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Electric field dependence of the capture cross section of ion-implantation-induced traps in SiO2 layers
Thfl7 SolidFihns, 99(1983j 331 337
331
ELECTRONICS AND OPTICS
ELECTRIC FIELD D E P E N D E N C E O F T H E CAPTURE CROSS SECTION O F I O N - I M P L A N T A T I O N - I N D U C E D TRAPS IN SiO 2 LAYERS I. S T R Z A L K O W S K I , M. MARCZEWSK1 AND M. KOWALSKI
hl,~tittttc ~/ PIu',~'ics, Warsaw Techtlical L:nit,er,~'it.v, Kos: r/~owa 75, 00-662 Warsaw (Poland) (Received April 7, 1982: accepted May 20, 1982)
Trapping centres introduced into an SiO2 layer during boron implantation through the oxide into the silicon substrate were investigated. The internal photoemission method was used to determine their capture cross section and its electric field dependence. A possible microscopic model of these centres, with a dipolar character, is presented.
I. INTRODUCTION S i O 2 is a very important material in electronics technology and its physical properties have been widely investigated during the last few years 1. For instance, S i O 2 is extensively used as an insulator layer in metal/insulator/semiconductor structures forming metal/oxide/semiconductor(MOS)-type devices. A convenient doping technique which is widely used in the fabrication of semiconductor devices and integrated circuits based on MOS structures is the ion implantation technique. The use of this technique produces a large variety of defects acting as electron- or hole-trapping centres. Charge trapping in the SiO 2 layer of MOS structures is responsible for the deterioration in electrical properties and the instability of MOS-type devices. In order to remove the implantation-created traps high temperature (about 1000 C ) post-implantation annealing is typically used. It removes practically all implantation defects but causes the diffusion of dopant atoms and presumably creates some additional interface states. Our aim in this work was to investigate the character of traps remaining after low temperature (500 C ) annealing in the S J O 2 layer and produced by a typical MOS integrated circuit fabrication process, i.e. the implantation of B + ions through this layer into the silicon substrate. We have already studied some trapping properties of these sites z. In this work we investigated the electric field dependence of the trap centres.
2. EXPERIMENTAL DETAILS
The devices used in this study were MOS capacitors fabricated on p-type Si(100) wafers with a resistivity of 1-10 [2 cm. The silicon substrates were oxidized 0040-6090/83/0000-0000/$03.00
~ ElsevierSequoia/Printedin The Netherlands
332
1. S T R Z A L K O W S K I , M. M A R ( ' Z I i W S K I , M. K ( ) W A I , S K I
in dry oxygen at 1100 C without HC1 to a thickness of 150nm. Boron ion implantation was then performed at tin energy of 75 keV and a dose of 10 is ions cm 2. In this case, according to the kinhard Scharff Schi0tt theory, the mean range of B + ions in SiO2 is equal to 320 nm, thus practically all the B + ions lay in the silicon substrate. After the implantation, samples were annealed in an N e ambient lit 500 C for 120 min. Then rectangular semitransparent gold electrodes with an area of 0.06 cm 2 were deposited. Ohmic contacts were prepared on the back sides of the wafers. The reference sample was prepared by the same procedure, excluding the implantation process. Capacitance voltage ((" t') measurements showed that after fabrication the SiO 2 layer of the MOS structures contained quite a small amount of negative charge, the same for both the implanted lind the reference samples. Investigations were carried out with the internal electron photoemission method 3. The experimental set-up was typical'*'5. Traps in the SiO, layer were charged by means of electron photoinjection. This was achieved by illuminating the semitransparent gold electrode with the full spectrum of a 40 W deuterium lamp for various negative gate polarities. The injected charge density Q~,,i was determined to an accuracy of about 10 ~-' electrons cm -' by lime integration of the injection current density ](t). The injection current was measured with a U N I P A N 219 electrometer. The trapped charge in the SlOe layer was characterized by the