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Defect energy levels from current transient recording
Nuclear Physics B (Proc . Suppl.) 23A (1991) 333-339 North-Holland
333
Defect Energy Levels from Current ~ansient Recording Michael Momayezi DESY, 2000 Hamburg 52, Germany Silicon detectors are widely used in high energy physics in vertexing and calorimetry applications . The radiative environment will introduce defects with energy levels in the bandgap into the crystals. At the high levels of radation present at proton accelerators the defect concentration will easily approach or exceed the doping concentration of the usual high ohmic material. DLTS, the most common technique for defect characterization is known to fail under these conditions. To study heavy radiation damage in silicon detectors a new method has bcen developed . Using a DLTS-like pulser setup, the current transient from trap emptying is recorded on a fast digital scope bang rid out by a microcomputer . This is repeatedly done during a temperature scan. The time integral of the current transient equals the number of traps present and the activation enthalpy is found from the temperature dependence of the emission life time. If there is more than one enpr~ 1_evel present the individual components may be extracted by a fitting procedure from the then multiexpoaential current transient. The sensitivity reached so far is, noise and systematics considered, ~ 209 traps . Lifetimes between 5 bus and 5 ms are covered.
1
Introduction
The large scale use of silicon detectors at the future high intensity colliders increases the need to understand their radiation damage on the level of point defects up to the highest possible particle fluences . The information of interest are the concentration and the energy levels of the dïfferent charge states of the various introduced deep defects as well as their ( temperature dependent ) emission life times. The well known defects P-V, V-V, and V-O can be identified with this knowledge . DLTS' is perhaps the most widely used method to provide these data. It has had enormous success in low resistivity material ( few SZcm ) but is not applicable for the study of high level radiation damage in high ohmic ( few kStcm ) material . There are mainly two reasons for this: a) DLTS measurements rely on the assumptions of an exponential capacitance transient and an only small relative change in the capacitance !~C(t)lC « 1 . Both assumptions are badly violated when the defect concentration approaches or exceeds the doping concentration 2. b) DLTS analysis assumes that the high frequency capacitance is uniquely related to the depletion width
by C = e/w. Detector diodes, however, have a thickness of up to ti 400 ~cm and the finite transit time across the neutral base as well as generation - recombination processes in the base destroy this unique relationship. Near compensation the high frequency capacitance becomes heavily temperature dependent, rendering DLTS useless . In DLTS the capacitance transient is subjected to a filtering operation resulting in a one number output at each temperature . Practically all information about the transients time behaviour is lost. Thurber et 2 proposed a consistency check for DLTS. In repeated tempera ture scans the time window t i , t 2 is varied whereby the
al.
rate for maximum filter response 1/T = ln(tz/ti)/(t2 t i ) is held constant . If the assumptions of the DLTS analysis are valid the temperatures where the DLTS signal peaks must not change . However, the sensitivity and possible corrections in the analysis are again model dependent3.
Ofl20~bß32/91/~03 .b0 ® 19fl1 ~ Llseviee Science Publishecs 13.V. (North~liolland)
M. Momayezi/Defect energy levels from current transient recording
334
The aim of this paper is to introduce a new method avoiding the above stated problems. It is dedicated t~ a proof of principle, i.e. the theory, the experimental setup, and the analysis are presented in detail in the following sections . As an example the results for a detector irradiated with 14MeV-neutrons is given. A detailed discussion of the defects introduced by é, ~, and neutrons will be published elsewhere . T~IE'OT3T
2.1
Basic Idea
The basicidea is to drive the silicon detector into full depletion by a fast pulser thereby sweeping out all mobile carriers ûom the detector volume. Any defect whose energy level is located between the Ferrai level and the intrinsic level will emit the trapped electron with a cha racteristic temperature dependent emission time. This leads to a $uorescent current which is monitored by a fast current-to-voltage converter . Its output is fed to a digital oscilloscope read out by an ATARI microcomputer. If there is only one defect present the fluorescent current will exhibit an exponential time behaviour with the emission constant as the decay time. The total number of traps is the time integral over the fluorescent current . If there is more than one kind of trap a multiexponential time behaviour is observed and the deconvolution can be done ofF Line. By varying the sample temperature the activation enthalpies are obtained from the Arrhenius plots of the individual decay-emission times . Besides the enthalpy the trap occupation vs. temperature may also be studied . In the lowly doped base material used for particle detectors ( ND ~O(lO llcm' 3) ) the electron Ferrai level is a strong function of the temperature ( T ), rising as T falls. Only those defect levels located in energy between the Ferrai level and the intrinsic level will change their charge state after application of the depletion pulse. Hence, when the temperature is lowered the integrated fluorescent charge emitted from a defect level rises when the Ferrai level crosses the defect energy level .
Figure 1: A p+nn+-diode with little bias ( upper part ) and high bias ( lower part ) applied . Traps located between the Ferrai level and the intrinsic level will emit electrons . The total number of electrons equals the number of traps that have changed their charge state. The advantages of this new technique are : ® The number of defects that can be detected is not related to the background doping . ® No assumptions on the time behaviour ofthe charge emission are necessary since the whole transient is recorded.
