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Capacitive effects in neutron-irradiated silicon diodes
Nuclear Instruments and Methods in Physics Research A 488 (2002) 100–109
Capacitive effects in neutron-irradiated silicon diodes M. McPherson School of Mathematical Sciences, Department of Physics, University of the North (QwaQwa), Private Bag X13, 9866 Phuthaditjaba, South Africa Received 12 June 2001; received in revised form 12 December 2001; accepted 9 January 2002
Abstract The capacitance of two silicon diodes irradiated with 1 MeV neutrons has been measured. The capacitance–voltage characteristic demonstrates four effects (frequency dependence, negative capacitance, low-voltage peak, peak migration) that do not fit very well to what the lifetime theory predicts for p–n junction devices, but that are easily explained with relaxation theory. This suggests that the radiation damage has altered the semiconductor material from lifetime to relaxation. Possible mechanisms for the occurrence of the effects are suggested with an emphasis that relaxation theory be used for analysis. A defect introduction rate of 0.059 cm1 has been evaluated. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.80; 61.82.F; 71.55.A; 85.30 Keywords: Capacitance; Silicon; Neutron; Radiation; Diode
1. Introduction Several effects have been observed in the measured capacitance of irradiated silicon diodes that cannot be explained adequately by the wellknown lifetime theory of semiconductors [1]. The effects are seen to occur in high resistivity materials with an abundance of defect centres that can act as deep or shallow levels, as generation– recombination centres, or as compensation centres. These effects are a frequency dependence of the depletion region capacitance in reverse bias, a negative diffusion capacitance in forward bias, a low-voltage peak in the reverse bias capacitance and a migration of this peak to high voltages.
E-mail address: [email protected] (M. McPherson).
In this paper, the effects are discussed and a possible mechanism for their occurrence is suggested. Further, it is proposed that the lifetime diode theory (in which the minority carrier recombination lifetime, t0 exceeds the dielectric relaxation time, td ) may not be an accurate method to analyse the capacitance of irradiated silicon diodes. Indeed, this would apply to any devices that are fabricated from semiconductor material which has an abundance of slow and deep traps that are responsive to the AC test signal. Rather, the relaxation theory, which has been reviewed by several authors [2–5], has to be applied in the analysis. The situation is that t0 otd here. This paper also serves to reinforce the previous suggestion [6] that one of the main effects of radiation damage in silicon is to render the
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 0 4 8 0 - 1
M. McPherson / Nuclear Instruments and Methods in Physics Research A 488 (2002) 100–109
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material relaxation-like. The acquired relaxationlike properties of radiation-damaged silicon have been documented by many particle detector workers [7–13], although the interest was not in the relaxation likeness of the semiconductor and so the effect was somewhat overlooked. Neutron damage in silicon results from collisions of the secondary particles with nuclei of the material where the host lattice is destroyed, thereby introducing deep level defects that alter material properties. A varied number of defect levels are created by neutron damage. These have been observed by several workers and are compiled elsewhere [14], even though the list is by no means exhaustive. Carrier removal by trapping and reduction in lifetime are a direct consequence of the presence of the induced defects and this gives semi-insulating properties, thereby rendering the semiconductor relaxation-like.
They can increase considerably the recombination of free carriers, which are removed to reduce the conductivity. However, more carriers are created at midgap such that recombination also occurs at half bandgap where the process is more efficient and so there is a single quasi-Fermi level. Carrier densities then assume intrinsic values such that the Fermi level is pinned at the location for intrinsic behaviour. The material becomes semi-insulating with high resistivity [14] as a consequence. Defect centres can also act as compensation levels in the electrical neutral bulk of a semiconductor. Here, the deep levels are not easily ionised at equilibrium and have the effect of locking away free carriers [16] to shift the Fermi level and so to reduce the conductivity. Shallow donor (acceptor) traps remain empty in order to compensate deep acceptor (donor) traps with the result that the resistivity of the material increases.
1.1. Defect centres in semiconductors
1.2. Depletion region capacitance
The activity of defect centres in a semiconductor material differs as a consequence of where they are situated in the band gap. Their position determines this activity and hence the conduction mechanism in any devices made from such material. They can trap, recombine or generate e–h pairs and also act as compensation centres. Deep traps are defect centres whose ionisation energy is much greater than kT (that is DEbkT) at the temperature considered [15] and so are efficient as trapping centres. They reduce the conductivity considerably by trapping any free carriers which shifts the position of the Fermi level. In contrast, shallow traps are easily ionised at equilibrium (since DE5kT) and so give the conductivity [16] by releasing trapped carriers which also adjusts the position of the Fermi level. In depleted regions they contribute to the space charge and hence to the voltage required for full depletion. Thus, deep traps increase the resistivity of a material while shallow traps reduce it. Generation–recombination (g–r) centres, on the other hand, are situated near the centre of the band gap [17–19], in which position their trapping for electrons and for holes is comparable and so they easily generate or recombine e–h pairs [16].
The capacitance–voltage (C2V ) technique in reverse bias measures the depletion region capacitance in p–n junctions and so is used to determine doping profiles within a semiconductor. As such, measurements of the capacitance give information about fixed impurity states and defect centres in the bandgap. This capacitance is associated with the bending of energy bands in the junction [15], and this is determined by the net ionised charge density. For lifetime material diodes (in which t0 > td ) the space charge density is given by r ¼ eðNd nÞ; where e is the electronic charge, Nd is the donor density and n is the free electron density. In an extrinsic lifetime material n ¼ Nd in the bulk and so r ¼ 0; while n ¼ 0 in the depletion region so that r ¼ eNd : The junction acts as a capacitor with a small signal capacitance defined [17] as the rate of change of charge with applied voltage C ¼ dQ=dV ; which yields the relation WC ¼ es e0 A for lifetime diodes, where W is the depletion region width, es is the relative dielectric constant of the semiconductor, e0 is the dielectric constant of free space and A is the active diode area. The depletion region capacitance of a lifetime material diode at full depletion can thus be expressed as
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dCd ¼ es e0 A; where d is the full depletion width and Cd is the full depletion capacitance. In this situation, the donor density is evaluated from a relation of the form 2 1 Cd2 ¼ Vd ð1Þ 2 ees e0 A Nd
hence of the effective space charge density) on the temperature (and hence on the frequency) occurs in those devices with deep level defects that are responsive to the frequency of the AC test signal. This can be seen from
where Vd is the full depletion voltage. This relation shows that for a constant donor density in the depletion region Vd pCd2 ; which is the case for uniform doping and is assumed for lifetime material devices. For relaxation material diodes (in which t0 otd ) the analysis differs since the current under forward bias (which is exponential for lifetime devices [6] before irradiation) has become ohmic after irradiation [20] so that V ¼ IR; where R is the maximum resistance defined in RA ¼ rmax d: Here, ohmic means that the current is no more exponential but follows the maximum resistivity line. Then the current varies as the full depletion voltage from A Vd I¼ ð2Þ rmax d
