Microsyst Technol DOI 10.1007/s00542-015-2700-7 TECHNICAL PAPER Analytical modeling of a silicon‑polymer electrothermal microactuator Huu Phu Phan1 · Minh Ngoc Nguyen1 · Ngoc Viet Nguyen1 · Duc Trinh Chu1 Received: 13 July 2015 / Accepted: 30 September 2015 © Springer-Verlag Berlin Heidelberg 2015 Abstract This paper illustrates both thermal and mechanical analysis methods for displacement and contact force calculating of a novel sensing silicon-polymer microgripper when heat sources are applied by an electric current via its actuators Thermal analysis is used to obtain temperature profile by figuring out a heat conductions and convections model Temperature profile is then applied into the mechanical structure of the gripper’s actuators to form the final equation of displacement and contact force of the jaws Finally, the comparison among the calculation, simulation and actual measurement concludes that materialization methods are appropriate Achieving the final equation of gripper’s jaws displacement and contact force is a major step to optimize or reform this novel structure for different sizes to meet specific applications 1 Introduction In recent years, microelectromechanical systems (MEMS) have been widely applied in diverse science and engineering domains (Cheng et al 2008) MEMS-based microgrippers provide advantages in terms of their compact size and low cost, and hence play an important role in microassembly and micromanipulation fields for manipulating micromechanical elements, biological cells (Cheng et al 2008; Zhang et al 2013) During the past two decades, microactuators based on different actuation principles such as shape-memory alloys, electrostatic, electrothermal, * Huu Phu Phan phanhuuphu82@gmail.com University of Engineering and Technology, Vietnam National University, Hanoi, Vietnam piezoelectric, pneumatic and electromagnetic approaches have been employed to drive MEMS microgrippers (Jiang et al 2007; Hsu et al 2002; Chen et al 2009; Beyeler et al 2007; Chu Duc et al 2007) Moreover, the integrated position and force sensors can deliver real-time feedback signals to protect both the microgripper and grasped object from damaging (Menciassi et al 2003; Chu Duc et al 2006; Chronis and Lee 2005) Owing to different properties of actuators, the MEMS microgrippers exhibit diverse dedicated performances to various applications For example, electrostatic actuation microgripper can provide a large displacement with no hysteresis in a low operating temperature along with a simple structure (Chan and Dutton 2000) Specifically, two different types of movement configuration in terms of lateral comb drive and transverse comb drive can fulfill the objective of high precision and large movement, respectively (Beyeler et al 2007) In addition, electrothermal actuator can generate a large output force and displacements by making use of its thermal expansion with a small-applied voltage (Chu Duc et al 2007) On the other hand, the large force output, precision displacement and rapid response are the attractive points of the piezoelectric actuator Besides, electromagnetic actuator and pneumatic actuator driven microgrippers can provide a relatively large output force and displacement (Butefisch et al 2002; Lee et al 1997) It is known that force sensing is necessary for a delicate micromanipulation task Nonetheless, before the force feedback sensor is applied, the optical method has been widely studied (Miao et al 2004; Rembe et al 2001) Recently, researchers showed a great interest in the sensors with high resolution and sensitivity In order to enhance the reliability and safety of the manipulation, the integrated position and force sensors such as piezoelectric sensor, piezoresistive sensor and capacitive sensor were designed 13 to provide the real-time position and force information (Chu Duc et al 2006; Menciassi et al 2003; Chronis and Lee 2005) Thanks to the advances in the technologies, the sensitivity and resolution of the sensor have been improved substantially A novel design of polymer-silicon electrothermal integrating force sensor microgripper is presented and characterized (Chu Duc et al 2007b, c; 2008) The device consists of laterally stacked structures based on a three-element composite: the metal heating layer, heating conducting silicon structures and a polymer The heat is highly efficient transferred from the heater to the polymer by employing the high heat conduction rate of the deep silicon serpentine structures that have a large