2 .2
Steady State Occupation Statistics
Starting from the general formula for steady state occupancies simple expressions in the field region and the neutral base are derived . The number of traps is denoted by T, the occupied and unoccupied fraction by To and T~ . Let e~ and ey be the electron and hole emission rates and r~ and ry the corresponding capture coefficients . n,p are the electron and hole concentrations . For a trap with well separated energy levels the occupancy
M. Momayezi /Defect energy levels from current transient recording rcn + ev
To
ratio is4 :
Tv
33b
Remembering T = Tv + To and the steady state condi-
rvp ~- ec
tions (3) and denoting difference from the steady stale
The emission and capture coefficients are related to each
as ~To (t) = To(t)-To(oo) the solution of this ~uati~t
other by
is :
ec = rcKc ey
Ec-ET kT ~ ET-Ev
rc9cNc exP (= rygyNy exp (-
= ryKy
kT
~
(1) (2)
The total camer generation rate is:
G = Gn + Gp = ecTo + eyTv
where the g's are the degeneracy factors and the N's are the band densities of state . In the field region n=p=0 and
To T
For a trap well above the intrinsic level this simplifies to ( ey
ey ey+ec
« ec ):
G = eyT + ec~To(0)é`ct
From the exponential behaviour (1),(2) it is seen that a level located far from the middle of the band gap,
Besides the steady state dark current - eyT - ~ addi-
will be occupied if it is below the intrinsic level Ei and
tional current transient with the electron emission time
empty if it is above . In case it is located very close to the intrinsic level the occupation probability will depend
ec
and the total charge Q = OTo(0) is observed. The above presented arguments are rigorously ~r~P
on the relative size of the capture coefficients and the
only if the carrier drift time through the field region is
degeneracy factors .
small compared to the emission times.
In the diodes
In the neutral base we find for a level well above
used for this experiment the maximum drift times were
K rcrt, i .e .
less than 60 ns. The shortest emission times of concern
Ei the following relations ; ryp K
ec & ey
communication only with the conduction band .
The
were ti 5 ~s.
occupancy becomes independent of the capture coeffi-
3
cients : _To _ Tv
_ To _
n Kc
T
n
Kc + n
Experimental Setup
The diodes used for this experiment are p+nn+ ion im-
Note that rc = ND -- [To] since the defect concentration
planted diodes with a net doping concentration of N 10 12 cm-3 . Their area is ti 9 cm2 and the wafer thick-
is not negligible compared to the doping concentration .
ness is 280 gym.
2.3
The sample diode was mounted onto
an aluminum bar and placed inside a thermo box. Cooling was done by evaporating some liquid nitrogen inside
Emission rates
the box . The resistive heater, mounted near the diode,
Emission of electrons from a trap with well separated
allowed heating at a rate of typically 1 K/min. The tem-
energy levels leads to an exponential emptying until
perature was measured with a Pt 100 four wire sensor
In the field zone
where no capture processes occur the rate of change in
to an accuracy of 0.5 K as was estimated from comparing measurements in a cool down - heat up cycle. The
the number of traps being occupied is given by :
diode was connected to the pulser and the current-to-
steady state conditions are reached .
dTo dt
4 ev~b
®
ec~,®
voltage ( I-+V )converter by 50 St coaxial cables. A free running trigger unit switched the analog pulser whose
M. Momayezi/Defect energy levels from current transient recording
336
Figure 2: Experimental Setup: Pulser : Trigger & analog pulser DUT: Device under test inside thermobox I-->V : Current-to-voltage converter LC 9420: Digital oscilloscope 8 bit, 100 MHz Bash ADC AT.~RI: Microcomputerstation with mass storage, gra phics, and analysis software output amplitude and offset are set by multiturn potentiometers . During the rising edge of the pulser output all mobile charge carriers are swept out of the diode, resulting in a large displacement current to be delivered by the pulser . Afterwards the pulser voltage remains constant and the fluorescent current from emptying traps is converted by the I-~V-converter into a voltage transient which in turn is recorded by a digital storage oscilloscope. Having aquired and averaged 100 traces ( to reduce noise ) the oscilloscope is stopped and read out via an IEEEbus into an ATARI microcomputer . This is repeated in temperature inter vals of 2K to 5 K during heat up. The pulser and the I-~V-converter have to meet some special demands described below.
output voltage slew rate output current settling time thermal tail noise input voltage
-10 V . . . -{-60 V 00 V/fes 150 mA <1% 20 ~s DU=100 mV, RC=20 mS 40nV/ Hz at v~.10
Table 1: Performance of the Pulser
PULSER
DUT
I>V
Figure 3: Circuit schematic showing the class-B pulser output stage ( r° ,t ~ 6 SZ ), the diode to be measured with its depletion capacitance and the current to voltage converter based on a CLC 401 transimpedance amplifier .
