CDF/DOC/TRACKING/PUBLIC/6287
version 1.1
Jan.30, 2003

Characteristics of Prototype Silicon Sensors for Run2b (II)N. Bacchetta1, G. Bolla4, D. Bortoletto4, A. Canepa4, B. Flaugher1, I. Gorelov3, K. Hara5,
M. Hoeferkamp3, D. Pellett2, S. Seidel3, Y. Takei5, P. Watje3
1

Fermilab, Batavia, Illinois, USA
University of California, Davis, California, USA
3
University of New Mexico, Albuquerque, New Mexico, USA
4
Purdue University, West Lafayette, Indiana, USA
5
University of Tsukuba, Tsukuba, Ibaraki, Japan
2

Abstract
Five prototype silicon sensors were irradiated with neutrons up to 1.4 × 1014 n/cm2, as a part ofthe sensor quality assurance program for Run2b silicon detector. This note describes thecharacteristics of irradiated sensors. We comment on charge-up susceptibility of the new sensors
which employ wafers in <100> direction.

1. Introduction
The prototype sensors are AC coupled and single-sided, which are designed to have lifetime
extending to the end of Run2b. Due to the intense radiation, the full depletion voltage will, after
type inversion, increase up to about 200V (100V) at 15 fb-1 and to 380V (200V) at 30 fb-1 for theL0 (L1) sensors located 2 cm (3 cm) from the collision point. These estimates include a safetymargin of 1.5 in the radiation fluence. The corresponding 1 MeV equivalent neutron fluence at L0
is 1.4 × 1014 n/cm2 after 30 fb-1. This note describes the electrical performance of five sensors
irradiated with neutrons. The evaluations were performed at three universities, Tsukuba, Purdueand New Mexico. Characteristics of non-irradiated sensors are reported in CDF note 6286.
Long-term stability tests have been initiated to test the leakage current stability and durabilityof the coupling capacitors. The status results are presented.
In the early stage of testing, we experienced some charge up problem. The present sensors
which employ <100> wafers seem to have more susceptibility than for <111> wafers. Somepreliminary observations to understand this phenomenon are described.

2. Performance of Neutron-Irradiated Sensors
2.1 Neutron Irradiation
We have irradiated 5 prototype sensors with neutrons at MNRC Irradiation Facility at UC
Davis on September 27, 2002. Three of the sensors (Sensor Number 060, 063, 069) received-2
1.4 × 1014 cm 1-MeV neutron equivalent fluence and the other two (Sensor Number 001, 002)

15

-2

0.7 × 10 14 cm 1-MeV equivalent. The irradiation time was 69 min in total. The actual doses

1

evaluated by sulfer activation are (0.67 ± 0.02 ) × 10 and (1.40 ± 0.02 )× 10 n/cm .
The irradiated sensors were stored at a low temperature (-7oC). The sensor temperature wasthen increased for certain periods so that the sensors should almost complete the initial annealing
and to have the full depletion voltage almost at the minimum. The three sensors irradiated to22
1.4 × 1014 n/cm were characterized at Purdue, and the two irradiated to 0.7 × 10 14 n/cm at UNM
and Tsukuba.
Characterization of irradiated sensors is not straightforward due mainly to existence of large
surface charges and total leakage current. One guideline is to cool down the sensors to besensitive to the intrinsic properties which we want to evaluate. Tsukuba and Purdue Groups haveused environment chambers for this purpose. Connections to only limited number of channels
were provided by wire-bonding. Purdue Group has used in addition a cooled chuck so thatprobing is still possible. UNM Group has measured quickly at room temperature, and sent the
samples to Tsukuba Group for further testing.
14

