11 Mechanical techniques for the measurements of film thickness

 

Introduction

 

The measurement of the thickness of thin films is usually of great importance for examining the properties of the films, as it is the very thinness which often gives rise to the properties which cause the film to be different from those of bulk materials. As discussed in previous module, there are various techniques available for thickness measurement. Mechanical techniques are cheaper techniques amongst all. These techniques include Quartz crystal monitor, stylus method and Gravimetric weight measurement techniques. In this module we will discuss in detail about these thicknesses measurement techniques.

 

1. Quartz Crystal Monitor

 

The quartz crystal monitor is worldwide used to monitor the thickness of metals, non-metals and multicomponent films. In this monitor a quartz crystal oscillator is operated in a particular mode of vibration. The changes in the resonant frequency is measured with mass loading during the deposition of the film. A quartz crystal of AT-cut is generally used as shown in Figure 1. The original frequency and also the frequency changes of the quartz crystal oscillator can be measured by using a suitable pulse-digital counter. The maximum sensitivity of the monitor depends on the variation in the crystal frequency duo to the temperature, oscillator drive level and the oscillator circuit.

 

c-axis oriented AT cut quartz crystal is used for this method. Quartz crystal containing metal thin film electrodes on the both sides is mounted in the deposition chamber closer to the substrate onto which thin film has to be deposited as shown in the Fig. 2. The keyhole-shaped electrodes on both major faces of the quartz resonator are vacuum deposited gold or silver films, about 150 nm in thickness. The mass-sensitive area is situated in the central part of the resonator, covering about the area where the two electrodes overlap. These metal electrodes provide the power to the crystal. The fundamental frequency ‘f’ of the shear vibrational mode is given by

f= vq/2dq                                      (1)

 

where, vq is the elastic wave velocity and dq is the thickness of quartz crystal which is equal to half of the wavelength of transverse wave.

Figure 2: Schematic of thermal evaporation deposition technique in which Quartz crystal monitor is used for the thickness of the film.

 

When the film deposition takes place onto the surface of substrate, same amount of film is also deposited onto the surface of quartz crystal monitor. Let the mass of the material deposited onto the surface of crystal electrodes is dm, this increases the thickness of the quartz crystal by

δd= δm/Aρ

 

where A is the area of film and ρ is the density.

From equation 1 and 2, provides the frequency change

δf= -f2 δm/KAρ,

Where, K=vq/2 is defined as the frequency constant which is 1656kHz-mm for AT cut quartz.

 

In equation (3), it has been considered that the film whose thickness has to be measured is deposited over the quartz crystal. Thus, the ambiguity in the formula shown in equation (3) arises as the elastic properties of the film are not same as that of quartz crystal and A is not equal to the total crystal area which affects the frequency response analysis. Nevertheless, as long as the accumulated mass deposited on the crystal does not shift the resonant frequency by few amount of its original frequency (δf varies linearly with δm). Commonly, crystal of 6 MHz resonant frequency is used, where 1Hz shift in frequency after deposition of film is easily readable.

 

Since change in frequency is usually easier to detect with precision which is measured by using the oscillator circuit. The shift in frequency is measured by keeping the reference (undeposited) crystal and counting the frequency difference obtained after depositing mass over the crystal. Quartz crystal oscillators used for the measurement of the frequency shift are integrated with the electronic circuitry to mathematically differentiate the frequency shift with respect to time, display rate and thickness of the film achieved as shown in Figure 3.

In these functions it is essential to eliminate uncertainty in the frequency shift measurement. Few sources of error also arises due to the increase in temperature at the crystal due to radiant heat from the evaporant source and from the heat delivered to the crystal by the bombardment of atoms. To avoid this crystals are enclosed in water cooled jackets surrounding the crystal assembly.