photocurrent voltage (lph--V) technique complemented by the C I/technique. The photocurrent Iph induced with a non-modulated monochromatic UV beam was measured electrometrically at various bias voltages with a positive (V+ I and a negative (V t metal electrode. The wavelengths were 260 nm and 276 nm respectively. The parameters of the traps were determined by the method developed by DiMaria ~'. This method is based on the fact that charging of the bulk of the SiO, layer results in parallel shifts in the Iph- V characte[istics along the voltage axis (A l ~_ for positive gate polarity (silicon injectingl and A[ / for negative gate polarity (gold injecting)). The charge centroid 5: measured from the Au SiO, interface and the total trapped charge Q, per unit area are related to these shifts by the following": .~=L
1
Av,
Q, = !:<["tAV
~11
-Al,
I
(2~
where g is the oxide thickness, c0 is the free-space permittivity lind ~:~ is the low frequency permittivity of SiO2. The value of the trapped charge O~ was determined from eqn. (2) to an accuracy of about 5 x 101° electrons cm : The injection of electrons into the SiOe layer was accomplished under various voltage polarities. For a given gate polarity a sequence of photoinjections was performed and after each photoinjection the l~h- V characteristics were measured. The mean shifts in successive I V curves allowed us to determine the charge trapped during the successive steps of injection and hence the relation O,(Q~,i). By monitoring the change with time in Q, and .,7: as trapping under a given voltage proceeded, the capture cross section for a given field strength and the total number N, of traps per unit area were determined with the lirst-order kinetic equation (eqn. (3) belowl.
ELECTRIC FIELD DEPENDENCEOF CAPTURE CROSS SECTION IN SiO 2
333
3. RESULTSAND DISCUSSION In order to determine the electrophysical parameters of the trapping centres we made the following assumptions. (1) There are two dominating types of trapping centre in the implanted SiO2 layer investigated. (2) Traps of the first kind are located very near the interfaces of the oxide. They have a very large cross section. Since they were also observed in the reference unimplanted structure they are treated as an unwanted result of the contact preparation and are not the object of our interest. (31 Trapping centres created by the boron ion implantation through the layer and remaining after 500 C annealing are distributed in the bulk of the layer. They can be characterized by a single value of the electron capture cross section. It should be mentioned that the above assumptions do not exclude the existence in the investigated layers of other types of trap. with smaller capture cross sections, which could be revealed after the injection of higher charge densities than those used in this experiment. Analysing the experimental data we found that the Iph-V c u r v e s for implanted structures underwent parallel shifts after all subsequent photoinjections but not after the first injection. Such parallel shifts were not observed for unimplanted structures. The first injection for implanted and unimplanted samples not only caused a shift in the lph V curves under both plus and minus gate polarization but also changed the shapes of the curves. This is evidence that during the first photoinjection the interracial layers as well as the oxide bulk were charged I which strongly supports the assumption concerning the existence of the first kind of trap. The shifts observed after the second and further injections allowed us to compute the charge Q, captured at the bulk traps. Q, is presented in Fig. 1 as a function of the injected charge Q~.j for several injection electric fields. It should be explained that it is not possible to calculate Q~ for the first injection directly from the lph-V curve shifts for the above-mentioned reasons. We had to approximate this quantity as NFre(Q~,j) o, where (Qi,,j)o is the charge injected during the first photoinjection.
Q.
I
[
I
--~
--- --T
]
•
--
"-T
r
~
J
~----T~
100
g.~j
1011 ecru2 20I
/
15
°
_
10
./ 4o
6'o
80
1013e cm2
Fig. 1. The trapped charge Q, as a function of the injected charge Q~ojfor several values of the external field applied during photoinjection.
