment around had almost no influence on our measurements. Obvious peaks can be observed from the curves of amplitude of the bending. These peaks represent the first resonance of the microcantilevers. Also we can see from this figure that the coating thickness has significant influence on the vibration response of microcantilever. This conclusion is coincident with that obtained in references [10–12]. For the phase angle we noted that the resonant peaks were followed by a sharp change of 180° for phase angle as expected.

The comparisons between the resonance frequencies obtained from experimental measurement and that from theoretical calculation were shown in Table 1. The experimental resonance frequencies of microcantilever were measured using the experimental setup mentioned in section 2. The calculated resonance frequencies of microcantilever were obtained using the theoretical mode in section 3. It can be seen from this table that the resonance frequencies obtained by experiments agree well with that of theory calculation. The relative error are below 8%.

5. Conclusion

The vibrations of gold coating rectangular semiconducting microcantilevers induced by laser excitation were measured under different modulation frequencies. The small response signal can be obtained at high modulation frequency. The coupled plasma wave, thermal wave and elastic wave theories are used to theoretically simulate the deflection response under different frequencies. The comparisons between experiment and computation are made for different sized microcantilevers. The results showed that the resonance frequency obtained by measurements agree well with theoretical ones.

Footnotes

Acknowledgements

The work was supported by National Natural Science Foundation of China (grant No. 11672224) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2018JM2013). The authors would like to thanks Prof. Wu Yihui and Dr. Li Feng of Changchun Institute of Optics for their assistance with the experiments and valuable discussion.

References

Korsunsky

A. M.

Cherian

Raiteri

and Berger

, On the micromechanics of micro-cantilever sensors: property analysis and eigenstrain modelling, Sens. Actuat. A 139 (2007), 70–77.

Cretin

and Vairac

, Measurement of cantilever vibrations with a new heterodyne laser probe: application to scanning microdeformation microscopy, Appl. Phys. A 66 (1998), S235-s238.

Volden

Zimmermann

Lange

Brand

and Baltes

, Dynamics of CMOS-based thermally actuated cantilever arrays for force microscopy, Sens. Actuat. A 115 (2004), 516–522.

Bianco

Cocuzza

Ferrero

Giuri

Piacenza

Pirri

C. F.

Ricci

and Scaltrito

, Silicon resonant microcantilevers for absolute pressure measurement, J. Vac. Sci. Technol. B 24 (2006), 1803–1809.

Requa

M. V.

and Turner

K. L.

, Electromechanically driven and sensed parametric resonance in silicon microcantilevers, Appl. Phys. Lett. 88 (2006), 263508.

Alvarez

Tamayo

Plaza

J. A.

Zinoviw

Dominguez

and Lechuga

L. M.

, Dimension dependence of the thermo-mechanical noise of microcantilever, J. Appl. Phys. 99 (2006), 024910.

Campbell

Medina

M. B.

and Mutharasan

, Detection of staphylococcus enterotoxin B at picogram levels using piezoelectric-excited millmeter-sized cantilever sensors, Sens. Actuat. B 126 (2007), 354–360.

Wilkinson

P. R.

and Gimzewski

J. K.

, The film interference in the optomechanical response of micromechanical silicon cantilevers, Appl. Phys. Lett. 89 (2006), 241916.

Gaitas

and Zhu

, A probe with ultrathin film deflection sensor for scanning probe microscopy and material characterization, Sens. Actua. A 168 (2011), 229–232.

10.

Gotoh

, Photothermal technique using individual cantilevers for quality monitoring in thin film devices, Rev. Sci. Instrum. 80 (2009), 074902.

11.

Merced

Davila

Torres

Cabrera

Fernandez

F.E

and Sepulveda

, Photothermal actuation of VO2:Cr-coated microcantilevers in air and aqueous media, Smart Mater. Struct. 21 (2012), 105009.

12.

Kim

Lee

and Thundat

, Photothermal cantilever deflection spectroscopy, EPJ Tech. Instrum. 1 (2014), 7.

13.

Wang

X.D.

Pang

Y.J.

Xie

X.Y.

Stoica

and Wang

L.H.V.

, Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain, Nature Biotechnology 21 (2003), 803–806.

14.

M.H.

and Wang

L.H.V.

, Photoacoustic imaging in biomedicine, Review of Scientific Instruments 77 (2006), 041101.

15.

Huang

X.H.

EI-Sayed

I.H.

and Qian

, Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods, Journal of The American Chemical Society 128 (2006), 2115–2120.

16.

Jain

P.K.

Huang

X.H.

Ei-Sayed

I.H.

and EI-Sayed

M.A.

, Noble metals on the nanoscale: optical and photothermal properties and some applications in imaging, sensing, biology, and medicine, Accounts of Chemical Research 41 (2008), 1578–1586.

17.

Mandelis

, Photoacoustic and Thermal Wave Phenomena in Semiconductors, New York, 1987.

18.

Todorović

D.M.

Nikolić

P.M.

Bojičić

A.I.

and Radulovic

K. T.

, Thermoelastic and electronic strain contributions to the frequency transmission photoacoustic effect in semiconductors, Phys. Rev. B 55 (1997), 15631–15642.

19.

Todorović

D. M.

Nikolić

P. M.

and Bojičić

A. I.

, Photoacoustic frequency transmission technique: Electronic deformation mechanism in semiconductors, J. Appl. Phys. 85 (1999), 7716–7726.

20.

Todorović

D. M.

and Nikolić

P. M.

, Ch.9, Carrier transport contribution to thermoelastic and electronic deformation in semiconductor, in: Semiconductors and Electronic Materials, Washington, 2000.

21.

Stearns

P.G.

and Kino

G.S.

, Effect of electronic strain on photoacoustic generation in silicon, Appl. Phys. Lett. 47 (1985), 1048–1050.

22.

Song

Y.Q.

Cretin

Todorović

D.M.

and Vairac

, Study of laser excited vibration of silicon cantilever, J. Appl. Phys. 104 (2008), 10409.

23.

Song

Y.Q.

Cretin

Todorović

D.M.

and Vairac

, Study of phototheral vibrations of semiconductor cantilevers near the resonant frequency, J. Phys. D 41 (2008), 155106.

24.

Todorović

D. M.

Cretin

Song

Y.Q.

and Vairac

, Electronic and thermal generation of vibrations of optically excited cantilevers, J. Appli. Phys. 107 (2010), 023516.

25.

Chen

G.Y.

Thundat

Wachter

E.A.

and Warmack

R.J.

, Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers, J. Appl. Phys. 77 (1995), 3618–3622.