 

The main disadvantages of this technique are the cost of the quartz crystals and number of parameters of the materials need to be feed in the electronic circuitry. Every time deposition degrades the crystal quality which yield in inaccurate film thickness (especially in the range of < 100nm) and in many materials it is difficult to remove the film after the deposition for next use. External water cooling system is needed so as to cool the crystal assembly. Thus other simple techniques are also explored for the thickness measurement.

 

2. Gravimetric Method:

 

Another conventional method used for the thickness measurement is Gravimetric technique in which thickness is calculated from measurements of mass, area and density of substrate before and after film deposition. This method can provide more accurate average thickness of the films and mainly used for the thickness measurement of the embossed sheets.

 

Main working principle of this technique is the weighing of substrate before and after the deposition of film. The average film thickness is determined using equation (4)

T= 100Wf/AfDf

Where, Wf is the weight difference in micrograms, Af is the surface area of the substrate having film and Df is the density of the film. In this method film thickness may be over estimated .The major disadvantage of this technique is that relatively small error in weighing introduces large errors and also film density varies with deposition. Apart from these disadvantages, very delicate microbalances are available commercially and used worldwide to measure the film thickness during the deposition. These microbalances works on the principle of elongation of a thin quartz fiber helix, torsion of a wire or pivot mounted beam deflection. Advantage of this technique is that the large area substrates can measure fractions of monolayers. Very low density films of thickness less than 10Å and high density films of thickness around 1Å can also be measured accurately.

 

Stylus-Method Profilometry.

 

Most commonly and cost effective mechanical method used for the thickness measurement is the Stylus method Profilometry. Stylus Profilometry is one of the common tools to measure film thickness and surface characteristics of film. It is based on the film contact measurement technique. In this technique stylus is made to move across the surface of the film and the vertical displacement of the stylus in the z-direction gives the step height of the film. Stylus profilometer includes both mechanical and electronic parts of the instrument to perform the measurement. The sample is placed on the motor driven X,Y, θ wafer stage and the resolution of this wafer stage is very critical for the high accuracy of thickness measurement. Then the stylus is made to drag over a straight line in Y direction across the wafer. For studying the surface characteristics including surface roughness multiple scans can be traced using stylus to give 3D information mapping. Figure 4 shows the photograph of a surface Profiler by Veeco Pvt. Ltd.

 

Wafer Stage: In Profilometer, wafer is mounted on the X, Y, θ stage in which the movements are controlled by stepper motors or servo motors. The motors are connected to stage using the screws which helps to align the stage and provide good resolution. The pace of the screw determines the resolution in conjunction with the reduction gear set.

 

Stylus: A diamond needle stylus with a tip diameter of 12.5 microns serves as the electromagnetic pickup. The stylus force is adjustable from 1 to 30 mg, and vertical magnifications of a few thousand up to a million times are possible. Film thickness is directly read out as the height of the resulting step-contour trace as shown in Figure 5.

Accuracy of the measurement depends on the following factors:

 

1.  Stylus penetration and scratching of films: Stylus penetration depends on the force and the surface of the film. The problem of scratching arises if the film is very soft.

 

2.  Substrate roughness: Surface roughness plays a crucial role as it may introduce number of small steps which creates excessive noise in the measurements. Smoother the surface, more accurate will be the measurements.

 

3.  Vibration of the equipment: The instrument is placed on the vibrational free bench which is shock proof so as to minimize the background vibrations in the vicinity.

 

Stylus based thickness measurement technique is advantageous over other techniques as it provides higher accuracy and low maintenance cost.

 

Summary:

 

In this module we have learnt about

  1. Mechanical techniques for film thickness measurement
  2. Studied about Quartz Crystal Monitor
  3. Gravimetric Method
  4. Stylus based Profilometry

 

List of References and Suggested Reading

  • Thin Film Materials- Stress, Defect Formation and Surface Evolution By L. B. Freund
  • Handbook of Thin Film Technology-By Leon I. Maissel, Reinhard Glang
  • The Material Science of Thin film by M. Ohring