## Abstract

Aluminum heavy wire bonds interconnects are a potential alternative to laser or resistance welded bus bars due to its ease of manufacturability, long term reliability and low cost for battery banks. They can also be utilized as a fault protection solution in case of a surge current, dead short, etc, and to isolate a bad cell preventing synchronous failure. Typically, the current-carrying capability of a wire is estimated using standard data generated by testing in free air. However, a deviation in the capacity limits can occur due to the proximity of interconnect to larger thermal masses and different heat extraction techniques found in present day lithium battery packs; e.g., fluid channel cooling, encapsulated wires, etc. The cylindrical cell cathode, anode, and the busbar material constitute a large thermal mass to increase the fusing current in wire bonds above conventional levels. To better predict and design the interconnects advanced and system-specific models should be developed. This paper presents a new mathematical approach which includes the effect of convective cooling inside the battery pack to do an early step estimation of the current handling capacity and fusing time of different diameter wires. The paper also presents a finite element model that includes the impact of boundary conditions, wire length and wire diameter on steady-state current handling capacity of 99.99 % Al wire. Both steady-state and transient simulations were performed to estimate fusing times at different time rated conditions. The paper concludes by providing new curve-fit patterns to give future battery pack designers further insight aiding new designs.

## I. Introduction

Commercialization of lithium-ion batteries has been driven by the rise in portable consumer electronics devices, electric vehicle (EV), rechargeable household and grid energy storage solutions. Lithium-ion batteries have higher energy densities, low self-discharge rate and no memory effect compared to Lead-acid and Nickel Metal Hydride batteries [1] making it widely popular. With the recent development in heavy wire bonding technology, the battery pack assembly has been further streamlined utilizing wire bonds as interconnects. Heavy aluminum bonding wires and aluminum bonding ribbons are used for a wide variety of purposes as aluminum has twice the current-carrying capacity of copper per unit of weight and low cost compared to gold and silver. Wire bonding also allows low-temperature processing (Au processed at 150°C and Al at RT) [2] and is relatively fast (1–20 wire/sec).

In EV applications, the Al wire bond can also double for fault protection by fusing to prevent battery pack failure in case of a single cell failure due to internal or external short circuits. Internal, chemical faults occur when a conductive dendrite forms and pierces the thin membrane between the cell anode and cathode of the cell. This fault occurs gradually over the life cycle of the battery pack due to reductive electrodeposition nonuniformly during cell operation [3]. The single cell failure can cause the other parallel cells to discharge through the low impedance path leading to sequential failure of cells in parallel. This can be mitigated through fusing for example with wire bonds. The other fault is categorized as an external fault. An external fault is due to physical damage to the pack when interconnects or busbars to short one or more parallel blocks of cells. This fault occurs instantaneously and often requires a Solid State Circuit Breaker (SSCB) along with fusing wire to prevent damage to the power system [4].

### A. Fusing of Wire

*I*of a wire can be represented as : Here

_{f}*d*is the diameter of the wire,

*σ*is the electrical conductivity and

*h*is the heat transfer coefficient applied to the wire for heat extraction. However, the derivation relied on empirical data to define a fuse curve and is based on long wires (half-inch and upwards) where heat loss dominates. It also assumes wire is in free air and excludes the effect of heat extraction through the bond foot, effect of potting around the wire and other alternative paths for heat extraction. The equation (1) is derived by assuming no conductive or radiant cooling of the wire.

Reference [6] provided experimental test data which helps establish the minimum current to fuse platinum wires of different gauges and also derives resistivity of conductors. Tests were performed by slowly increasing current until the conductor glowed. Reference [7] also highlighted a fusing equation that related fusing current to wire diameter, however, the equation was only applicable over short periods of a few seconds.

## II. Problem Approach

Current carrying capacity is defined as the amperage a conductor can conduct in a steady-state without fusing. Fusing is defined as the melting of the interconnect under heat produced by an excess current, opening the circuit. The joule heating due to the current through the wire will determine the current carrying capacity of the wire. The capacity is dependent on the diameter and length of the wire, ambient temperature and heat extraction coefficients.

