Appendix A - The High-Voltage CV Measurement
Instrument
A.1 - Introduction
Capacitance-voltage profiles are widely used as a diagnostic tool in the study semiconductors. In
particular, the C-V profiles provide insight to the doping profiles of semiconductor junctions, and in special
cases can be related directly to the doping profile [Hili60]. Although numerous instruments are commercially
available to measure the small-signal differential capacitance of semiconductor junctions [Palm90], these
instruments generally do not allow DC biases of more than 200V. As an example, the Boonton 71-AR meter allows a DC
bias to be directly applied for voltages up to 200V. For measurements at higher voltages, the bias can be applied
by connecting the test capacitance to the meter through a large DC-blocking capacitor, and by applying the DC bias
to the test capacitance through two parallel resonant filters [Boon]. This leads to several difficulties. The
parallel filters must be closely tuned to 1 MHz, and the Q of the inductors used in the filter must be greater than
200. Inductors with such high Q are not widely available. Furthermore, both the DC-blocking capacitor and the
bypass capacitor on the DC bias power supply must have a voltage rating greater than the maximum
bias.
The circuit presented here eliminates these difficulties. Only one component requires the full DC
bias rating, and no high Q inductors are required.
A.2 - Theory
A pn junction can be modeled as a parallel combination of a voltage-dependent current source and
a voltage-dependent capacitance, as shown in Figure A.1. If a DC bias voltage, A, is applied to the cathode of a
diode, and a small AC signal Bsin(ωt) is applied to the anode, as shown in Figure A.1,
the voltage across the diode will be
(A.1)
and the resultant current will be
(A.2)
As a simplifying assumption, one can assume the leakage current and the capacitance depend only on the DC component of the diode voltage, such that
(A.3)
In general, this is a reasonable assumption for large values of ωand
for small values of B and IL. This is not a good assumption in forward bias or in reverse breakdown.
However, it is generally the C-V profile in the reverse bias before breakdown that is of interest.
If this current flows through a resistance R, the resultant voltage will be
(A.4)
Thus by observing the AC component of this voltage on an oscilloscope or on an AC voltmeter, the
capacitance C(A) can be measured, since R, B, and ω are known. Also, the diode leakage
current can be measured by observing the DC component.
A.3 - Circuit Implementation
The circuit shown in Figure A.2 implements equations (A.1) - (A.4) directly. The DC bias, A, is
applied to the cathode of the diode under test (DUT). The LH0032 is a high-speed, low bias current op amp used as a
unity gain voltage follower to apply the AC test signal Bsin(ωt) to the anode of the
DUT. Since the inverting input of the LH0032 has such a small bias current (typically < 500 pA), the diode
current must flow through the resistor R, yielding a voltage across the resistor given by equation (A.4). The
AMP-05 is a high-speed, low bias current instrumentation amplifier, used in this circuit as a unity gain voltage
buffer. Since the voltage at the non-inverting and inverting inputs of the LH0032 will be equal (ignoring, for now,
a small DC offset), the voltage across the input of the AMP-05 will equal the voltage across the resistor
R.
The inverting input of the AMP-05 is connected to the non-inverting input of the LH0032, rather
than the inverting input, to minimize the parasitic capacitance present at the anode of the DUT. The inverting
input of the LH0032 will contribute some parasitic capacitance, which can not be removed. However, this
capacitance, and any other stray capacitances to ground will appear as a constant offset in the measurements, which
can be accounted for by measuring the output with the DUT removed.
By separating the DC bias and the AC test signal, the amplifiers and the sensing resistor R can
all be standard low-voltage components. The only component that requires a high voltage rating (aside from the DUT
itself) is the bypass capacitor Cb on the DC bias power supply. This capacitor serves two functions; it
provides the AC path to ground for the AC test signal, and secondly, in conjunction with the inductor L, it
suppresses any ripple present in the DC power supply. The circuit will actually measure the series combination of
the DUT capacitance C(A) and Cb, so one should have Cb > 100 C(A) over the voltage range
of interest for Cb to introduce less than 1% error.
