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Technical Field
The invention is in the field of the measurement of the electrical properties of solid-state materials intended for electronic usage. In particular, apparatus for measuring the Hall angle of semiconductor wafers is described.
Background of the Invention
The measurement of the Hall angle of
semiconductor material is an important aspect of its electrical characterization. The sign of the Hall angle indicates whether the material is p-type or n-type while the magnitude of the Hall angle is proportional to the Majority carrier mobility. However, prior Hall effect measurements require some sort of contacting arrangement and/or special sample geometry and are therefore
damaging or at least contaminating in nature. Thus, a noncontacting measurement of Hall angle is desirable.
A noncontacting method for the measurement of

Hall mobility in semiconductor materials is described by Nyberg et al. in the Canadian Journal of Physics 40 , (1962) November 1974. In this method a circular electrical current is inductively coupled into a spherical or
cylindrical sample of semiconductor material. An imposed d-c magnetic field then produces a rotation of the plane of the inductively coupled current which is detected as a signal related to the Hall mobility. However, Nyberg described this technique as being sensitive to the precise relative position of the pickup coil and the sample, and, as disclosed, it is not applicable to wafers of the geometry commonly used in industry.
Summary of the Invention
In accordance with this invention, an
apparatus is provided comprising a pair of circular
concentric coplanar electrodes which are placed adjacent to the wafer. An alternating voltage applied to the electrodes produces, by means of capacitive coupling, an alternating radial current in the adjacent portion of the wafer. A perpendicular magnetic field is provided which produces a circular component of the capacitively coupled current. This circular current produces an alternating magnetic field parallel to the imposed magnetic field.
This alternating magnetic field is inductively coupled to a pickup coil, the resulting signal being related to the Hall angle of the semiconductor material. If the imposed magnetic field is varied at a rate slow compared to the alternating radial current, a modulation of the Hall
signal in the pickup coil is produced. Phase sensitive detection of the modulated pickup signal then yields the magnitude and sign of the Hall angle of the semiconductor material.
Brief Description of the Drawing
FIG. 1 is an elevational view in section of a portion of an exemplary apparatus of the invention;
FIG. 2 is a plan view of an exemplary concentric electrode structure;
FIG. 3 is a perspective view of a semiconductor wafer with arrows representing the current flow pattern with (solid lines) and without (dotted lines) the
application of a magnetic field.
FIG. 4 is a schematic view, in simplified form of an exemplary apparatus of the invention;
FIG. 5 is a schematic view of a portion of an exemplary apparatus of the invention showing drive current control and cancellation of spurious pickup;
FIG. 6 is a schematic view of a portion of the inventive circuitry including details of the drive current control and signal input circuitry; and
FIG. 7 shows details of an exemplary magnetic pole piece and electrode configuration.
Detailed Description
The mechanical parts of a measurement apparatus for the noncontacting measurement of Hall angle are shown schematically in FIG. 1. In this figure a pair of co-planar concentric electrodes consisting of an inner electrode 11 and outer electrode 12 are placed adjacent to a
semiconductor wafer 13 whose properties are to be measured. A magnetic field perpendicular to the plane of the wafer 13 is produced by an electromagnet 14 which is energized by field coil 16. The signal which ultimately results in the Hall measurement is obtained from the pickup coil 15 which is also situated in the magnet gap adjacent to the
semiconductor wafer 13. The plane of the pickup coil 15 should be approximately parallel to the plane of the wafer 13 for optimum pickup of the Hall signal.
An exemplary electrode configuration is shown in FIG. 2. Here the inner electrode 11 is a disc and the outer electrode 12 is a ring. If variation of the magnetic field of magnet 14 is contemplated (e.g., for purposes of synchronous demodulation, as described hereinafter) any ring-shaped electrode, such as electrode 12, should
preferably include at least one gap 17 to minimize
inductively produced circulating currents.
The basic principle of operation of this
apparatus can be understood from consideration of FIG. 3. This figure shows the semiconductor wafer 13 with the area 31 adjacent to the inner electrode 11 and the area 32 adjacent to the outer electrode 12 indicated by the concentric dashed circles. When a high frequency
alternating voltage is imposed upon the electrodes 11, 12, an alternating current at the same frequency is
capacitively coupled into the adjacent wafer 13. This current flows radially between the capacitively coupled areas 31, 32 of the wafer 13. This current flow pattern is indicated by the dotted lines 33.
