- Email: [email protected]
Study of E3 trap annealing in GaAs by DDLTS technique
Solid State Communications, ’ Printed in Great Britain.
Vol. 44, No. 1, pp. 41-45,
1982.
STUDY OF E3 TRAP ANNEALING
0038-1098/82/370041-05$03.00/O Pergamon Press Ltd.
IN GaAs BY DDLTS TECHNIQUE
S. Loualiche, A. Nouailhat and G. Guillot Laboratoire
de Physique de la Mat&e,* Institut National des Sciences Appliquees de Lyon, 20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France (Received 8 March 1982, in revised form 6 April 1982 by E. F. Bertau t)
Double correlation deep level transient spectroscopy (DDLTS) has been used to determine the profile of the electron trap E3 (E, - 0.33 eV) introduced in n-type GaAs after proton irradiation at 300 K and annealing at 190°C. We show that E3 anneals without long range migration by close pair recombination mechanism. and after a 30 min annealing at 190°C and we compare these two profiles. If a long range migration exists during annealing, we should observe a spreading of the profile [IO], but in the case of local recombination mechanism between close pairs, just a diminution of the trap concentration without a spreading of the profile shall be seen. The result obtained for the E3 trap shows unambiguously that the annealing of this defect occurs without diffusion.
1. INTRODUCTION IN RECENT YEARS, the defects created by electron irradiation at room temperature on n-type GaAs have received particular attention. The work of Lang [l-4] gives seven defects created during these experiments: five electron traps (E, to Es) and two hole traps (He, Hr). All these defects have been studied [2,5] and the main results arising from the different works are the following: these different traps have been identified as being simple intrinsic defects which anneal at about 2OO’C (Stage III of Thommen [6]) with first order kinetics. But there are two different interpretations about the annealing mechanism: (i) Lang [3] suggests that this annealing mechanism is a long range migration of a defect to the donor atoms which act as sinks for this defect. (ii) Pons and co-workers [S] interpreted their annealing experiment results by a direct recombination between close pairs like vacancy-interstitial or vacancy-antisite defects. From these experiments they concluded that the Ez trap can be identified with a vacancy. More recent work [7] shows that all electron irradiation defects created on n-type GaAs are related to a displacement of As atoms and not to Ga atoms [4] as previously believed. In this work, we are principally interested in the annealing of the E, level created under proton irradiation on n-GaAs at room temperature. This level and the Hr trap are attributed by Lang [2] to two different charge states of the same defect, and the E3 level is found to be an acceptor-like trap [8]. To observe how this level anneals, we use the property of the protons to cause localized damage in solids. We draw then the profile of E3 by DDLTS [9] after the proton irradiation before
2. EXPERIMENTS 2.1, Experimental conditions The samples used in this study come from the same ( 10 0) n-type GaAs layer grown by VPE technique. The first sample is used to study the initial carrier concentration, native defects and irradiation conditions. This sample has a surface of 4 x 4 mm2 on which after etching and cleaning a thin Au layer (2 5008) has been evaporated to fabricate a Schottky barrier of 4.15 mm2. The carrier profde of this material obtained by C(V) is uniform (n = 7.3 x 10” cm-j). A DLTS scan performed on this material before irradiation shows no native trap having a concentration greater than 1013 cme3 (low limit of our measure). After these experiments a proton implantation (90 keV; 6 x 1Or0 H+ cmw2) is performed at room temperature on this Schottky diode. A DLTS study after irradiation shows that the usual traps (E3, E4, ES) observed above nitrogen temperature have been introduced [ 111. After the C(V) measurements of the carrier profile we do not observe a complete carrier compensation in the irradiated zone of the sample (around proton range RP) for our dose. A second set of two samples coming from the same wafer has been used. These two samples have been cleaned and positioned on the same sample holder to be irradiated at the same time. The implantation was performed at room temperature with a proton energy of
* Equipe de recherche associee au CNRS. 41
42
E3 TRAP ANNEALING
Vol. 44,lNo. 1
IN GaAs BY DDLTS TECHNIQUE
90 keV and a dose of 5 x 10” cmu2. One of these two samples was cleaned after the proton bombardment to be used for the fabrication of a Schottky barrier. DLTS and DDLTS experiments are then done on this diode to observe the created traps and their concentration profile. The other sample has been annealed at 190°C during 30 min under hydrogen atmosphere before the fabrication of the Schottky barrier used to study the annealing of the E3 level. 2.2. DDL TS method This method known as a double correlation DLTS has been introduced by Lefevre and Schulz [9] and helps to draw trap concentration profiles. This method is used as follows: (i) first, a DLTS scan is performed on the sample to select the level to be studied, to know its thermal energy and to choose the temperature at which the trap concentration will be drawn for a given experimental window rate (e,); (ii) second, the sample is cooled (or heated) to the chosen temperature and the concentration profile of the selected trap will be drawn.
