The plasma decay time in semiconductor detectors for energetic heavy ions

Nuclear Instruments and Methods 198 (1982) 547-556 North-Holland Publishing Company

547

THE PLASMA DECAY TIME IN SEMICONDUCTOR FOR ENERGETIC HEAVY IONS

DETECTORS

E.C. F I N C H , A.A. C A F O L L A * University of Dublin, Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland and M. A S G H A R Institut Laue-Langevin, 156X, 38042 Grenoble Cedex, France Received 18 September 1981

The decay times tp of the electron-hole plasmas formed in the wake of fission fragments and alpha particles stopped in a number of silicon surface barrier detectors are measured from the resulting current pulse rise times. Detector field and fragment mass and energy dependence data are presented for the five detectors used. Use of the field strength F~ at the charge centroid of the plasma column for both fragments and alphas removes or reduces a systematic detector resistivity dependence observable in the results obtained when the front face maximum detector field F0 is used as a parameter. We obtain tp~ Fc°85+-°°6 for fragments and tp ~ Fc-0"7+ 0.1 for alphas. These are slightly weaker field dependences than the commonly used inversely proportional relationship, which we too observe when Fo is used. No appreciable fragment mass dependence is observed, while the fragment energy (E) dependence is tp ~ E 0"47. These results are shown to accord with theoretical expectations.

1. Introduction The density of ionization produced in semiconductor radiation detectors by energetic heavy ions such as fission fragments or alpha particles is so great that the collection of charge is retarded by plasma effects. This is because the detector electric field is unable to disperse for several nanoseconds the dense electron-hole column formed in the wake of each fragment. As a result a neutral, field-free plasma of electrons and holes is created. The existence of the "plasma effect" was first proposed by Miller et al. [I] in order to explain long charge pulse rise times observed with fission fragments. The concept of a "plasma time" has evolved from analysis of the plasma effect and, although several definitions of the plasma time have been proposed, it may roughly be defined as the time taken for the plasma to disperse sufficiently for normal charge collection to proceed. Although the detector charge or voltage pulse can be studied to examine the effect, more detailed information can be obtained from the current pulse [2-7] as this

* Now at Physics Department, University of Virginia, Charlottesville, Virginia 22901, U.S.A. 0167-5087/82/0000-0000/$02.75 © 1982 North-Holland

directly monitors the actual motion of the carriers out of the plasma into the electric field. This permits a clearer separation to be made between plasma' decay and charge collection effects then would be possible with charge or voltage pulses. Several different methods of deriving the plasma time from the current pulse shape have been used. Examples include, for totally depleted detectors, the subtraction either linearly [3] or quadratically [4] of the calculated depletion layer charge transit time from the current width, and use of the shape of the current rise [4]. Our work here includes measurements on partially depleted detectors with a wide range of detector biases and depletion depths, and hence of field strengths and uniformities. In all cases we have characterized the plasma time by the 10-90% rise time of the current pulse, that is, the time it takes for the detector current to reach its maximum value. Comparisons between our results and existing data enable the effects of the different definitions to be examined. The time measured in these ways does not of course include any preliminary time delay which may exist between the incidence of a particle on a detector and the subsequent appearance of a pulse from the detector. This delay time has been investigated by several groups including ourselves [5-11]. The present article essen-

548

E.C. Finch et aL / Plasma decay time

tially considers the subsequent plasma "decay time". In this work are presented a wide range of measurements in several detectors for mass and energy separated fission fragments and also for alpha particles for different detector electric fields. The importance of plasma effects is not simply confined to their intrinsic theoretical interest or the influence they have on the physics of the detector charge collection process [1-4,11-18]. The resulting slowing down in the detector pulse rise time affects the use of such detectors for nanosecond timing applications, and it necessitates for example a careful consideration of pulse discriminations techniques for optimum timing performance. The existence of a plasma also increases the probability of electron-hole recombination during its lifetime, and this affects the charge pulse height response of such detectors through the pulse height defect. In refs. 19 and 20 we have discussed the relationship between the defect and the plasma lifetime.