If a magnetic field is imposed generally
perpendicular to the wafer 13, the current flow pattern is rotated by magnetic forces as indicated by the solid arrows 34. This rotation of the current flow pattern by the presence of the magnetic field is what is generally known as the Hall effect, the magnitude of this rotation being proportional both to the magnitude of the magnetic field and to the mobility of the electrical carriers (i.e., electrons or holes) producing the current flow.
It is the measurement of this rotation (i.e., the Hall angle) which is the purpose of this apparatus. This rotated current flow pattern can be decomposed into a radial component and a circular component. This circular component of current, alternating at the same high
frequency imposed upon the electrodes 11, 12, produces a high frequency alternating magnetic field perpendicular to the plane of the wafer 13. This alternating magnetic field is inductively coupled to the pickup coil 15
producing the desired signal related to the magnitude of the Hall angle of the material of the wafer 13. The phase of this pickup signal, relative to the phase of the signal imposed upon the electrodes 11, 12, will differ by 180 degrees depending upon whether the semiconductor wafer 13 is n-type or p- type. It is the purpose of the electronic circuitry described below to measure the magnitude and phase of the Hall signal.
In practice the choice of the particular high frequency to be used (referred to hereinafter as the rf frequency) presents conflicting requirements. On one hand it needs to be high enough to permit the capacitive coupling of sufficient electric current into the
semiconductor wafer 13, while on the other hand it must be low enough to avoid skin effect problems in low
resistivity semiconductor samples. A preferred range is from 105Hz to 106Hz. The rf frequency selected for
the construction of an exemplary apparatus was
approximately 600 kHz. This frequency was selected for use with semiconductors ranging in sheet resistance from of the order of 10-3 to 105 ohms per square.
While the principle of this measurement can be simply understood, the practitioner must consider a number of physical effects which operate to make the measurement difficult. The first of these is the direct coupling of rf signal between the drive electrodes 11, 12 and the pickup coil 15. This direct transmission of signals is referred to as crosstalk. There is one property of this crosstalk signal, used in the exemplary apparatus, which can be employed to differentiate the crosstalk signal from the Hall signal. This property is the fact that the crosstalk signal is independent of the magnetic field produced by the magnet 14. In the exemplary apparatus the magnetic field was varied at a frequency low compared to the rf frequency, by varying the current in the magnet drive coil 16. This results in a Hall signal which is modulated at the magnet frequency. The Hall signal was picked out of the much larger crosstalk signal by
synchronous demodulation at the magnet frequency. In order to produce sufficient signal separation the magnet frequency should be at least a factor of 102 lower than the rf frequency. A preferred range is from 10 Hz to
103Hz. In the exemplary apparatus the magnet frequency was chosen to be approximately 300 Hz. This frequency is referred to below as either the magnet frequency or the audio frequency.
The basic elements of a measurement system which can be used to measure the Hall angle by the method
outlined above are schematically shown in FIG. 4. The concentric electrodes 11, 12 are driven at the rf
frequency, f1 , by oscillator 41. The amplitude of the drive is monitored by the level sensing circuit 42. The level sensing circuit 42 provides a level control signal 52 to the oscillator 41 and also a rf phase reference signal through lead 53. The indicated arrangement in which the outer electrode 12 is driven by the oscillator 41 and the current level is monitored from the inner electrode 11 is preferred since the dependence of the test result upon the diameter of the semiconductor wafer 13 is reduced.
The electromagnet 14 is energized by the magnet drive coil 16. This coil 16 is driven by the magnet oscillator 45 at the magnet frequency, f2. The
oscillator 45 also provides a phase reference signal at the magnet frequency at lead 54.
The pickup coil 15 is electrostatically shielded by means of a resistive shield 64 (a carbon coating in an exemplary apparatus) and is connected to the input
amplifier 43. The amplified signal is synchronously demodulated in the phase sensitive detector 44 using the rf phase reference signal from lead 53. The demodulated signal, now at the magnet frequency, f2 , is amplified by means of amplifier 46. The amplified signal is
synchronously demodulated in the magnet frequency phase detector 47 using the magnet frequency phase reference signal from lead 54. The demodulated d.c. signal is again amplified by amplifier 48 and produces the output signal at terminal 49 whose sign and magnitude are related to the conductivity type and mobility of the material of the semiconductor wafer 13.
