An Oxide Wear Model of Ultrasonic Bonding Open Access

Ultrasonic bonding is widely used in different industries, such as electronic packaging [1]. Obtaining a comprehensive model of ultrasonic bonding is an important step in uncovering a thorough understanding of the dependencies between process parameters and outcomes on both the microscopic and macroscopic scale. Several macroscopic models have been developed to describe different types of ultrasonic bonding. Finite Element Method (FEM) is commonly used to more closely model microscopic behaviors. Friction heating was modeled in ribbon bonding by assuming the friction power was caused by the shear stress at the interface [2]. An FEM model was used to determine the pressure distribution at the bonded interface. These FEM results were then used in a holistic model of the wedge-wedge wire bonding process [3]. Oxide fracture in wedge-wedge wire bonding was modeled using a shear lag model developed for cold rolling [4]

Another popular approach is to link the rate of bond growth to the friction power at the interface. A bond growth model by Mayer and Schwizer [5] was developed that can be used for determining the relative amplitude between the ball and substrate, and the ratio of unbonded interface area to the total interface area. It assumes that the rate of bond growth is proportional to the power supplied to the interface. It also lets the transverse force acting at the interface be composed of the friction and the shear strength of the bonds formed. These two forces are weighted by the percentage of the unbonded and bonded areas respectively [5].

The model derived by Mayer-Schwizer [5] has been expanded upon. An equation was derived for the contact height [6] [7]. Experimental observations have been used to relate the ultrasonic transducer current to relative amplitudes in this model [8]. Recently, this model has been expanded to take into account the activated area to model ultrasonic cleaning [9].

In the present work, we propose to develop a modified version of the Mayer-Schwizer model that uses the Archard Equation to determine the relationship between the bond growth rate and wear. This model was conceived through earlier work about how the Archard wear Equation could be used to better understand oxide fracture [10]. Lumped parameters models also have been used to understand the system level dynamics of ultrasonic bonders [11]. A modified version of the lumped parameter piezoelectric model developed by Goldfarb and Celanovic [12] is used to model the ultrasonic transducer. The main purpose of this work is to present a modified modeling approach, which is less dependent on experimentally obtained parameters, and compare it to the existing model. The overall system level model is first reviewed. Then the procedure on how the Archard Equation is incorporated into the model is described.

The overall approach is to replace the relationship between the bond growth ratio and friction power used in the Mayer and Schwizer model with the Archard Equation. There are two sections of the model. The first section, referred to as the System Level model, accounts for the dynamics of the ultrasonic transducer. The second section, referred to as the Oxide Wear and Bond Growth model, replaces the friction power relationship in the Mayer and Schwizer model. This relationship is described briefly in this section.

The model of the entire bonding system is depicted in Figure 1 and Figure 2. The circuit depicted in Figure 1 is meant to capture the electrical side, while the diagram in Figure 2 is meant to capture the mechanical side

In developing the model, three assumptions are made, the first assumption, assumption (A1), is that the oxide wear height is a function of x_b and t or h = h(x_b,t). Based on how the coordinate system is defined, the interface area is assumed to be rectangular such that S = 2Lr, where r is the width out of the page. To get the dependence upon x_b, we let the stress F/S = W(x_b)/r, where W(x_b) is the force per unit length. The ball diameter 2L is brought into the force to turn it into a force per unit length.

The second major assumption, assumption (A2), is that once h(x,t) reaches a critical value, i.e. h_crit, a bond forms. Assumption (2) is not far from what occurs in ultrasonic ball bonding. Surface oxides are removed due to the ultrasonic vibrations and the normal force. Before the ultrasonic vibrations begin, the normal force and the surface roughness of the ball and substrate lead to the formation of cracks in the oxide layer. After ultrasonic vibration, the cracks grow and the oxides eventually detach. These oxide particles move around the interface due to the ultrasonic vibration, tending to move out to the periphery [13]. Once this process occurs and the ball and substrate are separated by a small distance, i.e. h_jump, bonding occurs. Recently this jump to contact behavior for aluminum-aluminum bonding was simulated. It was found that the critical separation distance for jump to contact to occur is 5.8 Å ± 0.05 Å [14]. From this discussion, letting |h_jump| = |h_oxide − h_crit| gives this the assumption of bond formation once h = h(x_b,t) = h_crit some physical basis.

It is fair to point out that since h_oxide > h_crit, the model predicts that there will be an oxide layer with a thickness h_jump remaining, which in reality would prevent any bonding from occurring. This is because the Archard Equation does not account for the cracking and detachment of the oxide layer, or the motion of resulting oxide particles. Both of these processes lead to the exposed surfaces and jump to contact behavior. Since the oxides are not extracted from the interface during bonding, oxides particles are still present in the interface among micro-welds. The presence of oxide particles in bonded regions has been experimental confirmed [15]. To account for these processes would require a more thorough investigation that is beyond the scope of this work. Therefore, these processes are ignored when it is assumed that at h(x_b,t) = h_crit bonding occurs.

Because of the second assumption (A2), the form of W(x_b)will determine how the bond grows. There have been several investigations on how the interface evolves in wedge-wedge wire bonding. Evidence suggests that bonding begins in the central regions for wedge-wedge wire bonding [15]. A second bonding pattern has also been reported that begins in the periphery and moves towards the center, greatly strengthening the bond [16]. In situ analysis of wedge-wedge bonding shows the total interface area S grows. The analysis also shows that there is both a static central region, where there is micro-weld bond growth among interspersed oxide particles, and a friction region that starts in the peripheral region. In the final stages of bonding, the strongest bonded areas are in the regions adjacent to the peripheral regions [17].