2. Experiment 2.1. Initial m e a s u r e m e n t s

Our main aim is to observe the variation of plasma decay time with fragment energy and mass for different detector conditions. For initial measurements at Trinity College we used a spontaneously fissile 252Cf source. This provides fragments of unseparated masses and energies (it also provides alpha particles which we have also studied). Separation of such fragments can be achieved by time-of-flight techniques, for example [21], but this was not feasible in our case because of the comparatively low strength (less than 1000 fissions s - i ) of our source. However, we were able to obtain partial separation of the fragment masses and energies by an electronic discrimination method. By looking only at fragments within a small energy range one also performs a partial mass selection - for example most fragments around 100 MeV are light fragments whereas around 80 MeV most are heavy [21]. Such a selection was achieved by integration of the current pulses to give the total charge deposited, which (neglecting pulse height defect effects [21]) is proportional to the fragment energy. The resulting pulses were passed through a single channel analyser with a window set to accept pulses only of a selected narrow energy band. The current-time waveforms corresponding to these selected pulses were then displayed in a manner described in ref. 22. In this way we could separate light and heavy fragments and obtain some plasma decay time data which showed the same trends as the results given in sections 3 and 4. Our subsequent experiments were however per-

formed with fragments completely separated according to mass and energy by electromagnetic means. 2.2. M a i n m e a s u r e m e n t s

The main experiments used the focussing parabola fragment separator "Lohengrin" at the Institut LaueLangevin, Grenoble. The instrument provides fission fragments separated according to their mass, energy and ionic charge [23]. The detectors being studied are mounted one at a time on the exit slit of the separator. The specifications of the detectors, which are all manufactured by Ortec, are listed in table 1. Each detector has an aluminium collimator placed directly in front of it to prevent edge effects. The electronics used to display on an oscilloscope the shapes of the current pulses are shown in fig. 1. The bias resistor has a value of 13 M~2 except in the case of the radiation damaged detector (TF-070-400-60) where it has a value of 0.2 Mf~ because of the large reverse current. These currents are monitored on the microammeter in the Ortec 210 detector control bias unit. The Hewlett-Packard 8447D 50 [2 current preamplifier provides 26 dB of gain per stage (two stages are available) with a rise time of 0.4 ns. The output from a single stage of the amplifier is split. One half is fed directly to the external trigger of a Hewlett-Packard 1810A 1 GHz sampling plug-in mounted in a 180A oscilloscope main frame. The other half after being delayed is fed to the 50 ~2 input of the sampling plug-in. This .permits the leading edge of the current to be displayed on the oscilloscope, which would not have been possible if internal triggering had been used. The pulses are photographed for later measurements with a Tektronix C27 oscilloscope camera. This fast rise time (-- 1 ns) system can thus be used to record the shapes of current pulses produced by any particles provided they are of uniquely defined mass and energy (otherwise the sampling oscilloscope will display a mixture of traces). In our work we use the system not only for fission fragments but also for the 6.1 MeV alpha particles produced from the main decay mode of 252Cf (the other decay mode being that of spontaneous fission referred to in section 2.1). Both

BIAS BIAS RESISTOR

II -n

l~ I ]T~GER

p,l-

Fig. 1. Electronics for displaying the current pulse shapes.

