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Delta-doping in diffusion studies
François Bénière, René Chaplain, Marcel Gauneau, Viswanatha Reddy, André Régrény
To cite this version:
François Bénière, René Chaplain, Marcel Gauneau, Viswanatha Reddy, André Régrény. Delta- doping in diffusion studies. Journal de Physique III, EDP Sciences, 1993, 3 (12), pp.2165-2171.
�10.1051/jp3:1993259�. �jpa-00249074�
Classification Physics Abstracts
66.30 66.30Q 61,70W
Delta-doping in diffusion studies
Frangois Bdnibre (I), Rend Chaplain (2), Marcel Gauneau (2), Viswanatha Reddy (I)
and Andrd Rdgrdny (2)
1') Groupe Matikre Condensde et Matdriaux, URA CNRS 804, Universitd de Rennes, 35042 Rennes, France
(2) D6partement MPA, Centre National d'Etudes des Tdldcommunications, 22302Lannion, France
(Received 20 April J993, revised 9 September J993, accepted16 September J993)
Rdsumd. Le dopage-delta, oh le dopant est confin6 h l'6chelle du paramdtre du r6seau, fournit les conditions parfaitement iddales pour dtudier les processus de transport atomique. Nous avons dtud16 des 6chantillons de GaAs obtenus par 6pitaxie par jet moldculaire dopds par des couches~
delta de Si et Al. Des traitements de diffusion de longue dur6e ont 6t6 r6alis6s dans l'intervalle de temp6rature 550 h 800 °C. Les profils de distribution sont examin6s par spectrom6trie d'6mission d'ions secondaires. Nous obtenons des coefficients de diffusion de Si en bon accord avec les autres Etudes r6centes utilisant des techniques diff6rentes (traitement thermique ultrarapide, profil de
distribution par la m6thode capacit6~voltage, diffusion d'une couche
« sandwich »). Ceci diffdre
des mesures antdrieures qui, bastes sur la diffusion de dopants implant6s, 6taient beaucoup plus
dispers6es, Nous concluons que les donn6es plus prdcises rendues possibles par le dopage~delta
montrent que le coefficient de diffusion est un paramdtre intrinsdque h la condition que la quantit6
de dopant et la densit6 de dislocation demeurent assez faibles.
Abstract. The &doping where the dopant is confined on the length-scale of the lattice constant
provides perfectly ideal conditions to study the atomic transport processes. We have studied MBE-
grown GaAs samples B-doped with Si and Al layers, Long time diffusion anneals have been
performed in the temperature range 550-800 °C, The distribution profiles are examined by SIMS- profiling. We obtain Si diffusion coefficients in good agreement with the other recent studies using
different techniques (rapid thermal annealing, capacitance-voltage profiling, sandwiched diffusion sourcej. This contrasts with the earlier measurements based on diffusion of implanted dopants which were much more widely spread. We conclude that the more accurate data allowed with the B-doping show that the diffusion coefficient is an intrinsic parameter provided that the amount of dopant and the dislocation density are kept sufficiently small.
1. Introduction.
The most accurate measurements of the mass transport processes are obtained in the
experimental arrangement of the « infinitely thin » layer where the marked isotope or foreign
atom is let to diffuse into a crystalline sampIe ill- With atoms bearing an electric charge, an
2166 JOURNAL DE PHYSIQUE III N° 12
external electric field provokes an electromigration shift. In such solids, the same experiment gives simultaneously the diffusivity and electrical mobility, as originally observed in ionic
crystals [2]. The diffusion source is deposited as a thin layer at the surface of the sample or
better as a « sandwich
» in between two adjoining identical samples, The initial and
boundary conditions can be written as :
t = 0 N
~, o~ = Q3 (x)
where 3 is the Dirac's function, and Q the number of atoms which are deposited per unit area.
