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time also much higher than the hole capture (from valence
band) one. It is the dynamic behavior of a level that deter-
mines whether it is a trap or not. Traps can be experimen-
tally observed by means of majority carrier deep level
transient spectroscopy (DLTS). When employed in n-type
(p-type) samples, this measurement gives us information
about electron (hole) traps.
and from it we obtain the free carrier concentrations. The
1
resistivity is given by q ¼
, where n is the electron
enlnþeplp
concentration, p the hole concentration, ln is the electron
mobility, lp is the hole mobility and e is the electron
charge. The sheet resistance, then, is given by Rs ¼ q, where
d
d is the conductive layer depth.
In the specific case of implant isolation, the most com-
mon structure of the samples employed [16] is constituted
by a semi-isolating bulk on top of which a uniform doped
conductive layer is grown. The resistance is measured using
two contacts over the doped layer, allowing us to approx-
imate the structure with a two parallel resistors scheme,
one of them being the high resistivity bulk and the other,
A compensating center is a level whose introduction
effectively reduces the majority free carrier concentration
in the sample, compensating the effect of majority dopant
levels [12,13]. The level position relative to Fermi level
and its corresponding charge state transition determine
whether a level will act as a compensating center or not.
Consequently, a trap might or might not act as a com-
pensating center. Fig. 1 helps to demonstrate this idea: in
Fig. 1(a), we have GaAs semiconductor only with the
donor species. Free electrons concentration (n) is close to
dopant concentration (Nd) in this case. Introducing a
defect level adequately close to the conduction band, it will
communicate practically only with this band. Assuming an
acceptor-like level (with 0 defect charge state when empty
and ꢀ when filled (0/ꢀ), see Fig. 1(b)), we do achieve a con-
siderable reduction in the free electron concentration. In
this case, the level can be characterized as an electron trap
and a compensating center. But if we consider a donor-like
level (with +/0 defect charge states, Fig. 1(c)), again we
have n ꢁ Nd, revealing that the trap level no longer acts
as a compensating center. Actually, the introduction of this
kind of level can even decrease the total free hole concen-
tration in a p-type sample (see Fig. 1(f)). Figs. 1(d)–(f)
exemplify the analogous phenomenon in p-type GaAs.
In the implant isolation specific case, although the word
‘‘trap’’ has been previously assigned to centers responsible
for free carrier reduction, defects dynamic behavior is not
relevant, and, to achieve proper results, one must consider
all possible compensating centers in simulations. In the
case of majority carrier DLTS data, for example, levels
observed in both n-type and p-type samples should be
taken into account.
the top conductive layer. Using this description, the mea-
Rs1Rs2
Rs1þRs2
sured sheet resistance will be given by Rs ¼
, where
Rs1 is the top layer sheet resistance and Rs2 is the bulk
one. Rs2 can be assumed constant (ꢁ2 · 109X/h for GaAs
[16]) and Rs1 should be estimated using the model.
It is very relevant to obtain information about the
defects introduced by the implantation and their corre-
sponding levels. This very simple model can be useful in
this sense, since this kind of information can be suggested
as input to the model, and a comparison between the mod-
el’s results and experimental data will reveal how close to a
good estimation the suggestion is.
4. GaAs proton implant isolation
The simple model described above can be used to esti-
mate GaAs samples sheet resistance evolution as a function
of ion fluence if we know accurately the parameters of the
defect levels introduced by this implantation. For proton
implantation, there are some experimental data previously
obtained by our group [3–5,16] or by other authors
[17–20] that, together with defect models described in the lit-
erature, [21–24] allow us to take a closer look on a few inter-
esting schemes. The first one concerns the previously
obtained [16] association between anti-site defects (GaAs
and AsGa) and the isolation process. There are a few levels
accredited to these defects in the literature [22–24]. Using
these data, we can build a level structure like the one
exposed in Table 1 and the inset of Fig. 2. As gallium and
arsenic have close masses and similar displacement energies
[25], we assumed equal introduction rates for both anti-sites,
estimated by Monte Carlo TRIM program [25]. Fig. 2 also
shows calculated sheet resistance curves as function of flu-
ence for 600 keV protons. The simulation results show dis-
tinct isolation behaviors for n-type and p-type cases. The
n-type curve reveals a region with an abrupt increase in
Rs. This region ends in a plateau, corresponding to the bulk
sheet resistance, for a given proton normalized dose value
that is called threshold dose. In the p-type curve, the thresh-
old dose is not observed in the proton dose interval used.
This is not, however, the experimentally observed result.
As pointed out in [5] and exposed by the experimental data
points in Fig. 2, p-type and n-type samples must have close
3. Using a null charge model sheet resistance simulation to
analyse implant isolation data
We will suppose a semiconductor with a well-known dis-
tribution of levels inside its band gap and assume a given
charge transition and uniform depth distribution for each
one of these levels. In order to estimate the electrical resis-
tivity of this material, one should find a way to obtain the
free carrier concentrations and their mobilities. There are
several empirical estimations for mobility values as a func-
tion of Coulomb scattering centers concentration that can
be used [14,15]. The idea is to calculate the carrier concen-
trations from the null total charge condition. As we know
the energies of the levels, their concentrations and the
charge states associated, it is straightforward to calculate
the total charge for a given Fermi level value. The actual
Fermi level will be the one leading to a null total charge,
Coelho, Fernando