where f and T are the frequency and temperature of measurement, respectively, k is the Boltzmann constant and Ea is the activation energy of the material. Clearly, log f and 1=T are equivalent parameters which means that a universal curve is defined for a known activation energy given by Ea ¼ kT logð f =f0 Þ:
where rmax is the maximum resistivity evaluated from the mobilities and the device geometry by ½2eðmn mp Þ1=2 ni 1 ; where mn and mp are the electron and hole mobilities, respectively, and ni is the intrinsic carrier density. In this ohmic case, the current determines the region empty of free carriers (or the depleted distance) since it is generated throughout the whole length of the depletion region [16] and so IpVd pW : Also, because any AC changes in the charge are produced at the edges of the depletion region, the capacitance is controlled mainly by the width such that Cp1=W : In consequence, the effective space charge density is not constant [14]. It is given as Neff ¼
2Cd2 Vd ees e0 A2
ð3Þ
by rearranging Eq. (1). This means that Neff pVd for a constant Cd so that the Debye length becomes variable in Nd ð¼ Neff Þ: Further, by Eqs. (2) and (3), IpNeff so that a rise in temperature increases the current since carriers become thermally activated to increase Neff : The dependence of the full depletion voltage (and
f ¼ f0 expð Ea =kTÞ
ð4Þ
1.3. Diffusion capacitance The C2V technique in forward bias measures the charge storage capacitance. In forward bias there is an excess of majority and minority carriers in the bulk regions, which cannot be removed immediately when the bias is suddenly discontinued. The technique is thus used to determine the rate at which charge is injected since in this situation carriers require a non-zero time to diffuse and recombine [14]. The diffusion capacitance can, as such, be explained by the stored charge or the current through the diode. It is given as eI Cd ¼ t0 ð5Þ kT for an ideal diffusion diode where I is the DC component of the current. The total voltage in forward bias is Vbi V ; where Vbi is the built-in voltage. Since the diffusion capacitance is given by dQp =dV ; any injected charge will alter the built-in charge. The relation of Eq. (5) is thus safely assumed for lifetime material diodes. For relaxation material diodes, the diffusion lengths for minority carriers are very small and so the currents are governed by space charge effects. In the situation when full depletion has been attained, the relation of Eq. (2) is substituted into Eq. (5) to give e AVd Cd ¼ t0 ð6Þ kT rmax d where I is the forward diffusion current, which, just like the reverse current, is ohmic for relaxation
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devices [6,14,20]. The current here gives details of the way carriers are distributed in the depletion region. Injected holes then recombine with electrons to deplete all carriers and so to increase the full depletion width to its maximum, the distance between the contacts, and hence to reduce the capacitance. In this way, the forward bias capacitance decreases with increasing voltage. This infers that an increase in the voltage produces a decrease in the charge.
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The forward bias data were acquired only up to 15 V. These measurements were taken at 10 kHz between 280 and 330 K ðCFB V TÞ; at 300 K between 10 and 400 kHz ðCFB V f Þ and also at 10 kHz, 300 K for all the different radiation doses (CRB V F). The AC test signal was maintained at a voltage level of 6 mV rms but the current limit was increased to 10 mA. Here, large value capacitors were placed in series with the input voltage for instrument protection and a resistance was placed in the DC bias circuit to prevent an AC short circuit through this path.
2. Experimental set-up 3. Results and discussion Two p–i–n photodiodes fabricated from high purity, high resistivity (400 O cm) silicon material were acquired from Hamamatsu. The active device area is 1 cm2 and the thickness is 240 mm. The diodes were then irradiated to different fluences at ISIS (RAL) with 1 MeV neutrons. Capacitance– voltage measurements in reverse bias and in forward bias were performed before and after irradiation using a Hewlett Packard LCR meter. In all cases the diodes were mounted under fairly good vacuum in which environment the measurements were carried out. The non-irradiated diodes were termed CSD1 and CSD2. The first diode was irradiated to two successive fluences of F1=3.4 1013 n cm2 and F3=25 1013 n cm2 while the second diode was irradiated to a fluence of F2=8.3 1013 n cm2. The irradiated diodes were termed CSD1i, CSD2i and CSD3i according to the dose, the highest dose being specified by 3i. It is clear that CSD1i and CSD3i are the same diode. Prior to irradiation, the diodes were tested and found to display nearly similar current–voltage and capacitance–voltage characteristics. The reverse bias data were acquired in the dark up to 200 V. The measurements were taken at 10 kHz over a temperature range from 230 to 350 K ðCRB V TÞ; at 300 K over a frequency range from 10 to 400 kHz ðCRB V f Þ and at 10 kHz and 300 K for all fluences (CRB V F). For all experiments the AC test signal was set to a voltage level of 6 mV rms and a current limit of 6 mA.
The general discussion of the results is based on the capacitance measured in both bias directions. The specific effects discussed here are due to the capacitance measured in reverse bias (depletion region capacitance) and that measured in forward bias (diffusion capacitance). The two interact to result in a low-voltage peak that has been observed in reverse bias. 3.1. Capacitance in reverse bias In reverse bias the depletion region width increases. The potential barrier also rises to reduce the flow of majority carriers. If the reverse voltage is increased the width, W is increased further until it equates to the device thickness, d: The capacitance should thus fall until saturation. The reverse bias capacitance of non-irradiated silicon (or lifetime) diodes generally falls with increasing voltage [18–19] until it saturates to a value equal to the capacitance between the metal contacts. At this voltage the diode is said to be fully depleted and it is possible to determine the doping profile by Eq. (1). The profile has been measured and found to be fairly uniform at B1012 cm3 over large voltages in the nonirradiated devices CSD1 and CSD2. Because lifetime diodes are made from fairly high-purity material and so with shallow donors and acceptors and no deep, slow defects, their capacitance is very weakly variable with temperature as to be assumed constant. This ‘‘lack’’ of temperature dependence
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means that the capacitance in these diodes can also be considered as frequency independent by Eq. (4). This has been shown before [6,14]. The activation energy has been evaluated from the current as Ea ¼ 0:86 eV for the CSD1 device and suggests that the conduction mechanism in this diode is due to shallow acceptor (or donor) traps in the lower (or upper) half of the band gap and so carrier values are extrinsic. A similar effect can safely be assumed for the CSD2 device. The expected fall in capacitance is not observed in radiation-damaged silicon (or relaxation) diodes. Instead, an initial peak at low voltages is observed that precedes the fall. This is shown in the frequency variation of the C2V characteristic of Fig. 1 for the irradiated silicon diode CSD1i at 300 K. The peak is caused by a decrease in the capacitance at low voltages. The decrease in C occurs because the injected carriers rapidly recombine with the built-in charge near the contact to produce a negative capacitance (DQ=DV ) contribution. We have shown the assumed electrostatics previously [21]. Carrier injection occurs because the ohmic behaviour depends on the maximum resistivity which is a dynamic property.
Fig. 1. A variation of the reverse C2V characteristic with frequency at 300 K for the irradiated device CSD1i. The dependence of capacitance on frequency means that the traps present are slow and therefore responsive to the test signal. Here, the current limit is set at 6 mA.
