A Normal Incidence Scanning Reflectometer of High Precision
Ulrich Gerhardt and Gary W. Rubloff
A near-normal incidence (6°) reflectometer system is described that records continuously and directly
the reflectance R(co) as a range of photon energies is scanned. The system has an absolute error of ±2 X
10-2 and a relative error of ±t2 X b5. It incorporates a quartz light pipe rotating at 70 Hz which captures light from the incident and the reflected beam, respectively, during about 20% of its period of rotation
in either case. A gating circuit separates the output signal of the photomultiplier into two channels, corresponding to the incident and the reflected beam, respectively. The signal corresponding to the incident
beam is kept constant by a servo system which regulates the gain of the photomultiplier. The reflectance
is thus proportional to the signal of the second channel, which is recorded as a function of photon energy.
Portions of the reflectance spectrum of Ge are given as examples. No trace of a fine structure in the reflectance of Ge below 2 eV is found.
1. Introduction
The complex dielectric function (co) of a solid is
closely connected with its electronic structure. Thus,
the accurate eperimental determination of this quantity
is of great importance. One method to determine e
consists of measuring the reflectance at or close to
normal incidence over a sufficiently large range of
photon energies and then performing a Kramers-Kronig
inversion.I
Reflectance measurements require a separation of the
incident and the reflected beam. This requirement
gives rise to two major difficulties. First, the noise
spectrum of the light source, such as a high pressure
discharge, and of the detector quite frequently contains
large low frequency components. Such a noise spectrum is particularly harmful when measuring the reflectance by a point-by-point method, in which one
normalizes the incident beam to 100%, changes the
optical path of the light, and then measures the reflected
beam. The change of the optical path takes typically
10 see or longer, thus making the method susceptible to
instabilities with a time constant of this order of magnitude.
Second, Io, the output of the detector, is normally a
strong function of photon energy, so that intensity
variations of several orders of magnitude often occur
within the spectral range of interest. It is possible to
record Io () and then R(cw) Io(W) and divide the two
quantities afterwards in order to get the reflectance.
However, this method performs poorly if Io (co) depends
The authors are with The James Franck Institute, The University of Chicago, Chicago, Illinois 60637.
Received 15 August 1968.
strongly on c, because it requires a very high reproducibility of the wavelength setting.
The point-by-point method is capable of very accurate results, provided the low frequency components of
the noise spectrum are small enough.2 The method
consisting of first recording o (co) and then R(w) Io(W)
requires both a good long-term stability and a weak
dependence of o on in order to be accurate. An ideal
method should be capable of bypassing both difficulties,
i.e., it should alternate between Io and RIO at high frequency in order to avoid the low frequency components
of the noise spectrum and it should be capable of operating under strong variations of lo(U). Furthermore, a
high signal-to-noise ratio requires that a large fraction of
the photons available are used in the measurements,
i.e., the on-time should be a large fraction of the period
of the system.
The purpose of this paper is to describe a reflectometer
which approaches the ideal system mentioned above.
The paper describes the optical and electronic components of the system and its characteristics in operation.
It also gives some portions of the reflectance spectrum
of germanium samples recorded with this system.
11
The Scanning Reflectometer
Design of the System
Our procedure for continuously recording R () at near
normal (.6)
incidence is shown schematically in Fig.
1. The beam emerging from the monochromator is
focused on the surface of the sample. A Suprasil
fused quartz light pipe 4.8 mm in diameter rotates at
about 70 Hz, sampling incident (Io) and reflected (RIo)
beams alternately. Figure 2 shows the top view of the
light pipe, the top part of which is bent slightly off-axis
so that it does not interfere with the incident beam
February 1969 / Vol. 8, No. 2 / APPLIED OPTICS
305
Sample
is attached to the light pipe and which sweeps across the
poles of two induction coils, Fig. 1. The gating signals
are adjusted to sample the output signal of the multiplier during the flat part of the pulses. The relative
duration of the gating signals with respect to the period
of the light pipe is about 11%; it is given by the separation of the two little spikes on top of the flat parts of the
main pulses in the lower half of Fig. 3.
The lo voltage signal is applied to a high input impedance differential preamplifier with variable bias voltage as a reference. The output of the differential amplifier determines the power applied to a servomotor. A
multiturn potentiometer which is mechanically coupled
to the servomotor controls the high voltage, and therefore the gain, of the photomultiplier. Hence the anode
current of the multiplier corresponding to the incident
beam is kept constant even as the monochromator output intensity changes due to the scanning of h and to
fluctuations in the light source.
Light Pipe
Fig. 1. Schematic diagram of the system.
Incident
Beam Io
B
Reflected Beam RIO
Fig. 2. Top view showing the geometry of the sample and bent
light pipe.