For the measurements presented here, the values R = 31.9 kΩ, B = 100
mVpp (35.3 mVRMS), ω = 2π x 1 MHz were
used. This yields a capacitance sensitivity of BR = 20.0 mVpp/pF, and a leakage current sensitivity of
1/R, or 31.3 mVdc/Adc. The AC output voltage, and hence the capacitance, was measured using a
Hewlett-Packard HP400F AC millivoltmeter. With no DUT in the circuit, a parasitic offset capacitance of 4.0 pF was
observed.
To generate the 100 mV, 1 MHz sine wave a standard crystal oscillator circuit [Matt83], which
generates a stable 1 MHz square wave, followed by a 4 pole 0.5dB-ripple Chebyshev lowpass filter [Horo89]nominally
tuned to 1.2 MHz was used. A Kepco ABC1000M power supply was used to generate the DC bias.
A.4 - Discussion
The primary advantage of this circuit is the relative ease with which small-signal capacitances
can be measured at kilovolt DC biases. There is no inherent limit on the maximum DC voltage that can be applied to
the DUT, other than practical considerations. That is, the bypass capacitor Cb must have a voltage
rating greater than the maximum DC bias, and the physical construction of the circuit must be appropriate for
high-voltage use.
Since the amplitude of the AC test signal, B, can be measured accurately with less than 1% error
using an oscilloscope or by other means, and the frequency is crystal-controlled, the accuracy of the circuit is
primarily limited by the tolerance of R and the gain-setting resistors of the instrumentation amplifier. These
errors can be reduced by measuring the output with a known capacitance and adjusting the gain accordingly,
otherwise one could expect 2% error. The nonlinearity of the AMP-05 amplifier is typically 0.001%, and can be
ignored. As mentioned earlier, Cb must be sufficiently large to eliminate its effect on the measured
capacitance.
The LH0032 and AMP-05 were chosen for their low input bias currents. The LH0032 typically has
Ib < 500 pA, and AMP-05 has Ib < 30 pA. Since the AC current induced in the diode will
be on the order of several microamps for the circuit values used above, these input bias currents can be neglected.
Both amplifiers will introduce a small DC offset voltage, however this will not affect the capacitance measurement,
which is based on an AC signal. Although the DC component can be used to measure the leakage current, better
instruments are available for this purpose. However, monitoring the DC component does allow the user to avoid the
onset of diode breakdown.
If the current-sensing resistor R is made too large, the instrumentation amplifier slew rate may
be exceeded. The typical AMP-05 slew rate is 7.5 V/μs, which limits the output voltage to 2.4 Vpp for a 1 MHz signal. Thus, in consideration of equation
(A.4), R can not exceed 190 kΩ for a 20 pF capacitance. In practice, it is wise to make
R smaller, such that the resistive component of R is much smaller than the impedance of the parasitic capacitance
that will exist in the resistor(s). (For this reason, when implementing R in a circuit, it is desirable to use
resistors in series rather than resistors in parallel, to reduce parasitic capacitance across R. Parasitic
inductance can be neglected at these frequencies.)
The input sine wave must be relatively pure, since the measured current is a function of the
derivative of this input. The sinewave output available from typical function generator instruments and integrated
circuits are often formed using diode forming networks, which will produce slight "knees" in the generated sine
wave, which are magnified in the derivative [AD76]. A filter is necessary to remove the undesired
harmonics.
For special cases, doping profiles can be related directly to the C-V profiles [Hili60]. However,
these relationships generally involve C and dC/dV. Since C varies so slowly at higher voltages a digital AC
millivoltmeter must be used to obtain the necessary precision, rather than the analog HP400F. There is no inherent
limitation in the circuit of Figure A.1, other than the noise floor, preventing a satisfactory degree of precision
from being obtainable.
The results presented here have also been reported by this author in [Chud95a].