*cm*b*p; a
0
XfP
‘fr
xr
Nevertheless, we cannot use the formula given by Lefevre and Schulz in our case for the following reasons: (i) these authors use for their calculation a solution of Poisson’s equation in the case of a donor-like trap (acceptor-like defect in our case); (ii) there is a confusion in their calculation between the exact carrier concentration profile and the profile n,(x) obtained by C(V) techniques [8] given in formula (1); (iii) their calculations one deep trap.
are made only in the case of
Therefore, we develop here the exact calculations to have the good theoretical expression of the trap concentration. To measure the trap profile on a sample, the carrier profile of this sample is needed. On a Schottky barrier this can be drawn by C(V) method. It is known that in the presence of an acceptor-like trap, the solution of Poisson’s equation is written as: ‘f Z;
=
J!
2xn,(x)
dx - 1 2xnT(x)
0
loz
=
--&m+
0
dx + J‘ 2xnT(x)
dx,
0
vfd,
where Vn is the built-in potential, Vn is the applied reverse voltage, No is a normalization concentration, ~Vono(x) is the initial carrier concentration, Nero, is the trap concentration, I is the total depleted zone of the junction and If is the point in the depleted region I
Fig. 1. (a) Electronic structure of a Schottky barrier (right) during a quiescent reverse voltage ( VR: left) and in presence of an acceptor-like trap. VB: built in potential; EC: conduction band edge; E,: Fermi level position; ET: acceptor trap level; I: depletion zone limit; If: position in the depletion region where the trap level crosses the Fermi level. The crosses (+) show the ionized donors, the minus (-) and (0) the filled and empty traps respectively. (b) Structure of a Schottky barrier during (upper right) and after (low right) the refiling pulse V’ (upper left). VR is the quiescent reverse voltage. xp, xfp are respectively the depletion zone limit and the crossing point between the trap level and the Fermi level during the pulse VP. x,, xfr have the same signification after the pulse I’, at time t. The variation of the measured capacitance AC at time t (low left) comes from the emission of electrons by the filled traps situated between the positions xfp and xfr (low right). (c) The upper left scheme shows a sequence of a double height pulse V, and I$ used in the DDLTS technique, The right diagram shows a Schottky barrier at time t after the applied pt$se vp (or V,). The positions xr, xti, xp, xfp (or xr, xfr, xp, x&) after the pulse V, (or Vi) have the same signification as described in the case of a single height pulse scheme of(b). The AC shown in low left figure is the difference between the measured capacitance after the pulse V, and I’d at time t. This difference comes from the emission of electrons by the filled traps situated between (x fr, xir) and (xfp, xi,) as shown by the calculations in the text.
E3 TRAP ANNEALING
Vol. 44, No. 1
43
IN GaAs BY DDLTS TECHNIQUE
where the trap level is crossing the Fermi level [seTFig. l(a)]. In this case, if the usual C(V) method is applied to calculate the carrier concentration, we obtain [S] :
+ C nTi(X;Zri - x&i) - e+[nTO(xfr)(xC i -
+,>I.
trO(XfPw$J
By using the expression of n,(x) (1) we have:
= NO&(0 with 1 = E/C;C = capacitance/unit
-x$)
at quiescent voltage
area and n,(Z) =
no(l) - M) + (~f/OMf). If more than one acceptor trap is present, as is the case under proton irradiation, the result is:
+ C nTi(Xfri)XrXfria
and: i runs over all the active traps. If we apply this result to the problem under study, and if we choose a temperature at which only one defect (nTO) can be observed, we arrive [case of Fig. l(b)], after a refilling pulse V, and at the time t, to: xi,
= i’2xne(x) 0
dx -x
7 i 0
Xfri +x
- eet”’ j
0
2xnTO(x)dx.