14

2

2.1 Total Leakage Current

n irradiation 002

1000

100000

Dtc 60
Dtc 69Dtc 63

10000

Measured at 13degC
Data Renormalized to 20degC

Leakage Current (uA)Leakage current (uA) at T=20degC

Figure 1a shows I-V curves of three sensors irradiated to 1.4 × 1014 n/cm2 measured at 13oC but
the currents are renormalized at 20oC. The three sensors have been annealed at room temperaturefor 1700 min (060), 1200 min (063) and 2800 min (069). Sensor 069 has experienced additional
annealing at higher temperature (4 min at T=80oC) to complete the initial annealing, which
explains smaller leakage current than others. Figure 1b shows I-V curves of one of the sensors(002) irradiated to 0.7 × 10 14 n/cm2. The temperatures were in the range –30 to –10oC. This sensor
was kept at room temperature so that the initial annealing should have completed. The two
sensors 063 and 069 showed a gradual leakage current increase at 490 V and 180V, respectively,

1000-10 degC-15 degC-20 degC-25 degC-30 degC

100

10

1

100

0

2 00

4 00

6 00

8 00

1 00 0Bias Voltage (V)Fig. 1a I-V curves of three sensors irradiated to 1.4 × 1014
n/cm2. The data are renormalized to T=20oC. Note
different annealing time for 69 (see text).

0

200

400
600
800
Bias Voltage (V)1000

Fig. 1b I-V curves of a sensor irradiated to
0.7 × 1014 n/cm2. HV was raised to 1 kV only at–15 and –30oC.

1

The error does not account for the error in sulfer activation cross section. Also, the uncertainty arising whentranslating the damage at different energies to that at 1 MeV is not added: The neutron energy spectrum has a peak at 1
MeV, ranging from 1 eV to 10 MeV.

16

before irradiation. As shown in Fig. 1a the onset voltage of Sensor 069 is shifted toward higher
voltage 350V. It is not very distinct for 063 since the increase is moderate. We note that 060, 002
and 001 (not shown) have I-V curves extending to 1000V without any micro-discharge.
Previous studies have shown that the leakage current of irradiated sensors decreases(annealing) with time approaching to an asymptotic value. The damage constant α is expressedby α = φ ⋅ ∆I / V , where φ is the neutron fluence, ∆I is the increase in the total leakage current
measured at full depletion voltage, and V is the volume of the sensor. Because of the features ofannealing and temperature dependence of the leakage current, α is usually calculated after theannealing is almost completed and at 20oC.
Systematic study of the annealing phenomena is available such as from Rose Collaboration. At
room temperatures, the current decreases substantially within a month, approaching to an
asymptotic damage constant of 3 × 10 −17 A/cm.
The present results are used to evaluate the neutron fluence. Using 069, which has beenannealed extensively, the fluence is evaluated to 1.1 × 10 14 /cm2 for nominal of 1.4 × 1014 /cm2.
Similarly with use of 001 and 002, and other data measured at different annealing, the neutron
fluence is evaluated to (0.33-0.64) × 1014 /cm2 for nominal of 0.7 × 10 14 /cm2. The present results
prefer somewhat smaller neutron fluence but are in reasonable agreement.

2.2 Full Depletion Voltage
The measurement of full depletion voltage is strongly affected by high leakage current andtherefore is performed in the environmental chamber at –25oC. For Sensor 060, the LCR is set to
f=1kHz and VAC=1V, and the full depletion voltage is calculated from the 1/C2 –Vbias plot. The
obtained value is then normalized to the nominal frequency and temperature f=10kHz and T=20o
C (ROSE/TN/2000-10). The normalized full depletion voltage is 128 V. Sensor 063 showedsimilar value of 130 V.
The curves for 0.7 × 10 14 /cm2 sensors are taken with the LCR frequency of 100 Hz. Since thecurves are quite dependent on the temperature and somewhat on the LCR frequency, we do not
quote the full depletion voltage. The two sensors, though, show a full depletion consistent witharound 50V.
Time evolution of the full depletion voltage is calculated using the parameters given by ROSE
Collaboration. Appendix summarizes the equations and the parameters we used, where the plots
are also given. In the present calculation, we assume that the initial full depletion voltage is 150 V
and the sensors are irradiated to equivalent neutron fluence of 0.7 × 10 14 /cm2 or 1.4 × 10 14 /cm2. We
expect that the full depletion voltage be around 40V and 120V, respectively.
n irradiation