If the pickup signal produced by the direct leakage between the drive electrodes 11, 12 and the pickup coil 15 is large enough to drive amplifier 43 out of its linear range of operation the Hall signal, modulated at the magnet frequency, will be degraded. FIG. 5 indicates schematically the reduction of the crosstalk signal through the use of a crosstalk nulling circuit 51 to introduce a crosstalk cancelling signal at the rf frequency into the input of amplifier 43 by means of lead 55. In an exemplary apparatus two such feedback loops were utilized. One of these operated from the output of phase detector 44 while the other operated from the output of a second phase detector whose reference phase was at 90 degrees to the phase of the first phase detector 44 (phase quadrature). Each detector output phase drives a separate varactor diode through a long time constant filter. The varactors each form part of a two capacitor bridge, driven from the amplifier 43 output. Overall action of this feedback system is then to null out the average crosstalk to the input amplifier 43 no matter what the drive level of current generator 41. The time constant of this feedback system should be at least ten times the time constant corresponding to the magnet frequency. In this case it was approximately one second. Thus the Hall signal (modulated at the magnet frequency of approximately 300 Hz) is not affected while the unmodulated pickup crosstalk signal is cancelled assuring that the rf amplifiers operate within their linear range.
In an exemplary constructed system, Hall data was obtained to an accuracy of approximately plus or minus 10 cm2/volt second over a range of sheet resistance from approximately 10-2 to 105 ohms per square following
calibration at a single point. The accuracy was limited by the noise level which was approximately 10cm2/volt-sec. This performance was achieved when operating with a one second overall averaging time, a radial current of
approximately 100 microamps and a sampling area of
approximately one square cm. The magnetic field alternates over a peak-to-peak range of approximately one kG while the rf and audio frequencies were 600 kHz and 300 Hz,
In one embodiment of the apparatus of the
invention, some dependence of the measurements upon the thickness and diameter of the semiconductor wafer 13 was observed. For many users these effects produce no
difficulty since wafers of the same size and thickness are repeatedly measured and a single calibration will still lead to consistent results over a wide range of carrier mobilities. These geometric effects are reduced by methods involving confining the electrical and
magnetic couplings close to the gap between the magnet pole pieces 14. The previously mentioned expedient of driving the outer electrode 12 and monitoring current flowing into the inner electrode 11 is one such
expedient. Another is the use of a cup core 68 such as illustrated in FIG. 6. The material of the cup core should be selected so as to maintain high permeability at the rf frequency so that the magnetic field coupled to the pickup coil 15 is confined to the region of magnetic pole pieces 14. The use of ferrite or powder iron cup cores is indicated for most uses. In an exemplary
construction it proved to be advantageous to round the corners of the cup core 68 to eliminate the possible saturation of the material at sharp corners. In an
apparatus which utilizes phase sensitive detection at the magnet frequency, it is particularly important that the material of the magnet 14 and cup core 68 are
magnetically soft and of appropriate dimension to be nonsaturating up to the magnetic field to be used for the Hall measurement.
The use of a simple air-core pickup coil of the type shown in FIG. 4 can lead to Hall measurements that are a function of sample size. This is because of the
contribution of rf current flowing in the semiconductor sample at some distance from the disc 11 and ring 12 assembly. This can be alleviated, as shown in FIG. 6, by the two steps of confining the region of the f2 magnetic field to the region of interest on the sample and
simultaneously confining the pickup coil in a ferrite cup core.
It may be possible to further limit these effects through the use of a symmetrical structure with a cup core both above and below the semiconductor material as shown in FIG. 7. An alternate means of introducing the pickup cancellation signal would be by means of inductive coupling via a loop 113 below the wafer 13. It has been found expedient to round the edges of the ferrite cup core, somewhat as indicated in FIG. 6. This minimizes noise generated by the Barkhausen effect arising from high field region of the ferrite material saturating at the peaks of the applied field.