If we use two refilling pulses [Fig. l(c)] with different heights VP and Vi, after the first pulse VP at the time t, we arrive at the same expression as above for the solution to Poisson’s equation. After the pulse I’d at the time t [Fig. l(c)], this solution stays having the same form as above but the distances (xor, x,, xfp, xfr . . .) become (x&.,x: . . .). If we make the difference at time t between the measure after VP and I$, we have: xr 2x J %I
(
+ c i
If we put x, - xfri =
dx - emt17
i,
2xnTo(x)
~1 -x;,i
-xZ)
eetj7(. .
= hi, we
.
.).
can then write:
- C hi(x;ri -xfri) i
.).
To arrive to an applicable formula, we make the assumption that: ~,(x,)(x:~ -x:) 3 Ci nTi(xfpi) hi(x;,i -xfri); if we do not forget that Xi < X, and thi s assumption gives 2n,(x,) 3 xh - xfri =x;-x~, pi nTi(xfri) (i.e. there is no carrier compensation). If we remember that we are working;t constant reverse voltage Vn [Fig. l(c)], we have x0,. = xi, = (2e/qN,)( I’, + I’,) and knowing that the pulse heights are such that VP> Vi, we conclude that: (i) xp < XL and xfp < xkp; (ii) x, > XL and xfr > xir (more traps filled during the pulse VP than during Vi).
nTo(xfp)
= et’rn,(x,)
+r
J’ 2xnTi(x) Xfri
-e-t’7(.
We arrive at the definite formula:
no(x) - z n&x) dx i 1
Xfri
+ C nTi(Xfr)
X [(X;2r-Xx3p)-(X;,iX:.-Xxf,iX,)]
X IZTi(Xfri) -
%fP
I2 2=' xor-xor
-xr’)
f2 2 = n,(x,)(x;2 xor - xor
dx
Xfr
2xnn(x)dx
1 i
2xnn
I2 2 = n,(x,)(x$ xor - xor
dx
X r2
4P
(XfP
-
$1 +
%dxfr) QdxfP)
(2) 7.
(Xfr
-
4:)
“fr -
j
2xn.,(x)dx
with x, = e/C and C measured at the reverse voltage V,. xk =x, - (x:/Ax); Ax = (e/AC), AC measured as shown in Fig. l(c). hz = (2e/@e)(E~ -ET).
. i
XfP
If we choose small distance amounts (x,, XL), (xf,, xip), we can consider that the carrier and defect concentrations no(x) and II~(X) stay constant; we are then led to:
(Xfp)
=
(xf,.)' =
nO(xr)-
x i
(xi2 -xf>
(xp)'-k
(xr)' -A
with Xi =
1 x-h
2(x - z)n,(z)
For the reasons cited above, formula (2), which
dz.
E3 TRAP ANNEALING
IN GaAs BY DDLTS TECHNIQUE
Vol. 44, No. 1
(Fig. 2). This profile can be expressed as follows, by using radiation damage theory: nTO(x) x
02
04
06
08
IO
Pm
Fig. 2. Profiles obtained by C(V) and DDLTS method after a proton im ldntation at room temperature (90 keV - 5 x 10% cme2) on n-GaAs. Before annealing: (. . .) dotted lines. The upper curve is the carrier concentration obtained by the C(V) method [n,(Z) in the text]. The low curve is the E3 trap (created by the irradiation) profne obtained by the DDLTS method as described in the text. After annealing: 190 + 5°C 30 min (AM) triangle curves. Upper curve: carrier concentration [n,(Z)]. Lower curve: E3 trap profile. The experimental conditions used to draw the trap profiles byDDLTSareEc-EE,=0.33eV;T= 190K;r= 39msec;t=lOmsec;I’~=0.6V;T/d=0.4V. gives n&x), is a little different from that given by Lefevre et al. [9]. The experimental technique used in this work, is to choose the temperature at which the DLTS peak is maximum for the trap under study with a given experimental window rate. At this temperature, the C(V) profile n,(x) is drawn and stored in a computer. After that for a given applied voltage the value of n,(x) andx are known, and after the measure of AC [Fig. l(c)] the profile nT(x) is deduced from formula (2) [see Fig. l(c) for the experimental technique and Fig. 2 for the E, level profile and experimental conditions].
