DESIGN AND SIMULATION OF PARALLEL MICROHEATER

This paper presents the design and simulation of a thin film microheater. This can have promising applications in bio-medical analysis, explosive detection, gas sensing, and micro-thrusters. An approach is presented to enhance the thermal uniformity of parallel microheater. The modeling of microheater is done using glass as a substrate material. The analysis is carried out with different resistive material for the heater. To study the response of the microheater to the different supply voltage, substrate thickness, and time interval, finite element simulation is carried out with commercial FEM analysis toolCOMSOL Multiphysics 5.2a. The proposed design in Model 1 have high contact resistance and it suffers from the contact-heating problem; however, Model 2 offers an excellent thermal uniformity with a tolerance of 1°C. There is a good agreement between the simulated and the theoretical results.


INTRODUCTION
Most of the bio-medical analysis and sensing applications require an elevated temperature. Therefore, systems like microfluidic Polymerase Chain Reaction (PCR) chip, gas sensors, and micro-chemical sensors need an integrated heating component with the device. Microheaters are one of the most important functional blocks for the systems such as microfluidic PCR chip for bio-medical analysis (Park et al., 2011;Nie, et al., 2014) humidity sensors for industrial application (Smetana and Unger, 2008;Dai, 2007), and Methanol sensors for chemical sensing (Ha et al., 2005;Korotcenkov, 2014).
There are two types of microheater: the wire and the thin film based. The thin film microheaters are preferred over the wire microheaters due to their low thermal mass, less power consumption and ease of integration with other functional units of the system. At the early stage, heavily p-doped silicon microheaters were used because of its compatibility with integrated circuit fabrication process and its attractive mechanical properties. However, huge power consumption is the major drawback of the silicon microheaters. To overcome the problem of large power requirement, the proposed heaters are modeled on the Glass substrate, which offers low thermal conductivity (1.38 Wm -1°C-1 ) and high electrical resistivity (1 ×10 14 Ωm); desirable to achieve better thermal uniformity and low power consumption.
The commonly used resistive materials for the microheater are Aluminum (Phanakun et al., 2012), Copper (Pandya et al., 2012), Gold (Kim, 2006), Nickel-Chromium (NiCr) alloy (Das and Akhtar, 2014), Platinum (Hsieh et al., 2008), Titanium (Guan and Puers, 2010), and Tungsten (Santra et al., 2010). Aluminum and Copper are susceptible to corrosion and oxidation; therefore, they are avoided as the resistive material for the microheater. Gold and Platinum are chemically inert materials but they are very expensive; therefore, to keep the device cost low, they are not used. The melting temperature of Titanium and Tungsten are higher compared to NiCr. Therefore, it is easier to evaporate the NiCr compared to Titanium and Tungsten. Hence, this work uses NiCr as a resistive element for the microheater. Figure 1 shows the schematic of microheaters.

DESIGN AND GOVERNING EQUATIONS
Joule heating is the phenomena in which the current is passed through a resistive material to generate the heat. The heating power P of a microheater is produced by connecting a voltage source V across the two ends of a heating circuit with a resistance R due to the current I. The basic configurations of the heating circuit are categorized as series and parallel type, respectively. Figures 1(a) and 1(b), shows the series and parallel resistance microheater, respectively. In Fig. 1(a), the contact pad and the resistive elements are connected in series. Therefore, power dissipation of the heater is given by, From Eq. (1) the power is directly proportional to the resistance of the heating element. Therefore, the higher resistance values are favorable in achieving the large heating power. In Fig. 1(b) there is no voltage difference in the resistive element across the line 1-1' therefore the power across 1-1' line is given by,