Electron–hole pairs are drawn into (or created in) the space charge region on demand. The built-in charge arises from the built-in voltage and refers to a region of free carrier space charge distributed over a certain distance. The injection of carriers results in an opposite effect to the depletion of carriers and so leads to a rise in the capacitance, thus the initial peak. However, the recombination with the built-in charge leads to a depression of the peak and so the system shifts to negative values. This is the negative capacitance contribution. The total capacitance is then the sum of the charge change near the electrode and that at the far edge of the depletion region. Also, if the radiation has created defect levels that are slow compared to the frequency of measurement the capacitance becomes frequency dependent. This is also shown in the figure and occurs because the device now has responsive traps and so is not a lifetime diode anymore. Rather, it is semi-insulating with high resistivity and therefore relaxation-like. The activation energy for the CSD1i device has been evaluated from the current as Ea ¼ 0:54 eV and means that the conduction mechanism in this diode is due to midgap defect centres. A similar effect is therefore assumed in devices CSD2i and CSD3i. Another interesting feature of the profile of Fig. 1 is that the capacitance increases with decreasing frequency at the same voltage. The relation of Eq. (4) can be written as log f p 1=T and indicates that frequency and temperature are inversely related. It follows then that the capacitance will increase with increasing temperature at the same voltage. This is the case as shown for the heavily irradiated device CSD3i in the reverse bias part of the C2V profiles of Fig. 2. The frequency dependence further indicates that there are slow traps in the substrate material of this diode that are responsive to the frequency of measurement. Relaxation devices are known to be frequency dependent in capacitance due to the presence of traps [22] which are thermally activated and which only respond to certain frequencies. This is also true for lifetime diodes with deep and slow traps. Thus, the frequency dependence of the capacitance is demonstrated to be an effect resulting from defect levels that act as trapping centres.
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Fig. 2. A variation of the C2V characteristic (a) with temperature at 10 kHz and (b) with frequency at 300 K for device CSD3i. A fall in temperature or a rise in frequency moves the profile towards zero capacitance. The current limit is set at 10 mA and the circuit design is different from that of Fig. 1.
3.2. Capacitance in forward bias In a forward biased diode, there is injection of positive charge (holes) which recombines with fixed or mobile negative charge. The depletion width is reduced as a result and the potential barrier lowers to allow easy flow of carriers. It is therefore expected that the capacitance should increase in a temperature dependent measurement. The expected increase in capacitance is not observed in irradiated silicon (or relaxation) diodes, the reason being that there is a competition for the injected charge by the stored charge and the radiation-induced g–r centres. The former requires time to diffuse and recombine while the latter recombine almost immediately. The diffusion capacitance effect is therefore easily overcome by the depletion capacitance effect. In the situation described above, the large density of g–r centres increases the recombination rate such that the space charge region is reinforced. Furthermore, the forward bias injects holes that recombine with the electrons already present in the depletion region. The density of mobile carriers is reduced as a result and the space charge region is enhanced further. The width increases
and so the capacitance falls as the forward voltage increases and continues falling beyond 0 F (that is, it increases negatively). Negative capacitance is then recorded in these devices which increases with an increase in temperature at the same voltage. This effect is shown in the C2V characteristic of Fig. 2(a) for device CSD3i at 10 kHz. The space charge region expands also because the traps cannot respond to the frequency of the test signal, and so the capacitance decreases. At high temperature the profile is grouped closer together, showing that the effect is reduced at these temperatures. This is expected because nearly all of the remaining carriers have become ionised and a further temperature rise has a negligible effect on the space charge density (and region). The capacitance then remains constant for the same voltage. In contrast, it is expected that for low temperatures the capacitance profile will tend to become horizontal since there is carrier freeze-out. A similar behaviour occurs in the case of a frequency-dependent measurement but in a converse manner. This is shown for the same device (CSD3i) in Fig. 2(b). Here, for the same voltage, the negative capacitance increases with a decrease in frequency. The effect is expected since a rise in
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temperature is synonymous with a fall in frequency as has been discussed. Another significant feature in this plot is that the capacitance profile is becoming horizontal as the frequency increases, with C attaining positive values at 100 kHz (and higher frequencies) which confirms the assertion deduced from plot (a) that the profile will become horizontal at low temperature. This suggests that at high enough frequencies negative capacitance would not be observed anymore. This is expected since at these frequencies carriers do not respond well to the test signal such that C remains constant over a large voltage change. A variation of the negative capacitance as a function of radiation fluence, F is shown in Fig. 3 for the diodes with fluences of F1=3.4 1013 n cm2 (CSD1i), of F2=8.3 1013 n cm2 (CSD2i) and of F3=25 1013 n cm2 (CSD3i). In forward bias here, an increase in fluence induces a similar effect as an increase in frequency or a fall in temperature would—that is, the profile becomes horizontal. It is different in reverse bias, of course, where an increase in F is similar to a fall in f or a rise in T: The mechanism in the first case is based
on two competing effects. These are that the increase in the density of g–r centres ðNgr Þ makes the negative capacitance effect larger since carriers are being annihilated, but the increase in the density of deep level traps ðNt Þ moves everything to different temperatures (or frequencies). In the figure, the second effect overcomes the first. This collapses the space charge region as carriers are being trapped, and the negative capacitance effect decreases such that the profile becomes horizontal. The three effects that have been observed by means of the negative capacitance in terms of the temperature, frequency and radiation fluence show that the capacitance becomes small and positive. This is due to two effects; the creation of g–r centres that increase the recombination/generation rate and the creation of deep level defects that increase trapping effects. These two effects compete but the latter overcomes the former, such that the effect of negative capacitance is reduced. This and the occurrence of negative capacitance means that the devices are behaving as relaxation material diodes. Thus, somewhat contrary to what the authors of Ref. [23] suggest for their experimental conditions, the effect under the paper’s conditions may not be wholly a circuit effect. It has been shown here that it is a trap effect. 3.3. The peak effect
Fig. 3. A variation of the C2V characteristic with fluence at 300 K and 10 kHz for devices CSD1i, CSD2i and CSD3i at three different fluences. An increase in fluence increases the capacitance in both bias directions and so moves the forward bias profile towards zero (and positive) capacitance. The current limit is set at 10 mA.
