1. Ultrasonic investigation of Mesoporous Silicon
Julien Bustillo1, Jérôme Fortineau1, Gaël Gautier1, Marc Lethiecq1
1Université François Rabelais de Tours, CNRS, CEA, INSA CVL, GREMAN UMR 7347, Tours, France
Abstract: Ultrasonic characterization of mesoporous silicon is proposed to estimate the porosity and the thickness of porous silicon layer. Two sets of samples are formed in order to retrieve independently each parameter: one with similar porosity and another with similar thickness. Secondly, an immersion ultrasonic measurement technique is developed and a modeling based on material homogenization is used to simulate wave propagation through the porous layer. An optimization between simulated and experimental spectra, based on a genetic algorithm, allows porosity and thickness to be estimated. They are compared to destructive measurements and good estimation of porosity and thickness is observed, even when layer thickness is small compared to wavelength of the ultrasonic wave.
Sample presentation
Sample
Current density (mA/cm²)
Etching duration (min)
PoSi thickness (µm)
PoSi Porosity rate (%) A 42 30
115 39 B 20 81 37 C 10 41 36 D 80 97 E 45
114
<100> p-type silicon
HF based solution
Pulsed current electrochemical etching
Pore diameter of 20 nm
2 sets of porous silicon
Porosity measured by gravimetic method
Thickness measured using optical microscope
SEM Slice view
Ultrasonic measurement method d
Transducer
Transducer
Input
Output
tSi
cSi
ρSi
tPoSi
cPoSi
ρPoSi
Water d
Sample
Experimental and theoretical transmission spectra through sample 2
Modeling (a) and experimental setup (b) used for ultrasonic characterization.
Data processing
Wave propagation model
Frequency domain analysis
Optimisation based on Genetic Algorithm
Non monotone mutation
Good convergence behavior
Porosity deduced from acoustical impedance
One dimensional modeling
Biot’s theory modeling
Transfer matrix method
Transmission coefficient calculation and measurement
Parameter retrieval processing scheme
Porosity and thickness estimations
PoSi thickness (µm)
PoSi Porosity rate (%)
Sample A B C D E
Destructive Method
115 81 41 39 42 36
Acoustical Method
121 37 44
Relative error (%) 6 10 5 3
Retrieved values compared to values measured by destructive methods
Good agreement even for thin layers
Maximum discrepancy of 10% for thickness estimation
Maximum discrepancy of 6% for porosity estimation
Simultaneous and non destructive estimation of porosity and thickness
Conclusion: An ultrasonic method has been developed and applied to porous silicon characterization using an inverse problem solving. A model has been implemented to calculate theoretical transmission spectrum and an optimization has been performed using a genetic algorithm. A good agreement is observed between retrieved thicknesses and porosity rates and values obtained by destructive methods. Discrepancies are respectively of 10% and 6% for thickness and porosity. Therefore, this method seems promising to characterize mesoporous silicon layer made using electrochemical processes.
PSST 2014 – March 9th-14th –Alicante