Frontiers in Heat and Mass Transfer
Available at www.ThermalFluidsCentral.org Frontiers in Heat and Mass Transfer (FHMT), 10, 9 (2018) DOI: 10.5098/hmt.10.9 Global Digital Central ISSN: 2151-8629 Hence, the smaller resistances are favorable in achieving higher heating power and results in the faster response for the parallel configuration.
Resistance plays a critical role in power dissipation calculation. The resistance of any thin-film having the length, width and thickness L, w, and t, respectively is given by, The ρ represents the resistivity of the material. If L=w, then Eq. (3) represent the sheet resistance (RS) of the resistive layer and can be written as, Therefore, the resistance of any resistive thin film can be calculated as, The heat produced in a resistive element due to Joule heating is given by, Here, ∆t is the time. The heat generated by the microheater is dissipated in the surrounding medium. The thermal loss of microheater is divided into three types, viz., conduction in the device, convection cooling, and radiation. Therefore, to achieve steady state, the total heat produced by the microheater must be equal to the heat lost by conduction (Qcond), convection (Qconv), and radiation (Qrad).
2 cond conv rad The rate of heat loss by conduction in the glass substrate is given by, Here kglass, Aglass, ∆T, and ∆x, represents the thermal conductivity, area of the cross-section of the glass substrate, a temperature difference of two opposite surfaces and the thickness of glass substrate, respectively. The rate of heat loss by conduction can be reduced by selecting the substrate material with a lower thermal conductivity and by decreasing the area of conduction. The rate of heat loss by convection in the air is given by, Here, h is coefficient of convection, it depends on the geometrical factor, shape, and the orientation of the heated surface. Aconv and ∆T represent the surface area through which convection is taking place and the temperature difference between the heater and the ambient, respectively. The rate of heat lost by radiation is given by, The ε, σ, Arad, and ∆T are the emissivity, Stefan Boltzmann constant, surface area and the temperature difference between the heater and the ambient, respectively. Therefore, the total power lost can be obtained by, 24 glass glass conv rad The losses due to radiation can be neglected at the temperature range of interest of microheater and due to the very low emissivity of the materials involved (Courbat et al., 2011). Therefore Eq. (12) can be rewritten as 2 glass glass conv

Fig. 2
Parallel microheater (Model 1) Figure 2 shows the parallel microheater Model 1, the width of all the resistive elements RA to RE is taken 40µm. For the resistance calculation, the resistivity and thickness of all the resistive films are taken as 1.10×10 -6 Ωm and 0.2µm, respectively. The dimension and theoretical resistance values of all the resistive element used in Model 1 are given in Table 1. It can be seen from Table 1 that RA is having the highest resistance compared to all other resistive element. When a voltage source connected to the microheater circuit, it results in current flow through the resistive elements. As the current always takes the low resistance path, the minimum and the maximum current flowing through RA and RE, respectively, which leads to the minimum and maximum temperature near to circumferences of the heater and the resistive element RE, respectively. It can be seen from the Fig. 2 that resistive elements RB and RC are having two neighbor resistive elements whereas RA has the only neighbor. Due to more neighbor and conductive heat transfer in the glass substrate, the central region of heater acquires higher temperature. To overcome this problem, the separation between the resistive elements reduces as we move away in the top or bottom direction from the center of the heater. From Fig. 2, the separation 3 between RC and RB is 200µm whereas the separation of RB and RA is 150µm.

Fig. 3 Modified parallel microheater (Model 2)
To overcome the problem of nonuniform heating of Model 1, a modified parallel microheater is proposed in Model 2 shown in Fig. 3. In the Model 2, the resistance of the resistive elements is selected in such that if a voltage source connected to the heater the minimum current (I) flows through the resistance RC1, and as we move away from the center in the top or bottom direction current gets doubled of its neighboring branch.
The heating power in resistive element RC1 can be calculated as, Here L and w1 represent the length and width of resistance RC1. Similarly, the power in resistive element RB1 due to current 2I can be calculated as, Here w2 represent the width of resistive element RB1. By equating Eqs. (14) and (15), and solving for w2 Similarly, the width of all the resistive elements is calculated by taking a constant length 10000µm and shown in Table 2. Once the L:w ratio of all the resistances are known, then as per spacing between the resistive elements of Model 2 shown in Fig. 3, the dimensions of all the resistive members are calculated using Eq. (5), and given in Table 3.
As per the calculation, the length and width of RE1 are 5355µm and 1050µm, respectively. But to accommodate the heater on a 30×10mm 2 glass substrate, the length of RE1 is fixed to 1554µm. The major drawback of the design proposed in Model 2 is if the number of parallel branches increases the width of the resistive elements increases exponentially. Hence for more than 5 parallel branches, the proposed design is not practical.

SIMULATION
The simulations are carried out using a commercial FEM simulation tool COMSOL Multiphysics 5.2a. The specifications of the Model 1 and Model 2 are shown in Table 4.  All the material properties for the simulation are taken from the COMSOL material library. For all the simulations, the ambient temperature, and the convection coefficient h are considered 20°C and 5 Wm -2 .°C -1 , respectively. The design of microheater targets the biomedical application where the maximum operating temperature is below 100°C, therefore the input voltage for all the heaters are fixed in such that the steady state temperature will be 90°C -100°C. To study the effect of substrate thickness on the heater behavior, the parametric sweep is used to vary the substrate thickness from 300µm to 1500µm in steps of 300µm. A time-dependent simulation is carried out from 0s to 1600s in steps of 50s, to find out the transient response of the microheater. A predefined extra fine size free tetrahedral type mesh is used to simulate the microheater models. The meshes are very fine near the heater element and get coarser as we move away from the heater where high accuracy is not needed Figs. 4(a) and 4(b) show the meshes of Model 1 and Model 2, respectively. 4