3.1
Requirements for the pulser
The pulser must exhibit a shôrt rise time and sufficient drive capability together with stability on the huge capacitive load of an undepleted diode ( ~3 nF ). Any change in voltage after the rising edge would cause additional displacement currents to flow, interfering with the measurement. Therefore the requirements on settling time and thermal tails are most demanding . The noise voltage generated in the pulser is amplified across the diode and the I-~V-converter in direct proportion to its frequency. Hence, a low high frequency noise density is a must. The table below lists the pulser properties.
3.2
The I--~V-converter
The circuit, as shown in fig. 3, is known to be unstable if a conventional operational amplifier is used. The inherent 90°-phase shift of any op-amp add to the 90° of the RjCDVT-low pass reducing the phase margin to zero. Employing a transimpedance amplifier instead allows to built a fast and simple I-}V-converter with the conventional circuit topologys . The transimpedance amplifier in use ( CLC 401, Comlinear Corp. ) shows no open loop phase shifts up to frequnciee of 50 MHz . Therefore, the device is stable on any capacitive input load
M. Momayezi /Defect energy levels from current transient recording with a phase margin of 90° . It also offers overload recovery and a settling behaviour far superior to what is needed here. The effective converter transimpedance is calculated by paralleling the feed back resistor Rf and the open loop transimpedaxice ( A=710 kSZ, f(-3dB)=0.28 MHz ) For Rf=1 kSZ, 10 kSZ, 100 kSZ the corner frequencies of the effective transimpedance are 80 MHz, 8.6MHz, and 1.2 MHz . In order to reduce noise the bandwidth was limited to Less than 2MHz for all Rf by introducing R~ = 1 kSt. The trap emptying current will cause voltage drops over the pulser output resistance ( r, ) and the hV converter input resistance ( rt ). These also give rise to a displacement current across the diode depletion ca pacitance ( ti 350 pF ). The resulting relative error in the measured charge is found to be equal to the ratio (ro -~ r~) ~ CDUTlT where T is the current decay time. From the data given in table 2 it follows that the resulting rC-times are small to the trap emission times of concern . Two protecting diodes and the resistor R~ help to reduce the severe overload during the pulser switching, when the displacement current reaches 100 mA. Compared with the maximum voltage swing of 4 V this represents an overload factor of ti 2 500 in the maximum sensitivity setting, Rf = 100 kSZ . The device recovers within 201cs to error voltages of DU < 1 rrtV. Summarizing, the circuitry allows recording of fast current transients from 4 mA down to the noise limit of ti 20 nA. The decay times accessible are limited from below by the pulser rise time and the overload recovery behaviour to ~ 51cs depending a little on the amplitude. On a time scale of ti 20 ms the pulser voltage relaxes by about 100 mV due to the changed thermal load of the output transistor after switching. This introduces an error charge on the order of 3 ~ 108 electrons and limits the decay time measurements to times shorter than 5 ms. As was tested on unirradiated diodes the total error charge is below 5 ~ 108 electrons for all configurations .
j 1 kSt transimpedance , 1 kSt ri DC ~ ~1.5St rs "~ 1 MHz 5 St settling time <1% ~ 4~rs nonlinearity ~I Rf =
337 10 kft 9.8kit 15fZ ~ St 4 us
100 kSZ $8kSt 150D 340 ft 6ics
Table 2: Performance of the current-to-voltage converter
4
Analysis
During the measurement the data read out from the oscilloscope are converted into physical data, i.e. time and current, and are stored in a format readable by a graphics package. For every transient the osc~ll~cope's time base has been chosen to ensure that the trace ex tends over at least four decay times of the slowest component . That way offsets and the steady state currents could be subtracted by graphical inspection . Starting values for the fit parameters were obtained by letting the graphics package do successive single exponential fitting and subtracting for every componnat of a certain transient . The decision of how many components the transient is composed was also made at this point . Final values for the amplitudes and decay times of the several ( typically two or three ) components were obtained from a dedicated multiparameter least square fitting procedure. It is provided with the full Hesse matrix ( calculated analytically ) and takes full Newton steps towards the minimum of the least square function taking into account all parameter correlations . The use of the Hessian further yields a scale free convergence criterion. Being scale free is important when parameters with different dimensions as amplitude ( ampere ) and emission times ( seconds ) are correlated in a mini-
mizing procedures. Over the total trace length the oscilloscope took 50000 data points employing a 100 MHz 8-bit flash ADC . Of these 50 000 points only every 50th was read out because of time and storage considerations . The fits ~rsually extended over the first 500 points being read out . The r.m.s. error of the measured current is the
M. Momayezi/Defect energy levels from current transient recording
338
same for all points . Hence, if the fit is good the least square sum divided by the number of degrees of freedom should reproduce the variance of the original data, i.e. the current noise. The r.m.s. noise deduced from the least square fulfilled this within a factor of two for all traces. The full charge corresponding to each component was then calculated as the product of the current amplitude and the decay time. Here the current amplitude was extrapolated to time zero, i.e. the rising edge of the poker voltage.