An increase in temperature T; or an increase in radiation fluence F; both have been found to have the same effect on the reverse bias capacitance of irradiated silicon diodes. The effective space charge density, Neff ; increases. A variation of the reverse C2V characteristic with temperature (C2V 2T) for device CSD1i at 10 kHz is shown in Fig. 4(a) for several temperatures from 300 to 350 K. The data are presented here in logarithmic form to better highlight this effect. The peak in C migrates to higher voltages as the temperature rises. This happens because at elevated temperatures more carriers become thermally activated and the effective space charge density increases and so does the capacitance. Then, since the maximum capacitance of the device is constant as it is measured between the contacts, the peak in C moves to higher
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Fig. 4. A logarithmic variation of the reverse C2V characteristic with temperature at 10 kHz (a) and a graph of the effective space charge density against temperature (b) for the irradiated device CSD1i. The peak in capacitance migrates to higher voltages and Neff increases as the temperature rises. The rise in Neff and the motion of the peak occur because the traps become ionised as the temperature increases. The slope of plot (b) is 1.6 109 K1 cm3.
voltages. The increase of charge enhances the built-in charge in the depletion region. A higher reverse bias is then required to overcome the charge, with the result that the maximum value of the capacitance occurs at a higher voltage than at lower temperatures. This type of charge enhancement is known to occur in relaxation devices [2–5,22]. The figure shows another interesting feature. The full depletion capacitance, Cd ; is observed to increase with an increase in temperature. This appears to suggest that the full depletion width decreases, which implies that the distance between the contacts is reduced. This is physically not possible, and can only mean that the charge measured between the contacts is enhanced [14]. This occurs because the built-up of charge at the opposite electrode induces an apparent reduction in the full depletion width. Then, since the depletion width is reduced, the capacitance is increased according to the discussion of Section 1.2. In the plot of Fig. 4(a), the depletion voltage at 350 K could be estimated at 850 V by extrapolating the data to the value of Cd : A linear fit to the data beyond the peak yields a voltage B900 V, from
which the effective space charge density has been calculated as 1:8 1013 cm3 by Eq. (3). The depletion voltage at 294 K is B112 V, which yields an effective space charge density of only 2.3 1012 cm3. An obvious increase in the full depletion voltage (from 112 to 900 V) and in the effective space charge density (from 2:3 to 18 1012 cm3 ) is indicated as the temperature rises from 294 to 350 K. This effect is shown in plot (b) of the figure where a slope of 1:6 109 K1 cm3 has been extracted. The effective space charge density increases because at high temperatures carriers are thermally activated from traps to increase Nt and so to increase Neff : The capacitance is then increased. A variation of the reverse C2V characteristic with fluence (C2V 2F) for all the devices at 300 K and 10 kHz has also been investigated for several fluences and is presented in logarithmic form in Fig. 5(a). A dependence of the capacitance on fluence has been observed that can be explained by the number of g–r centres ðNgr Þ generated by the irradiation. In general, the capacitance increases with increasing fluence for the same voltage, with the result that at high doses the diode requires a
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Fig. 5. A variation of the reverse C2V characteristic with fluence at 300 K and 10 kHz (a) and a plot of the effective space charge density against fluence (b) for the devices CSD1, CSD1i, CSD2i, and CSD3i. The peak in C migrates to higher voltages and Neff increases as the fluence increases. The rise in Neff and the peak motion occur due to a rise in g–r centres as the fluence increases. The slope of plot (b) yields a b value of 0.059 cm1.
higher voltage to attain full depletion. This has the advantage that the device can sustain higher electric fields since the space charge region does not easily reach the opposite electrode, but for use as a detector which needs a large depleted volume it is not so good. A second and more significant feature of this result is a migration of the lowvoltage peak towards higher voltages as the fluence increases. This effect is similar to that which is induced by an increase in temperature. A defect introduction rate of b ¼ 0:059 cm1 has been evaluated from the fluence dependence of the capacitance as shown in Fig. 5(b). The procedure to generate this plot is as outlined for Fig. 4, and the slope gives b: The calculated value of b is high as expected because no annealing was possible since the diodes were stored at sub-zero temperatures between measurements. It is, however, in fair agreement with b ¼ 0:05 cm1 reported by Wunstorf [24] for non-annealed samples. A lower value of b ¼ 0:017 cm1 has been reported by Chilingarov et al. [25] and this was measured after the diodes had undergone complete annealing. The damage constant, a has been found to range from 1.42 to 6:67 1017 A cm1 in these diodes [14,26], as expected
and in fair agreement with (5–10) 1017 A cm1 reported by Watts et al. [27] and compiled from several groups. Both a and b signify the level of radiation damage in the devices and can be used as measures of relaxation likeness. The effect of an increase in temperature or an increase in radiation fluence on the depletion region capacitance is similar. In both cases the effective space charge density is observed to increase and the capacitance peak to migrate to high voltages. A rise in temperature increases Neff by increasing Nt due to thermal activation from traps. An increase in fluence increases Neff by increasing Ngr due to the enhancement of generation activity from g–r centres. In both cases the peak in capacitance migrates to higher voltages.
4. Conclusions Four distinct capacitive effects have been demonstrated in silicon diodes irradiated with 1 MeV neutrons. These effects are somewhat contrary to what is expected in lifetime p–n junction diodes and suggest that the conventional lifetime semiconductor theory may not be an
M. McPherson / Nuclear Instruments and Methods in Physics Research A 488 (2002) 100–109
accurate method to analyse the depletion region capacitance of these devices. The effects can be explained by the relaxation theory, which means that the diodes have become relaxation-like. The relaxation likeness is explained by the presence of defect states in the bulk of the material. This means that after radiation damage the longneglected relaxation theory should be applied in analysing these diodes. By the frequency dependence of the capacitance, the radiation has been shown to create defect centres in the forbidden gap with a defect introduction rate of 0:059 cm1 evaluated from the fluence dependence of the capacitance. The existence of a negative capacitance and a peak in capacitance indicates that the irradiated devices have become relaxation-like diodes. By the peak in capacitance, it has been found that an increase in device temperature or radiation fluence will have a similar effect on the capacitance. This suggests that device properties may be optimised and increases in Neff easily monitored. It also means that relaxation-like samples can easily be identified. The migration of the peak may be used to detect any increases in device temperature or fluence and so the diodes may be used as detectors for any of the two parameters. The peak effect can also be used to monitor the onset of type inversion in the diodes. Acknowledgements Many thanks are due to M. Edwards for the irradiation runs, to B.K. Jones and T. Sloan for assistance with the analysis and to A. Chilingarov and J. Santana for fruitful discussions. References [1] S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1969.