3. RESULTS AND DISCUSSION The profile of the E’, level (EC - 0.33 eV) has been drawn by DDLTS technique as described in this work. This profile is Gaussian type in the region situated after the proton range R, toward the bulk of the sample
7
=
nTl(x
exp (- (x - R,)2/2ARi).
nT1 comes from the electronic stopping processes in the solid, and nm comes from the nuclear stopping processes. In our experiments we measure nn = 1.15 x 10i5 cm -3 for a proton irradiation dose of 5 x 10” cmm2 and an energy of 90 keV. The measured R, and AR, are respectively 0.75 and 0.1 pm before the annealing (Fig. 2). After annealing at 190 + 5°C for 30 min, we measure R, = 0.75 pm, AR,, = 0.09pm and nT2 = 3.8 x lOr4 cme3 (Fig. 2). We observe a decrease in the E, trap concentration by a factor 3. An annealing is observed, but the results show clearly that this annealing occurs without spreading of the defect profile. But we must bear in mind that the spatial resolution of the method cannot be less than the Debye length (0.03 pm in our experiment). An additional sample irradiated in the same conditions and annealed at 22O”C, shows that the E, level is completely annealed (its concentration is less than 1013 cmm3). These experiments show unambiguously that after proton implantation which gives us a very localized defect profile, the annealing of the Es level occurs without long range migration. This E, level is created during electron [2] and proton [ 11, 121 irradiation on n-type GaAs, it acts as an acceptor-like trap [8] and anneals with first order kinetics at 200°C [3]. As suggested by Pons et al. [S], and in opposition to the result of Lang [3], the annealing mechanism of E3 level is consistent with a mutual recombination of close pairs. Nevertheless we note that if there is a migration with a diffusion length less than the Debye length (0.03 pm), it cannot be be observed by these experiments. 4. CONCLUSION The result of this study is focused on the E, trap created by the irradiation in n-type GaAs. This trap is always present even after the bombardment at nitrogen temperature [ lo], it is introduced linearly with the electron dose [2], and we can reasonably say that it is a primary defect. Lang [2] suggests that E, level andH, level are the different charge state of the same defect. It probably comes from a primary defect involving As sublattice [7] and it is an acceptor-like trap [8]. In accordance with the result of Pons et al. [5], we show that E3 anneals without long range migration and this annealing mechanism is consistent with close pair recombination mechanism.
Vol. 44, No. 1
E3 TRAP ANNEALING
IN GaAs BY DDLTS TECHNIQUE
Acknowledgements - The authors wish to acknowledge L. Holland and J.P. Hallais of LEP for growth of VPE layers and financial support from the Delegation Generale a la Recherche Scientifique et Technique (Contract No. 79.7.0724).
5. 6. 7. 8.
REFERENCES 1. 2. 3. 4.
D.V. Lang, J. Appl. Phys. 45,3023 (1974). D.V. Lang & L.C. Kimerling, Inst. Phys. Conf: Ser. 23,581 (1975). D.V. Lang, Inst. Phys. Con5 Ser. 31,70 (1977). D.V. Lang, R.A. Logan & L.C. Kimerling, Phys. Rev. B15,4874(1977).
9. 10. 11. 12.