interface with the surrounding polymer The proposed device is based on the SU8-2002 polymer with a large thermal expansion coefficient This design overcomes the weakness of the other designs and it boats a large lateral jaw movement with low coupled vertical motion and fast response time Another advantage is that the device is made of regular silicon wafers which are compatible with CMOS technology fabrication process Thus, control circuits can be integrated into the structure with the sole manufacturing process For the characterization of the microgripper, HP4155A semiconductor parameter analyzer is used The displacement is monitored by the CCD camera on the top of the probe station The thermal behavior of the microgripper is investigated by using a built-in external heat source from the Cascade probe station A DSP lock-in amplifier SR850 is used to characterize the response frequency of this sensing microgripper The sensing microgripper (490 μm long, 350 μm wide, and 30 μm thick) can be used to grasp an object with a diameter of 8–40 μm A microgripper jaws displacement up to 32 μm at applied voltage of 4.5 V is measured with a maximum average working temperature change of 176 °C The output voltage of the piezoresistive sensing cantilever is up to 49 mV when the jaws displacement is 32 μm The force sensitivity is measured as being up to 1.7 nN/m and the corresponding displacement sensitivity is 1.5 kV/m The bandwidth frequency of this sensing microgripper is 29 Hz The minimum detectable displacement and minimum detectable force are estimated to be 1 nm and 770 nN, respectively (Chu Duc et al 2007b, 2008) These characteristics make the sensing microgripper entirely suitable for applications where force feedback is needed, such as microrobotics, microassembly, minimally invasive and living cell surgery Although measurements were conducted throughout, initial simulation model for this device was quite simple COMSOL—a finite element modeling tool is used to simulate the operation of this sensing micro-gripper Threedimensional models are employed to analysis the elasticity, displacement, temperature distribution of the microactuator The model only comprises one transmission which is 13 Microsyst Technol from assumed heat inputs to movements, while the gripper works base on a voltage source Therefore, completely model (with electrical input parameters) and careful analysis are needed to improve the accuracy of the simulated and calculated values and physical properties of the gripper The heat transfer and mechanical calculation of the microgripper basing on thermal, mechanical and thermal– mechanical combination analysis are presented in this paper Firstly, the operation principle of the sensing microactuator based on silicon-polymer electrothermal actuator and piezoresistive force sensing cantilever is thoroughly understood using thermal and mechanical analysis Following these steps, calculation results are compared with 3-D simulation and the fabricated sample characterized parameters for verification of gripper’s mathematical equations Finally, a method for structure optimization is proposed basing on combination of changing equations’ factors and the simulation 2 Design and operation of silicon‑polymer electrothermal microactuator The microgripper is designed for the normal opened operating mode with two actuators on opposite sides Each actuator has a silicon comb finger structure with the aluminum metal heater on top (Chu Duc et al 2007d) A thin layer of silicon nitride is employed as the electrical isolation between the aluminum structure and the silicon substrate Each actuator consists of silicon comb fingers with SU8 polymer layers in between When the heater is activated, the generated heat is efficiently transferred to the surrounding polymer through the deep silicon comb finger structure that has a large interface area with the polymer layer The polymer layers expand along lateral direction which leads to bending displacement of the actuator arms The design of the actuator is shown on Figs. 1 and 2, which is the right arm of the sensing microgripper system Ideally, both arms of the gripper are similar geometry and characteristic Therefore, calculations and simulations of the gripper are took place on one arm The structure is based on the combination of a silicon-polymer electrothermal microactuators and piezoresistive lateral forcesensing cantilever beams When the electrothermal actuator is warmed up by applying electric current through its