549

E.C. Finch et al. / Plasma decay time

Table 1 Specifications from manufacturer of detectors used Detector

Nominal resistivity (f~m)

Active area (mm2)

Recommended normal bias (V)

Nominal resulting; sensitive depth (/~m)

Si slice thickness (/tm)

CF-040-100-60

3.42

100

65

> 60

550

CA-023-100-100

5.27

100

70

> 100

550

100 100 400

155 150 65

296 516 > 60

296 516 -

CB-022-100-300 a) CB-022-100-500 a) TF-070-400-60 b)

24.0 80.0 _

~) Designed for use as totally depleted detector; front face field when just totally depleted=0.9 V # m - i (CB-022-100-300) and 0.5 V /~m- J (CB-022-100-500). b) Detector previously damaged by 4× 109 fission fragments.

stages of amplification are however used for alpha particles because the pulses produced are smaller than with fission fragments. For fission fragments from "Lohengrin" the electric and magnetic deflection fields of the separator have first to be adjusted until the required mass and energy have been selected and separated out from other masses and energies. This is accomplished in each case with a charge sensitive electronics system attached to the detector under study, with the current measuring system disconnected. This gives, neglecting pulse height defect effects, the energy of the fission fragments selected. If the separator is not correctly adjusted a series of different energy peaks appears, each peak having also a different fragment mass. By fine adjustment of the separator fields it is readily possible to "tune out" the unwanted peaks and maximise the count rate o f the selected one. Mass and energy resolutions of 0.1% and 0.3% respectively are thus obtainable. This procedure is repeated each time a new mass and energy are required. It is possible to "tune out" unwanted fragments with the current sensitive system alone, since fragments of different energies and masses in general produce overlapping pulses of distinct shapes on the oscilloscope screen. However the charge sensitive system provides a more precise method of tuning, as well as an immediate check on the energies being received.

are read off from each photograph to an accuracy of about 10%. The plasma decay time t o is then given by (assuming the contributions to t r a r e independent of each other) tp2__ - - t r2

t2 '

where t A is the time constant of the instrumentation (cables, current amplifier and sampling unit), and is about 1 ns. This correction is usually only a few percent in magnitude. In all cases the possibility arises of a correction to the pulse rise due to the finite fall time. This effect is in fact not large, as we hope to show in a future publication. This will be true not only for totally depleted detectors, as used in earlier work, but also for partially depleted detectors. Both typ'es are used in our work (table 1). We also intend to give an analysis of the role of the current rise as a measure of the plasma decay time. The alpha particle and fission fragment energies are corrected for the small losses in energy in the gold front electrodes of the surface barrier detectors and the nickel foil mounted in front of the 252Cf source. (The nickel foil is necessary to prevent migration of the 252Cf through the vacuum chamber.) The largest effect is with fragments passing through the nickel foil, where about 5% of their energy is lost.

2.3. Data analysis

3. Mass dependence

The current pulses produced in the five surface barrier detectors by fission fragments of selected mass and energy are recorded on 320 photographs. There are also a further 50 photographs of the current pulses produced by 252Cf alpha particles and 100 photographs of 252Cf fission fragment pulses obtained with the energy selection electronics referred to in section 2.1. The 10% to 90% rise times, tr, of each current pulse

Of the various main factors examined which can influence the decay time, tp, the fragment mass dependence is considered first - in fact no significant mass dependence is observable within the range of fragment masses studied. Fig. 2 shows the plasma time as a function of mass for five light and five heavy masses for a fixed fragment energy and detector field. Any change in plasma time over the mass range studied as calculated

550

E.C. Finch et al.

/

Plasma decay time

dent term in the expressions concerned. Over the mass range considered here the fragment range varies from 12.9/zm for 60 MeV, 91 amu fragments to 11.6/.tm for 60 MeV, 143 amu fragments [24], which is a 6% decrease. This corresponds to a 6% increase in n x since the energy and hence, neglecting pulse height defect changes, the total charge deposited remains constant. Thus the expected increase in tp would be about 2%. This change would be too small to detect within the limits of the experimental method used.

tp (ns)

4. Field dependence

I

I

90

/~ l

?00

[

I

130

140 ~aS5

(a,mlU.)