Fig. 4 shows on a logarithmic scale the current transient after switching on the depletion pulse for a diode irradiated with 0.72 - 10 12 neutrons per cm2 ( T=14 MeV ) two years ago . One recognizes two exponential components of the transient .
I(t) [~A ] 50 10
0
100
Time [ ~s ]
400
Figure 4: Doubly exponential current transient at 5.2°C. Reverse bias switching occurs at t=0 . The two straight lines are the two components. Their sum is indistinguishable from the data for t>30~cs . Within the first 30~cs one observes the amplified ringing of the pulser . This range has usually been excluded from the fits except at the highest temperatures, where the signal was much larger than the ringing . The error charge introduced by the ringing has been 3~l0selectr®ns, typically.
The diodes in this experiment are encapsulated for ease of handling in a high energy physics application. They are glued on a ceramics board and are covered with black plastic . Due to the difFerent thermal expansion factors of the ceramics and silicon the temperature range that could be covered without breaking the diodes extended only from -40° to -~30°. Within this limited temperature range two trap energy levels were found. There activation enthalpies are ( 0 .396E 0.006 ) eV and ( 0.41E 0.02 ) eV respectively as has been derived from an Arrhenius plot of their emission times, fig . 5. For this the emission time was parametrized as T = To .
~ 300 K~ T
2
.
enFr~kT
The erstwhile level is attributed to the doubly negative charge state of the divacancy. The findings here 3.6ps < To < 6.0 ps and DH = 0.396 eV f 6 meV compare well with findings from DLTS-measurements of Borchi et ah. - 2.1 ps and (0.40 f 0.02)eV - and Wunstorf et alb 6.9ps and (0.3910.02) eV. The dark current ofthe diode shows an activation enthalpy of (0.607f0.003)eV which is then attributed to the divacancy midgap level (0/-) . The second level may be the P-V (0/-)level, but the errors in To and its energy are considerable . To is found to range in between 0.34ps and 1 .7 ps. Its energy is (0.41f0.02) eV. Data taken from Asom9 and Watkinsio give DH = 0.44 eV and To = 0.64ps, 0.87ps respectively. Fig .6 shows the number of traps, for each component, vs. temperature . The concentration of the large component is 2 ~ 101°/0 .11cm3 0.18 ~ 1012 /cms. Note, that this is about 20 % of the total doping density ( ND = 0.85 ~ 1012cm3 ), already reached at a very moderate level of neutron irradiation . The divacancy ( filled points ) shows the expected behaviour of remaining empty in the neutral base when the temperature is high enough . The second trap level present lies even deeper and does not change its occupancy over the temperature range addressed .
M. Momayezi/Defect energy
levels from current transient recording
339
No. of Traps e
100
2 " 10 10
-®
® ® ®®
10
®®
®®
1 " 1010
0 r
_40
°
o
°
o
0 ° 0 0 ° 0 °° 0
-20
0
Temp. [°C)
o
° ° -f20
Figure 5: The product T " TZ vs. 1/kT for both traps . The slope of the expected straight line is the activation enthalpy. Filled points correspond to the more abundant trap; compare fig .6.
Figure 6: Number of electrons emitted from each of the two traps vs. temperature.
6
References
Conclusion
Current Transient Recording ( CTR ) gives clear and unambigous insight into the dynamics of charged carrier emission from deep traps. The number of traps present follows immediately from the integral over the fluorescent current . Energy levels are derived without relying on assumptions that can not be checked . The trap occupancy vs. temperature can be measured directly and the sensitivity is in no way related to the background doping density. On the other hand the electronics equipment needed is comparatively simple. CTR will thus allow studies on defect introduction even at the highest levels of irradiation present at future hadron colliders .
Acknowledgements This work has been performed as a part of the development of a silicon counter based hadron electron separator for the ZEUS calorimeter . The author gratefully acknowledges the support from R .Klanner and E.Lohrmann and is indebted to A.Seiciman for reading the manuscript .
