Chemical Mechanical Planarization (CMP)
The CMP Process
The primary function of CMP is to smooth a nominally macroscopically flat wafer at the feature (or micro-level), i.e., planarize features. Therefore, to evenly planarize features across the whole wafer it is crucial to have a uniform material removal rate across the wafer. This removal rate uniformity ensures that the entire wafer is uniformly reduced in height. A schematic of a typical CMP machine is shown in Figure 1. The wafer is held on a rotating carrier face down and is pressed against a polishing pad attached to a rotating disk. For oxide or silicon polishing, an alkaline slurry of colloidal silica (SiO2 particles in a KOH solution or NH4OH) is continuously fed to the pad/wafer interface.
Figure 1. Schematic of a CMP System.
Figure 2. CMP Process inputs and outputs.
Figure 2 shows an input-output diagram of the CMP process. The primary inputs to the CMP process are as follows: (1) rotational speeds of the pad and wafer (both constant), (2) load pressure magnitude, (3) ring pressure, and (4) pad conditioning (friction coefficient between pad and wafer). The primary output of interest is the uniformity of the material removal rate across the wafer as measured by the within wafer non uniformity, WIWNU, and the average removal rate.
Physical Models for CMP
The typical geometrical configuration for polishing the wafer is shown in Figure 3. The rotating wafer, which we will refer to as the top body, rests on a rotating pad system, which we will refer to as the bottom body, consisting of two pads, a top pad, the IC1000, immediately below the wafer, and a relatively soft sub-pad, the SUBA IV, located below the top pad. A retaining ring surrounds the wafer and holds it in place. A uniform (except at the edges of the wafer) load pressure distribution acts on the wafer. A uniform pressure distribution of lower magnitude acts on the ring.
Figure 3. Geometrical configuration for the contact mechanical analysis.
Based on the inputs to the process, the local material removal rate is given by Preston’s equation:
Removal Rate = K p v
where K is a constant of proportionality, p is the interface pressure, and v the speed difference between the point of interest on the wafer and its point of contact on the pad.
Detailed contact mechanical models for removal rate uniformity
A three dimensional contact mechanical model, which takes into account the frictional force due to the relative motion of the pad with respect to the wafer, was created to simulate the interfacial pressure between the pad and the wafer. The normalized removal rate distribution obtained from simulating the 3D contact model is shown in Figure 4.
Figure 4. Radial distribution of the Removal Rate (3D Model).
The model compares favorably with experimental results for 0 < r < 98 mm. In particular, it is important to note that the model does predict the edge peak, observed in experiments, at r = 98mm. Therefore, this 3D model was used as the basis for developing reduced models for the effect of ring pressure as well as pad conditioning on the within wafer-non-uniformity, WIWNU, a global measure of the uniformity of removal rate across the wafer.
Reduced Models for Control-1: Effect of Ring Pressure on uniformity
Figure 5. Within Wafer Non-Uniformity (WIWNU) versus pressure ratio.
Reduced Models for Control-2: Effect of Pad Conditioning (friction coefficient) on uniformity
Figure 6. Within Wafer Non-Uniformity (WIWNU) versus friction coefficient.
Run-to-Run control of uniformity and removal rate
The outputs at each run are shown in Figure 7(a) and the corresponding inputs are shown in Figure 7(b). It is seen that run-to-run control gives the desired value of the removal rate in 7 runs and within 17 runs both removal rate and uniformity reach their desired values. It is seen that run-to-run control successfully compensates for process disturbances. Furthermore, increasingly aggressive control (pressure ratio) is necessary to compensate for sensor noise or, equivalently, process disturbances. The run-to-run control can adjust pressure ratio to compensate for pad wear in order to control uniformity.
Figure 7. Run-to-run control simulation results.
Services and Products
SC Solutions provides the following services for CMP: detailed finite-element contact mechanical modeling for prediction and control of the within wafer non-uniformity (WIWNU) of removal rate across the wafer, development of run-to run control algorithms for controlling uniformity and removal rate, and implementation of the sensing/control algorithms on CMP equipment using embedded control.
SC Solutions provides the following products for CMP: physical modeling software for CMP, integrated model-based run-to-run control software for CMP, and embedded controllers for uniformity and removal rate control in CMP.