Fig. 2. Plasma decay time vs mass for 60 MeV fragments in the CF-040-100-60 detector biased at 65 V.

from a least squares fit is much smaller than the error in the mean of the ten plasma times. This conclusion agrees with theoretical considerations. Refs. 3 and 15 for example predict that for a given detector field and fragment energy tp varies as nl/3 Here n x is the mean linear charge density along x ' the track [see also eq. (1)] and is the only mass-depen-

In order to determine the electric field dependence of the plasma decay time it becomes necessary to consider what is the effective field acting on the plasma. The front face field F0, for example, is simply 2 V / d , where V and d are the detector bias and depletion layer thickness respectively. However particularly for the 60 /~m and 100/xm depletion depth detectors the ranges x of a fission fragment ( - - 1 5 ~m) and alpha particle ( ~ 30/~m) are appreciable fractions of d. It will be seen that in view of the experimental results to be described a more appropriate effective field strength may be the rather lower value at the charge centroid of the plasma formed along the track. To a first approximation the electronic stopping

I

20 •

\

o CF-040-100-6V

\

•

\

1E

CA- 023-I00-I00

x CB- 022-I00-300

tp (ns)

0

9 8

0

7 6 X

5

4

I

I

I

I

I

I

0.3

0.4

0.5

0.6

0.7

0.8

I

I

0.9 1.0

I

I

1.5

2.0

Fc (V ~m-')

Fig. 3. Log-log plot of plasma decay time vs centroid field for 100 MeV fragments. Dashed line indicates Seibt's data [3] for light fragments (energy ~ 100 MeV), but as a function of front face field.

E..C. Finch et al. / Plasma decay time I

551

i

15 o

CF-040-100-60

• CA-023-I00-I00

O

* TF-070-400-60

tp (ns) 10 O

9

•

l

[

|

0.4

0.5

0.6

l

0.7

l

0.8

I

I

0.9 1.0

O

I

I

I

1.5

2.0

2.5

3.0

Fc (V~m -f)

Fig. 4. Log-log plot of plasma decay time vs centroid field for 80 MeV fragments. power and linear charge density along the plasma can be considered for fission fragments to be proportional to the distance from the plasma end away from the entrance window, the ionization decreases as a fragment

slows), and for alpha particles to the distance from the entrance window end (the ionization increases as an alpha particle slows) [15], The charge centroid is thus located a distance x / 3 along the plasma from the high

15 o CF- 040-100-60

X

•

CA-023-100-100

x CB-022-100-300

tp (ns) lC

O Q X 0

0

I

0.3

0.4

I

I

I

I

0.5

0.6

0.7

0.8

I

I

I

0.9 1.0

1.5 Fc (V ~Jrn-r )

Fig. 5. As fig. 4, but for 60 MeV fragments.

I

2-0

E.C. Finch et al. / Plasma decay time

552

i

I

,

J

i

12 tp (ns) t

10

o CF-040-100-60 •

9

CA- 023-100-100

x CB-022-I00- 300

X

~O

I

I

I

I

I

I

0.3

0-/.

0.5

0.6

0-7

0.8

I

I

I

0.9 1-0

,

1.5

Fc (V/urn -I )

Fig. 6. As fig. 4, but for 40 MeV fragments.

41

' t

i

I

10

o CF-040-100-60

9

• CA-023-100-100

8 tp (ns} 6

x CB-022-100-300

\

7

* CB-022-100-500

\ •

X

\ \ ÷ X o

\ \ •\ x

\ \ \ \

o\

o o

\ 1-5 I

0-1,5

I

l

I

I

I

I

I

I

0.2

0.3

0.4

0.5

0.6

0.7

0-8

0-9

I

i

1.0

1-5

2.0

Fe (V pm -I)

Fig. 7. As fig. 4, but for 6.1 MeV alphas. Dashed line indicates Seibrs model [3] for 5.3 MeV alphas as a function of front face field,

E.C. Finch et al. / Plasma decay time

553

Table 2 Slopes of log-log plots of plasma decay time against centroid field (slopes using front face field in brackets). Detector

Energy (MeV)

CF-040-100-60 CA-023-100-100 CB-022-100-300 CB-022-100-500

100

80

60

- 0.75 (-0.88) --0.85 (--0.96) -- 0.79 (--0.82) .