1. D.V.Lang, J.Appl.Phys. 45(7) 3023 (1974) 2. W.R.Thurber, J.Appl.Phys . 53(11) 7397 (1982) 3. P.T.Landsberg et (1987)
al., J.Appl.Phys. 61(11) 5055
4. P.T.Landsberg, Semiconductor Statistics in T.Moss, Handbook of Semiconductors, Voll, chapter 7, North Holland Publ. (1982) 5. S.Franco, EDN J-.~~.5, ?61 (1989) 6. F.James,Function Minimization in Proc. of the 1972 CERN Comp. and Data Process . School, Pertisau, Austria, (1972), CERN 72-21 7. Borchi et al.,Nucl.Instr .lVleth . A 249
244
(1989)
8. Wunstorf et al., Radiation Damage of silicon Detectors by Monoenergetic Neutrons . . . , this proceedings 9. Asom et al.,Appl .Phys .Lett. 51(4) 256 (1987) 10. Song,Benson,Watkins, Phys.Rev.B 33(2)1452 (1986)
333
Defect Energy Levels from Current ~ansient Recording Michael Momayezi DESY, 2000 Hamburg 52, Germany Silicon detectors are widely used in high energy physics in vertexing and calorimetry applications . The radiative environment will introduce defects with energy levels in the bandgap into the crystals. At the high levels of radation present at proton accelerators the defect concentration will easily approach or exceed the doping concentration of the usual high ohmic material. DLTS, the most common technique for defect characterization is known to fail under these conditions. To study heavy radiation damage in silicon detectors a new method has bcen developed . Using a DLTS-like pulser setup, the current transient from trap emptying is recorded on a fast digital scope bang rid out by a microcomputer . This is repeatedly done during a temperature scan. The time integral of the current transient equals the number of traps present and the activation enthalpy is found from the temperature dependence of the emission life time. If there is more than one enpr~ 1_evel present the individual components may be extracted by a fitting procedure from the then multiexpoaential current transient. The sensitivity reached so far is, noise and systematics considered, ~ 209 traps . Lifetimes between 5 bus and 5 ms are covered.
1
Introduction
The large scale use of silicon detectors at the future high intensity colliders increases the need to understand their radiation damage on the level of point defects up to the highest possible particle fluences . The information of interest are the concentration and the energy levels of the dïfferent charge states of the various introduced deep defects as well as their ( temperature dependent ) emission life times. The well known defects P-V, V-V, and V-O can be identified with this knowledge . DLTS' is perhaps the most widely used method to provide these data. It has had enormous success in low resistivity material ( few SZcm ) but is not applicable for the study of high level radiation damage in high ohmic ( few kStcm ) material . There are mainly two reasons for this: a) DLTS measurements rely on the assumptions of an exponential capacitance transient and an only small relative change in the capacitance !~C(t)lC « 1 . Both assumptions are badly violated when the defect concentration approaches or exceeds the doping concentration 2. b) DLTS analysis assumes that the high frequency capacitance is uniquely related to the depletion width
by C = e/w. Detector diodes, however, have a thickness of up to ti 400 ~cm and the finite transit time across the neutral base as well as generation - recombination processes in the base destroy this unique relationship. Near compensation the high frequency capacitance becomes heavily temperature dependent, rendering DLTS useless . In DLTS the capacitance transient is subjected to a filtering operation resulting in a one number output at each temperature . Practically all information about the transients time behaviour is lost. Thurber et 2 proposed a consistency check for DLTS. In repeated tempera ture scans the time window t i , t 2 is varied whereby the
al.
rate for maximum filter response 1/T = ln(tz/ti)/(t2 t i ) is held constant . If the assumptions of the DLTS analysis are valid the temperatures where the DLTS signal peaks must not change . However, the sensitivity and possible corrections in the analysis are again model dependent3.
Ofl20~bß32/91/~03 .b0 ® 19fl1 ~ Llseviee Science Publishecs 13.V. (North~liolland)
M. Momayezi/Defect energy levels from current transient recording
334
The aim of this paper is to introduce a new method avoiding the above stated problems. It is dedicated t~ a proof of principle, i.e. the theory, the experimental setup, and the analysis are presented in detail in the following sections . As an example the results for a detector irradiated with 14MeV-neutrons is given. A detailed discussion of the defects introduced by é, ~, and neutrons will be published elsewhere . T~IE'OT3T
2.1
Basic Idea
The basicidea is to drive the silicon detector into full depletion by a fast pulser thereby sweeping out all mobile carriers ûom the detector volume. Any defect whose energy level is located between the Ferrai level and the intrinsic level will emit the trapped electron with a cha racteristic temperature dependent emission time. This leads to a $uorescent current which is monitored by a fast current-to-voltage converter . Its output is fed to a digital oscilloscope read out by an ATARI microcomputer. If there is only one defect present the fluorescent current will exhibit an exponential time behaviour with the emission constant as the decay time. The total number of traps is the time integral over the fluorescent current . If there is more than one kind of trap a multiexponential time behaviour is observed and the deconvolution can be done ofF Line. By varying the sample temperature the activation enthalpies are obtained from the Arrhenius plots of the individual decay-emission times . Besides the enthalpy the trap occupation vs. temperature may also be studied . In the lowly doped base material used for particle detectors ( ND ~O(lO llcm' 3) ) the electron Ferrai level is a strong function of the temperature ( T ), rising as T falls. Only those defect levels located in energy between the Ferrai level and the intrinsic level will change their charge state after application of the depletion pulse. Hence, when the temperature is lowered the integrated fluorescent charge emitted from a defect level rises when the Ferrai level crosses the defect energy level .