45
D. Pons, A. Mircea & J.C. Bourgoin, J. Appl. Phys. 51,4150(1980). K. Thommen. Rad. Eff 2.201 (1970). D. Pons & J.C. Bourg&t,ihys. kev. iett. 47, 1293 (1981). S. Loualiche, A. Nouailhat & G. Guillot, Solid State Electron. 25,577 (1982). H. Lefevre & M. Schulz, Appl. Phys. 12,45 (1977). F. Richou, G. Pelous & D. Lecrosnier, Appl. Phys. Lett, 31,525 (1977). G. Guillot, A. Nouailhat, G. Vincent & M. Baldy, Rev. Phys. Appl. 15,679 (1980). G. Guillot, S. Loualiche, A. No&hat & G.M. Martin, Inst. Phys. Confi Ser. 59, 323 (1981).
Vol. 44, No. 1, pp. 41-45,
1982.
STUDY OF E3 TRAP ANNEALING
0038-1098/82/370041-05$03.00/O Pergamon Press Ltd.
IN GaAs BY DDLTS TECHNIQUE
S. Loualiche, A. Nouailhat and G. Guillot Laboratoire
de Physique de la Mat&e,* Institut National des Sciences Appliquees de Lyon, 20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France (Received 8 March 1982, in revised form 6 April 1982 by E. F. Bertau t)
Double correlation deep level transient spectroscopy (DDLTS) has been used to determine the profile of the electron trap E3 (E, - 0.33 eV) introduced in n-type GaAs after proton irradiation at 300 K and annealing at 190°C. We show that E3 anneals without long range migration by close pair recombination mechanism. and after a 30 min annealing at 190°C and we compare these two profiles. If a long range migration exists during annealing, we should observe a spreading of the profile [IO], but in the case of local recombination mechanism between close pairs, just a diminution of the trap concentration without a spreading of the profile shall be seen. The result obtained for the E3 trap shows unambiguously that the annealing of this defect occurs without diffusion.
1. INTRODUCTION IN RECENT YEARS, the defects created by electron irradiation at room temperature on n-type GaAs have received particular attention. The work of Lang [l-4] gives seven defects created during these experiments: five electron traps (E, to Es) and two hole traps (He, Hr). All these defects have been studied [2,5] and the main results arising from the different works are the following: these different traps have been identified as being simple intrinsic defects which anneal at about 2OO’C (Stage III of Thommen [6]) with first order kinetics. But there are two different interpretations about the annealing mechanism: (i) Lang [3] suggests that this annealing mechanism is a long range migration of a defect to the donor atoms which act as sinks for this defect. (ii) Pons and co-workers [S] interpreted their annealing experiment results by a direct recombination between close pairs like vacancy-interstitial or vacancy-antisite defects. From these experiments they concluded that the Ez trap can be identified with a vacancy. More recent work [7] shows that all electron irradiation defects created on n-type GaAs are related to a displacement of As atoms and not to Ga atoms [4] as previously believed. In this work, we are principally interested in the annealing of the E, level created under proton irradiation on n-GaAs at room temperature. This level and the Hr trap are attributed by Lang [2] to two different charge states of the same defect, and the E3 level is found to be an acceptor-like trap [8]. To observe how this level anneals, we use the property of the protons to cause localized damage in solids. We draw then the profile of E3 by DDLTS [9] after the proton irradiation before
2. EXPERIMENTS 2.1, Experimental conditions The samples used in this study come from the same ( 10 0) n-type GaAs layer grown by VPE technique. The first sample is used to study the initial carrier concentration, native defects and irradiation conditions. This sample has a surface of 4 x 4 mm2 on which after etching and cleaning a thin Au layer (2 5008) has been evaporated to fabricate a Schottky barrier of 4.15 mm2. The carrier profde of this material obtained by C(V) is uniform (n = 7.3 x 10” cm-j). A DLTS scan performed on this material before irradiation shows no native trap having a concentration greater than 1013 cme3 (low limit of our measure). After these experiments a proton implantation (90 keV; 6 x 1Or0 H+ cmw2) is performed at room temperature on this Schottky diode. A DLTS study after irradiation shows that the usual traps (E3, E4, ES) observed above nitrogen temperature have been introduced [ 111. After the C(V) measurements of the carrier profile we do not observe a complete carrier compensation in the irradiated zone of the sample (around proton range RP) for our dose. A second set of two samples coming from the same wafer has been used. These two samples have been cleaned and positioned on the same sample holder to be irradiated at the same time. The implantation was performed at room temperature with a proton energy of
* Equipe de recherche associee au CNRS. 41
42
E3 TRAP ANNEALING
Vol. 44,lNo. 1
IN GaAs BY DDLTS TECHNIQUE
90 keV and a dose of 5 x 10” cmu2. One of these two samples was cleaned after the proton bombardment to be used for the fabrication of a Schottky barrier. DLTS and DDLTS experiments are then done on this diode to observe the created traps and their concentration profile. The other sample has been annealed at 190°C during 30 min under hydrogen atmosphere before the fabrication of the Schottky barrier used to study the annealing of the E3 level. 2.2. DDL TS method This method known as a double correlation DLTS has been introduced by Lefevre and Schulz [9] and helps to draw trap concentration profiles. This method is used as follows: (i) first, a DLTS scan is performed on the sample to select the level to be studied, to know its thermal energy and to choose the temperature at which the trap concentration will be drawn for a given experimental window rate (e,); (ii) second, the sample is cooled (or heated) to the chosen temperature and the concentration profile of the selected trap will be drawn.