1/C^2

0.8

1.0

0.7
0.8

1/C(nF)2

0.6

0.6

Sensor 060

0.4

f =1kHz &ACVoltage =1V @T = -25C

001

0.5

002

0.4
0.3

T= -25degC
f=100 Hz

0.2

0.2

0.1
0.0

0.0

0

50

100

150

Bias Voltage (V)

200

250

0

100

200

Bias Voltage (V)Fig. 2 1/C2-V curves of n-irradiated sample. (Left) 060 Sensor and (Right) 001/002 Sensors. Note the differenceof C at plateaux is due to the frequency settings.

17

2.3 Poly-silicon Resistance
The poly-silicon resistance is measured and compared before and after irradiation. Figure 3
shows the bias dependence measured for a particular strip. Although the resistance is set saturated
at about 100V before irradiation, it requires much larger bias voltage, about 350V, to reach thesaturated value. The intrinsic poly-silicon should not be degraded but the surface charge
obviously degrades the isolation after irradiation. The measured poly-silicon resistance after
irradiation seems slightly smaller. Again, we interpret this is due to that the surface isolation isdegraded. In any case the changes are small and acceptable.
2.E+06

Bias Reistance (Ohm)Bias Resistance (Ohm)

2.0E+06

1.E+06

1.0E+06

sensor 63
Before Irradiation

sensor 60 before
sensor 63 before
sensor 63 after

After Irradiation

sensor 69 after

0.0E+00
0

100

200

300

400

500

600

700

800

0.E+00-250-150Bias Voltage (V)

-50

50

150

250

strip # (from D250 to U250)

Fig. 3 (Left) Bias resistance measured as a function of bias.(Sensor 063) . (Right) Bias resistance versus strip
number.

2.4 Interstrip Resistance
The interstrip resistance is one of the key parameters to evaluate the radiation effect on silicondetectors. The oxide layer between strips accumulates positive charges created due to radiation,
which degrades the interstrip resistance.
Figure 4a shows bias dependence of the resistance. The plots show the temperature dependence-25degC-20degC

82n001
Strip Isolation (Gohms)

Interstrip Resistance (Gohms)

10-15degC-10degC

64
2

T= −10degC

n001-n51n001-n4n001-n3n001-n2n001-n1

0

0
0

100

200
300
Bias Voltage (V)

400

0

100

200

300

400

500

Bias Voltage (V)Fig. 4b Interstrip resistance as a function of bias voltage. (Left) Temperature dependence
measured for 001 Sensor. (Right) channel dependence measured at –10oC.
18

(Sensor 001) and variations among strips (Sensor 001) measured at –10oC. The resistance issubstantially degraded: it is greater than 40 GΩ before irradiation. In order to keep the resistanceto be more than 1G Ω, bias of 250V (50V) is required at –10oC (–25oC). Since the oxide charge
plays the essential role whose effects should be larger at higher temperatures, we have to respect
the temperature where we evaluate the interstrip resistance. Although the bias voltage 250V issubstantially larger than the full depletion voltage of 50V, where we naively expect that the strips
are isolated, the required voltage is small enough and manageable.

2.5 Interstrip Capacitanceafter irradiation T=14C
f=1MHz & AC signal = 5V

7.0E-12sensor 63 U250
sensor 63 D120
sensor 60 U256

6.5E-12Interstrip capacitance (F)Figure 5a shows the bias
dependence of the interstrip
capacitancemeasuredforparticular sets of neighboring
strips. The LCR frequency is 1
MHz. The shoulders around
130V are consistent with the full
depletion voltage. The interstrip
capacitance decreases graduallywith bias voltage, approaching toasymptotic values consistent
with those of non-irradiatedsensors. The asymptotic value is
3.3 pF (3.17 pF) for Sensor 063(Sensor 060), which is to becompared with 3.4 pF (3.46 pF)
obtained before irradiation. We
notice, though, that the bias
should be substantially larger
than the full depletion voltage toreach the asymptotic value.