Figure 1: A p+nn+-diode with little bias ( upper part ) and high bias ( lower part ) applied . Traps located between the Ferrai level and the intrinsic level will emit electrons . The total number of electrons equals the number of traps that have changed their charge state. The advantages of this new technique are : ® The number of defects that can be detected is not related to the background doping . ® No assumptions on the time behaviour ofthe charge emission are necessary since the whole transient is recorded.
2 .2
Steady State Occupation Statistics
Starting from the general formula for steady state occupancies simple expressions in the field region and the neutral base are derived . The number of traps is denoted by T, the occupied and unoccupied fraction by To and T~ . Let e~ and ey be the electron and hole emission rates and r~ and ry the corresponding capture coefficients . n,p are the electron and hole concentrations . For a trap with well separated energy levels the occupancy
M. Momayezi /Defect energy levels from current transient recording rcn + ev
To
ratio is4 :
Tv
33b
Remembering T = Tv + To and the steady state condi-
rvp ~- ec
tions (3) and denoting difference from the steady stale
The emission and capture coefficients are related to each
as ~To (t) = To(t)-To(oo) the solution of this ~uati~t
other by
is :
ec = rcKc ey
Ec-ET kT ~ ET-Ev
rc9cNc exP (= rygyNy exp (-
= ryKy
kT
~
(1) (2)
The total camer generation rate is:
G = Gn + Gp = ecTo + eyTv
where the g's are the degeneracy factors and the N's are the band densities of state . In the field region n=p=0 and
To T
For a trap well above the intrinsic level this simplifies to ( ey
ey ey+ec
« ec ):
G = eyT + ec~To(0)é`ct
From the exponential behaviour (1),(2) it is seen that a level located far from the middle of the band gap,
Besides the steady state dark current - eyT - ~ addi-
will be occupied if it is below the intrinsic level Ei and
tional current transient with the electron emission time
empty if it is above . In case it is located very close to the intrinsic level the occupation probability will depend
ec
and the total charge Q = OTo(0) is observed. The above presented arguments are rigorously ~r~P
on the relative size of the capture coefficients and the
only if the carrier drift time through the field region is
degeneracy factors .
small compared to the emission times.
In the diodes
In the neutral base we find for a level well above
used for this experiment the maximum drift times were
K rcrt, i .e .
less than 60 ns. The shortest emission times of concern
Ei the following relations ; ryp K
ec & ey
communication only with the conduction band .
The
were ti 5 ~s.
occupancy becomes independent of the capture coeffi-
3
cients : _To _ Tv
_ To _
n Kc
T
n
Kc + n
Experimental Setup
The diodes used for this experiment are p+nn+ ion im-
Note that rc = ND -- [To] since the defect concentration
planted diodes with a net doping concentration of N 10 12 cm-3 . Their area is ti 9 cm2 and the wafer thick-
is not negligible compared to the doping concentration .
ness is 280 gym.
2.3
The sample diode was mounted onto
an aluminum bar and placed inside a thermo box. Cooling was done by evaporating some liquid nitrogen inside
Emission rates
the box . The resistive heater, mounted near the diode,
Emission of electrons from a trap with well separated
allowed heating at a rate of typically 1 K/min. The tem-
energy levels leads to an exponential emptying until
perature was measured with a Pt 100 four wire sensor
In the field zone
where no capture processes occur the rate of change in
to an accuracy of 0.5 K as was estimated from comparing measurements in a cool down - heat up cycle. The
the number of traps being occupied is given by :
diode was connected to the pulser and the current-to-
steady state conditions are reached .
dTo dt
4 ev~b
®
ec~,®
voltage ( I-+V )converter by 50 St coaxial cables. A free running trigger unit switched the analog pulser whose
M. Momayezi/Defect energy levels from current transient recording
336
Figure 2: Experimental Setup: Pulser : Trigger & analog pulser DUT: Device under test inside thermobox I-->V : Current-to-voltage converter LC 9420: Digital oscilloscope 8 bit, 100 MHz Bash ADC AT.~RI: Microcomputerstation with mass storage, gra phics, and analysis software output amplitude and offset are set by multiturn potentiometers . During the rising edge of the pulser output all mobile charge carriers are swept out of the diode, resulting in a large displacement current to be delivered by the pulser . Afterwards the pulser voltage remains constant and the fluorescent current from emptying traps is converted by the I-~V-converter into a voltage transient which in turn is recorded by a digital storage oscilloscope. Having aquired and averaged 100 traces ( to reduce noise ) the oscilloscope is stopped and read out via an IEEEbus into an ATARI microcomputer . This is repeated in temperature inter vals of 2K to 5 K during heat up. The pulser and the I-~V-converter have to meet some special demands described below.
output voltage slew rate output current settling time thermal tail noise input voltage
-10 V . . . -{-60 V 00 V/fes 150 mA <1% 20 ~s DU=100 mV, RC=20 mS 40nV/ Hz at v~.10
Table 1: Performance of the Pulser
PULSER
DUT
I>V
Figure 3: Circuit schematic showing the class-B pulser output stage ( r° ,t ~ 6 SZ ), the diode to be measured with its depletion capacitance and the current to voltage converter based on a CLC 401 transimpedance amplifier .