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[2] W. van Roosbroeck, Phys. Rev. 123 (1961) 474. [3] N.M. Haegel, Appl. Phys. A 53 (1991) 1. [4] H. Queisser, In: P.N. Robson (Ed.), Solid State Devices, IOP Conference Series, Vol. 15, 1973, p. 145. [5] W. van Roosbroeck, Phys. Rev. Lett. 28 (1972) 1120. [6] M. McPherson, B.K. Jones, T. Sloan, Semicond. Sci. Technol. 12 (1997) 1187. [7] Z. Li, W. Chen, H.W. Kraner, Nucl. Instr. and Meth. A 308 (1991) 585. [8] F. Lemeilleur, M. Glass, E.H.M. Heijne, P. Jarron, E. Ocelli, IEEE Trans. Nucl. Sci. NS-39 (1992) 551. [9] D. Pitzl, et al., Nucl. Instr. and Meth. A 311 (1992) 98. [10] V. Eremin, Z. Li, IEEE Trans. Nucl. Sci. NS-41 (1994) 1907. [11] Z. Li, Nucl. Instr. and Meth. A 342 (1994) 105. [12] Z. Li, IEEE Trans. Nucl. Sci. NS-42 (1995) 224. [13] V. Eremin, Z. Li, I. Iljashenko, Nucl. Instr. and Meth. A 360 (1995) 458. [14] M. McPherson, Irradiated silicon detectors as relaxation devices, Ph.D. Thesis, Lancaster University, UK, 1998. [15] P. Blood, J.W. Orton, In: N.H. Marsh (Ed.), The Electrical Characterization of Semiconductors: Majority Carriers and Electron States, Academic, London, 1992. [16] B.K. Jones, J. Santana, M. McPherson, Nucl. Instr. and Meth. A 395 (1997) 81. [17] B.G. Streetman, Solid State Electronic Devices, 3rd Edition, Prentice Hall, New Jersey, 1990. [18] D.K. Schroder, Semiconductor Material and Device Characterization, Wiley, New York, 1990. [19] H.F. Wolf, In: H.K. Henisch (Ed.), Silicon Semiconductor Data, Pergamon, Oxford, 1969. [20] B.K. Jones, J. Santana, M. McPherson, Solid State Commun. 105 (1998) 547. [21] B.K. Jones, J. Santana, M. McPherson, Solid State Commun. 107 (1998) 47. [22] K. Zdansky, B.K. Jones, J. Santana, T. Sloan, J. Appl. Phys. 79 (1996) 3611. [23] K.S.A. Butcher, T.L. Tansley, D. Alexiev, Solid State Electron. 39 (1996) 333. [24] R. Wunstorf, IEEE Trans. Nucl. Sci. NS-44 (1997) 806. [25] A. Chilingarov, H. Feick, E. Fretwurst, G. Lindstrom, S. Roe, T. Schultz, Nucl. Instr. and Meth. A 336 (1995) 432. [26] M. McPherson, T. Sloan, B.K. Jones, J. Phys. D 30 (1997) 3028. [27] S.J. Watts, J. Matheson, I.H. Hopkins-Bond, A. HolmesSidle, A. Mohammadzadeh, R. Pace, IEEE Trans. Nucl. Sci. NS-43 (1996) 2587.
Capacitive effects in neutron-irradiated silicon diodes M. McPherson School of Mathematical Sciences, Department of Physics, University of the North (QwaQwa), Private Bag X13, 9866 Phuthaditjaba, South Africa Received 12 June 2001; received in revised form 12 December 2001; accepted 9 January 2002
Abstract The capacitance of two silicon diodes irradiated with 1 MeV neutrons has been measured. The capacitance–voltage characteristic demonstrates four effects (frequency dependence, negative capacitance, low-voltage peak, peak migration) that do not fit very well to what the lifetime theory predicts for p–n junction devices, but that are easily explained with relaxation theory. This suggests that the radiation damage has altered the semiconductor material from lifetime to relaxation. Possible mechanisms for the occurrence of the effects are suggested with an emphasis that relaxation theory be used for analysis. A defect introduction rate of 0.059 cm1 has been evaluated. r 2002 Elsevier Science B.V. All rights reserved. PACS: 61.80; 61.82.F; 71.55.A; 85.30 Keywords: Capacitance; Silicon; Neutron; Radiation; Diode
1. Introduction Several effects have been observed in the measured capacitance of irradiated silicon diodes that cannot be explained adequately by the wellknown lifetime theory of semiconductors [1]. The effects are seen to occur in high resistivity materials with an abundance of defect centres that can act as deep or shallow levels, as generation– recombination centres, or as compensation centres. These effects are a frequency dependence of the depletion region capacitance in reverse bias, a negative diffusion capacitance in forward bias, a low-voltage peak in the reverse bias capacitance and a migration of this peak to high voltages.
E-mail address: [email protected] (M. McPherson).
In this paper, the effects are discussed and a possible mechanism for their occurrence is suggested. Further, it is proposed that the lifetime diode theory (in which the minority carrier recombination lifetime, t0 exceeds the dielectric relaxation time, td ) may not be an accurate method to analyse the capacitance of irradiated silicon diodes. Indeed, this would apply to any devices that are fabricated from semiconductor material which has an abundance of slow and deep traps that are responsive to the AC test signal. Rather, the relaxation theory, which has been reviewed by several authors [2–5], has to be applied in the analysis. The situation is that t0 otd here. This paper also serves to reinforce the previous suggestion [6] that one of the main effects of radiation damage in silicon is to render the
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 0 4 8 0 - 1
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material relaxation-like. The acquired relaxationlike properties of radiation-damaged silicon have been documented by many particle detector workers [7–13], although the interest was not in the relaxation likeness of the semiconductor and so the effect was somewhat overlooked. Neutron damage in silicon results from collisions of the secondary particles with nuclei of the material where the host lattice is destroyed, thereby introducing deep level defects that alter material properties. A varied number of defect levels are created by neutron damage. These have been observed by several workers and are compiled elsewhere [14], even though the list is by no means exhaustive. Carrier removal by trapping and reduction in lifetime are a direct consequence of the presence of the induced defects and this gives semi-insulating properties, thereby rendering the semiconductor relaxation-like.
They can increase considerably the recombination of free carriers, which are removed to reduce the conductivity. However, more carriers are created at midgap such that recombination also occurs at half bandgap where the process is more efficient and so there is a single quasi-Fermi level. Carrier densities then assume intrinsic values such that the Fermi level is pinned at the location for intrinsic behaviour. The material becomes semi-insulating with high resistivity [14] as a consequence. Defect centres can also act as compensation levels in the electrical neutral bulk of a semiconductor. Here, the deep levels are not easily ionised at equilibrium and have the effect of locking away free carriers [16] to shift the Fermi level and so to reduce the conductivity. Shallow donor (acceptor) traps remain empty in order to compensate deep acceptor (donor) traps with the result that the resistivity of the material increases.
1.1. Defect centres in semiconductors
1.2. Depletion region capacitance
The activity of defect centres in a semiconductor material differs as a consequence of where they are situated in the band gap. Their position determines this activity and hence the conduction mechanism in any devices made from such material. They can trap, recombine or generate e–h pairs and also act as compensation centres. Deep traps are defect centres whose ionisation energy is much greater than kT (that is DEbkT) at the temperature considered [15] and so are efficient as trapping centres. They reduce the conductivity considerably by trapping any free carriers which shifts the position of the Fermi level. In contrast, shallow traps are easily ionised at equilibrium (since DE5kT) and so give the conductivity [16] by releasing trapped carriers which also adjusts the position of the Fermi level. In depleted regions they contribute to the space charge and hence to the voltage required for full depletion. Thus, deep traps increase the resistivity of a material while shallow traps reduce it. Generation–recombination (g–r) centres, on the other hand, are situated near the centre of the band gap [17–19], in which position their trapping for electrons and for holes is comparable and so they easily generate or recombine e–h pairs [16].