6.0E-12After Irradiation
Depletion Voltage
sensor 63 V = 130V

5.5E-125.0E-12

Cint: Before Irradiation
sensor 63 3.17 +/- 0.01 pF
sensor 60 3.46 +/- 0.17 pF

sensor 60 V = 128V

After Irradiation
sensor 63 3.3 pF
sensor 60 3.4 pF

4.5E-124.0E-12
3.5E-123.0E-12
0

100

200

300

400

500

600

700

800

900 1000

Bias Voltage (V)Fig. 5a Interstrip capacitance of irradiated 063 and 060 sensors,
measured as a function of bias voltage.

n002
10

10
1-2

8

8

8-9

6

6-7
7-8

4

Cint (pF)

Cint (pF)

2-3
6
4
2

2

0

0
0

100

200

300

Bias Voltage (V)

400

500

10

100

1000

LCR frequency (kHz)Fig. 5b (Left) Interstrip capacitance for sampled strips of Sensor 002. The LCR frequency is 1MHz.
o(Right) Frequency dependence of interstrip capacitance at bias of 300V. The temperature is –25 C.

19

Figure 5b shows the interstrip resistance of Sensor 002 measured as a function of bias with
LCR frequency of 1 MHz. Again, a bias substantially larger than the full depletion voltage (about
50V) is required to reach the asymptotic value. From the frequency dependence, measured atbias voltage of 300V, it is still possible that the interstrip capacitance decreases further if the LCR
frequency is raised.

1.5E-10Figure 6 shows the uniformity of thecoupling capacitance measured after
irradiation. The data are shown for two
sensors. The average values measured on
Sensor 060 and 069 are 136.3 ± 1.2(134.4 ± 0.5) pF and 134.5 ± 5.3(126.5 ± 1.0) pF after (before) irradiation.
The data before and after are comparable
for both sensors. Similarly, essentially no
degradation is observed also for Sensor
001 and 002.

Coupling Capacitance (F)2.6 Coupling Capacitance

1.0E-10

Sensor 60 f=100Hz
Sensor 69 f=100Hz
5.0E-11After Irradiation
f=100kHz &ACVoltage =1V
0.0E+00
-250

-200

-150

-100

-50

0

50

100

150

200

250

strip # (fromD250 to U250)

Fig. 6 Coupling capacitance versus strip number,measured for Sensor 060 and Sensor 069.

2.7 Summary of Irradiation Tests
We have characterized various electrical parameters of the sensors irradiated with neutrons up
to 1.4 × 1014 n/cm2. The full depletion voltages are uniform among the samples irradiated to thesame dose, and are consistent with previously known values. Many parameters such as interstrip
capacitance, interstrip resistance, and bias resistance are apparently degraded to some extent due
to positive charges accumulated in oxide layer and type inversion.
The p+ strips are in the ohmic contact side after the bulk is inverted to p type. The strips are notwell isolated unless the bulk is fully depleted. However, we expect that the interstrip capacitanceand other parameters should reach rapidly the asymptotic values if the bias exceeds the full
depletion voltage. Our observation is that this transient is moderate and it requires additional
voltage to reach the asymptotic value. Consequently, we need to set the bias at substantiallylarger than the full depletion voltage to obtain best detector performance. Typically a bias of 250300V is required for the depletion voltage of around 130V.
Hamamatsu sensors, which show superior durability against high voltages, are best suited forour application, and fulfill the specifications required for Run2b Detector.