334
I. S T R Z A L K O W S K I ,
M. M A R ( ' Z E W S K I ,
M. K O W A L S K I
The values of 5-/L found after each injection step are close to 0.5, which could show" 7 that the distribution of the implantation-induced traps and their charging are practically uniform in the SiO2 layer. However, after the last prolonged injections was significantly shifted towards smaller values, In order to describe changes in the trap occupation numbers during photoinjection we used the first-order kinetic equation
2,/L
_6nat= {N(x)-n{xj}i'a"-n{\34}{-\)~r'
{31
where x is the distance from the gate, N{x) is the trap concentration, n{.';) is the concentration of filled traps, a,. is the effective electron capture cross section. 4~{x) is the light intensity, at-is the trap centre photoionization effective cross section and/ is the injected current density'. The effective electron capture cross section is related to the microscopic capture cross section a: /'lh
% = ---a
141
Ud
where v,, {t,a} is the thermal {drift} electron velocity. For electric fields in the range f r o m 2 x l 0 s t o 3 x l 0 {'Vcm ~ , c e i s t h o u g h t t o b e c l o s e t o c , j , S ; t h e n % = a . Integrating eqn. (31 over the oxide thickness and time we obtain AOt - N , % - A~iiT. a~ i f A Q ' d O ' " i AOi.} where
AQaf :,-,
£ ' , f o nq) dx dt
(5)
j"
AQi,,i =
.j dt
11
is the injected charge per unit area. AQ, =
n(.,c}dx }
is the trapped charge per unit area and N, =
N i x I d.\ }
is the effective trap density per unit area. The time t was related only to the duration of the injections, because during the measurements of the ]ph V characteristics changes in Ot were negligible. In these integrals the first injection 10, t~} was omitted, so we carried out an integration from t~ to t and thus used the symbols AQ~,.i and AQ, instead of O~,j and O,. The last term in eqn. {5} can be estimated from the photodepopulation experiment. It appeared to be negligible in our investigations. Thus AQ,
G j'AQt dQ,. i
Figure 2 shows the plots of AQt//AQini as a function of {J'AQ, dQi,j}/;AQi,,i for several applied electric fields. The lines are fitted through the points calculated from the
E L E C T R I C FIELD D E P E N D E N C E OF C A P T U R E CROSS SECTION IN S i O 2
6Q~
335
10-2
1.50
180
0.50
"--~~
-8,, •
-
o
~
-20V
o o
~
O
~
-28V .
.
.
.
0
,
,
,
,
5
I
i
jZ~q~dO,~
AQ~j
1011
ecm
,
i
,
i
15
10
2
Fig. 2. The ratio AQt/AQi,j of the trapped charge and the injected charge as a function of (SAQtdQi.:,)/AQinj for several values of the external electric field applied during photoinjection. The lines are fitted through the points calculated from experimental results. experimental results. A comparison of the parameters for these lines (the slope and the intersection) with the parameters of eqn. (6) gives the values of a~ and N,ae. All the values o f N t found from eqn. (6) are close to 3 x 10 ~2 cm 2 Some samples, however, were degraded after a few injections; thus only the product Nto- e could be determined. If N ~ n, then
dn
NaJ-
dt
(7)
e
and
N,o" e --
AQ, AQinj
(8)
In practice as few as two injections are enough for determining Nto-e. The first injection is necessary to fill the interfacial traps (see assumption (2)). F r o m the lph--V curve shifts after the second injection we can determine AQ, and then Nto e. Therefore, inserting the mean value of N t (3 × 1012 cm 2) in the product Nto- e obtained from eqn. (8), we obtained the value ofa~ for that case.
336
I. S T R Z A L K O W S K I , M. MAR('ZEWSKI, M. KOWALSKI
The capture cross section a~ v e r s u s the external electric field applied to the sample during photoinjection is presented in Fig. 3. The figure shows that the electron capture cross section decreases with increasing average oxide electric field, approximately as E ~~, approaching a value of 10 15cm2 at about 10~'Vcm 1. The electron capture cross sections for the coulombic attractive centres are greater (10 ~ 10 ~a cm-'t ~' and vary with the electric field ~ as E 3:2. For the "simple" neutral centres, however, the electron capture cross sections are smaller ( 10 ~' 10 ~s cm-') and arc a very weak function of the electric field ~. Taking these remarks into consideration we suppose that the trapping centres due to the boron ions implanted through the SiO2 layer have a dipolar character. One of the possible models for such a trapping centre is ~Si"
Si~
It contains two threefold-coordinated silicon atoms. If the trap is "'empty" one of the silicon atoms binds two electrons in a dangling sp 3 orbital (negative pole) while the other has no electron in a broken bond !positive pole). The simplest way in which the dipole-type centre may be formed is by the displacement of the oxygen atom. The trapping of an electron by an ideal electric dipole and bound energy levels in the dipolar field have been considered by Belmont 1", Wallis e t a l . ~ and Fox and
Turner
~2
CT'ecrn2i lff I~-
\\\\
~
N,\
0
\\\ \ \\
\
\
"5\ \ \
\
•
\.