3
while measuring the reflected beam. The light pipe
catches each beam fully for about 20% of its period,
producing wide, flat pulses, shown schematically in
Fig. 1. The actual signal is reproduced in Fig. 3. An
induction motor rotates the light pipe assembly. The
coupling between motor and light pipe consists of two
pulleys and a flexible rubber belt. The rubber belt
decouples the high frequency vibrations of the motor
from the light pipe. The light pipe assembly, which is
mounted in ball bearings, is balanced dynamically to
minimize vibrations.
The gating circuit shown in Fig. 4 separates the 1 and
RIO channels and measures the peak values of the signals. The field effect transistors act as switches to
apply the voltage across the 10-kQ anode resistor alternately to the load capacitors as long as the gating signals
persist. The gating signals are the output voltages of
two monostable multivibrator circuits. They are
triggered by pulses produced by a small magnet which
306
APPLIED OPTICS / Vol. 8, No. 2 / February 1969
Fig. 3. Photomultiplier output measured across 10 kg of the
gating circuit (see Fig. 4). The larger peaks correspond to the Io
channel and the smaller peaks to the Rlo channel. The upper
trace is with the gating circuit turned off and the lower trace is
with the gating circuit operating.
From Photomultiplier
20/± A
RI,
10
sv
5V
0
7l-7Jl 1L
-57V
trp J~
-
From Monostoble Multivibrators
Fig. 4.
Gating circuit.
0.7
Ge, 3000 K
w
, 0.6
IU
0.5
2
3
4
PHOTON ENERGY
5
(eV)
Fig. 5. The reflectance of P type Ge (0.074 02cm) from 1.6 eV to
5.2 eV. Vibration coupling to the monochromator causes a
wavelength modulation, which produces a bump in the reflectance near the strong xenon line at 4.85 eV. The energy resolution given in the bottom part is the half-width of atomic mercury
lines, as recorded with our system.
The RIo voltage signal is amplified by a Keithley 150B
Microvolt-Ammeter and then applied to the Y channel
of an X-Y recorder. The Y channel is calibrated for
absolute values of the reflectance by applying the Io
signal to the RIO channel and adjusting the gain to full
scale of the recorder. The X channel of the recorder
monitors the wavelength setting of the monochromator.
A variable offset voltage is available at the input of the
Keithley amplifier to compensate for most of the RIo
signal. We are thus able to record fine structure in
R (w) by using a much higher gain of the amplifier or the
recorder.
Optimization of the System
The servo system keeps the lo signal constant to within
This is achieved by using a large dc gain
of the feedback loop. A damping force proportional to
the velocity of the motor reduces the tendency of the
system to oscillate and reduces the response time. An
aluminum flywheel mounted on the shaft of the servomotor moves in a strong magnetic field to provide the
damping mechanism.
The values of the anode resistance and the load capacitance in Fig. 4 are chosen to fulfill two requirements.
First, the RC time constant is set equal to the gating
time, resulting in a fast response while still averaging
over variations of the intensity during the gating time,
which are about 5%. Second, the anode resistance is
kept small compared with the load resistances of the
differential preamplifier in the I channel and of the
amplifier in the RIO channel. In this way the capacitors
discharge negligibly when not connected to the anode
resistance; hence the signal levels read are very close to
the peak values and independent of differences in the
load resistances of the two channels.
Dynamical balancing of the light pipe assembly is
essential to the success of this method, since vibrations
cause microphonics of the photomultiplier and wavelength modulation of the monochromator output.
i 2 X 10-'.
Furthermore, high precision, low friction ball bearings
in the mounting of the light pipe are needed to minimize
vibrations generated in the bearings themselves.
The 70-Hz rotation speed of the light pipe is well
above the frequency response of the servo system, which
is about 10 Hz. Thus, low frequency signals from
intensity fluctuations and wavelength scanning are
compensated by the feedback circuit, whereas higher
frequency signals are attenuated by the filter circuits of
the system.
The absolute error of the reflectance measured with
our system is (AR/R)bsoluto = ±i2 X 10-2. This is the
deviation of the measured reflectance of quartz from the
theoretical reflectance, calculated using the tabulated
refractive index. This value is the maximum error
within the spectral range of the system, i.e., from 1.5 eV
to 5.5 eV. The absolute error depends smoothly on
photon energy. Therefore, the ability of the system to
detect fine structure in the reflectance superimposed on
a smoothly varying background is given by the performance of the servo system, i.e., the relative error of the
system is (R/R)oiative = 2 X 10-5.
111.
Experimental Examples: Germanium
The room temperature reflectance of P type Ge ( =
0.074 Q cm) is given in Figs. 5-7. The surface of this
sample is prepared by grinding with increasingly finer
abrasives down to mesh 1000 and subsequently etching
in a mixture of nitric, hydrofluoric, and acetic acid
(ratio 3:1: 1). The etching process is stopped by
rinsing in methanol and quickly removing the thin
methanol layer on the surface by a warm stream of air.