In practice however, the mathematical approximation consisting in assuming a delta-function
was seldom satisfactory and the experimental accuracy was very strongly limited by the
inevitable width of the diffusion source [3]. The electromigration experiments were even more
difficult to carry out because of the poor mechanical and electrical contact between the different layers. A major forward step has been achieved with the « &doping » where the
dopant is confined to one or a few atomic monolayers. Then the initial conditions of the diffusion sources can really be described by the Dirac 3 function, as for the initial conditions of Fick's second law.
The production of 3-doped layers has been motivated with the new requirements of the
modem semiconductor technology where it was becoming desirable to make doping over
narrower and narrower distributions. This has been made technically possible by the new
epitaxial crystal growth techniques. Experimentally &doping has been achieved in GaAs [4]
by growth interruption during epitaxial growth by molecular beam epitaxy (MBE) with silicon [5-10] and beryllium [I I], by metalorganic chemical vapor deposition [12] and by chemical beam epitaxy [13].
This paper describes the measurements of D for Si in GaAs in the conditions of time and temperature usually the most appropriate to accurate measurements. There was a large scatter between the data reported in the literature [14, 15] before the &doping technique appeared.
Even with this technique, the &doped results may depend on parameters such as the diffusion
time [8], amount of dopant (atoms.cm~~) [16], dislocation density [12] and substrate
temperature [7].
The Si 3-doping of GaAs has already recently enabled Ashwin et al. [10] to determine
precisely the position and the ionic charge of the silicon atoms on the GaAs lattice the Si
atoms only occupy the Ga lattice sites of the 3-doped plane and give as many conduction
electrons up to a coverage of 10'~ cm~ ~. These authors have shown that diffusion
occurs within the 3 plane in samples from a heat treatment at 500 °C for 30 min. They also showed that the Si
atoms diffuse out of the 3 plane if the growth temperature was significantly in excess of 400 °C.
2. Experimental.
The GaAs substrates are (100) oriented wafers having a dislocation density ~ ? x 10~ cm~ ~ and a resistivity of 1.6 x 10~ ~ f1. cm at 300 K. An epitaxial layer of pure GaAs is then grown by MBE at the rate of 0.32 nm. s~ until a thickness of 1500 nm is reached. A Si &doped plane of 5 x lo ~~ atoms. cm ~ is then formed. Another epitaxial layer of 500 nm of undoped GaAs is deposited, followed by an Al &doped plane, which is finally covered by a last
epitaxial layer of 500 nm of GaAs (Fig. I). The respective temperatures of the sources are 268 °C (As), 970 °C (Ga), 090 °C (Al) and 100 °C (Si) while that of the substrate is~500 °C during the growth.
The Al layer is formed to act as a reference. The mobility of the aluminium atoms is
expected to be negligible relative to that of the silicon atoms in the conditions of our diffusion anneals. The SIMS indications of the position, shape and width of this Al layer give the
experimental resolution on the effective layer thickness.
500 iS00 lS00 I'
, ,
, ,
, ,
i ,
, ,
i ,
,
, .
, ,
i
GaAs GaAs nJGaAo
i i
# ,
# ,
, o
, ,
, ,
, ,
, ,
o i
, a ,
, '
Sl $-d
o pod
Al $-doped
Fig. I, Experimental preparation of &doped samples for diffusion studies.
The coating with epitaxial GaAs is meant to diminish the influence of surface decomposition
due to some arsenic evaporation also leading to depth resolution lowering. This effect is also
partly prevented by an imposed pressure of argon atmosphere,
The samples are thereafter introduced in a quartz vessel for diffusion inside an electric fumace where the temperature is carefully kept constant and measured within ± 0,5 °C. Both the temperature and the time of diffusion are essential parameters for accurate diffusion data.
We thought that instead of using very short times like in the rapid quenching experiments used
in the III-V compounds technology, much longer times of several hours would be easier to
control and allow to neglect the periods necessary for the temperature to reach the fixed values.