Based on these observations, the third major assumption, assumption (A3), assumes W(x_b) is parabolic, with a local maximum at the center. Assumption (A3) is also supported by FEM analysis based on an unpublished work by Tszeng [18]. The results are shown in Figure 4 and Figure 5. The stress achieves a maximum magnitude near the center. Also the stress near the ends of the ball, or at L = 17μm, is nearly zero.

If W(0) F_max/2L and W(±L) = F_min/2L, this gives

Imposing these condition as t goes to infinity shows that F_min must be zero for γ → 1 as → ∞. This also matches the FEM results shown in Figure 5. F_max is then determined by integrating Equation (18) for −L ≤ x_b ≤ L. This gives F_max= 3/2Fn.Equations (21) – (23) are solved numerically for five voltages V₀ = {80,90,100,110,120}V with h_crit = 4.42 nm and the following boundary conditions: y₁(0) = 0, y₂(0) = 0, and y₃(0) = 0.05. The initial bond growth ratio is set to a nonzero value to account for the cracks that form due to contact before ultrasonic vibration is applied [6]. This initial bond growth is equivalent to assuming there is an initial wear height h_crit Also because of the presence of 1/y₃ in Equation (26), setting y₃(0) = 0 would result in an initially infinite bond growth rate. The constants used for the model are shown in Table I. These constants are presented for demonstration purposes. Most constants are taken from other work [12] [5] [10] [14] [6]. The spring constant k was set such that the transducer is resonating at f = 130 kHz by using Equation (10).

The estimation of the free air vibration amplitude using A₀(t) = A₀,_est(t) in Equation (12), and the free air response using Equation (7) are both calculated with V₀ = 100V. As shown in Figure 6, A₀,_est(t) is a good estimation of the free air response amplitude. Using an exponential function in the form of A₀,_est(t) is similar to using a constant value, since the rise time is only about 10⁻⁴ seconds.

The relative amplitude as a function of the transverse force for the five voltage amplitudes are calculated using Equations (5) and (6). The relative amplitudes in Figure 7 are calculated using A₀(t) = A₀,_est(t) or Equation (12), while the relative amplitudes in Figure 8 use A₀(t) = A₀,_ss or Equation (11). For both Figures, the power is calculated using Equation (13).

The results in Fig. 7 using A₀,_est(t), show the relative amplitude has two regions. In the first region the relative amplitudes sharply increase for nearly constant transverse forces. Initially the bond does not grow very fast, which causes the bonding ratio γ(t) in Equation (5) to be nearly zero. At this stage the transverse force mostly comprises the friction force. In the second region, the relative amplitude is linear with respect to the transverse force. As the power increases, the relative amplitude increases since the transducer produces larger forces at higher powers. Also as the transverse force increases, the relative amplitude decreases since the transverse force restricts the motion of the ball.

There is only a linear region present in the results shown Fig. 8. This is because A₀,_ss is a constant, which does not account for when the transducer is initially starting up. Because A₀,_ss is also the steady state value of A₀,_est(t), results in the linear region in Figure 7 match the results in Figure 8.

Equation (27) follows from Equation (14). The results of the Mayer-Schwizer model are shown in Figure 10 using a β = 55 × 10⁻⁵m²/J [5]. Comparing Figure 9 and Figure 10, it can be seen that the bond growth for the Archard Equation model is much slower. It takes about 0.8 ms to achieve a γ of 0.5 for the Archard Equation model, while it takes about 0.04 ms to achieve a γ of 0.5 for the Mayer-Schwizer model.

From Equation (28), Figure 11 is generated. Initially β_eq is calculated as 50 × 10⁻⁶m²/J. This value is one order of magnitude smaller than the β used in the Mayer-Schwizer model, which explains why the bond growth is much slower for the Archard Equation model [5]. It is much slower also because β_eq is inversely proportional with time, as shown in Figure 11.

In this work, a modeling approach was developed for ultrasonic bonding. The model uses lumped parameters to describe the kinetics of the transducer and tool, and the Archard Equation to describe oxide cleaning and bond growth. The modeling approach has three major assumptions: (A1) the oxide wear height a function of x_b and t h(x_b,t), (A2) once h(x_b,t) = h_crit oxide cleaning process is complete which allows a bond to form, and (A3) the normal force per unit length distribution is parabolic. Using an exponential estimation of the free air amplitude, the relative amplitude between the bonding material and the substrate was determined. It was found that as the power increases the relative amplitude increases, and that with larger transverse forces the relative amplitude decreases. Compared to the Mayer-Schwizer model, the Archard Equation model predicts a longer time for bond formation. The longer bond formation time is because the equivalent bonding coefficient is initially much smaller and is also inversely proportional to time. As a result, the bond increases at a slower rate compared to the Mayer-Schwizer model.

Several future adjustments can be made to the model; the constant parameters, such as the interface area S, could be replaced with functions, the model could be extended to a function of 3 variables with an additional bonding coordinate for the direction out of the page, equations could be introduced to account for stronger bonding in the periphery, and additional parameters, such as the initial surface roughness and contamination, could be brought into the model.

This work was supported by the National Science Foundation (CMMI-1728652).