aluminum heater, the microactuator’s arm and also the sensing cantilever are bent This causes a difference in the longitudinal stress on the opposite sides of the cantilever, which changes the resistance values of the sensing piezoresistors Due to the correlation of the displacement of the microactuator jaws and resistance of piezoresistors, positions of the actuator jaws can be monitored by the output voltage of the Wheatstone bridge of the piezoresistive sensing cantilever Microsyst Technol Aluminum heater Polymer GND V+ Anchor Silicon MoƟon direcƟon Fig. 1 Schematic drawing of the silicon-polymer electrothermal microactuator HSi L Fig. 3 SEMS pictures of a fully sensing electrothermal silicon-polymer microactuator; b removed silicon cantilever configuration HAl L comp HSU8 Wbone Wgap Wcan L jaw Silicon SU- polymer (see Fig. 3) The configuration without silicon cantilever removes the heat conduction through the sensing cantilever for analyzing the mechanism operation of the electrothermal actuator (Fig. 3b) The actuator displacement is then calculated by using a traditional mechanical method Aluminum 3.1 Thermal analysis Fig. 2 Front-side view of the silicon-polymer electrothermal microactuator with geometry symbols and parameters beam Besides that, the contact force between the microactuator jaws and clamped object is then determined, relying on displacement and stiffness of microactuator arms (Chu Duc et al 2007b) Readers are referred to the Ref (Chu Duc et al 2007b, c, 2008) for further information on this proposed sensing microactuator 3 Silicon‑polymer electrothermal actuator The fabricated electrothermal silicon-polymer microactuator and its geometry dimension parameters is shown in Fig. 3 and Table 1 respectively A full sensing microactuator illustrates with 490 µm long, 110 µm wide and 30 µm thick The design, fabrication and initially characterization of the proposed sensing microgripper are reported (Chu Duc et al.) Figure 3a is SEM picture of the sensing microgripper based on silicon-polymer electrothermal actuator with a force sensing silicon cantilever Beside the sensing function, the cantilever heat energy in the electrothermal actuator is conducted to the anchor through this cantilever In this work, the heat transfer is analyzed based on two configurations without and with the silicon cantilever The whole structure is heated by the aluminum layer on the surface of silicon bone which is considered the main heat source of the microgripper When aluminum filament terminals are connected to a power source, that layer is heated by the Joule-Lenz’s law In that case, the thermal energy is transferred to the silicon-polymer stack The polymer layers, after heated up, expand in the x-axis, causing bending displacement of the actuator arms In general, conduction, convection and radiation are three mechanisms of heat flow The electrothermal actuator is operated in the air ambient where two heat transfer mechanisms in analysis: conduction in the actuator and convection to the surrounding air are considered Because the working temperature is lower than 500°K, the radiation transfer can be neglected (Howell and Robert Siegel) The major thermal dissipation is caused by the conduction to the silicon substrate and the convection to the air Temperature can be assumed to be uniform throughout the thickness because it is very thin; therefore the actuator is regarded as a one-dimensional case Eventually, calculations and analysis are conducted in x-axis while y-axis is ignored In the steady state, the heat is stored in volume unit between x and x + ∆x given by (Stephen 2001): x + ∆x QG = qG y.dx (1) x 13 Microsyst Technol The heat loss from left and right side of polymer-silicon stack is given by: ∂T (x + ∆x) ∂T (x) − ∂x ∂x QC = t.y (a) (2) The heat loss due to convection is expressed by: (b) (3) Qconv = −2α(T (x) − T0 ).y.