20

3. Long-term stability tests
The long-term stability tests have been initiated at Tsukuba and UNM. At Tsukuba, eight
sensors (4 axial and 4 stereo sensors) are biased for nearly two months. The bias-ring and Nsub
pad, a pad resistively coupled to the back-plane, are wire bonded to external traces to which+500V is applied with the bias-ring at ground. In addition, in order to test the oxide durability, 30
AC pads per sensor are wire-bonded to an external electrode to which +100V is applied. The
setup is placed in an environment chamber at 20oC. At UNM, two axial sensors are biased. The
stability test consists of two one-week long sets, one set for coupling capacitance durability where
120V was applied across the DC and AC pads of adjacent four strips, and another set for leakage
current stability where 500V was applied between the back-plane and the bias-ring.

3.1 Leakage Current Stability
The leakage current stability data obtained by Tsukuba Group are shown in Fig. 5a. The data
were taken typically once per day. When Vcp (=100V) is applied across the AC pad and theimplant electrode, the total leakage current increases substantially, typically to 100 µA whereas
the leakage current without Vcp is less than 1 µA. Actually this increase, evident for Vcp above
80V, is reproducible and uniform among the eight sensors. We employ extended Al electrodestructure, which makes the electric field at this region strong and initiates micro-discharge.
Therefore, we set Vcp to zero when we take the leakage current data. Since Dec 7, we decided toturn off Vcp for typically 1 hr prior to the leakage current measurement. After that the leakage
current became fairly stable.
The stability data obtained by UNM Group are shown in Fig. 5b, where temperature data areplotted together. We observe that the leakage current of both sensors tracks very closely thevariances in temperature, and that when the temperature is fairly stable so is the value of sensor
leakage.
Comparing the two results, we notice that the Tsukuba sensors are less stable. Also some ofsensors, e.g. S23 and A54, have a tendency to increase the leakage gradually. Such a variation
could be explained by fluctuation of micro-discharge onset voltage. However, we measured I-V
curves and observed that no sensors show micro-discharge up to 1000V. We suspect that edge
current may be continuously high as Nsub pad is used for biasing.
10
S 25
S 23
A12
Leak Current at 500V (uA

A54
A23
1

A29
S 57
S 53

0 .1

Switched off Vcp for ~1hr prior to I meas.
0 .0 11 2 /3 /2 0 0 2

1 2 /1 7 /2 0 0 2

1 2 /3 1 /2 0 0 2

1 /1 4 /2 0 0 3

1 /2 8 /2 0 0 3

Fig. 5a Leakage current stability for eight sensors biased at 500V. Note the change in themeasurement procedure (see text) after 2002/12/07.
21

Fig. 5b Leakage current stability for two sensors. The temperature (RHS) is shown ingreen.

3.2 Coupling Capacitor Stability
The coupling oxide punch-through is specified not to occur below 100V. Although, in ourapplication, no voltage is applied to the oxide, this requirement is retained in engineering point ofview to ensure that the process is properly completed: HPK oxide layers should stand up to100V.
HPK applies 120V across the oxide for 1/6 sec (actually they do twice, so in total 1/3 sec) inorder to ensure the durability at 100V for years.
The coupling capacitor stability is measured to find out how robust the coupling capacitors arewhen subjected to worst case conditions, applying 120V between the AC and DC pads. Fouradjacent strips are ganged together. The results are shown in Fig. 6c, where the leakage current
with the applied voltage is seen to be much less than the 1 nA level. Figure 6d plots the values ofthe four coupling capacitors which had the 120V potential applied, along with their neighbors. A
decrease of approximately 1.5% is seen. It is possible that our measurement, made 0.5 h afterswitching off the 120V, have recorded transient values before the oxide condition is stabilized.
Among the eight sensors with 100V applied for nearly two months, one axial sensor A23 failed
after one day due to punch-through. This is unfortunate but HPK testing of axial sensors wasincomplete (See CDF 6286) to ensure 100V durability. Since then, no other sensor showedcreation of punch-through.