RESULT AND DISCUSSION
The simulation of Model 1 and Model 2 are carried out using Aluminium, Copper, Gold, Nickel-Chromium, Platinum, Titanium and Tungsten. For all the simulation Glass (1.5mm thick) is taken as substrate. To find the resistance of microheaters modeled with the different resistive material, 1A current is applied as the input to each model and the voltage across each heater is measured. From Ohm's law, we know that V=IR, therefore, the voltage is equal to the resistance of the heater. Once the resistance is known, by applying the fixed voltage across the heater, the power is calculated for Model 1 and Model 2 and given in Tables 5 and 6, respectively. Once the power is known the time required to reach to the steady state temperature is calculated theoretically for microheater Model 1 and Model 2, and given in Table 5 and Table 6, respectively. Figures 5 and 6 shows the time versus temperature plot for microheater Model 1 and Model 2, respectively. It is observed from the Tables 5, 6 and Figs. 5 and 6 that there is a good agreement between the theoretically calculated time required to reach to the given steady state temperature and the result obtained from the FEM simulation. Figures 7  and 8 shows the zoomed view of time versus temperature plot shown in Figs. 5 and 6, respectively. It is observed that to reach the steady state temperature microheater Model 1 takes longer time compared to Model 2 (Cengel and Ghajar, 2011). Focusing on PCR application, simulation have been carried out to find the time required to reach to the temperatures 90-95°C (denaturation), 50-55°C (annealing), and 70-75°C (extension) steady state temperature for the NiCr microheater Model 1 (Fig. 9) and Model 2 (Fig. 10), It is observed from the Figs. 9 and 10 that time required for lower steady state temperature is less compared to the elevated temperature and rate of change of temperature is more for the higher steady state temperature.
From Figs. 5 to 10, it is observed that the time required for both the microheater models to reach to its steady state temperature is greater than 1000s. Therefore, to achieve the steady state temperature quickly, initially 12V supply voltage applied to the heater (Model 1) and after the 50s the voltage is decreased to 4V. Similarly, for the heater (Model 5 2) initially 9V input is applied and after the 50s it is reduced to 3V, the time versus temperature plot of Model 1 and Model 2 are shown in Figs. 11 and 12,respectively. From Figs. 11 and 12,it is observed that both the heaters achieve the 90 percent of steady state temperature in less than 200s. The problem involves in this approach is the kink in the temperature during the voltage transition. It is observed that Model 2 (Fig. 12) has smaller temperature kink compared to Model 1 (Fig. 11), it is due to larger size of contact-pad.    Figure 15 shows the isothermal contour of NiCr microheater Model 2. The bar graph is shown in Fig. 16 shows the temperature of hottest and coolest region of microheater Model 2. It is observed the average temperature difference is around 1°C for the different resistive material based heater. Hence modified parallel heater proposed in Model 2 offers excellent thermal uniformity with the tolerance of 1°C.  For the applications such as PCR, the temperature control is very crucial, the heater and the microfluidic reservoir are fabricated at the opposite surface of the glass substrate. Therefore, it is necessary to carry out the transient analysis to find the time required for the heater to reach to the steady state temperature and the temperature difference of the two opposite faces of the glass substrate. Figures 17 and 18 show the time required to reach the steady state temperature for different substrate thicknesses for Model 1 and Model 2, respectively. It can be observed that as the substrate thickness increases the time required to reach the steady state temperature also increases. Therefore, thinner substrates are favorable for achieving steady state temperature quickly. Figures 19 and 20 show the substrate thickness versus temperature plot for Model 1 and Model 2, respectively. In the Figs. 19 and 20, x=0 represents the bottom surface of the glass substrate and the terminal value of the x represents surface where the heater is located. It is observed from the Figs. 19 and 20 that the thinner substrate gives the better temperature control. Table 7 shows the comparison of the present work with the experimental work with respect to the substrate used, heating element, maximum operating temperature, and power. The proposed heater in Model 2 is the most power efficient.

CONCLUSIONS
The design and the simulation of a microheater have been carried out with two microheater models. Higher values of the thermal and the electrical resistivity are the desirable ones for the substrate to achieve the better heat confinement. The Model 1 and the Model 2 are the parallel type of microheater. Simulations are carried out using varied materials and found that the NiCr microheaters are using comparatively high power but it is cost-effective compared to other material based microheaters. Model 1 suffers overheating of contact pads due to higher resistance and current near the contact pads. To solve this problem microheater Model 2 is proposed. This offers an excellent thermal uniformity with more than 72 percent area of the heater falling within the tolerance of 1°C and most suitable for applications such as stationary PCR.