Whenever length measurements are required over a wide range with nanometer precision, laser interferometers are commonly used. Standard interferometer designs, of which the Michelson type is the most common, exploit the interference effect of two laser beams propagating in the same direction. They suffer several disadvantages, including the use of at least two optical axes, and the need for additional components such as multiple mirrors and beam splitters.
An alternative approach for high-precision length measurements is the so-called ‘standing-wave interferometer’.1 This uses the interference effect of two laser beams propagating in opposite directions, so that the superposed beams form an optical standing wave. The standing-wave interferometer is attractive for its simplicity: the optical setup consists only of a laser, a movable mirror, and a special transparent detector. All the components are arranged on a single axis (see Figure 1), which makes optical alignment extremely simple.
Figure 1. Principle of a standing-wave interferometer. With a single optical axis and just three basic components, the device is simpler and intrinsically more robust than a conventional interferometer of Michelson or similar type.
The working principle of the standing-wave interferometer is based on sampling the optical standing wave using two transparent photodiodes. The standing wave is created by a HeNe laser (wavelength λ=632.8nm), which is orthogonally incident on a movable plane mirror. The intensity profile of the standing wave contains minima and maxima which appear with a period of λ/2 along the optical axis and can be measured by the photodiodes (Figure 2).
Figure 2. The standing-wave interferometer uses two photodiodes to detect minima and maxima in the standing wave generated as laser light from the HeNe source is reflected back from the mirror.
The intensity profile of the standing wave is firmly coupled at the mirror: if the mirror is moved, the intensity profile is shifted along the optical axis. The task of each photodiode is to provide a photocurrent that is proportional to the intensity of the standing wave at the location of the diode, and dependent on the position of the mirror. These currents can be used for bidirectional fringe counting, a standard method of interferometric length measurement, allowing the relative displacement of the mirror to be determined.
Displaying the two photocurrents on the x- and y-axes of a Cartesian coordinate system results in elliptical Lissajous figures. In the ideal case, the measured photocurrents are sinusoidal, and their phase shift is close to 90°. The Lissajous figure is then a circle, at which point error is minimized, and measurements with nanometer precision are possible.
Key to the standing-wave interferometer is the integrated phase-selective transparent detector (PSTD) (Figure 3).2 This three-terminal device is assembled on a glass substrate, with the two PIN photodiodes embedded between three transparent conductive oxide (TCO) layers. The PIN diodes themselves consist of amorphous silicon and are less than 100nm thick. The TCO contact layers are of aluminum-doped zinc oxide.
Figure 3. The phase-selective transparent detector incorporates two PIN photodiodes on a glass substrate. TCO: transparent conductive oxide.
To fabricate the PSTD, plasma-enhanced chemical vapor deposition (PECVD) was used for the amorphous silicon layers and RF magnetron sputtering for the zinc oxide layers. The patterning of the detectors was done using photolithography and reactive ion etching under cleanroom conditions.
The PSTD needs to exhibit remarkable properties. High transmission at the laser wavelength is crucial to allow the ‘undisturbed’ formation of the standing wave. However, enough light must be absorbed by the PIN photodiodes to generate the photocurrents.
Our PSTD design was developed with the aid of numerical simulations.3 For high transmission, layers TCO 1 and TCO 3 must act as anti-reflection coatings with an optical thickness of ¾λ, while TCO 2 needs to be λ thick. The intrinsic (‘i’) layer of each photodiode should have an optical thickness close to λ/4, which for our laser wavelength is around 43nm. The optical thickness of the amorphous diodes must be close to λ/2. Thus, the amorphous silicon layer stack is only around 90nm thick. The p- and n-layer thicknesses (λ/8 each) are chosen to meet the λ/2 thickness requirement for the whole PIN structure. The p-layer of diode 1 has to be slightly thicker (λ/4) to make the phase shift of the photocurrents close to 90°, which causes a slight mismatch in the layer thicknesses.3
Our PSTDs exhibit quantum efficiencies at 632.8nm of around 1.4% for both diodes. The transmission is greater than 70%.3 Photocurrents ‘inside’ the standing wave with a phase shift of around 114° were measured. Figure 4 shows the corresponding normalized Lissajous figures (solid line), as well as the results of numerical simulations (symbols), which agree well with the experimental data. The deviation of the phase shift from the desired 90° is attributed to thickness inaccuracies of the thin-film layers.3 The best measurement error achieved up to now is ±15nm,4 which demonstrates the great potential of the standing-wave interferometer.
Figure 4. Measured Lissajous figures (solid line) show good agreement with simulation results (symbols), and the phase shift is relatively close to the ideal value of 90°.
Figure 5. The laboratory setup of the standing-wave interferometer.
This work was performed in collaboration with the Institut für Prozess-, Mess- und Sensortechnik, TU Ilmenau, Germany.