- 0.82 (-0.93) -0.91 (--0.99) -

- 0.93 ( - 1.03) -0.95 (-- 1.03) -- 0.88 (--0.91) .

TF-070-400-60

.

-

Mean Slope

. --0.80 (-0.87)

-0.80--+0.05 (-0.90-+0.07)

-0.83--+0.06 (-0.93-+0.06)

40

-0.92--+0.03 (-0.99-+0.07)

6.1 a) -

-0.89 (--0.93) -- 0.83 (--0.86) . -0.86-+0.04 (-0.89-+0.05)

- 0.59 ( - 1.13) --0.74 (-- 1.21) -- 0.58 (--0.74) 0.78 (--0.85) -0.7-+0.1 ( - 1.0-+0.2)

a) Alpha particles. ionization end. Since the detector field varies linearly with distance between values 2 V / d at the entrance window and 0 at the other end of the depletion layer, the centroid field is given by Fc=-~(1--~)

x

and

~(1--~),

2x

for fission fragments and alpha particles respectively. Figs. 3 - 7 show l o g - l o g plots of tp as a function of F~ for fission fragments of different energies and for 6.1 MeV alpha particles. In the fragment plots each data point represents tp averaged over all the masses examined at the given field value. We do this because tp is essentially independent of mass over the fragment mass range (section3). The error bars show the standard deviation in the average value of the decay time. Table 2 lists the slopes of these graphs as determined by least-squares fitting. The overall average slopes for all fragments and for alphas are - 0 . 8 5 - + 0 . 0 6 and -- 0.7 -+ 0.1 respectively, i.e., tp ~ Fc-0"85 for fragments and tp ~ F~-°'7

for alphas.

The slopes obtained if the front face field F 0 rather than the centroid field F~ is used are also given in table 2. In this case the overall average slopes become -0.94-4-0.07 and - 1 . 0 -+ 0.2 for fragments and alphas respectively. Two representative plots of log tp VS log F 0 are shown in figs. 8 and 9. The conclusions to be drawn from this data thus depend on how the detector field is defined. (The TF070-400-60 detector is treated as a special case later.) If the front face field F 0 is used then the plasma decay time, within the limits of experimental error, is inversely

proportional to the electric field. This is in agreement with the theoretical models and experimental work of other authors [3,4,12,15-17]. However, it can be seen that there appears to be a distinct detector dependence observable, with the decay time increasing at constant field as the resistivity (i.e. depletion layer thickness) decreases. The decay time increases is therefore occurring as the, field further inside t h e depletion layer is decreasing. When the centroid field F¢ is used then a smaller detector dependence is observable. However the field dependence is now weaker than inversely proportional, because at low fields and therefore thinner depletion layer thicknesses F¢ is reduced more strongly below F 0 than at higher fields. It would therefore appear that F~ is a more appropriate parameter to consider than F 0, especially when the field varies appreciably along the plasma column. This would concur with theoretical predictions and with existing results for detectors where F 0 --F~ [3,4] in that no detector dependent effects are anticipated. It can be seen that in general there is broad agreement between the magnitude of our results and the work of Seibt et al. [3] (figs. 3 and 7) (although especially for fragments our results appear to be a little lower). Experimental agreement with the alpha data of Williams et al. [4] in the limited region of field overlap is also quite good. This would indicate that the several methods of deriving the plasma time from the current pulse shape (section 1) can turn out to give in general terms equivalent results. We note that our fragment times are a factor of about 3 longer than for alphas, in distinction to the much larger factor predicted by Seibt's model. This confirms Seibt's well established conclusion that the simple cylindrical charge erosion geometry assumed in

E.C. Finch et al. / Plasma decay time

554 15

o CF -01.0-100- 60

X

• CA-023-100 -I00 x CB-022-100-300

tp (ns) 10

9

7 O

sl 5~

O

O

3 I

I

I

I

I

I

I

I

I

I

0-3

0./4

0-5

0.6

0-7

0.8

0.9

1.0

1.5

2.0

Fo (V pro-')

Fig. 8. L o g - l o g plot of plasma decay time vs front face field for 60 MeV fragments.