"N
1C 15
\
©
O
\\ \\
q0 6
E %m
Fig. 3. The capture cross section a as a l'unclio~l of the external clcclric fidd t: applied d u r i n g p h o l o i n j e c t i o n : ( ) , c a l c u l a t e d from cqn. (61: O. c a l c u l a t e d [rom CL]I). {~) tl~,il/g ~l Ille~ll/ ~alUC of N~ o1 3 × 10 ~ cm x: , obtained b~ filling through the points \~ith the ~caM-squarc% lllcthod Islopc /, 1.~1,
ELECTRIC FIELD DEPENDENCE OF CAPTURE CROSS SECTION IN S i O 2
337
We suppose that the capture of an electron probably proceeds by the singlephonon cascade emission process ~3 involving successive transitions to the deeper bound states created by the dipole field, which finally results in the trapping of the electron at the positive pole of the dipolar trap centre. The increase in the external field shrinks the volume in which an electron may be captured by the dipolar field and induces a reduction in the capture cross section. The screening effect of the negative pole can make the observed capture cross section smaller and its field dependence a little higher than that for a single coulombic attractive centre. The exact explanation of our results needs some theoretical investigations for which knowledge of the dipole site parameters and its angular distribution in the oxide is necessary. REFERENCES
1 S.T. Pantelides (ed.), The Physics O/SiO 2 andlts hlte~jitces, Pergamon, New York, 1978. 2 M. Marczewski and I. Strza|kowski, Appl. Phys. A, 29 (1982), in the press.
3
R.J. PoweIlandC, N. Berglund, J. AppI. Phys.,42(1971)4390.
4 5
D.J. DiMaria, J. Appl. Phys., 45 (1974) 5454. 1. Strzatkowski, M. Marczewski. T. Asifiski, H. D r ~ y k and Z. Majewski, Pr. hT.s't. Technol. Elektron., 4 (1980) 1. D.J. DiMaria, J. Appl. Phy.~.,47(1976)4073.
6
7 8 9 10 11 12 13
D.J. DiMaria, Z . A . WeinbergandJ. M. Aitken, J. Al~pI. Phys.,48(1977) 898. R.C. Hughes, Phys. Ret'. Lett.,30(1973) 1333. D . J . DiMaria, in S. T. Pantelides (ed.), The Physics ~?/ SiO 2 and It.~ h~tel;/hces, Pergamon. New York, 1978, p. 160. M . R . Belmont, Thin SolidFihns, 28(1975) 149.
R.F. Wallis, R. HermanandH. W. Milnes, J. Mal. Spectrosc.,4(1960) 51. K. F o x a n d J. E. Turner, J. C71em. Phys.,45(1966) 1142. M. Lax, Phys. Rer., 119(1960) 1502.
331
ELECTRONICS AND OPTICS
ELECTRIC FIELD D E P E N D E N C E O F T H E CAPTURE CROSS SECTION O F I O N - I M P L A N T A T I O N - I N D U C E D TRAPS IN SiO 2 LAYERS I. S T R Z A L K O W S K I , M. MARCZEWSK1 AND M. KOWALSKI
hl,~tittttc ~/ PIu',~'ics, Warsaw Techtlical L:nit,er,~'it.v, Kos: r/~owa 75, 00-662 Warsaw (Poland) (Received April 7, 1982: accepted May 20, 1982)
Trapping centres introduced into an SiO2 layer during boron implantation through the oxide into the silicon substrate were investigated. The internal photoemission method was used to determine their capture cross section and its electric field dependence. A possible microscopic model of these centres, with a dipolar character, is presented.