The capacitance–voltage (C2V ) technique in reverse bias measures the depletion region capacitance in p–n junctions and so is used to determine doping profiles within a semiconductor. As such, measurements of the capacitance give information about fixed impurity states and defect centres in the bandgap. This capacitance is associated with the bending of energy bands in the junction [15], and this is determined by the net ionised charge density. For lifetime material diodes (in which t0 > td ) the space charge density is given by r ¼ eðNd nÞ; where e is the electronic charge, Nd is the donor density and n is the free electron density. In an extrinsic lifetime material n ¼ Nd in the bulk and so r ¼ 0; while n ¼ 0 in the depletion region so that r ¼ eNd : The junction acts as a capacitor with a small signal capacitance defined [17] as the rate of change of charge with applied voltage C ¼ dQ=dV ; which yields the relation WC ¼ es e0 A for lifetime diodes, where W is the depletion region width, es is the relative dielectric constant of the semiconductor, e0 is the dielectric constant of free space and A is the active diode area. The depletion region capacitance of a lifetime material diode at full depletion can thus be expressed as
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dCd ¼ es e0 A; where d is the full depletion width and Cd is the full depletion capacitance. In this situation, the donor density is evaluated from a relation of the form 2 1 Cd2 ¼ Vd ð1Þ 2 ees e0 A Nd
hence of the effective space charge density) on the temperature (and hence on the frequency) occurs in those devices with deep level defects that are responsive to the frequency of the AC test signal. This can be seen from
where Vd is the full depletion voltage. This relation shows that for a constant donor density in the depletion region Vd pCd2 ; which is the case for uniform doping and is assumed for lifetime material devices. For relaxation material diodes (in which t0 otd ) the analysis differs since the current under forward bias (which is exponential for lifetime devices [6] before irradiation) has become ohmic after irradiation [20] so that V ¼ IR; where R is the maximum resistance defined in RA ¼ rmax d: Here, ohmic means that the current is no more exponential but follows the maximum resistivity line. Then the current varies as the full depletion voltage from A Vd I¼ ð2Þ rmax d
where f and T are the frequency and temperature of measurement, respectively, k is the Boltzmann constant and Ea is the activation energy of the material. Clearly, log f and 1=T are equivalent parameters which means that a universal curve is defined for a known activation energy given by Ea ¼ kT logð f =f0 Þ:
where rmax is the maximum resistivity evaluated from the mobilities and the device geometry by ½2eðmn mp Þ1=2 ni 1 ; where mn and mp are the electron and hole mobilities, respectively, and ni is the intrinsic carrier density. In this ohmic case, the current determines the region empty of free carriers (or the depleted distance) since it is generated throughout the whole length of the depletion region [16] and so IpVd pW : Also, because any AC changes in the charge are produced at the edges of the depletion region, the capacitance is controlled mainly by the width such that Cp1=W : In consequence, the effective space charge density is not constant [14]. It is given as Neff ¼
2Cd2 Vd ees e0 A2
ð3Þ
by rearranging Eq. (1). This means that Neff pVd for a constant Cd so that the Debye length becomes variable in Nd ð¼ Neff Þ: Further, by Eqs. (2) and (3), IpNeff so that a rise in temperature increases the current since carriers become thermally activated to increase Neff : The dependence of the full depletion voltage (and
f ¼ f0 expð Ea =kTÞ
ð4Þ
1.3. Diffusion capacitance The C2V technique in forward bias measures the charge storage capacitance. In forward bias there is an excess of majority and minority carriers in the bulk regions, which cannot be removed immediately when the bias is suddenly discontinued. The technique is thus used to determine the rate at which charge is injected since in this situation carriers require a non-zero time to diffuse and recombine [14]. The diffusion capacitance can, as such, be explained by the stored charge or the current through the diode. It is given as eI Cd ¼ t0 ð5Þ kT for an ideal diffusion diode where I is the DC component of the current. The total voltage in forward bias is Vbi V ; where Vbi is the built-in voltage. Since the diffusion capacitance is given by dQp =dV ; any injected charge will alter the built-in charge. The relation of Eq. (5) is thus safely assumed for lifetime material diodes. For relaxation material diodes, the diffusion lengths for minority carriers are very small and so the currents are governed by space charge effects. In the situation when full depletion has been attained, the relation of Eq. (2) is substituted into Eq. (5) to give e AVd Cd ¼ t0 ð6Þ kT rmax d where I is the forward diffusion current, which, just like the reverse current, is ohmic for relaxation
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devices [6,14,20]. The current here gives details of the way carriers are distributed in the depletion region. Injected holes then recombine with electrons to deplete all carriers and so to increase the full depletion width to its maximum, the distance between the contacts, and hence to reduce the capacitance. In this way, the forward bias capacitance decreases with increasing voltage. This infers that an increase in the voltage produces a decrease in the charge.
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The forward bias data were acquired only up to 15 V. These measurements were taken at 10 kHz between 280 and 330 K ðCFB V TÞ; at 300 K between 10 and 400 kHz ðCFB V f Þ and also at 10 kHz, 300 K for all the different radiation doses (CRB V F). The AC test signal was maintained at a voltage level of 6 mV rms but the current limit was increased to 10 mA. Here, large value capacitors were placed in series with the input voltage for instrument protection and a resistance was placed in the DC bias circuit to prevent an AC short circuit through this path.
2. Experimental set-up 3. Results and discussion Two p–i–n photodiodes fabricated from high purity, high resistivity (400 O cm) silicon material were acquired from Hamamatsu. The active device area is 1 cm2 and the thickness is 240 mm. The diodes were then irradiated to different fluences at ISIS (RAL) with 1 MeV neutrons. Capacitance– voltage measurements in reverse bias and in forward bias were performed before and after irradiation using a Hewlett Packard LCR meter. In all cases the diodes were mounted under fairly good vacuum in which environment the measurements were carried out. The non-irradiated diodes were termed CSD1 and CSD2. The first diode was irradiated to two successive fluences of F1=3.4 1013 n cm2 and F3=25 1013 n cm2 while the second diode was irradiated to a fluence of F2=8.3 1013 n cm2. The irradiated diodes were termed CSD1i, CSD2i and CSD3i according to the dose, the highest dose being specified by 3i. It is clear that CSD1i and CSD3i are the same diode. Prior to irradiation, the diodes were tested and found to display nearly similar current–voltage and capacitance–voltage characteristics. The reverse bias data were acquired in the dark up to 200 V. The measurements were taken at 10 kHz over a temperature range from 230 to 350 K ðCRB V TÞ; at 300 K over a frequency range from 10 to 400 kHz ðCRB V f Þ and at 10 kHz and 300 K for all fluences (CRB V F). For all experiments the AC test signal was set to a voltage level of 6 mV rms and a current limit of 6 mA.