10

9

o C F - 0&0-100- 60 • CA - 023 - 100 - 100

8

x CB-022-100-300 7 tp (ns)

+ CB- 022 - t00 - 500 O

6 @

X

@ ÷ X

0

0

O O

!

0.15

I

[

I

I

I

i

I

I

0.2

0,3

0.4

0-5

0,6

0.7

08

0-9

Fig. 9. As fig. 8, but for 6. I MeV alphas.

I

1.0

Fo (V pm-h

I

I

1.5

2.0

555

E.C. Finch et al. / Plasma deca~' time

The slopes of these plots are the same within experimental error for each detector, giving an average of m =0.47---0.01, i.e., t p ~ E °'47 in the range studied. This is in agreement with other experimental results, in which it is concluded that 0.3 < m < 0.5 [12]. The detector dependence observable in fig. 10 would, as in section 4, be lessened if the centroid field were used. This result is in agreement with theoretical expectations. From refs. 3 and 15 it can be seen that

his model is not applicable to short range particles such as fragments. At the lowest fields a decrease in the field dependence of tp for alphas may be observed. For the F and A series detectors this may be explained by the influence of punch-through effects, which occur below 0.12 and 0.09 V/tin-~ respectively. This corresponds to when the depletion layer thickness becomes less than the alpha range. As a result the number of charge pairs created in the depletion layer (the detector sensitive volume) decreases; thus a shorter plasma decay time may be expected, giving a decrease in the field dependence. This effect will be especially significant for alphas since the maximum ionization occurs at the end of their tracks. Field funnelling, especially for comparatively lightly doped silicon as used in detectors, may reduce such punch-through effects [25]. Nevertheless at fields around (and even just above) punch-through, non-linearities such as we observe are not surprising, since it is just then that the field variation along the plasma track is becoming large, thus making the definition of an effective detector field rather critical. The radiation damaged detector (TF-070-400-60), although it shows the same field dependence as for the other detectors, has generally longer plasma times, presumably because of the resulting reduced charge mobility slowing the plasma erosion rate.

/

~xl/3

tp~nxl~

)

,

(1)

where, as in section3, n x is the mean linear carrier density, given by E/x,

n x ~

(2)

x being the particle range. In the LSS theory for partially ionized ions [26] the electronic stopping power -dE/dx varies as E 1/2, which leads to (neglecting atomic collision losses) (3)

x ~ E 1/2

for a given ion. Thus from eqs. (1)-(3) we obtain tp~El/2.

In fact the dependence of - - d E / d x on E is less strong for fission fragments than predicted by LSS (cf refs. 19, 24 and 27); - d E / d x ~ E °'4 would be a better fit. This gives x ~ g 0'6,

5. Energy dependence

(rather than E °'5) and hence (perhaps rather fortuitously!)

Fig. 10 shows tp plotted against the fragment energy E for three detectors at the same front face field. Each point gives the mean time averaged over all the masses studied at the given energy (section 3 and cf. section 4).

tp ~ E 0"47. These trends are clearly reproduced by our results. i

9

i

8 7

O

!

tp (ns) 6

o C F - 040-100-60

3

• CA- 023-100-100 x CB-022-100-300 I

20

1

30

I

40

50

-

I

[

I

60

70

80

I

I

90 100

E (MeV)

Fig. 10. Log-log plot of plasma decay time vs fragment energy at front face fields of 1.05 V #m- ~.