3.1
Requirements for the pulser
The pulser must exhibit a shôrt rise time and sufficient drive capability together with stability on the huge capacitive load of an undepleted diode ( ~3 nF ). Any change in voltage after the rising edge would cause additional displacement currents to flow, interfering with the measurement. Therefore the requirements on settling time and thermal tails are most demanding . The noise voltage generated in the pulser is amplified across the diode and the I-~V-converter in direct proportion to its frequency. Hence, a low high frequency noise density is a must. The table below lists the pulser properties.
3.2
The I--~V-converter
The circuit, as shown in fig. 3, is known to be unstable if a conventional operational amplifier is used. The inherent 90°-phase shift of any op-amp add to the 90° of the RjCDVT-low pass reducing the phase margin to zero. Employing a transimpedance amplifier instead allows to built a fast and simple I-}V-converter with the conventional circuit topologys . The transimpedance amplifier in use ( CLC 401, Comlinear Corp. ) shows no open loop phase shifts up to frequnciee of 50 MHz . Therefore, the device is stable on any capacitive input load
M. Momayezi /Defect energy levels from current transient recording with a phase margin of 90° . It also offers overload recovery and a settling behaviour far superior to what is needed here. The effective converter transimpedance is calculated by paralleling the feed back resistor Rf and the open loop transimpedaxice ( A=710 kSZ, f(-3dB)=0.28 MHz ) For Rf=1 kSZ, 10 kSZ, 100 kSZ the corner frequencies of the effective transimpedance are 80 MHz, 8.6MHz, and 1.2 MHz . In order to reduce noise the bandwidth was limited to Less than 2MHz for all Rf by introducing R~ = 1 kSt. The trap emptying current will cause voltage drops over the pulser output resistance ( r, ) and the hV converter input resistance ( rt ). These also give rise to a displacement current across the diode depletion ca pacitance ( ti 350 pF ). The resulting relative error in the measured charge is found to be equal to the ratio (ro -~ r~) ~ CDUTlT where T is the current decay time. From the data given in table 2 it follows that the resulting rC-times are small to the trap emission times of concern . Two protecting diodes and the resistor R~ help to reduce the severe overload during the pulser switching, when the displacement current reaches 100 mA. Compared with the maximum voltage swing of 4 V this represents an overload factor of ti 2 500 in the maximum sensitivity setting, Rf = 100 kSZ . The device recovers within 201cs to error voltages of DU < 1 rrtV. Summarizing, the circuitry allows recording of fast current transients from 4 mA down to the noise limit of ti 20 nA. The decay times accessible are limited from below by the pulser rise time and the overload recovery behaviour to ~ 51cs depending a little on the amplitude. On a time scale of ti 20 ms the pulser voltage relaxes by about 100 mV due to the changed thermal load of the output transistor after switching. This introduces an error charge on the order of 3 ~ 108 electrons and limits the decay time measurements to times shorter than 5 ms. As was tested on unirradiated diodes the total error charge is below 5 ~ 108 electrons for all configurations .
j 1 kSt transimpedance , 1 kSt ri DC ~ ~1.5St rs "~ 1 MHz 5 St settling time <1% ~ 4~rs nonlinearity ~I Rf =
337 10 kft 9.8kit 15fZ ~ St 4 us
100 kSZ $8kSt 150D 340 ft 6ics
Table 2: Performance of the current-to-voltage converter
4
Analysis
During the measurement the data read out from the oscilloscope are converted into physical data, i.e. time and current, and are stored in a format readable by a graphics package. For every transient the osc~ll~cope's time base has been chosen to ensure that the trace ex tends over at least four decay times of the slowest component . That way offsets and the steady state currents could be subtracted by graphical inspection . Starting values for the fit parameters were obtained by letting the graphics package do successive single exponential fitting and subtracting for every componnat of a certain transient . The decision of how many components the transient is composed was also made at this point . Final values for the amplitudes and decay times of the several ( typically two or three ) components were obtained from a dedicated multiparameter least square fitting procedure. It is provided with the full Hesse matrix ( calculated analytically ) and takes full Newton steps towards the minimum of the least square function taking into account all parameter correlations . The use of the Hessian further yields a scale free convergence criterion. Being scale free is important when parameters with different dimensions as amplitude ( ampere ) and emission times ( seconds ) are correlated in a mini-
mizing procedures. Over the total trace length the oscilloscope took 50000 data points employing a 100 MHz 8-bit flash ADC . Of these 50 000 points only every 50th was read out because of time and storage considerations . The fits ~rsually extended over the first 500 points being read out . The r.m.s. error of the measured current is the
M. Momayezi/Defect energy levels from current transient recording
338
same for all points . Hence, if the fit is good the least square sum divided by the number of degrees of freedom should reproduce the variance of the original data, i.e. the current noise. The r.m.s. noise deduced from the least square fulfilled this within a factor of two for all traces. The full charge corresponding to each component was then calculated as the product of the current amplitude and the decay time. Here the current amplitude was extrapolated to time zero, i.e. the rising edge of the poker voltage.
