Analysis of Microelectrode Arrays for Dielectrophoresis using the Finite Element Method

Dielectrophoresis (DEP) is a widely used separation technique for polar or polarizable particles based on the movement of the sample species which occurs when the particles are subjected to a non-uniform electric field [1]. The work presented is focused on the analysis of the DEP force distribution at nanoscale heights above the electrodes dependence on microelectrode size parameters. Results of the investigation may already find application in the fabrication of microfluidic lab on chip devices to separate or control motion of the particles in nanometer scale microfluidic channels [2]. DEP force theoretical analysis was performed using the finite element method and the dependence on microelectrode width, spacing and thickness was acquired. The electrode structure modelled was the interdigitated golden electrodes with thin Cr ahesion layer on glass substrate. Research results are applicable for any microelectrode structure that inherits rectangular structure of single microelectrode finger in its design. Using numerical calculations the influence on the gradient of electric field of each microelectrode’s size parameter when the other two size parameters are altered was investigated. Taking into account resultant data, respective microelectrode structure design adjustments for future fabrication were discussed. DEP force dependence on electrode size parameters plots and research conclusions are also presented in this work.


Introduction
Dielectrophoresis (DEP) is a widely used separation technique for polar or polarizable particles based on the movement of the sample species which occurs when the particles are subjected to a non-uniform electric field [1].The work presented is focused on the analysis of the DEP force distribution at nanoscale heights above the electrodes dependence on microelectrode size parameters.Results of the investigation may already find application in the fabrication of microfluidic lab on chip devices to separate or control motion of the particles in nanometer scale microfluidic channels [2].DEP force theoretical analysis was performed using the finite element method and the dependence on microelectrode width, spacing and thickness was acquired.The electrode structure modelled was the interdigitated golden electrodes with thin Cr ahesion layer on glass substrate.Research results are applicable for any microelectrode structure that inherits rectangular structure of single microelectrode finger in its design.Using numerical calculations the influence on the gradient of electric field of each microelectrode's size parameter when the other two size parameters are altered was investigated.Taking into account resultant data, respective microelectrode structure design adjustments for future fabrication were discussed.DEP force dependence on electrode size parameters plots and research conclusions are also presented in this work.

Mathematical analysis
Dielectrophoresis (DEP) is a phenomenon that takes place when a polar or polarizable particle, e.g., a biological cell is being subjected to a non-uniform electric field which results in the motion of the particle [3,5].This technique is widely used to characterize and separate polarizable particles.Particle range can vary from micrometer to nanometer size dimensions [6].The DEP force affecting the specimen is produced because of the interaction between particle dipole moment m (permanent or induced) and the non-uniform electric field [6].The force is defined as where ∇ is the gradient of the electric field .Dipole moment m is defined as where is the effective polarizability of the particle, is the volume, is the absolute permittivity of the medium, is the Clausius-Mossotti factor and is the radius of the particle [6].
From (1) and (2) DEP force is given by [6] Clausius-Mossotti factor is defined as [6] = * − * where , are the relative permittivity of the particle and the medium, respectively.Positive value refers to a positive DEP when the particle is attracted to the electrodes, negative refers to the negative DEP and the particle is repelled from the electrodes [6].A transition from one type of DEP to another may occur when the frequency is being altered.The frequency when the transition occurs is the crossover frequency and is defined as From (3) it can be seen that one of the most crucial parameters affecting the DEP force is the gradient of electric field.Therefore, the DEP force will strongly

P force depen
In Fig. 3 ∇| th is shown.T ng 5 and 10 del showed an ues compared t  As it is sho eved using th ording to num kness is effec ghts.Above th ative or no ef rage increase nm thick elec kness microe ease of ∇| | ues between th 2 %.A tenden trodes the hi ained in the 0 120 nm elec | by 38% an influence of dient is nonlin The plot sum ameters on ∇| 6.It can be o most effective d and DEP fo ween the electr ctive only in reover, in this e beneficial th th reduction ctive in the 0 ement rates of efit is negligib The influence of electrode spacing reduction on the gradient of electric field is not strongly dependent on the other two size parameters and can be negligible.Alteration of the electrode thickness is also independent from the influence of other two size parameteres.Therefore, only when electrode width is reduced other size parameters should be taken into account due to the fact they so strogly affect the effectiveness of width reduction.Moreover, as it was mentioned above reducing width of the electrode fingers results in a more uniform gradient of electric field across the whole microelectrode array.

Conclusions
DEP force theoretical analysis was performed using the finite element method and the dependence on microelectrode width, spacing and thickness was acquired.The research results are applicable for any microelectrode structure that inherits rectangular structure of single microelectrode finger in its design.It was determined that the strongest influence on the DEP force has the spacing alteration between the electrodes.The wider the spacing is, the lower DEP force will be obtained.Spacing reduction also proved to be effective on the whole range of heights that were investigated.Reduction of microelectrode structure width parameter resulted in a steady increase of the gradient of electric field.However, the increment rates are lower by a factor of 10 compared to the effectiveness of spacing reduction.Also a strong dependency of width alteration on other two parameters has been observed.Reduction of width below 10 μm when the spacing of the electrodes is less than 5 μm doesn't have any impact on the ∇| | .Thickness reduction proved to be effective in order to increase DEP force only in the 0 -100 nm range of heights.However, thickness alteration effectiveness is independent from the influence of the other two parameters.Results obtained in this work may already find application in the fabrication of microfluidic lab on chip devices to separate or control motion of the particles in nanometer scale microfluidic channels.Also the data obtained from numerical calculations can be used in order to create the most suitable electrode array design for nanoparticle separation applications where a specific DEP force value is required.