*cm*b*p; a
0
XfP
‘fr
xr
Nevertheless, we cannot use the formula given by Lefevre and Schulz in our case for the following reasons: (i) these authors use for their calculation a solution of Poisson’s equation in the case of a donor-like trap (acceptor-like defect in our case); (ii) there is a confusion in their calculation between the exact carrier concentration profile and the profile n,(x) obtained by C(V) techniques [8] given in formula (1); (iii) their calculations one deep trap.
are made only in the case of
Therefore, we develop here the exact calculations to have the good theoretical expression of the trap concentration. To measure the trap profile on a sample, the carrier profile of this sample is needed. On a Schottky barrier this can be drawn by C(V) method. It is known that in the presence of an acceptor-like trap, the solution of Poisson’s equation is written as: ‘f Z;
=
J!
2xn,(x)
dx - 1 2xnT(x)
0
loz
=
--&m+
0
dx + J‘ 2xnT(x)
dx,
0
vfd,
where Vn is the built-in potential, Vn is the applied reverse voltage, No is a normalization concentration, ~Vono(x) is the initial carrier concentration, Nero, is the trap concentration, I is the total depleted zone of the junction and If is the point in the depleted region I
Fig. 1. (a) Electronic structure of a Schottky barrier (right) during a quiescent reverse voltage ( VR: left) and in presence of an acceptor-like trap. VB: built in potential; EC: conduction band edge; E,: Fermi level position; ET: acceptor trap level; I: depletion zone limit; If: position in the depletion region where the trap level crosses the Fermi level. The crosses (+) show the ionized donors, the minus (-) and (0) the filled and empty traps respectively. (b) Structure of a Schottky barrier during (upper right) and after (low right) the refiling pulse V’ (upper left). VR is the quiescent reverse voltage. xp, xfp are respectively the depletion zone limit and the crossing point between the trap level and the Fermi level during the pulse VP. x,, xfr have the same signification after the pulse I’, at time t. The variation of the measured capacitance AC at time t (low left) comes from the emission of electrons by the filled traps situated between the positions xfp and xfr (low right). (c) The upper left scheme shows a sequence of a double height pulse V, and I$ used in the DDLTS technique, The right diagram shows a Schottky barrier at time t after the applied pt$se vp (or V,). The positions xr, xti, xp, xfp (or xr, xfr, xp, x&) after the pulse V, (or Vi) have the same signification as described in the case of a single height pulse scheme of(b). The AC shown in low left figure is the difference between the measured capacitance after the pulse V, and I’d at time t. This difference comes from the emission of electrons by the filled traps situated between (x fr, xir) and (xfp, xi,) as shown by the calculations in the text.