∆x Implying the conservation law: (4) QG + QC + Qconv = The equation of temperature by x is then obtained as: ′′ T (x) − qG + 2αTair qG + 2αT0 2α T (x) = − =− t t t (5) This is the quadratic differential equation which has the root given by: T (x) = C1 e 2α tx − + C2 e 2α tx + C3 (6) =0 Applying boundary conditions: T(0) = T0; dT (x=L) dx The coefficients C1, C2 and C3 are given by: 2α tL qG − 2α e C1 = − 2α tL e − +e qG 2α e C2 = − 2α tL e C3 = T0 + 2α tL (7) 2α tL +e − 2α tL qG t (8) (9) For the fabricated microgripper, the resistor of aluminum layer is about 149.018 Ω When it is applied a voltage of 4 V, the heat power is calculated about 0.107 W Thus, qG ∼ = 6.941e6 W/m2 (it is the power dissipation over the aluminum filament area) The value of α is in the range from to 25 W/m2K (Howell and Robert Siegel), thus, the highest value of 2αTair is 15 × 103 W/m2 Comparing to the value of qG = (6.941) × 106, the convection is neglected, therefore: ′′ T (x) = − qG t (10) Following is the outcome of a similar method, we have the function describes the temperature distribution in the actuator: T (x) = − qG qG L x + x + T0 t t (11) Figure 5 shows the calculated temperature distribution in the microgripper It is clear that the steady state temperature 13 Fig. 4 Cross-side and front-side view of the removed silicon cantilever structure for thermal analysis Table 1 Geometry of the sensing microactuator design Parameters Symbol Str Unit Actuator/cantilever length L 390 Actuator/cantilever thickness T 30 µm Silicon finger width HSi µm SU-8 layer width HSU8 µm Aluminum heater width HAl µm Comb finger width Wc 75 µm Silicon bone structure width Wb 10 µm Gap between actuator and silicon cantilever Wgap 22 µm Cantilever width Wcan 12 µm µm Microactuator jaw length Ljaw 100 µm Aluminum thickness TAl 0.6 µm The heat capacity of actuator C J/kg.K The mass density of actuator The cross section area ρ A kg/m3 m3 The temperature in x-axis T K The conductivity coefficient The convection coefficient λ α W/m.K W/m2K The heat source Q J distribution rises dramatically along the actuator in form of half parabola The maximum temperature of actuator peaks nearly 270 °C at the tip when 4 V between two terminals of the aluminum heater is applied 3.2 Mechanical analysis Considering that the microgripper is a bimorph cantilever that consists of two different materials: the silicon-polymer stack layer and silicon layer It can be supposed as single material bars because these parts are calculated to obtain apparent parameters Therefore, this simplified model is Microsyst Technol (a) (b) Fig. 7 Cross-side and front-side view of the silicon-polymer electrothermal microactuator for thermal analysis Fig. 5 Calculated temperature distribution on the microgripper The displacement d of the bimorph cantilever is: d= kcur Lact for (13) Lact ≪ ρ It is assumed that the zero point of x-axis is the border between the anchor and the actuator (Fig. 4a) Considering component dx with temperature is T(x), radius of the activating actuator’s curvature can be calculated by applying the Timoshenko calculation at x (Stephen 2001), as illustrates below: 6(αstack − αSi )(1 + m)2 ∆Tx kcur−x = (Wc + Wb )(3(1 + m)2 + (1 + mn) m2 + mn ) (14) Fig. 6 Sketch of the bimorph structure consisting of the silicon bone and the silicon-polymer lateral stack composite The average temperature: x probably appropriate for the structure When the bimorph cantilever is heated, causing the different expansion of two materials, the cantilever is bent as shown in Fig. 6 (Chu Duc et al 2007c) It is assumed that the average temperature increases ∆T, and the bending displacement of microgripper is d Thus, the curvature of cantilever can be calculated as follows: Tx = x (− qG qG L qG q G L x + x + T0 )dx = − x + x + T0 t t t t (15) The average temperature increase ∆T: ∆Tx = − qG qG L x x + t t (16) The curvature of whole structure based on x coordinate: kcur 6(αstack − αSi )(1 + m)2 ∆T = = ρ (Wcomb + Wbone )(3(1 + m)2 + (1 + mn) m2 + mn ) (12) where αSi is the thermal expansion coefficient (CTE) of silicon; αstack is the apparent CTE of the silicon-polymer Si b stack; n = EEstack , m= W Wc ; ESi is the Young’s modulus of silicon; Estack is the Young’s modulus of silicon-polymer stack kcur = = ρ 6(αstack − αSi )(1 + m)2 (Wc + Wb )(3(1 + m)2 + (1 + mn) m2 + − qG qG L x + x t t mn ) (17) 13 Microsyst Technol Thus, the displacement d of cantilever based on x coordinate: d= = 2α tx T (x) = C1 e kcur x 2 2α tx − + C2 e (24) + C3 Inserting the Eq. (23) into (24), we obtain: 6(αstack − αSi )(1 + m)2 Lact (Wc + Wb )(3(1 + m)2 + (1 + mn) m2 + qG 2α C3 = T0 + mn ) x4 qG (− + Lx ) t (25) Applying boundary conditions: T(0) = T0 Thus, (18) 4 Microgripper based on silicon polymer electrothermal actuator with sensing function C1 + C2 + C3 = T0 4.1 Thermal analysis The sensing actuator has a silicon cantilever beam (Chu Duc et al 2007b, d) where existence of heat transfer between silicon-polymer stack and cantilever beam is: Figure shows the cross-side and front-side view of the proposed silicon-polymer electrothermal microactuator for thermal analysis Thermal energy in the