L OCAL

The change to the effective impurity concentration was measured using the capacitance voltage technique. Measurement was performed over a voltage range of 0 V to - 100 V. A plot of the capacitance per unit area versus the reverse voltage is shown in Figure 3.16 for all detectors. The plotted data was not corrected for the MOS capacitor effect associated with the bonding pad which can be seen in the 0 - 15 V region.

It can be seen that the curve becomes ‘flattened’ for detectors irradiated with a higher neutron fluence. The curve shape no longer appears to follow the C-V relationship described by Equation 3.1. This is most likely the result of radiation induced deep level defects present in concentrations comparable to the shallow level impurity concentration.

To correctly understand this result the effect of deep level defects on the capacitance was considered from a theoretical point of view. This was done by considering the effect of a mid band acceptor state in the form of a radiation induced defect present within the high resitivity n- type bulk of a p+-n junction device. In this analysis the acceptor impurity was assumed to have two charge states, -1 if occupied by an electron, and 0 if unoccupied. The band structure of the reverse biased junction is shown in Figure 3.17. No features are detailed in the p+ region. In the n-type region the electrical states of shallow level donor impurities, with energy ED and concentration ND, are shown close to the conduction band edge. Similarly, the electrical states of

Figure 3.16: C-V curves for the detectors U4a, b and c and U5a, b and c following neutron irradiation.

Figure 3.17: Energy band diagram of a p+-n junction with a deep level defect at an energy Et and concentration Nt. The ionised shallow donors, shown as a dash at energy ED are positively charged.

0 20 40 60 80 100 Reverse voltage (V) 0 50 100 150 200 250 Capacitance (pF/cm 2 ) U4a U4b U4c U5c U5b U5a Ev Ec Et (Nt) xd x1 ED (ND) EA (NA) EF

shallow level acceptor impurities, with energy EA and concentration NA, are shown close to the valence band edge. A deep level defect is shown with energy Et located at mid band positions through the material. To simplify the text, from here on this deep level defect will be referred to as a ‘trap’. The concentration of the trap is Nt. The Fermi level (EF) is shown. The depletion region edge, xd, is shown at the point where the bands become flat.

To understand the measured capacitance in this model the space charge within the depletion region needs to be considered. For distances less than xd the shallow level donor impurities are ionised and contribute a space charge density of +qND. In the same region, the shallow level acceptor impurities are occupied by an electron and contribute a charge density of −qNA. The net charge density due to the shallow level impurities is therefore qND− qNA. The contribution of the trap to the space charge in this region will depend on its charge state. Due to band bending the trap energy level will cross the Fermi level at some distance x1. Assuming

steady state conditions, traps located at distances less than x1 will be unoccupied by an electron

and will have a charge state of zero. These traps will make no contribution to the space charge density. Those traps located at distances greater than x1 but less than xd will be occupied by an electron and be in a charge state of -1. They will make a contribution of −qNt to the space charge density.

The total space charge density within the depletion region is summarised by:

x < x1 Charge density = q(ND− NA) x1 < x < xd Charge density = q(ND− NA− Nt)

If the reverse voltage is increased by a small increment ∆V then further band bending will occur and the depletion region will extend by ∆xd. The space charge about the depletion region edge due to shallow level impurities will increase by q(ND− NA)∆xd. A contribution from traps located about xd will also contribute a charge of qNt∆xd (a response from the trap is not required

as its charge state is not altered under this situation). The band bending will also cause the Fermi level to decrease about x1. This will cause some filled traps to be raised above EF. These traps will seek to emit the electron under thermal stimulation. The rate of emission will be en. Hence, after a long period compared to en-1, there will be a decrease in the space charge of magnitude qNt∆x1 as the trap charge state changes from -1 to 0.

Now, if the reverse voltage is decreased by the initial increment ∆V, the space charge density due to the shallow level impurities will almost immediately resume the situation prior to the application of ∆V. The traps about x1 will move below the Fermi level again. They will seek

to trap an electron in order to become occupied. Under the conditions imposed by the depletion approximation no free electrons can exist within the depletion region. In a real situation however electrons are able to diffuse into the depletion region to a distance characterised by the debye length, LD. These electrons are available to be captured by the trap at a rate equal to the capture rate, cn. It can be shown that for Et≈ EF, as is the case about x1 that cn≈ en [181]. So that the response of the trap to either an increase or decrease of the reverse voltage is dependent upon the emission rate of the trap and its value relative to the rate of change of ∆V. If the frequency of the capacitance meter test signal is ωtest, then when en >>ωtest the trap can respond

to the signal and make a contribution to the change in space charge. If en<<ωtest then the trap is

not capable of responding to the signal and will not make a contribution to the changing space charge. Hence for situations where the concentration of traps is comparable or greater than the net concentration of shallow level impurities, the capacitance measurement will be frequency dependent. In the high frequency limit the trap cannot contribute to the measured capacitance.

While the contribution of these traps cannot be detected in a high frequency capacitance measurement it is important to realise that in the steady state they will still contribute space charge and as such will affect the net effective impurity concentration and hence the full depletion voltage of the detectors.

less evident as the capacitance of all detectors approaches a minimum capacitance. This minimum in capacitance is given by the geometrical capacitance:

d Si o

w

A

C=ε

ε

where: wd = the detector thickness.

For these detectors the geometrical capacitance can be calculated to be 28.7 pF⋅cm-2. All experimental curves can be seen to be approaching this value.

The small change of C as a function of V gives a C-2 versus V curve with a substantially reduced slope. Calculation of the effective impurity concentration from the slope will give an erroneous result. Neff can however still be obtained from a C versus V curve. For detector U4b the C-V curve is shown in Figure 3.18. The slope can be seen to change at a reverse voltage of approximately 60 V. The transition to an almost flat type region is indicative of the full depletion capacitance having been reached. Construction lines were extrapolated from both regions and the point of interception obtained. This occurred at a voltage of 60 V. Using Equation 3.1 the effective impurity concentration can be calculated from the full deletion voltage to give 5.9×1011 cm-3.

Verification of this result can be obtained by an independent measurement of the full depletion voltage. This was done by measuring the charge collection characteristics of the detector to ionisation produced just within the non junction side of the detector. Collection of charge from this region can only occur when the depletion region extends throughout the detector volume. Alpha particles from 241Am were used to deposit energy at the rear side of the detector. The detector holder was modified to include a small hole in the brass base to permit the alpha particles to reach the rear of the detector. The range of the Am-241 alpha particles in

silicon is only 20 µm. Type inversion of the detector bulk was not anticipated on account of the modest neutron fluence. The junction should still exist at the front of the detector. The response of the detector as a function of reverse voltage is shown in Figure 3.19. The full depletion voltage was estimated from the point of intersection between a line extrapolated from the undepleted region and a line extrapolated from the fully depleted region of the charge collection curve. A full depletion voltage of 68 V was determined. The corresponding value of Neff is 6.7×1011 cm-3. This is in good agreement with the value calculated from the C-V measurement.

Figure 3.18: Full depletion depth (and hence the effective impurity concentration) can

still be obtained from the C-V curve of a neutron irradiated detector.

20 40 60 80 100 Reverse voltage (V) 26.5 27.0 27.5 28.0 28.5 29.0 Capacitance (pF/cm 2 ) VFD

Figure 3.19: Detector response to 5.5 MeV alpha particles incident on the rear contact.

Full depletion estimated at a reverse voltage of 68 V.