The general discussion of the results is based on the capacitance measured in both bias directions. The specific effects discussed here are due to the capacitance measured in reverse bias (depletion region capacitance) and that measured in forward bias (diffusion capacitance). The two interact to result in a low-voltage peak that has been observed in reverse bias. 3.1. Capacitance in reverse bias In reverse bias the depletion region width increases. The potential barrier also rises to reduce the flow of majority carriers. If the reverse voltage is increased the width, W is increased further until it equates to the device thickness, d: The capacitance should thus fall until saturation. The reverse bias capacitance of non-irradiated silicon (or lifetime) diodes generally falls with increasing voltage [18–19] until it saturates to a value equal to the capacitance between the metal contacts. At this voltage the diode is said to be fully depleted and it is possible to determine the doping profile by Eq. (1). The profile has been measured and found to be fairly uniform at B1012 cm3 over large voltages in the nonirradiated devices CSD1 and CSD2. Because lifetime diodes are made from fairly high-purity material and so with shallow donors and acceptors and no deep, slow defects, their capacitance is very weakly variable with temperature as to be assumed constant. This ‘‘lack’’ of temperature dependence
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means that the capacitance in these diodes can also be considered as frequency independent by Eq. (4). This has been shown before [6,14]. The activation energy has been evaluated from the current as Ea ¼ 0:86 eV for the CSD1 device and suggests that the conduction mechanism in this diode is due to shallow acceptor (or donor) traps in the lower (or upper) half of the band gap and so carrier values are extrinsic. A similar effect can safely be assumed for the CSD2 device. The expected fall in capacitance is not observed in radiation-damaged silicon (or relaxation) diodes. Instead, an initial peak at low voltages is observed that precedes the fall. This is shown in the frequency variation of the C2V characteristic of Fig. 1 for the irradiated silicon diode CSD1i at 300 K. The peak is caused by a decrease in the capacitance at low voltages. The decrease in C occurs because the injected carriers rapidly recombine with the built-in charge near the contact to produce a negative capacitance (DQ=DV ) contribution. We have shown the assumed electrostatics previously [21]. Carrier injection occurs because the ohmic behaviour depends on the maximum resistivity which is a dynamic property.
Fig. 1. A variation of the reverse C2V characteristic with frequency at 300 K for the irradiated device CSD1i. The dependence of capacitance on frequency means that the traps present are slow and therefore responsive to the test signal. Here, the current limit is set at 6 mA.
Electron–hole pairs are drawn into (or created in) the space charge region on demand. The built-in charge arises from the built-in voltage and refers to a region of free carrier space charge distributed over a certain distance. The injection of carriers results in an opposite effect to the depletion of carriers and so leads to a rise in the capacitance, thus the initial peak. However, the recombination with the built-in charge leads to a depression of the peak and so the system shifts to negative values. This is the negative capacitance contribution. The total capacitance is then the sum of the charge change near the electrode and that at the far edge of the depletion region. Also, if the radiation has created defect levels that are slow compared to the frequency of measurement the capacitance becomes frequency dependent. This is also shown in the figure and occurs because the device now has responsive traps and so is not a lifetime diode anymore. Rather, it is semi-insulating with high resistivity and therefore relaxation-like. The activation energy for the CSD1i device has been evaluated from the current as Ea ¼ 0:54 eV and means that the conduction mechanism in this diode is due to midgap defect centres. A similar effect is therefore assumed in devices CSD2i and CSD3i. Another interesting feature of the profile of Fig. 1 is that the capacitance increases with decreasing frequency at the same voltage. The relation of Eq. (4) can be written as log f p 1=T and indicates that frequency and temperature are inversely related. It follows then that the capacitance will increase with increasing temperature at the same voltage. This is the case as shown for the heavily irradiated device CSD3i in the reverse bias part of the C2V profiles of Fig. 2. The frequency dependence further indicates that there are slow traps in the substrate material of this diode that are responsive to the frequency of measurement. Relaxation devices are known to be frequency dependent in capacitance due to the presence of traps [22] which are thermally activated and which only respond to certain frequencies. This is also true for lifetime diodes with deep and slow traps. Thus, the frequency dependence of the capacitance is demonstrated to be an effect resulting from defect levels that act as trapping centres.
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Fig. 2. A variation of the C2V characteristic (a) with temperature at 10 kHz and (b) with frequency at 300 K for device CSD3i. A fall in temperature or a rise in frequency moves the profile towards zero capacitance. The current limit is set at 10 mA and the circuit design is different from that of Fig. 1.
3.2. Capacitance in forward bias In a forward biased diode, there is injection of positive charge (holes) which recombines with fixed or mobile negative charge. The depletion width is reduced as a result and the potential barrier lowers to allow easy flow of carriers. It is therefore expected that the capacitance should increase in a temperature dependent measurement. The expected increase in capacitance is not observed in irradiated silicon (or relaxation) diodes, the reason being that there is a competition for the injected charge by the stored charge and the radiation-induced g–r centres. The former requires time to diffuse and recombine while the latter recombine almost immediately. The diffusion capacitance effect is therefore easily overcome by the depletion capacitance effect. In the situation described above, the large density of g–r centres increases the recombination rate such that the space charge region is reinforced. Furthermore, the forward bias injects holes that recombine with the electrons already present in the depletion region. The density of mobile carriers is reduced as a result and the space charge region is enhanced further. The width increases
and so the capacitance falls as the forward voltage increases and continues falling beyond 0 F (that is, it increases negatively). Negative capacitance is then recorded in these devices which increases with an increase in temperature at the same voltage. This effect is shown in the C2V characteristic of Fig. 2(a) for device CSD3i at 10 kHz. The space charge region expands also because the traps cannot respond to the frequency of the test signal, and so the capacitance decreases. At high temperature the profile is grouped closer together, showing that the effect is reduced at these temperatures. This is expected because nearly all of the remaining carriers have become ionised and a further temperature rise has a negligible effect on the space charge density (and region). The capacitance then remains constant for the same voltage. In contrast, it is expected that for low temperatures the capacitance profile will tend to become horizontal since there is carrier freeze-out. A similar behaviour occurs in the case of a frequency-dependent measurement but in a converse manner. This is shown for the same device (CSD3i) in Fig. 2(b). Here, for the same voltage, the negative capacitance increases with a decrease in frequency. The effect is expected since a rise in
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temperature is synonymous with a fall in frequency as has been discussed. Another significant feature in this plot is that the capacitance profile is becoming horizontal as the frequency increases, with C attaining positive values at 100 kHz (and higher frequencies) which confirms the assertion deduced from plot (a) that the profile will become horizontal at low temperature. This suggests that at high enough frequencies negative capacitance would not be observed anymore. This is expected since at these frequencies carriers do not respond well to the test signal such that C remains constant over a large voltage change. A variation of the negative capacitance as a function of radiation fluence, F is shown in Fig. 3 for the diodes with fluences of F1=3.4 1013 n cm2 (CSD1i), of F2=8.3 1013 n cm2 (CSD2i) and of F3=25 1013 n cm2 (CSD3i). In forward bias here, an increase in fluence induces a similar effect as an increase in frequency or a fall in temperature would—that is, the profile becomes horizontal. It is different in reverse bias, of course, where an increase in F is similar to a fall in f or a rise in T: The mechanism in the first case is based
on two competing effects. These are that the increase in the density of g–r centres ðNgr Þ makes the negative capacitance effect larger since carriers are being annihilated, but the increase in the density of deep level traps ðNt Þ moves everything to different temperatures (or frequencies). In the figure, the second effect overcomes the first. This collapses the space charge region as carriers are being trapped, and the negative capacitance effect decreases such that the profile becomes horizontal. The three effects that have been observed by means of the negative capacitance in terms of the temperature, frequency and radiation fluence show that the capacitance becomes small and positive. This is due to two effects; the creation of g–r centres that increase the recombination/generation rate and the creation of deep level defects that increase trapping effects. These two effects compete but the latter overcomes the former, such that the effect of negative capacitance is reduced. This and the occurrence of negative capacitance means that the devices are behaving as relaxation material diodes. Thus, somewhat contrary to what the authors of Ref. [23] suggest for their experimental conditions, the effect under the paper’s conditions may not be wholly a circuit effect. It has been shown here that it is a trap effect. 3.3. The peak effect
Fig. 3. A variation of the C2V characteristic with fluence at 300 K and 10 kHz for devices CSD1i, CSD2i and CSD3i at three different fluences. An increase in fluence increases the capacitance in both bias directions and so moves the forward bias profile towards zero (and positive) capacitance. The current limit is set at 10 mA.