An anomalous influence of the diffusion time has been reported for the shortest times [8]. The
diffusion spreading conveniently expressed as FWHM (full width at half-maximum) is only
proportional to the square root of t. An anomalous influence of the diffusion time has been
reported for the shortest times [8]. At the other hand, long diffusion anneals render the samples
more subject to contamination. In order to minimize this possible effect, the crystals are kept in a quartz tube filled with a lo Hg cm atmosphere of purified argon.
The impurity profiles are measured before and after the diffusion anneals using SIMS
(Secondary ion mass spectrometry) with primary Cs+ ions at a current of 50 nA for a swept square of 125 x 125 ~Lm. Both positive and negative secondary ions have been utilized to determine the profiles (5.5 kev Cs + ions are used for the positive secondary ions and 14.5 kev ions for the negative ones), The negative ions are chosen for better signal/noise ratio while the positive ions are chosen for better resolution. The results of the aluminium 3-doped layer show
a limit of resolution of 5 nm, in good agreement with the similar analysis of Ashwin et al. [10]
of the SIMS resolution of Si delta-doped layer in GaAs using a low energy (3keV)
O( primary ion beam. Some broadening of a few tens nm of the aluminium layers can be observed at the extreme temperatures.
2168 JOURNAL DE PHYSIQUE III N° 12
3. Results.
Three diffusion profiles determined with negative Si~ ions analysis are shown in figure 2. The influence of temperature is seen on the spreading of the Si atoms originally confined on one or two atomic planes. Assuming a perfect Dirac function for the initial concentration of Q atoms
per unit area, the diffusion profile should be given by the Gaussian distribution [1] :
~ 2
,~
~~~ 4~t ~~~where N is the concentration (atoms,cm~~) at the distance,; from the initial 3-plane, t the diffusion time and D the diffusion coefficient. One of those experiments (800 °C, 8 h) is
represented in figure 3 as Ln (N) vs.-x~. The fact that straight and symmetric lines are observed provides a good confirmation of the theoretical equation (I j, in contrast with some
circumstances [7] in which non symmetrical profiles can be obtained. The diffusion coefficient is readily given by the slope of Ln (N)-vs.-x~. D can also be derived from the profile full width
when the concentration N has decayed by a factor of 2 (FWHM) or preferably by a factor of lo-
atoms.Cm~~
is lo
,~17
is
id~
o i z 3 a
x microns
Fig. 2. Diffusion profiles (log N-vs.-x) of Si in GaAs. 550 °C. 20 h 645 °C, 30 h
800 °C, 6h.)
Figure 4 shows the variation of the diffusion coefficient as a function of temperature. For
comparison, are also reported
. the results of Schubert et al. [6] determined by ultra-short diffusion anneals (5 s) in the temperature range 600-1000 °C through capacitance voltage (C-V) profiling ;
. those derived from the data of Beall et al. [16] for longer diffusion anneals (2-3.5 h) in the
range 560-648 °C obtained by C-V and SIMS from a Si plane &-doped with
,~17 atoms.cnc~
lo
~2
(i~£~)
O 1 2 3 4 5 6 7
Fig. 3. Diffusion profile (log N-vs.-x~j of Si in GaAs (800 °C, 6 h).