actuator is diffused to the anchor as the heat-sink by heat conduction transfer through the actuator-anchor interface and also silicon cantilever, see Fig. 7b Beside the conduction, heat energy is lost by convection to the surrounding air, see Fig. 7a The temperature can be assumed to be uniform throughout the thickness due to the thickness of the structure is much smaller than other geometry parameters Thus, the temperature of y-axis is uniform so that the actuator is regarded a one-dimensional case Therefore, the electrothermal microactuator can be simplified as a bar shown in Fig. 7b In the steady state, the heat is stored in volume unit between x and x + ∆x given by (Arfken 1985; Trodden 1999): Si dT (x = L) = −qcond dx C1 2α e t 2α tL (19) qcond C1 = − QC = t.y 2α tL e (20) The heat loss due to convection is expressed (Arfken 1985; Trodden 1999; Snieder 1994): 2α tL =− (21) +e C3 = T0 + + 2α t Si C2 = − 2α tL (29) 2α tL 2α tL qG 2α e +e − (30) 2α tL qG 2α (31) Temperature profile on the silicon cantilever is also calculated by: Tcan (x) = qcond x + T0 (32) At x = L, T (L) = Tcan (L), so that: Applying the conservation law: QG + QC + Qconv = (22) The equation obtains: qG + 2αTair qG + 2αT0 2α T (x) = − =− T (x) − t t t ′′ qcond = Si 2α t This is the quadratic differential equation which has the root given by: 13 qG 2α ( (23) (28) Si Si Qconv = −2α(T (x) − T0 ).y.∆x qcond 2α tL qG − 2α e − qcond e ∂T (x + ∆x) ∂T (x) − ∂x ∂x + 2α t Si x The heat loss in the left and right side of silicon-polymer stack is given by [36]: 2α − e t − C2 The coefficients C1, C2, C3 are given by − qG y.dx (27) The equation becomes: x+∆x QG = (26) 2α L − t +e e − e e 2α L t −e 2α L − t +e 2α L t 2α L t 2α L t − 1) (33) −L The temperature distribution in the actuator is given by inserting the Eq. (33) into the Eqs. (29), (30), (31) Microsyst Technol 2α t Let τ = L ( eτ +e −τ −1) qG C1 = − 2α e−τ −eτ eτ +e−τ −τ + e−τ (34) eτ + e−τ − qG C2 = − 2α ( eτ +e −τ −1) e−τ −eτ eτ +e−τ eτ −τ + eτ (35) + e−τ Thus, τ τ T (x) = C1 e L x + C2 e− L x + T0 + qG 2α (36) C1, C2 are given in Eqs. (34) and (35) Basing on the function of temperature with real parameters coming from fabricated version of the gripper, Fig. 8 plots profile of temperature versus the length (the resistor of aluminum layer is about 149.018 Ω, heat power is 0.136 W when applied voltage of 4.5 V, and qG ∼ = 8.784e6W/m2) As shown in the results of temperature distributions chart, temperature is varied from the base to tip with a parabolic form appropriate to earlier calculation The arrangement on the cantilever is linear and peaks at nearly 200 °C at the tip Due to the existence of cantilever, the former analytical manner to attain tip’s displacement is ineffective The displacement and gripping force at the tip is calculated by the direct displacement method Fig. 8 The calculated temperature profile on sensing microactuator A EAB, AAB, IAB B h1 C E ECD, ACD, ICD D h h2 F EEF, IEF G L Ljaw Fig. 9 Frame structure to analyse the sensing microactuator A ∆Τ B C ∆Τ D 4.2 Thermal–mechanical analysis A simplified structure which is used to analyze the sensing microactuator under the change of temperature is shown in Fig. 9 It can be seen from the figure that lines AB, CD and EF denote beam elements representative of silicon-polymer stack, silicon bone, and silicon sensing layers, respectively Those beam elements are fixed on one end, and connected together by a rigid beam BDF on the other end Denote Eij, Aij and Iij to be Young’s modulus of material, cross-section area and moment of inertia of cross-section for the beam ij, respectively The silicon-polymer stack beam AB length increases when power is applied The performance of the siliconpolymer stack is analyzed based on the hydrostatic pressure according to the constraint effect (Chu Duc et al 2007d) Note that for the beam AB, equivalent values of the above parameters are adopted on (Chu Duc et al 2007d) In this calculation, it is assumed that the change of average temperature on elements AB and CD is ΔT E F Z1 B’ D’ Z2 y(T) F’ Fig. 10 Deformation of the structure 4.3 Sensing microactuator displacement analysis Figure 10 shows the deformation of the structure under the change of temperature in beams AB and CD As shown in the graph, Z1 and Z2 denote the unknown rotation and vertical deflection of the rigid beam BDF Here, it is assumed that the axial expansion of elements EF is neglected In order to calculate the displacement and the output force at the jaw tip of the sensing