E3 TRAP ANNEALING
Vol. 44, No. 1
43
IN GaAs BY DDLTS TECHNIQUE
where the trap level is crossing the Fermi level [seTFig. l(a)]. In this case, if the usual C(V) method is applied to calculate the carrier concentration, we obtain [S] :
+ C nTi(X;Zri - x&i) - e+[nTO(xfr)(xC i -
+,>I.
trO(XfPw$J
By using the expression of n,(x) (1) we have:
= NO&(0 with 1 = E/C;C = capacitance/unit
-x$)
at quiescent voltage
area and n,(Z) =
no(l) - M) + (~f/OMf). If more than one acceptor trap is present, as is the case under proton irradiation, the result is:
+ C nTi(Xfri)XrXfria
and: i runs over all the active traps. If we apply this result to the problem under study, and if we choose a temperature at which only one defect (nTO) can be observed, we arrive [case of Fig. l(b)], after a refilling pulse V, and at the time t, to: xi,
= i’2xne(x) 0
dx -x
7 i 0
Xfri +x
- eet”’ j
0
2xnTO(x)dx.
If we use two refilling pulses [Fig. l(c)] with different heights VP and Vi, after the first pulse VP at the time t, we arrive at the same expression as above for the solution to Poisson’s equation. After the pulse I’d at the time t [Fig. l(c)], this solution stays having the same form as above but the distances (xor, x,, xfp, xfr . . .) become (x&.,x: . . .). If we make the difference at time t between the measure after VP and I$, we have: xr 2x J %I
(
+ c i
If we put x, - xfri =
dx - emt17
i,
2xnTo(x)
~1 -x;,i
-xZ)
eetj7(. .
= hi, we
.
.).
can then write:
- C hi(x;ri -xfri) i
.).
To arrive to an applicable formula, we make the assumption that: ~,(x,)(x:~ -x:) 3 Ci nTi(xfpi) hi(x;,i -xfri); if we do not forget that Xi < X, and thi s assumption gives 2n,(x,) 3 xh - xfri =x;-x~, pi nTi(xfri) (i.e. there is no carrier compensation). If we remember that we are working;t constant reverse voltage Vn [Fig. l(c)], we have x0,. = xi, = (2e/qN,)( I’, + I’,) and knowing that the pulse heights are such that VP> Vi, we conclude that: (i) xp < XL and xfp < xkp; (ii) x, > XL and xfr > xir (more traps filled during the pulse VP than during Vi).
nTo(xfp)
= et’rn,(x,)
+r
J’ 2xnTi(x) Xfri
-e-t’7(.
We arrive at the definite formula:
no(x) - z n&x) dx i 1
Xfri
+ C nTi(Xfr)
X [(X;2r-Xx3p)-(X;,iX:.-Xxf,iX,)]
X IZTi(Xfri) -
%fP
I2 2=' xor-xor
-xr’)
f2 2 = n,(x,)(x;2 xor - xor
dx
Xfr
2xnn(x)dx
1 i
2xnn
I2 2 = n,(x,)(x$ xor - xor
dx
X r2
4P
(XfP
-
$1 +
%dxfr) QdxfP)
(2) 7.
(Xfr
-
4:)
“fr -
j
2xn.,(x)dx
with x, = e/C and C measured at the reverse voltage V,. xk =x, - (x:/Ax); Ax = (e/AC), AC measured as shown in Fig. l(c). hz = (2e/@e)(E~ -ET).
. i
XfP
If we choose small distance amounts (x,, XL), (xf,, xip), we can consider that the carrier and defect concentrations no(x) and II~(X) stay constant; we are then led to:
(Xfp)
=
(xf,.)' =
nO(xr)-
x i
(xi2 -xf>
(xp)'-k
(xr)' -A
with Xi =
1 x-h
2(x - z)n,(z)
For the reasons cited above, formula (2), which
dz.