Fig. 6c Leakage current through four coupling capacitors
at neighbor. 120V is applied across the coupling
capacitors. The temperature was stable within 2oC
during this test.

Fig. 6d Coupling capacitance values compared
before and after the 7-day durability test. The
central four strips had 120V on them.

224. Effects of Charge-up
In early stage of testing, we
recognized that the sensors are easier
to charge up compared to ISL/L00
sensors. This tendency was observed
at Tsukuba and Purdue (UNM



recorded some hint of the effect).
Figure 10a is an example of suchdata obtained at Tsukuba. In this case,typically 30-40 central strips showed
smaller resistances (R in the figure).
Also some non-uniformity is seen for
the coupling capacitors (Ccp) in the









same region. From the location and
spread, Tsukuba Group suspectedthat the vacuum tweezers used toFig.10a Example AC scan plot for a sensor with charge-up.
pick up the sensor was causing thetrouble. After eliminating use oftweezers, this effect turned to be hard to appear2.
The charge-up mechanism can be explained that a thin p-type layer, an inversion layer, iscreated on the surface of n-type bulk by external static charges. This deteriorates the electricalisolation between strips, which was actually identified from strip isolation test as well. This typeinversion is easier to occur for <100> than for <111> because the positive charge trapped at the
Si-SiO2 interface and fixed oxide charge in SiO2 layer are about one order abundant for <111>3.
This explains qualitatively why we did not see charge-up for ISL/L00 sensors, which employ<111> wafers. It is important to note that HPK is checking the isolation for every strip. This
insures that the isolation degradation must have occurred during handling. Actually all the sensors
have recovered from charge-up when they were placed back in the envelope which is used by
HPK at sensor delivery. But it is also the observation that the charge-up can remain for long time
if the sensor is just kept on the test stage.
The inversion layer could remain for a long time if there is no route for the charges to move. In
our detector application, though, there are a couple of routes possible: (1) Al electrodes areconnected to ASICs, (2) Signal currents are created by particles passing through, and (3) Positive
ions are accumulated in oxide layer due to radiation. The positive ions (3) attract electrons at theoxide-silicon boundary, thus removing the inversion layer.
Purdue Group observed irregular resistance values for one sample. This sample was thenirradiated with neutrons. As shown in Fig. 10b, a cluster of strips which initially showed small
resistance have recovered to nominal resistance after irradiation. Although it is probable thatcharge up effect disappeared by other effects, an assumption is that positive charge trapped in thesilicon dioxide helped to diminish the inversion layer ((3) described above).
We have made several tests such as to investigate time constants for the inversion layer todisappear. The tests included studying the effect of wire-bonding simulating the connection to
ASICs, of epoxy applied on the surface for hybrid gluing, and of UV illumination. Preliminary
observations we have are:(1) Inversion layers seem to diminish quickly if the sensors are wire-bonded.

2

Four consecutive sensors showed similar effects before Tsukuba Group stopped using tweezers. Since
then, we observed degraded isolation for a couple of strips but much less frequently. We suspect probe tips
which were not properly discharged before use caused this. Recently, in order to carry out the study
described here, we are back to use the same tweezers to intentionally reproduce charge-up sensor but failed.
3
See, for example, S. M. Sze, “Semiconductor Devices”: John Wiley & Sons 1985.
23

(2) If the sensors are not wire-bonded, the surface charge could remain at least for days.
(3) Removal of inversion layer is accelerated if the sensor is illuminated with UV.
(4) Epoxy on the surface helps to remove the charge, but too much epoxy degrades thesurface isolation, which in turn makes the sensor easily affected by external conditions.
The above are preliminary since the study is not complete. We tried to carry out more
systematic studies, but failed to do because we have not succeeded to reproduce charge-up
sensors. Comparing the easiness of charge-up we encountered at earlier time, the sensors, threemonths after delivery, must have changed the susceptibility. One of such changes could be thatoxide layer has accumulated positive charges enough to prevent the sensor from charge-up.