More accurate means to define fusing currents for wire bonds as lithium battery interconnects were sought through classical derivations and multiphysics simulations. Prior works did not include conduction or convection. This paper also provides a new mathematical model that considers the effect of convective cooling and the results are applicable to small wires (>100 mm).

### 1. Mathematical Approach

This section discusses a new mathematical approach which includes the impact of the convection coefficient on the steady-state current handling capability of different diameter wire bonds. The model is designed to estimate the current-carrying capability of a wire bond when the bond is convectively cooled and the resistance of the wire dynamically changes with temperature.

Model Assumptions :

Material conductivity of Al is considered infinite, bulk treatment is assumed. The model only considers the effect of temperature on electric specific resistivity of Al.

Designed for a constant

*h*rate and not for turbulent flow (Prandtl, Reynolds number, etc are ignored)The model does ignore melting enthalpy.

*I’*current [A] through a loop that is conductively cooled by with an ‘

*h’*heat transfer coefficient [W/m

^{2}K]. The gain of thermal energy is directly equivalent to the difference of heat generated due to Joule heating and the energy dissipated by convection with respect to time such that: Here,

*C*

_{ρ}is specific heat capacity [J/K.kg],

*M*is mass of wire [Kg],

*h*is the heat transfer coefficient [W/m

^{2}K],

*S*is the surface area of the cross-section [m

^{2}]. R is the total resistance of the wire [Ω] and is temperature-dependent and represented as : Where,

*L*is the length of the wire [m],

*A*is the cross-section area [m

^{2}] and α

*is the temperature coefficient of resistivity of wire [ppm/*

_{ref}^{0}C]. The ρ

*is the electrical resistivity of wire [Ω.m],*

_{ref}*T*is the ambient temperature [K] and Δ

_{ref}*t*is the time [s] to fuse (melt) the wire. The mass M [kg] is calculated from : Here, ρ is the density of wire [kg/m

^{3}]. Substituting (3) and (4) in (1). The time taken for the wire to fuse can be represented as : Here, K, B and C are constants and are dependent on the material properties and dimensions of the wire bond. They are represented as : For values of B and C, where K<0 the wire is shown to continuously conduct ‘

*I*’ current.

Equations (5)–(8) are utilized to calculate the current handling capability of 8, 12, 24 mil bond wire which is convectively cooled by 100 W/m^{2}K heat transfer coefficient. The length of the wire bond is held constant at 7.5 mm and the material properties of pure Al bond wire is listed in Table I. Table II shows fusing time in seconds for rated current.

Inferring from Table II, 8 mil Al bond wire can conduct 4 A of current in steady-state, 12 mil Al bond wire can conduct 8 A and similarly 24 mil Al bond wire can conduct 20 A current under the same convective cooling forced airflow. However, in an EV application, the actual fusing time and the current handling capability will be more due to the proximity of interconnect to larger thermal masses such as batteries and DC bus bars and different heat extraction techniques. The presence of a larger thermal mass where the interconnect is attached makes conduction transfer dominate over convective cooling of wire. Thus, an alternative FEA model is discussed below.

### 2. FEA Model

The 3D models were created of typical lithium battery arrangements with 8, 12, and 24 mil diameter aluminum wire bonds to a central Cu busbar. Earlier work of such kind of modeling [8] reported 98 % accuracy to actual hardware measurement as long as the material properties and dimensions are to scale. The same approach is applied here. The form factor of the 18650-battery cell was chosen due to its popularity, but the choice of any other cylindrical cell should represent little or no deviation from the results described here as long as the battery is volumetrically the same. A 3D rendering of the battery pack along a typical bond wire profile is shown in Fig.1 (a) and (b) respectively. The overall bond profile can change depending on the application.

## III. Simulation Results

The model was simulated in COMSOL multiphysics under steady-state and transient conditions to mimic the fusing of the wire bond. Material properties used in COMSOL are listed in Table III.

Simulation setup: The external cell wall is assumed to be the heat dissipation surface and an *‘h’* rate is defined as mimicking heat extraction. The wire bond is considered to be potted and the *h*=0 W/m^{2}K on the wire bond outer surface. Anode cap of the cell is considered as an electrical current terminal with a current *‘I’* is passed through the wire bond into the bus bar was held at electrical ground to set the direction of the current flow. The model was made to scale.