I. INTRODUCTION S i O 2 is a very important material in electronics technology and its physical properties have been widely investigated during the last few years 1. For instance, S i O 2 is extensively used as an insulator layer in metal/insulator/semiconductor structures forming metal/oxide/semiconductor(MOS)-type devices. A convenient doping technique which is widely used in the fabrication of semiconductor devices and integrated circuits based on MOS structures is the ion implantation technique. The use of this technique produces a large variety of defects acting as electron- or hole-trapping centres. Charge trapping in the SiO 2 layer of MOS structures is responsible for the deterioration in electrical properties and the instability of MOS-type devices. In order to remove the implantation-created traps high temperature (about 1000 C ) post-implantation annealing is typically used. It removes practically all implantation defects but causes the diffusion of dopant atoms and presumably creates some additional interface states. Our aim in this work was to investigate the character of traps remaining after low temperature (500 C ) annealing in the S J O 2 layer and produced by a typical MOS integrated circuit fabrication process, i.e. the implantation of B + ions through this layer into the silicon substrate. We have already studied some trapping properties of these sites z. In this work we investigated the electric field dependence of the trap centres.
2. EXPERIMENTAL DETAILS
The devices used in this study were MOS capacitors fabricated on p-type Si(100) wafers with a resistivity of 1-10 [2 cm. The silicon substrates were oxidized 0040-6090/83/0000-0000/$03.00
~ ElsevierSequoia/Printedin The Netherlands
332
1. S T R Z A L K O W S K I , M. M A R ( ' Z I i W S K I , M. K ( ) W A I , S K I
in dry oxygen at 1100 C without HC1 to a thickness of 150nm. Boron ion implantation was then performed at tin energy of 75 keV and a dose of 10 is ions cm 2. In this case, according to the kinhard Scharff Schi0tt theory, the mean range of B + ions in SiO2 is equal to 320 nm, thus practically all the B + ions lay in the silicon substrate. After the implantation, samples were annealed in an N e ambient lit 500 C for 120 min. Then rectangular semitransparent gold electrodes with an area of 0.06 cm 2 were deposited. Ohmic contacts were prepared on the back sides of the wafers. The reference sample was prepared by the same procedure, excluding the implantation process. Capacitance voltage ((" t') measurements showed that after fabrication the SiO 2 layer of the MOS structures contained quite a small amount of negative charge, the same for both the implanted lind the reference samples. Investigations were carried out with the internal electron photoemission method 3. The experimental set-up was typical'*'5. Traps in the SiO, layer were charged by means of electron photoinjection. This was achieved by illuminating the semitransparent gold electrode with the full spectrum of a 40 W deuterium lamp for various negative gate polarities. The injected charge density Q~,,i was determined to an accuracy of about 10 ~-' electrons cm -' by lime integration of the injection current density ](t). The injection current was measured with a U N I P A N 219 electrometer. The trapped charge in the SlOe layer was characterized by the photocurrent voltage (lph--V) technique complemented by the C I/technique. The photocurrent Iph induced with a non-modulated monochromatic UV beam was measured electrometrically at various bias voltages with a positive (V+ I and a negative (V t metal electrode. The wavelengths were 260 nm and 276 nm respectively. The parameters of the traps were determined by the method developed by DiMaria ~'. This method is based on the fact that charging of the bulk of the SiO, layer results in parallel shifts in the Iph- V characte[istics along the voltage axis (A l ~_ for positive gate polarity (silicon injectingl and A[ / for negative gate polarity (gold injecting)). The charge centroid 5: measured from the Au SiO, interface and the total trapped charge Q, per unit area are related to these shifts by the following": .~=L
1
Av,
Q, = !:<["tAV
~11
-Al,
I
(2~
where g is the oxide thickness, c0 is the free-space permittivity lind ~:~ is the low frequency permittivity of SiO2. The value of the trapped charge O~ was determined from eqn. (2) to an accuracy of about 5 x 101° electrons cm : The injection of electrons into the SiOe layer was accomplished under various voltage polarities. For a given gate polarity a sequence of photoinjections was performed and after each photoinjection the l~h- V characteristics were measured. The mean shifts in successive I V curves allowed us to determine the charge trapped during the successive steps of injection and hence the relation O,(Q~,i). By monitoring the change with time in Q, and .,7: as trapping under a given voltage proceeded, the capture cross section for a given field strength and the total number N, of traps per unit area were determined with the lirst-order kinetic equation (eqn. (3) belowl.