Fig.10a Poly-silicon resistanceversus strip number. While some
irregular values before irradiation(blue circles) indicate existence of
charge up, the resistance is uniform
after irradiation (red triangles).

Bias Reistance (Ohm)

2.0E+06

1.0E+06

0.0E+00
-250

-150

-50
50
strip # (from D250 to U250)

150

250

5. Conclusions
We have evaluated the electrical performance of prototype silicon sensors fabricated for the
SVX2b Detector. As shown in this note and in CDF-6286, the prototypes fulfill our specifications.
Five sensors irradiated with neutrons are characterized. The performance after irradiation isconsistent with characteristics previously known. Because of bulk type inversion and positive
charge accumulation, we require a bias voltage of typically 200V (full depletion is about 50V) for
the sensors irradiated to 0.7 × 10 14 /cm2 and 300-350V (full depletion is 130V) for those irradiatedto 1.4 × 1014 n/cm2 in order to accomplish the best electrical performance.
We have addressed susceptibility of sensors against charge-up. It seems this susceptibility isdegraded with time and the effect should diminish when the sensors are wire-bonded to ASICs.
We need to pay attention not to create charge-up.

24

Appendix. Equations used to calculate evolution of full depletion voltage
The full depletion voltage of silicon sensor with thickness of d is given by
V FD =

N eff ed 22εunder planer diode assumption. Here permittivity of silicon is ε = 11.9 × 8.85 × 10 −14 F/cm. The
same equation is used to calculate the initial impurity density N eff 0 using the initial full depletion
voltage (150 V).
The initial n type impurity density decreases with radiation (and time) since new levels ofdisplacement damages induced by radiation act as effectively p type:
N eff = N eff 0 − N damage (φ , t , T )The radiation effects can be classified into three types.
N damage (φ , t , T ) = N c (φ ) + N a (φ , t , T ) + N Y (φ , t , T )The first effect is stable damage, representing increase of donor type impurities and creation of
acceptor type impurities, which is expressed by the following equation:
N c (φ ) = N c 0 (1 − exp( −cφ ) ) + g c φ

The fraction N c 0 / N c refers to “incompleteness” in donor removal.
The second effect is short-term annealing after irradiation.
N a (φ , t , T ) = g a φ exp(− k a 0 t exp(− E aa / k B T ))where the model assumes activation energy E aa and time constant k a 0 .
The last effect is long-term reverse annealing:1N Y (φ , t , T ) = g Y φ 1 − 1 + k Y 10 t exp(− E aY / k B T ) 
The parameters used in the calculation are listed below.
N c 0 = 0.65 N eff 0
c = 1.1 × 10 −13 cm2
g c = 1.49 × 10 −2 cm-1

g a = 1.81 × 10 −2 cm-1
g Y = 5.16 × 10 −2 cm-1
k a 0 = 2.4 × 1013 s-1
k Y 10 = 1.5 × 1015 s-1
E aa = 1.09 eV
E aY = 1.33 eV

25

200

Full Depletion Vol (V)T=20degC
150

T=10degC
T=0degC
T=-10degC

100

50

0
1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08Time since irradiation (sec)Fig. 12c Evolution of full depletion voltage since completion of irradiation.
Parameters are taken from ROSE Collaboration. Initial full depletion voltage 150V,
and neutron fluence 0.7 × 1014 /cm2.

1h

1day

1mon

1yr

300

Full Depletion Vol (V)

250
200
150
100
50
0
1.E+03

T =20degC
T =10degC
T =0degC
T =-10degC
1.E+04

1.E+05

1.E+06

1.E+07

1.E+08T ime since irradiation (sec)

Similar to Fig. 11e, but for neutron fluence 1.4 × 1014 /cm226