micro gripper, the direct 13 Microsyst Technol E AB I AB E AB I AB L ECD I CD ECD I CD ∆Τ B C ∆Τ D L Z1 = L A E L F h1 B’ h h2 D’ G F’ F h3 Manipulating object EEF I EF EEF I EF L F L Fig. 13 Structure for solving the output force Fig. 11 Diagram of the bending moment due to Z1 = 1 E AB I AB ECD I CD Note that axial forces in elements AB and CD due to Z2 = 1 are zero Based on conditions for static balance of the structure, stiffness coefficients are given by: L2 r11 = r22 = L r12 = EEF I EF L2 Z2 = 4EAB IAB AAB + 4ECDL ICD + 4EEFL IEF + h EAB L L 12ECD ICD 12EAB IAB 12EEF IEF + + , L3 L3 L3 6ECD ICD 6EAB IAB 6EEF IEF + L2 + L2 r21 = − L2 + h22 ECD ACD , L Components R1(T) and R2(T) of the force vector are calculated basing on axial forces on elements AB and CD due to the change of temperature ΔT We have R1 (T ) = α1 ∆TEAB AAB h + α2 ∆TECD ACD h2 , R2 (T ) = Fig. 12 Diagram of the bending moment due to Z2 = 1 (37) Z1 (T ) = r12 R1 (T ) r22 R1 (T ) ; Z2 (T ) = − det K det K r11 r12 ; Z(T ) = r21 r22 Z1 (T ) Z2 (T ) ; and R(T ) = R1 (T ) R2 (T ) (38) Equations (38) denote stiffness matrix of the structure, displacement vector and output force vector, respectively To determine stiffness coefficients, unit displacements are applied Diagrams of bending moments in structural elements are performed in Figs. 11 and 12 in the cases of Z1 = 1 and Z2 = 1 Axial forces in elements AB and CD under the applied unit displacement Z1 = 1 are given by: AB N = ∆LAB ELAB AAB = CD N = ∆LCD ELCD ACD = 13 hEAB AAB , L h2 ECD ACD L (39) (42) where det K = r11r22 − (r12)2 Vertical displacement y(T) of the microactuator jaw tip under the change of temperature is therefore given by where K= (41) Solving the Eq. (1), we yield displacement method is used Under the change of temperature ΔT, the governing equation for the system is given by: KZ(T ) = R(T ) (40) y(T ) = Z1 (T )LJaw + Z2 (T ) = R1 (T ) r22 Ljaw − r12 det K (43) Sensing microactuator output force analysis Figure 13 illustrates the structure which estimates the contact force between the microactuator jaw and the manipulating object The unknown force F is calculated from the following condition: y(T ) + y(F) = h3 (44) where y(F) denotes the vertical displacement due to the reaction force F Like the above procedure, the governing equation for solving the displacement y(F) is given by: KZ(F) = R(F) (45) Microsyst Technol Fig. 14 Displacement of the microgripper jaw tips at steady state vs average working temperature where R1 (F) = −FLjaw ; R2 (F) = −F Solving the Eq. (45), we yield Z1 (F) = det1 K {r22 R1 (F) − r12 R2 (F)}, Z2 (F) = − det1 K {r12 R1 (F) − r11 R2 (F)} (46) The vertical displacement of the jaw tip due to the reaction F is given by: y(F) = Z1 (F)LJaw + Z2 (F) = det1 K r22 R1 (F) − r12 R2 (F) Ljaw + R2 (F)r11 − R1 (F)r12 (47) Taking the above result into Eq. (44), we obtain the value of gripping force: F= R1 (T ) r22 Ljaw − r12 − h3 det K r11 − 2r12 Ljaw + r22 (Ljaw )2 (48) 5 Measurement, calculation, simulation results and discussions The design, fabrication and initially characterization of the proposed sensing microgripper is reported in the ref (Chu Duc et al 2007b; Chu Duc et al.) and calculation results were mention in this paper In addition, a 3-Dimention computer model of this device which comprises two conversions (electricity to heat and heat to movement) for simulating in virtual medium Elasticity, movement, temperature profile, power consumption of the actuator are generated by COMSOL (Comsol Inc.)—a finite element modeling tool - based on conversion of electricity to heat Fig. 15 The temperature profile on sensing microactuator and then heat to movement It is necessary to make comparisons with relevant results to conclude the consistency of each deductive method Therefore, those methods are tethered for an effective reconfirmation of the new size sensing microgripper system such as optimization parameters for a specific application before fabrication steps are carried out Figure 14 shows calculation, simulation and measurement results over the average working temperature of the sensing microgripper As can be seen from the chart, there are similar patterns of calculation and simulation which have approximately 30 % of deviation To clarify, errors of each method can contribute to this nonconformity Firstly, in calculation, there was not mention resistance changes of aluminum layer when temperature varies, and some variables such as convection and radiation were neglected Besides, there could