556

E.C. Finch et al, / Plasma decay time

6. Conclusions We have considered primarily the energy, mass and detector field dependence of the plasma decay time for several surface barrier detectors over the energy and mass ranges accessible by fission fragments. In general there would appear to be broad agreement between the experimental results obtained and theoretical expectations. However the work does show the importance of defining carefully what is meant by the detector field strength when the field varies significantly over the length of the plasma column. Use of the field strength at the charge centroid of the plasma column for fragments and also for alpha particles removes or reduces a systematic detector dependence observable in the results obtained when the front face maximum detector field is used as a parameter. It also however makes the dependence of the plasma time on the field somewhat weaker than the commonly used inversely proportional relationship. We have pleasure in thanking the many people who have helped us in this work, especially Prof. C.F.G. Delaney (T.C.D.), who has given us invaluable advice and assistance throughout. For their support we also thank G.E. Nolan, S. Currivan and T. Burke (T.C.D.), P. Perrin (C.N.R.S. Grenoble), M. Forte (J.R.C. Ispra) and the staff of I.L.L. Grenoble involved in the work. The National Board for Science and Technology, Ireland, and C.N.R.S., France, have given financial grants, and one of us (A.A.C.) acknowledges receipt of research student maintenance allowances from Trinity College and the Irish Department of Education.

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[3] W. Seibt, K.E. Sundstr/Sm and P.A. Tove, Nucl. Instr. and Meth. 113 (1973) 317. [4] R.N. Williams and E.M. Lawson, Nucl. Instr. and Meth. 120 (1974) 261. [5] H. Henschel, H. Hipp, A. Kohnle and F. G6nnenwein, Nucl. Instr. and Meth. 125 (1975) 365. [6] H. Henschel and R. Schmidt, Nucl. Instr. and Meth. 151 (1978) 529. (7] L. Hannappel, H. Henschel and R. Schmidt, Nucl. Instr. and Meth. 151 (1978) 537. [8] A. Alberigi Quaranta, A. Taroni and G. Zanarini, Nucl. Instr. and Meth. 72 (1969) 72. [9] M. Moszynski and B. Bengtson, Nucl. Instr. and Meth. 91 (1971) 73. [10] H.-O. Neidel and H. Henschel, Nucl. Instr. and Meth. 178 (1980) 137. [l 1] E.C. Finch, C.F.G. Delaney and M. Asghar, IEEE Trans. Nucl. Sci. NS-27 (1980) 286. [12] A.H. Krulisch and R.C. Axtmann, IEEE Trans. Nucl. Sci. NS-14 (4) (1967) 58. [13] P.A. Tove, and W. Seibt, Nucl. Instr. and Meth. 51 (1967) 261. [14] A. Taroni and G. Zanarini, Nucl. Instr. and Meth. 67 (1969) 277. [15] E.C. Finch, Nucl. Instr. and Meth. 121 (1974) 431. [16] V.K. Eremin, N.B. Strokan and N.I. Tisnek, Sov. Phys. Semicond. 10 (1976) 33. [17] H. Meyer, IEEE Trans. Nucl. Sci. NS-13 (3) (1966) 180. [18] A. Alberigi Quaranta, A. Taroni and G. Zanarini, IEEE Trans. Nucl. Sci. NS-15 (3) (1968)373. [19] E.C. Finch, Nucl. Instr. and Meth. ll3 (1973) 41. [20] E.C. Finch, M. Asghar and M. Forte, Nucl. Instr. and Meth. 163 (1979) 467. [21] See for example E.C. Finch and A.L. Rodgers, Nucl. Instr. and Meth. 113 (1973) 29. [22] A.A. Cafolla, Thesis, University of Dublin (1978). [23] E. Moll et al., Nucl. Instr. and Meth. 123 (1975) 615. [24] L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233. [25] C.M. Hsieh, P.C. Murley and R.R. O'Brien, IEEE Electron Dev. Lett. EDL-2 (1981) 103. [26] J. Lindhard and M. Scharff, Phys. Rev. 124 (1961) 128. [27] C.D. Moak and M.D. Brown, Phys. Rev. 149 (1966) 244.