ELECTRIC FIELD DEPENDENCEOF CAPTURE CROSS SECTION IN SiO 2
333
3. RESULTSAND DISCUSSION In order to determine the electrophysical parameters of the trapping centres we made the following assumptions. (1) There are two dominating types of trapping centre in the implanted SiO2 layer investigated. (2) Traps of the first kind are located very near the interfaces of the oxide. They have a very large cross section. Since they were also observed in the reference unimplanted structure they are treated as an unwanted result of the contact preparation and are not the object of our interest. (31 Trapping centres created by the boron ion implantation through the layer and remaining after 500 C annealing are distributed in the bulk of the layer. They can be characterized by a single value of the electron capture cross section. It should be mentioned that the above assumptions do not exclude the existence in the investigated layers of other types of trap. with smaller capture cross sections, which could be revealed after the injection of higher charge densities than those used in this experiment. Analysing the experimental data we found that the Iph-V c u r v e s for implanted structures underwent parallel shifts after all subsequent photoinjections but not after the first injection. Such parallel shifts were not observed for unimplanted structures. The first injection for implanted and unimplanted samples not only caused a shift in the lph V curves under both plus and minus gate polarization but also changed the shapes of the curves. This is evidence that during the first photoinjection the interracial layers as well as the oxide bulk were charged I which strongly supports the assumption concerning the existence of the first kind of trap. The shifts observed after the second and further injections allowed us to compute the charge Q, captured at the bulk traps. Q, is presented in Fig. 1 as a function of the injected charge Q~.j for several injection electric fields. It should be explained that it is not possible to calculate Q~ for the first injection directly from the lph-V curve shifts for the above-mentioned reasons. We had to approximate this quantity as NFre(Q~,j) o, where (Qi,,j)o is the charge injected during the first photoinjection.
Q.
I
[
I
--~
--- --T
]
•
--
"-T
r
~
J
~----T~
100
g.~j
1011 ecru2 20I
/
15
°
_
10
./ 4o
6'o
80
1013e cm2
Fig. 1. The trapped charge Q, as a function of the injected charge Q~ojfor several values of the external field applied during photoinjection.
334
I. S T R Z A L K O W S K I ,
M. M A R ( ' Z E W S K I ,
M. K O W A L S K I
The values of 5-/L found after each injection step are close to 0.5, which could show" 7 that the distribution of the implantation-induced traps and their charging are practically uniform in the SiO2 layer. However, after the last prolonged injections was significantly shifted towards smaller values, In order to describe changes in the trap occupation numbers during photoinjection we used the first-order kinetic equation
2,/L
_6nat= {N(x)-n{xj}i'a"-n{\34}{-\)~r'
{31
where x is the distance from the gate, N{x) is the trap concentration, n{.';) is the concentration of filled traps, a,. is the effective electron capture cross section. 4~{x) is the light intensity, at-is the trap centre photoionization effective cross section and/ is the injected current density'. The effective electron capture cross section is related to the microscopic capture cross section a: /'lh
% = ---a
141
Ud
where v,, {t,a} is the thermal {drift} electron velocity. For electric fields in the range f r o m 2 x l 0 s t o 3 x l 0 {'Vcm ~ , c e i s t h o u g h t t o b e c l o s e t o c , j , S ; t h e n % = a . Integrating eqn. (31 over the oxide thickness and time we obtain AOt - N , % - A~iiT. a~ i f A Q ' d O ' " i AOi.} where
AQaf :,-,
£ ' , f o nq) dx dt
(5)
j"
AQi,,i =
.j dt
11
is the injected charge per unit area. AQ, =
n(.,c}dx }
is the trapped charge per unit area and N, =
N i x I d.\ }
is the effective trap density per unit area. The time t was related only to the duration of the injections, because during the measurements of the ]ph V characteristics changes in Ot were negligible. In these integrals the first injection 10, t~} was omitted, so we carried out an integration from t~ to t and thus used the symbols AQ~,.i and AQ, instead of O~,j and O,. The last term in eqn. {5} can be estimated from the photodepopulation experiment. It appeared to be negligible in our investigations. Thus AQ,
G j'AQt dQ,. i
Figure 2 shows the plots of AQt//AQini as a function of {J'AQ, dQi,j}/;AQi,,i for several applied electric fields. The lines are fitted through the points calculated from the
E L E C T R I C FIELD D E P E N D E N C E OF C A P T U R E CROSS SECTION IN S i O 2
6Q~
335
10-2
1.50
180
0.50
"--~~
-8,, •
-
o
~
-20V
o o
~
O
~
-28V .