An increase in temperature T; or an increase in radiation fluence F; both have been found to have the same effect on the reverse bias capacitance of irradiated silicon diodes. The effective space charge density, Neff ; increases. A variation of the reverse C2V characteristic with temperature (C2V 2T) for device CSD1i at 10 kHz is shown in Fig. 4(a) for several temperatures from 300 to 350 K. The data are presented here in logarithmic form to better highlight this effect. The peak in C migrates to higher voltages as the temperature rises. This happens because at elevated temperatures more carriers become thermally activated and the effective space charge density increases and so does the capacitance. Then, since the maximum capacitance of the device is constant as it is measured between the contacts, the peak in C moves to higher
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Fig. 4. A logarithmic variation of the reverse C2V characteristic with temperature at 10 kHz (a) and a graph of the effective space charge density against temperature (b) for the irradiated device CSD1i. The peak in capacitance migrates to higher voltages and Neff increases as the temperature rises. The rise in Neff and the motion of the peak occur because the traps become ionised as the temperature increases. The slope of plot (b) is 1.6 109 K1 cm3.
voltages. The increase of charge enhances the built-in charge in the depletion region. A higher reverse bias is then required to overcome the charge, with the result that the maximum value of the capacitance occurs at a higher voltage than at lower temperatures. This type of charge enhancement is known to occur in relaxation devices [2–5,22]. The figure shows another interesting feature. The full depletion capacitance, Cd ; is observed to increase with an increase in temperature. This appears to suggest that the full depletion width decreases, which implies that the distance between the contacts is reduced. This is physically not possible, and can only mean that the charge measured between the contacts is enhanced [14]. This occurs because the built-up of charge at the opposite electrode induces an apparent reduction in the full depletion width. Then, since the depletion width is reduced, the capacitance is increased according to the discussion of Section 1.2. In the plot of Fig. 4(a), the depletion voltage at 350 K could be estimated at 850 V by extrapolating the data to the value of Cd : A linear fit to the data beyond the peak yields a voltage B900 V, from
which the effective space charge density has been calculated as 1:8 1013 cm3 by Eq. (3). The depletion voltage at 294 K is B112 V, which yields an effective space charge density of only 2.3 1012 cm3. An obvious increase in the full depletion voltage (from 112 to 900 V) and in the effective space charge density (from 2:3 to 18 1012 cm3 ) is indicated as the temperature rises from 294 to 350 K. This effect is shown in plot (b) of the figure where a slope of 1:6 109 K1 cm3 has been extracted. The effective space charge density increases because at high temperatures carriers are thermally activated from traps to increase Nt and so to increase Neff : The capacitance is then increased. A variation of the reverse C2V characteristic with fluence (C2V 2F) for all the devices at 300 K and 10 kHz has also been investigated for several fluences and is presented in logarithmic form in Fig. 5(a). A dependence of the capacitance on fluence has been observed that can be explained by the number of g–r centres ðNgr Þ generated by the irradiation. In general, the capacitance increases with increasing fluence for the same voltage, with the result that at high doses the diode requires a
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Fig. 5. A variation of the reverse C2V characteristic with fluence at 300 K and 10 kHz (a) and a plot of the effective space charge density against fluence (b) for the devices CSD1, CSD1i, CSD2i, and CSD3i. The peak in C migrates to higher voltages and Neff increases as the fluence increases. The rise in Neff and the peak motion occur due to a rise in g–r centres as the fluence increases. The slope of plot (b) yields a b value of 0.059 cm1.
higher voltage to attain full depletion. This has the advantage that the device can sustain higher electric fields since the space charge region does not easily reach the opposite electrode, but for use as a detector which needs a large depleted volume it is not so good. A second and more significant feature of this result is a migration of the lowvoltage peak towards higher voltages as the fluence increases. This effect is similar to that which is induced by an increase in temperature. A defect introduction rate of b ¼ 0:059 cm1 has been evaluated from the fluence dependence of the capacitance as shown in Fig. 5(b). The procedure to generate this plot is as outlined for Fig. 4, and the slope gives b: The calculated value of b is high as expected because no annealing was possible since the diodes were stored at sub-zero temperatures between measurements. It is, however, in fair agreement with b ¼ 0:05 cm1 reported by Wunstorf [24] for non-annealed samples. A lower value of b ¼ 0:017 cm1 has been reported by Chilingarov et al. [25] and this was measured after the diodes had undergone complete annealing. The damage constant, a has been found to range from 1.42 to 6:67 1017 A cm1 in these diodes [14,26], as expected
and in fair agreement with (5–10) 1017 A cm1 reported by Watts et al. [27] and compiled from several groups. Both a and b signify the level of radiation damage in the devices and can be used as measures of relaxation likeness. The effect of an increase in temperature or an increase in radiation fluence on the depletion region capacitance is similar. In both cases the effective space charge density is observed to increase and the capacitance peak to migrate to high voltages. A rise in temperature increases Neff by increasing Nt due to thermal activation from traps. An increase in fluence increases Neff by increasing Ngr due to the enhancement of generation activity from g–r centres. In both cases the peak in capacitance migrates to higher voltages.
4. Conclusions Four distinct capacitive effects have been demonstrated in silicon diodes irradiated with 1 MeV neutrons. These effects are somewhat contrary to what is expected in lifetime p–n junction diodes and suggest that the conventional lifetime semiconductor theory may not be an
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accurate method to analyse the depletion region capacitance of these devices. The effects can be explained by the relaxation theory, which means that the diodes have become relaxation-like. The relaxation likeness is explained by the presence of defect states in the bulk of the material. This means that after radiation damage the longneglected relaxation theory should be applied in analysing these diodes. By the frequency dependence of the capacitance, the radiation has been shown to create defect centres in the forbidden gap with a defect introduction rate of 0:059 cm1 evaluated from the fluence dependence of the capacitance. The existence of a negative capacitance and a peak in capacitance indicates that the irradiated devices have become relaxation-like diodes. By the peak in capacitance, it has been found that an increase in device temperature or radiation fluence will have a similar effect on the capacitance. This suggests that device properties may be optimised and increases in Neff easily monitored. It also means that relaxation-like samples can easily be identified. The migration of the peak may be used to detect any increases in device temperature or fluence and so the diodes may be used as detectors for any of the two parameters. The peak effect can also be used to monitor the onset of type inversion in the diodes. Acknowledgements Many thanks are due to M. Edwards for the irradiation runs, to B.K. Jones and T. Sloan for assistance with the analysis and to A. Chilingarov and J. Santana for fruitful discussions. References [1] S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1969.
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