The Fig. 2 shows the COMSOL surface plot result for an example simulation. For this example 95 A was passed through a 24 mil wire bond with 7.5 mm total length. The cell wall has a heat flux coefficient of 10 W/m^{2}K applied to the cell wall. Inferring from the plot, the wire can conduct 95 A in steady-state without fusing (Fusing temp = 660.5°C > 565°C) and the hottest point is in the center of the wire bond.

Simulations were conducted to study how the current handling capability of the wire bond is affected by different boundary conditions for heat extraction (i.e. different *h* values), diameter of wire bond and the wire bond profile. Also noted was the time taken for 99.9 % pure Al wire to reach melting temperature as a percentage of overcurrent.

### Study 1: Current handling capacity and fusing time of different Al wire diameter at constant current density

This study monitors the change in fusing time for different diameter Al wire bonds for fixed loop length, fixed *h=10 W/m ^{2}K* (applied to the cell wall) and constant current density. All 8, 12 and 24 mil wire bonds diameters were simulated. The current density was fixed to 350 A/mm

^{2}, therefore as the diameter of the wire bond scales, the current is scaled such that the joule heating per unit length remains constant. The actual values of the current are listed in Table IV.

The plot of maximum wire temperature at different percentage rated current is shown in Fig 3. Inferred from the graph, 100% rated current can flow through the 610 um wire bond in steady-state, 106 % rated current can flow through 300 um wire bond in steady-state and 121 % rated current can flow through the 200 um wire bond for the given conditions. Thus, the smaller the diameter of the wire bond the higher the current can be passed through the system for any given boundary condition and the wire bond was then subjected to 120% – 150% overcurrent. The time taken to reach the melting temperature is shown in Fig. 4.

Results show that the smaller the diameter of the wire bond the longer the time it takes to reach melting temperature and the time decreases as the current increases in the bond wire.

### Study 2: Effect of heat extraction boundary conditions on current handling capacity for 610 μm Al wire

This study investigates the effect of the heat transfer coefficient applied to the cell walls on the current handling capacity of the wire bond. For this simulation, the wire bond diameter and bond profile was fixed and the simulation was done for varying heat transfer coefficients from 5 W/m^{2}K to 100 W/m^{2}K, and the maximum steady-state current handling capacity was recorded. The result is shown in Fig. 5.

Inferred from the graph, the current density of the wire bond increases substantially with the heat transfer coefficient till 20 W/m^{2}K above which the rise in current handling capability is negligible.

### Study 3 : Effect of wire length on current handling capacity for 610 μm Al wire

This study explores the effect of wire length on the current handling capability of the device. A typical bond profile is shown in Fig. 1(b) where the apex height is referred to as loop height. For fixed bond pad separation an increase in loop height directly will increases the overall wire length. For fixed boundary conditions, with a constant *h=10W/m ^{2}K* applied to wall of the 18650 cell and for a fixed bond wire diameter the effect of loop length on steady-state current density is observed and is plotted in Fig 6.

*J*is the current density in A/mm

^{2}and

*L*is the length of the wire.

## Conclusion

This paper proposes a modeling approach using COMSOL Multiphysics to estimate the fusing current density and fusing time for different diameter wires. The paper also studies the change in the current handling capacity of a wire for different Al wire diameters, wire lengths and boundary conditions. The results indicate that smaller diameter wire bonds can have carrier higher current densities before fusing than larger diameter wire bonds, for the same heat extraction. This has important implications for design engineers who may opt for two small wire bonds in place of a single, heavier wire interconnect. Multiple parallel wire bonds also decrease wire resistance, contact resistance and inductance. The results also show that the current carrying capacity varies directly with the heat transfer coefficient for heat extraction but beyond a point the change is nearly negligible. This study can help design engineers in setting their own thermal system. The final result showed that the current handling capacity of the bond wire decreased with loop length. This showed the importance of having constant loop length across parallel wire bonds on parallel cells.

## References

*IEEE Transactions on Components, Hybrids, and Manufacturing Technology,*