Figure 5 shows the actual recorder trace of the reflectance of Ge from 1.6 eV to 5.2 eV. The zero of the reflectance scale is suppressed. The bump at 4.85 eV is
caused by a wavelength modulation of the monochromator output. The source intensity changes rapidly in
this region because of the strong xenon line at 4.85 eV,
superimposed on the continuum of the high pressure
xenon lamp used in our measurements. In Fig. 6, the
sensitivity has been increased fourfold compared with
O.
0
Z
0
i
1:
a:
0.45
2.0
Fig. 6.
2.5
PHOTON ENERGY
3.0
( eV)
The reflectance of Ge from 1.6 eV to 3.2 eV in expanded
scale (same sample as Fig. 5).
February 1969 / Vol. 8, No. 2 / APPLIED OPTICS
307
W
, 0.512
Z
W0.510
(
w
0.508
2.2
2.!1
PHOTON ENERGY (eV)
2.3
Fig. 7. The reflectance of Ge from 2.04 eV to 2.32 eV in drastically expanded scale (same sample as Fig. 5). The vertical
arrows indicate the relative error of the measurement.
Fig. 5. The figure is again an actual recorder trace and
spans the photon energy from 1.6 eV to 3.2 eV. A
trace taken with a fortyfold increased sensitivity is
shown in Fig. 7 for the region around the 2-eV doublet.
The energy resolution given in Figs. 5-7 is the halfwidth of atomic mercury lines, as recorded with our
monochromator. The relative error of the reflectance
is indicated on Fig. 7 only; it is given by the width of the
line enclosed by the arrows.
IV.
Discussion
The scanning reflectometer described in this paper
approaches the features of the ideal system discussed in
Sec. I. The relatively high operating frequency allows
us to take advantage of the high intensity of high pressure discharge lamps. The large low frequency fluctuations of these light sources do not appreciably affect the
operation of our system, except when ultimate stability
is required. We mention in this context that Figs. 5 and
6 were taken using a high pressure xenon lamp, whereas
Fig. 7 was taken using a tungsten-iodine lamp. Repeating the measurement given in Fig. 7 with the high
pressure xenon lamp increases the noise approximately
fivefold.
The combination of the small relative error with the
possibility to scan the spectrum makes our system
ideally suited to detect fine structure in reflectance.
We used this feature to investigate the reflectance of Ge
between 1.6 eV and 2 eV. Potter 4 previously reported
fine structure in this region which is about AiR = 0.01
above the background reflectance and assigned it to the
L3 ' -> L1 transition. The recorder trace given in Fig. 6
shows no indication of such a fine structure. Similar
measurements using differently doped samples show
no fine structure either. The accuracy of our method
enables us to detect fine structure 500 times smaller than
the one reported by Potter.
The absolute error of the reflectance of our system is
dominated by the asymmetries of the optical system,
i.e., the beam is convergent for the Io position and divergent for the RIO position of the light pipe, as shown in
Fig. 2. Furthermore, the cross section of the beam on
the front surface of the light pipe might be slightly
different in size for the I and the RIO position and the
light might not hit the same spot on the light pipe.
The asymmetries of the electronic circuit contribute
very little to the absolute error of the reflectance.
The on-time of our system is about 22% of its period.
One could, in principle, approach an on-time equal to the
period if a square wave motion of the light pipe were
used. However, the vibrations generated by such a
motion might be difficult to control. The on-time could
also be increased by an oscillatory motion of the light
pipe, with its extreme positions identical to the Io and
RIo position. The task of minimizing vibrations of the
multiplier and the monochromator would still be more
difficult than in the case of a rotary motion.
The spectral range of the scanning reflectometer described here can be extended into the vacuum uv by
coating the front surface of the light pipe with sodium
salicylate. We have in fact already used the system in
the vacuum uv.*
H. Fritzsche for his help and
The authors thankI
advice and for his interest in the subject. This work
was supported by the U.S. Air Force Office of Scientific
Research under a contract.
References
1. T. S. Robinson, Proc. Phys. Soc. London B65, 901 (1952);
H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
2. See, e.g., H. E. Bennett and W. F. Koehler, J. Opt. Soc. Amer.
50, 1 (1960).
3. The same geometry of the light pipe has been used previously
for reflectance measurements in the vacuum uv. For this application, the front surface was coated with a sodium salicylate
layer. The light pipe was turned by hand. Results obtained
with this set up were reported by U. Gerhardt and E. Mohler,
Phys. Stat. Sol. 18, K45 (1966).
4. R. F. Potter, J. Phys. Soc. Japan 21, 107 (1966). The optical
constants given in this paper were obtained from polarimetry
measurements, using large angles of incidence. This fact might
make polarimetry measurements more sensitive to surface
layers than measurements of the reflectance at normal incidence.
* We use the synchrotron radiation produced by the electron
storage ring located at the Physical Science Laboratory of the
University of Wisconsin in Stoughton, Wisconsin, for our measurements in the vacuum uv.
March 1969 features
Interferometry vs Grating Spectroscopy
308 APPLIED OPTICS / Vol. 8, No. 2 / February 1969