Fig. 4 shows on a logarithmic scale the current transient after switching on the depletion pulse for a diode irradiated with 0.72 - 10 12 neutrons per cm2 ( T=14 MeV ) two years ago . One recognizes two exponential components of the transient .
I(t) [~A ] 50 10
0
100
Time [ ~s ]
400
Figure 4: Doubly exponential current transient at 5.2°C. Reverse bias switching occurs at t=0 . The two straight lines are the two components. Their sum is indistinguishable from the data for t>30~cs . Within the first 30~cs one observes the amplified ringing of the pulser . This range has usually been excluded from the fits except at the highest temperatures, where the signal was much larger than the ringing . The error charge introduced by the ringing has been 3~l0selectr®ns, typically.
The diodes in this experiment are encapsulated for ease of handling in a high energy physics application. They are glued on a ceramics board and are covered with black plastic . Due to the difFerent thermal expansion factors of the ceramics and silicon the temperature range that could be covered without breaking the diodes extended only from -40° to -~30°. Within this limited temperature range two trap energy levels were found. There activation enthalpies are ( 0 .396E 0.006 ) eV and ( 0.41E 0.02 ) eV respectively as has been derived from an Arrhenius plot of their emission times, fig . 5. For this the emission time was parametrized as T = To .
~ 300 K~ T
2
.
enFr~kT
The erstwhile level is attributed to the doubly negative charge state of the divacancy. The findings here 3.6ps < To < 6.0 ps and DH = 0.396 eV f 6 meV compare well with findings from DLTS-measurements of Borchi et ah. - 2.1 ps and (0.40 f 0.02)eV - and Wunstorf et alb 6.9ps and (0.3910.02) eV. The dark current ofthe diode shows an activation enthalpy of (0.607f0.003)eV which is then attributed to the divacancy midgap level (0/-) . The second level may be the P-V (0/-)level, but the errors in To and its energy are considerable . To is found to range in between 0.34ps and 1 .7 ps. Its energy is (0.41f0.02) eV. Data taken from Asom9 and Watkinsio give DH = 0.44 eV and To = 0.64ps, 0.87ps respectively. Fig .6 shows the number of traps, for each component, vs. temperature . The concentration of the large component is 2 ~ 101°/0 .11cm3 0.18 ~ 1012 /cms. Note, that this is about 20 % of the total doping density ( ND = 0.85 ~ 1012cm3 ), already reached at a very moderate level of neutron irradiation . The divacancy ( filled points ) shows the expected behaviour of remaining empty in the neutral base when the temperature is high enough . The second trap level present lies even deeper and does not change its occupancy over the temperature range addressed .
M. Momayezi/Defect energy
levels from current transient recording
339
No. of Traps e
100
2 " 10 10
-®
® ® ®®
10
®®
®®
1 " 1010
0 r
_40
°
o
°
o
0 ° 0 0 ° 0 °° 0
-20
0
Temp. [°C)
o
° ° -f20
Figure 5: The product T " TZ vs. 1/kT for both traps . The slope of the expected straight line is the activation enthalpy. Filled points correspond to the more abundant trap; compare fig .6.
Figure 6: Number of electrons emitted from each of the two traps vs. temperature.
6
References
Conclusion
Current Transient Recording ( CTR ) gives clear and unambigous insight into the dynamics of charged carrier emission from deep traps. The number of traps present follows immediately from the integral over the fluorescent current . Energy levels are derived without relying on assumptions that can not be checked . The trap occupancy vs. temperature can be measured directly and the sensitivity is in no way related to the background doping density. On the other hand the electronics equipment needed is comparatively simple. CTR will thus allow studies on defect introduction even at the highest levels of irradiation present at future hadron colliders .
Acknowledgements This work has been performed as a part of the development of a silicon counter based hadron electron separator for the ZEUS calorimeter . The author gratefully acknowledges the support from R .Klanner and E.Lohrmann and is indebted to A.Seiciman for reading the manuscript .
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al., J.Appl.Phys. 61(11) 5055
4. P.T.Landsberg, Semiconductor Statistics in T.Moss, Handbook of Semiconductors, Voll, chapter 7, North Holland Publ. (1982) 5. S.Franco, EDN J-.~~.5, ?61 (1989) 6. F.James,Function Minimization in Proc. of the 1972 CERN Comp. and Data Process . School, Pertisau, Austria, (1972), CERN 72-21 7. Borchi et al.,Nucl.Instr .lVleth . A 249
244
(1989)
8. Wunstorf et al., Radiation Damage of silicon Detectors by Monoenergetic Neutrons . . . , this proceedings 9. Asom et al.,Appl .Phys .Lett. 51(4) 256 (1987) 10. Song,Benson,Watkins, Phys.Rev.B 33(2)1452 (1986)