be unknown structural ties that skipped in simplifying gripper’s structure for the calculation Secondly, some parameters of the model are fixed in ideal conditions and simulation results are gathered from perfectly surrounded environment Regarding measured results, most of discrete points are in the range of the two lines of simulation and calculation In addition, these plots can be linear fitted into a single line that in the same channel with previous lines In short, results of displacement versus average working temperature of three methods are uniform As regard to distribution of heat at steady state when voltage source (4.5 V) is applied to activate the gripper, Fig. 15 illustrates temperature profiles on both actuator and cantilever which are obtained by calculation and simulation Due to the limitation of the measurement method (Chu Duc et al.), temperature on each position of actuator and cantilever could not be gathered precisely Thus, the results measured in comparison with 13 these of other methods are ignored Obviously, there are striking similarities in the results of calculation and simulation, and therefore, not only the mathematics methodology but also simulation model of the microgripper are confirmed As is shown in the results comparison among methods, one methodology has confirmed the accuracy of others and vice versa Although there are some errors and tolerances of each method itself, the model for simulations and calculation scheme is appropriate Consequently, it is an important factor to improve or adapt the gripper’s structure to specific application Moreover, it can be used to optimize the structure in a particular aspect For example, a new microgripper which performs the same range of displacement with the original one, but the operating temperature below 100 °C can be designed Firstly, determine size of the gripper (the number of polymer stacks or the length of actuator) by using the final equation After that, conducting the simulation with model which has obtained parameters from the first steps, and therefore, the design via those results is affirmed 6 Conclusions The design of sensing polymer-silicon electrothermal microgripper was proposed, characterized and simulated This device has many advantages in comparison with other actuators, such as large movement, fast response time, low driving voltage and CMOS compatible However, it is required analytical modeling to fully comprehend each parameter of the design Therefore, optimization and adaptation for the new dimensional microgripper are based on mathematical functions that have obtained Analysis methods for this proposed sensing siliconpolymer microgripper are introduced in this paper Firstly, gripper’s temperature profile is calculated by using the heat conductions and convections model Secondly, final displacement and contact force equations are formed by inserting temperature profile into the mechanical model Finally, the direct displacement method is used for this device’s displacement and output force analysis Besides, functional parts of the gripper is considered and analyzed separately Microgripper operation is based on two main transformations: electricity to heat and then heat to mechanic The computation following these two models in turn to form displacement and clamp force of the actuator is applied Deviations between simulation, measurement and calculation results are not significant There are great steps to understand the devices better, and more scientific approaches to determine the new size of actuator to suit 13 Microsyst Technol each specific requirement or optimize the design This proposed microgripper could be potentially used for microparticle manipulation, minimally invasive surgery, and microrobotics References Arfken G (1985) Mathematical methods for physics, 3rd edn Academic Press, Waltham Beyeler F, Neild A, Oberti S, Bell DJ, Sun Y, Dual J et al (2007a) Monolithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells aligned in an ultrasonic field J Microelectromech Syst 16(1):7–15 Beyeler F, Neild A, Oberti S, Bell DJ, Sun Y, Dual J et al (2007b) Mono-lithically fabricated microgripper with integrated force sensor for manipulating microobjects and biological cells 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heat transfer... electrical input parameters) and careful analysis are needed to improve the accuracy of the simulated and calculated values and physical properties of the gripper The heat transfer and mechanical calculation