a
LOG D jam(
~~ ~-lj
' '
,~
' '
' ,
",~ ,
~
" '
' '
'
'
.l 6 ,
' '
'
.17 ,
'
1iiT '
'
~9 1 %2
Fig. 4. Influence of temperature on the diffusion coefficient of Si in GaAs. present work
Schubert et al. [6] ; Beall et al. [7] Cunningham et al. [8] A : Kavanagh
et al. [17]. )
2170 JOURNAL DE PHYSIQUE III N° 12
4 x 10~~ atoms. cm~ ~ These authors interestingly have also studied more heavily doped layers
up to 4 x 10'~ atoms. cm- ~ for which non-Gaussian distributions are observed
. the low temperature measurements of Cunningham et al. [8] performed for short times
under arsenic overpressure by C-V profiling. They report a lowering of the Arrhenius
activation energy at temperatures higher than 700 °C
. one value determined by Kavanagh et al. [17] at 900 °C from the diffusion analysis of the distribution profile of Si initially contained in a heavily doped GaAs layer sandwiched between two undoped GaAs layers grown by molecular beam epitaxy. The Si concentration profile (SIMS) after lo min anneal could be fitted to the error function according to the theoretical
expectations, leading to D
=
2.5 x lo- '~ cm~.s- at 900 °C. The good fit with the error function also showed that the Si diffusion coefficient in GaAs is independent of Si doping
concentration, at least below 5 x lo~~ atoms. cm- ~ The absolute value is however larger than
the results obtained by 6-doping.
Considering the small magnitude of the diffusivity, one may notice quite a satisfactory agreement between the various sets of data derived from the spreading of 3-doped layers. This is particularly interesting to point out in regard to the usual complexity of impurity diffusion in
III-V semiconductors. Even in the present case of diffusion of Si in GaAs, the earlier
diffusivities at a given temperature were differing by over four orders of magnitude [8]. The
new technology of the 3-doping is a major forward step in the mass transport field which will lead to improved results in diffusion.
The present results can be summarized by the Arrhenius equation
D 7.9 x exp (- ??5/kT) cm~, s- '
The activation energy of 2.25 ± 0.2 eV is close to the results of 2.45 eV reported by Schubert et al. [6] and 2.41eV by Cunningham et al. [8] using the same 3-doping as for the initial
conditions but other experimental parameters like the diffusion times and concentration measurements.
4. Discussion.
The delta-doping technique will be extended for more accurate diffusion data in addition to its intrinsic advantages in the microelectronic technology. The best results are obtained in the
following conditions.
. The amount of dopants deposited in the 3-plane should not exceed any critical value above
which segregation processes might occur, leading to a poly-component diffusion mechanism.
This limit can be estimated around 4 x 10~~ Si atoms, cm- ~ in GaAs [16] or 10'3 [10].
. The temperature of the substrate should be as low as possible so that the broadening of the
3-layer by diffusion during the sample epitaxial growth itself remains negligible. The careful study of Lanzillotto et al. [9] shows that the full width at half maximum does not exceed the
SIMS resolution as long as the substrate temperature is kept below 580 °C. The observations of Ashwin et al. [10] also imply that &doped layers could not be grown without diffusion of the
Si atoms out of the plane if the temperature growth temperature was significantly in excess of
400 °C.
. The temperature, surrounding atmosphere and time of the post growth diffusion conditions must be well controlled. In particular, it might have seemed that long times would be easier to monitor. Still, the present data obtained for several annealing time~ agree well with the 5 s experiments of Schubert et al. [6] so that this parameter is not as critical as expected.
. The precision of the profiling method must be in accordance with the narrowness of the diffusion distance. The 3-doped layer extends between I and 2 lattice constants. A better
resolution is probably achieved with the C-V technique as compared to SIMS [6]. The simultaneous use of the two techniques is even more advantageous since it gives separately the total atomic profile, the charge state of the ionized species as well as the electroactive profile.
This may be particularly useful if diffusion results from two or more simultaneous contributions.
5. Conclusion.
The &doping allows to study the atomic transport processes with an increased accuracy. The present case of Si in GaAs has already given rise to several studies [5-9, 16] motivated by the
technological importance of GaAs n-doping in microelectronics. However, many more applications of the technique can now be envisaged : diffusion of other dopants in GaAs and in other III-V compounds as well as diffusion in other materials, including possibly silicon. If feasible, this latter material would provide better chemical and mechanical opportunities to make atomic transport studies easier to be investigated. Application of a constant electric field
might also be added in order to obtain a direct measurement of the atomic mobility of the
doping ions simply by following the electrical shift due to the electrical force.
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