E3 TRAP ANNEALING
IN GaAs BY DDLTS TECHNIQUE
Vol. 44, No. 1
(Fig. 2). This profile can be expressed as follows, by using radiation damage theory: nTO(x) x
02
04
06
08
IO
Pm
Fig. 2. Profiles obtained by C(V) and DDLTS method after a proton im ldntation at room temperature (90 keV - 5 x 10% cme2) on n-GaAs. Before annealing: (. . .) dotted lines. The upper curve is the carrier concentration obtained by the C(V) method [n,(Z) in the text]. The low curve is the E3 trap (created by the irradiation) profne obtained by the DDLTS method as described in the text. After annealing: 190 + 5°C 30 min (AM) triangle curves. Upper curve: carrier concentration [n,(Z)]. Lower curve: E3 trap profile. The experimental conditions used to draw the trap profiles byDDLTSareEc-EE,=0.33eV;T= 190K;r= 39msec;t=lOmsec;I’~=0.6V;T/d=0.4V. gives n&x), is a little different from that given by Lefevre et al. [9]. The experimental technique used in this work, is to choose the temperature at which the DLTS peak is maximum for the trap under study with a given experimental window rate. At this temperature, the C(V) profile n,(x) is drawn and stored in a computer. After that for a given applied voltage the value of n,(x) andx are known, and after the measure of AC [Fig. l(c)] the profile nT(x) is deduced from formula (2) [see Fig. l(c) for the experimental technique and Fig. 2 for the E, level profile and experimental conditions].
3. RESULTS AND DISCUSSION The profile of the E’, level (EC - 0.33 eV) has been drawn by DDLTS technique as described in this work. This profile is Gaussian type in the region situated after the proton range R, toward the bulk of the sample
7
=
nTl(x
exp (- (x - R,)2/2ARi).
nT1 comes from the electronic stopping processes in the solid, and nm comes from the nuclear stopping processes. In our experiments we measure nn = 1.15 x 10i5 cm -3 for a proton irradiation dose of 5 x 10” cmm2 and an energy of 90 keV. The measured R, and AR, are respectively 0.75 and 0.1 pm before the annealing (Fig. 2). After annealing at 190 + 5°C for 30 min, we measure R, = 0.75 pm, AR,, = 0.09pm and nT2 = 3.8 x lOr4 cme3 (Fig. 2). We observe a decrease in the E, trap concentration by a factor 3. An annealing is observed, but the results show clearly that this annealing occurs without spreading of the defect profile. But we must bear in mind that the spatial resolution of the method cannot be less than the Debye length (0.03 pm in our experiment). An additional sample irradiated in the same conditions and annealed at 22O”C, shows that the E, level is completely annealed (its concentration is less than 1013 cmm3). These experiments show unambiguously that after proton implantation which gives us a very localized defect profile, the annealing of the Es level occurs without long range migration. This E, level is created during electron [2] and proton [ 11, 121 irradiation on n-type GaAs, it acts as an acceptor-like trap [8] and anneals with first order kinetics at 200°C [3]. As suggested by Pons et al. [S], and in opposition to the result of Lang [3], the annealing mechanism of E3 level is consistent with a mutual recombination of close pairs. Nevertheless we note that if there is a migration with a diffusion length less than the Debye length (0.03 pm), it cannot be be observed by these experiments. 4. CONCLUSION The result of this study is focused on the E, trap created by the irradiation in n-type GaAs. This trap is always present even after the bombardment at nitrogen temperature [ lo], it is introduced linearly with the electron dose [2], and we can reasonably say that it is a primary defect. Lang [2] suggests that E, level andH, level are the different charge state of the same defect. It probably comes from a primary defect involving As sublattice [7] and it is an acceptor-like trap [8]. In accordance with the result of Pons et al. [5], we show that E3 anneals without long range migration and this annealing mechanism is consistent with close pair recombination mechanism.
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E3 TRAP ANNEALING
IN GaAs BY DDLTS TECHNIQUE
Acknowledgements - The authors wish to acknowledge L. Holland and J.P. Hallais of LEP for growth of VPE layers and financial support from the Delegation Generale a la Recherche Scientifique et Technique (Contract No. 79.7.0724).
5. 6. 7. 8.
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D.V. Lang, J. Appl. Phys. 45,3023 (1974). D.V. Lang & L.C. Kimerling, Inst. Phys. Conf: Ser. 23,581 (1975). D.V. Lang, Inst. Phys. Con5 Ser. 31,70 (1977). D.V. Lang, R.A. Logan & L.C. Kimerling, Phys. Rev. B15,4874(1977).
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