.
.
.
0
,
,
,
,
5
I
i
jZ~q~dO,~
AQ~j
1011
ecm
,
i
,
i
15
10
2
Fig. 2. The ratio AQt/AQi,j of the trapped charge and the injected charge as a function of (SAQtdQi.:,)/AQinj for several values of the external electric field applied during photoinjection. The lines are fitted through the points calculated from experimental results. experimental results. A comparison of the parameters for these lines (the slope and the intersection) with the parameters of eqn. (6) gives the values of a~ and N,ae. All the values o f N t found from eqn. (6) are close to 3 x 10 ~2 cm 2 Some samples, however, were degraded after a few injections; thus only the product Nto- e could be determined. If N ~ n, then
dn
NaJ-
dt
(7)
e
and
N,o" e --
AQ, AQinj
(8)
In practice as few as two injections are enough for determining Nto-e. The first injection is necessary to fill the interfacial traps (see assumption (2)). F r o m the lph--V curve shifts after the second injection we can determine AQ, and then Nto e. Therefore, inserting the mean value of N t (3 × 1012 cm 2) in the product Nto- e obtained from eqn. (8), we obtained the value ofa~ for that case.
336
I. S T R Z A L K O W S K I , M. MAR('ZEWSKI, M. KOWALSKI
The capture cross section a~ v e r s u s the external electric field applied to the sample during photoinjection is presented in Fig. 3. The figure shows that the electron capture cross section decreases with increasing average oxide electric field, approximately as E ~~, approaching a value of 10 15cm2 at about 10~'Vcm 1. The electron capture cross sections for the coulombic attractive centres are greater (10 ~ 10 ~a cm-'t ~' and vary with the electric field ~ as E 3:2. For the "simple" neutral centres, however, the electron capture cross sections are smaller ( 10 ~' 10 ~s cm-') and arc a very weak function of the electric field ~. Taking these remarks into consideration we suppose that the trapping centres due to the boron ions implanted through the SiO2 layer have a dipolar character. One of the possible models for such a trapping centre is ~Si"
Si~
It contains two threefold-coordinated silicon atoms. If the trap is "'empty" one of the silicon atoms binds two electrons in a dangling sp 3 orbital (negative pole) while the other has no electron in a broken bond !positive pole). The simplest way in which the dipole-type centre may be formed is by the displacement of the oxygen atom. The trapping of an electron by an ideal electric dipole and bound energy levels in the dipolar field have been considered by Belmont 1", Wallis e t a l . ~ and Fox and
Turner
~2
CT'ecrn2i lff I~-
\\\\
~
N,\
0
\\\ \ \\
\
\
"5\ \ \
\
•
\.
"N
1C 15
\
©
O
\\ \\
q0 6
E %m
Fig. 3. The capture cross section a as a l'unclio~l of the external clcclric fidd t: applied d u r i n g p h o l o i n j e c t i o n : ( ) , c a l c u l a t e d from cqn. (61: O. c a l c u l a t e d [rom CL]I). {~) tl~,il/g ~l Ille~ll/ ~alUC of N~ o1 3 × 10 ~ cm x: , obtained b~ filling through the points \~ith the ~caM-squarc% lllcthod Islopc /, 1.~1,
ELECTRIC FIELD DEPENDENCE OF CAPTURE CROSS SECTION IN S i O 2
337
We suppose that the capture of an electron probably proceeds by the singlephonon cascade emission process ~3 involving successive transitions to the deeper bound states created by the dipole field, which finally results in the trapping of the electron at the positive pole of the dipolar trap centre. The increase in the external field shrinks the volume in which an electron may be captured by the dipolar field and induces a reduction in the capture cross section. The screening effect of the negative pole can make the observed capture cross section smaller and its field dependence a little higher than that for a single coulombic attractive centre. The exact explanation of our results needs some theoretical investigations for which knowledge of the dipole site parameters and its angular distribution in the oxide is necessary. REFERENCES
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