y kT, where k is the Boltzmann constant.

The nature of the measurement is ilustrated next [Figure 3] by this schematic epresentation of an n-p junction with two onor defects on the lightly doped p-type ide of the junction [defect indicated by star]. With zero bias applied to the unction, the space-charge region is very mall, extending from the junction to the

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10

ashed line [Figure 3A]. The nt region is
ssumed to be so heavily doped that the
pace-charge penetration into this region
ay be neglected. In the neutral region,
the negative charge on the acceptor atoms
is neutralized by valence-band holes, and
the positive charge on the donor defects
is neutralized by conduction-band electrons.
Under zero bias the junction is now
lowered to liquid nitrogen temperature.
Now, at this temperature, a reverse bias
is applied to the junction which widens
the space-charge region as illustrated here [Figure 3B). Valence-band holes and conduc-
tion-band electrons are removed from the space-charge region. At this temperature the
hole remains on both defect centers: the one in the space-charge region and the one in
the neutral region.

P-TYPE(DONOR DEFECTS)+
N+-TYPE

Figure 3. Charge state of defect centers in
nt-p junction.

As the temperature of the junction is increased, a critical temperature is reached, called the emission temperature, at which the hole on the defect in the space-charge region receives sufficient thermal energy to be released to the valence band. Through this process the defect center has changed charge state from positive to neutral and the release of the hole constitutes a current which can be measured in an external circuit. The change in charge state means that the space-charge region must shrink so as to maintain charge balance [indicated in Figure 3C]. This motion of the space-charge region constitutes a change in the junction capacitance which can also be measured in an external circuit. This example illustrates the case of the gold donor in a silicon nt-p junction.

+

Experimental results for such a junction will be shown next [with use of Figure 4]. The junction was first cooled to liquid nitrogen temperature. The donors were charged with holes by zero biasing the junction. After a reverse bias of 22.5 volts was applied, the junction was heated slowly at 0.61 kelvin per second and the current measured [Figure 4A]. The junction was again cooled to liquid nitrogen temperature and defects charged, but this time the junction was heated at 5 kelvin per second.

Figure 4. Response of a gold doped nt-p junction.

These dynathermal or dynamic-temperature measurements indicate that hole emission from the gold donor is heating-rate dependent, for at the slower heating rate the peak occurs at 125 kelvin and at the higher heating rate it occurs at 134 kelvin. Because the current response is governed by the rate at which holes are emitted per unit time, the sensitivity of this measurement depends on the heating rate. For a high heating rate of 10 kelvin per second it is possible with our equipment to detect 1010 defects/cm3

or one defect center in a trillion silicon atoms.

Next [Figure 4B] is shown the dynathermal capacitance response of the gold donor. This step in the capacitance response is directly related to the number of gold atoms which in this case is about 1015/cm3. Because the capacitance response is governed by the number of the holes emitted, the magnitude of the capacitance step is not heating rate dependent. For our equipment, defect centers are detectable if their density is greater than one defect in five hundred background dopant atoms.

For the non mid-gap defect shown here, the capacitance measurement is by far the easier in terms of the experimental apparatus and theoretical interpretation. For example, simple cryostats may be used, for icing is not a problem and low heating rates may be used. However, as will be shown, the dynathermal current measurements are superior when evaluating mid-gap defect centers which are the source of junction leakage. The next example is a process-induced defect center in a silicon p-n junction. This defect was unintentionally introduced into the junction. It resulted from the fabrication process. The dynathermal current and capacitance response for this defect [Figure 5] indicates that this center has two energy levels, as indicated by the emission processes at 150 and 225 kelvin. This example allows a comparison between the dynathermal response of a non-mid-gap energy level and a mid-gap energy level. The non-mid-gap energy level is initially completely full of electrons and finally completely emptied of elecThe mid-gap energy level is initially completely full of electrons but after the electrons have begun to be emitted, this level begins to generate both electrons

trons.

16

2.84

100

150

200

T (K)

Figure 5. Response of a p*-n junction with
process-induced defect centers.

er, a limitation of the measurements is
scussed [with the use of Figure 6]. The
ility of these measurements to detect de-
cts depends on whether the defects change
arge state. This in turn depends on the
sition of the defect energy level in the
ergy gap. As an example, consider an n-type semiconductor [Figure 6A] with an acceptor
fect center whose energy level is located well below mid-gap. In the neutral region,
noted by electrons in the conduction band, the center is negatively charged. In the
ace-charge region, denoted by the absence of electrons in the conduction band, the
ectron sticks on the center for at reasonable temperatures the electron cannot receive
ough thermal energy to be excited to the conduction band. This defect center does not
ange charge state and is therefore not detectable by these measurements.

For an energy level at mid-gap, the center is initially charged with an electron

t in its final state it acts as a generation site emitting holes and electrons [Figure 1. Its final charge state is governed by these emission rates which dictate its dectability.

For an energy level above mid-gap, centers are initially fully charged with electrons 1 finally fully discharged [Figure 6C]. These centers have optimum detection conditions. In summary [Figure 6D], the ability to detect defects in n-type silicon depends on e position of the energy level of the defect center. If the energy level lies in the wer half of the gap, then no measurement is possible (M=0). If the level is in the per half of the energy gap then the measurement has the best chance of succeeding (M=1).

If the level lies above the Fermi level, Ef, detectability is poor because the center is initially not charged with electrons.

The three kinds of measurement methods used to characterize defects are discussed now with respect to the process-induced defect in a silicon pn junction [Figure 5]. The measurements shown here are dynathermal measurements. The emission temperature and the heating rate are initial clues to the atomic identity of the defect center. The emission temperature is defined by the current peak or the maximum capacitance slope. A more definitive analysis of the emission rate, which involves the energy level determination, follows from isothermal capacitance measurements. In this measurement, made at a fixed temperature, the capacitance time constant is determined as the capacitance goes from its initial state to its final state. Measurements are taken at various temperatures and from the analysis comes both the energy level and the pre-exponential Bcoefficient. Such measurements were used to evaluate the electron emission rate for the 150 kelvin emission process.

The emission process at 225 kelvin is a mixture of both electron and hole emission. To evaluate these emission rates both isothermal capacitance and steady state leakage measurements are needed. The results of such evaluations are shown next [Figure 7] for the two emission processes. The non-mid-gap electron emission observed at 150 K is characterized by this emission rate, [e, 4.1 x 103 T2 exp (-0.23/kT)], and its energy level is in the middle of the upper half of the energy gap. The emission process observed at 225 K is given by these electron and hole emission rates, [e (-0.61/kT) and e

=

P

n

=

=

n

3.5 x 108 T2 exp is near mid-gap.

3.4 x 106 T2 exp (-0.55/kT)], and their energy level The defect density, N, for the two levels is the same within experimental error since both emission processes are coupled to the same defect center.

The shoulder shape of the dynathermal current response is a unique signature for the process-induced defect center [Figure 5]. This shape is distinctly different from the dynathermal current response for the gold acceptor defect in a silicon p+-n junction shown next [Figure 8A]. This response shows a peak and valley before it goes into steady state leakage. This dramatically demonstrates how dynathermal current measurements can be used to identify mid-gap defect centers. The currents shown here were measured at various heating rates. If the heating rate is slow enough, [0.17 K/s], electron emission is difficult to detect and the current response is essentially the steady state leakage The capacitance response is shown next [Figure 8B] for various heating rates. From this shift in characteristics the gold density was found to be about 3 percent of the background donor density.

response.

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