Changes in electrophysical properties of heavily doped n-Ge <As> single crystals under the influence of thermoannealings

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T11878 Solid-state spectroscopy and crystallography

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_Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 53-56._

doi: 10.15407/ spqeo18.01.053

PACS 61.82.Fk

# Changes in electrophysical properties of heavily doped n -Ge  As  single crystals under the influence of thermoannealings

G.P. Gaidar
_Institute for Nuclear Research, National Academy of Sciences of Ukraine,_
_47, prospect Nauky_, _03680 Kyiv, Ukraine; e-mail: gaydar@kinr.kiev.ua_

Abstract. Features of changes in the electrophysical parameters (concentrations of
charge carriers _ne_ and their mobilities  ) in heavily doped _n_ -Ge  As  single crystals,
which occur as a result of the series of thermoannealings (each for 0.5 h) over a wide
temperature range (540  _T_  900 °C), have been investigated and explained.

Keywords : germanium, thermoannealing, Hall effect, charge carrier concentration,
charge carrier mobility.

Manuscript received 19.09.14; revised version received 25.12.14; accepted for
publication 19.02.15; published online 26.02.15.

1. Introduction technological methods when creating modern solid-state

Up to date and probably in the following decade,
elementary semiconductors will remain a major material
of the electronic engineering [1]. Thus, germanium is
widely used in optical devices of infrared range. Very
large scale integration circuits and very-high-speed
integrated circuits, new elements of microelectronics,
_etc._ are based on silicon [2]. In relation with the
emergence of new technological materials and devices
manufactured on the basis of germanium and silicon, the
problem of controlling their physical properties after
various treatments is especially urgent [3, 4].

The thermal treatment of the solid-state electronic
devices based on the many-valley semiconductors under
various conditions is a common feature of their
production technique. Interaction of dopant with the
lattice defects and residual impurities in the bulk of
semiconductor crystals occur, in principle, at any
nonzero temperature. However, at higher temperatures
these processes run faster [5].

The doping of semiconductors with the necessary
impurities to the desired concentration is one of the main

technological methods when creating modern solid-state
electronic devices, which allows directed changing the
properties of materials. Impurity atoms introduced into
semiconductor create local levels in the band gap, which
act as suppliers of electrons to the conduction band
(donors) or traps for them, providing the appearance of
holes in the valence band (acceptors), or play the role of
radiative or nonradiative recombination centers of nonequilibrium charge carriers. Impurity atoms are
introduced into the bulk of ingots or layers at various
stages of their growth, to purposefully alter their
resistivity and to form the desired structures. The
existence of inhomogeneities in the electrical, optical
and other characteristics of real crystals is conditioned
by the presence of the impurity atoms in the
semiconductor bulk (which, in fact, are the defects in
crystal) as well as by irregularity of their distribution [6].

2. Features of the heavily doped semiconductors

Intensive study of the heavily doped semiconductors and
increased interest in them is mainly caused by two
reasons. First, using heavily doped semiconductors

_Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 53-56._

doi: 10.15407/ spqeo18.01.053

greatly expanded the capabilities of the semiconductor
engineering and electronics, since they are the basis of
such semiconductor devices as tunnel diodes, lasers,
tensometers, Hall sensors. The second equally important
reason is that in heavily doped semiconductors arises
substantial in cognitive terms qualitatively new physical
phenomena, compared with the studied crystals, which
have normal level of the impurity content. These
phenomena include manifestations of “individuality” of
dopants in the kinetic effects, polytropy of the impurity,
and appearance of “tails” inherent to the density of states
in the band gap [7]. Moreover, the high content and
associated non-uniform impurity distribution can lead to
formation of defects in the crystal bulk that have a
different physical nature.

First of all, we should define more specifically the
notion of “weakly” and “heavily” doped semiconductor.
Under weak doping, the impurity atoms that do not
interact with each other form local energy levels in the
band gap, and the charge carriers in this semiconductor
obey the classical Boltzmann statistics.

By increasing the degree of doping, the wave
functions of the neighboring impurity atoms begin to
overlap, which leads to increased efficiency of
interaction between the impurity atoms that removes the
permutable degeneration and leads to the appearance of
impurity bands on basis of the levels that were discrete
at weakly interaction between impurity atoms. In [8], the
doping level that leads to formation of an impurity band
is conventionally called as the average.

Finally, at strong doping the impurity band merges
with the conduction band ( _n_ -type semiconductor) or with
the valence band ( _p_ -type semiconductor). The charge
carriers, density of which is now very large, obey the
quantum Fermi-Dirac statistics, and semiconductors with
such a doping level are called as the heavily doped ones.

For example, the electrical conductivity of weakly
doped _n_ -Ge does not depend significantly on the type of
the dopant of V group (As, P, Sb) in the temperature
region where all donors are fully ionized. However, in
the case of _n_ -Ge heavily doped by these impurities this
statement is not fair. Thus, in [9, 10] the concentration
dependence of the resistivity is studied for _n-_ Ge doped
with As, P, Sb in a wide range of concentrations at the
temperature of 300 K. It was found that starting from a
certain concentration the resistivity depends on the type
of dopant. The highest resistivity in the region of high
concentrations was observed for Ge  As , and the least
resistivity – for Ge  Sb  . It should be also noted that the
limiting values of concentrations, at which
“individuality” of the impurities begins to manifest,
differ for the germanium crystals doped with various
impurities. Based on the study of the concentration
dependence of resistivity and Hall effect, the conclusion
was made concerning the effect that the electron
mobility in Ge at the high level of doping with elements
of V group depends on the type of dopant, beginning
with a certain threshold concentration _n_ 0.

The mentioned features of the electrical properties
of heavily doped Ge crystals become apprehensible to a
certain extent, if we assume that the charge carrier
concentration obtained from the Hall measurements is
less than the true concentration of impurity in the bulk of
the investigated crystal. Taking into account the fact that
the dopant atoms are completely ionized, and the Hall
factor in heavily doped Ge is not very different from
unity (though it is not exactly equal to unity up to the
highest concentration of the dopant), this discrepancy
can be explained by the fact that a part of the dopant
atoms is not included in the Ge lattice and is located in
its bulk in an inactive state. In [11], for germanium the
theoretical calculations were adduced, which show that
when the number of impurity atoms is changed from
10 18 up tо 10 22 cm –3, i.e., by 4 orders, the number of
charge carriers is changed only by 2 orders. Therefore, it
is conceivable that with a high level of doping, the
dopant is located in a germanium crystal in several
forms simultaneously. This property of the impurity in
the heavily doped Ge is called as polytropy.

There are many causes of generation of impurity
polytropy in germanium. The main among them are as
follows: formation of different types of structural
complexes, the dopant deposition on the various
structural defects (for example, formation of “impurity
atmospheres” on dislocations), the inclusions of second
phase, and the presence of the impurity atoms in the
interstitials. All these causes lead to the fact that the part
of impurities is not included into the substitutional solid
solution. Such system is not stable from the
thermodynamic point of view, because polytropy
appears at the impurity concentrations when the solid
solution is still far from saturation. Therefore, it is
natural to assume that over time there will be a gradual
recovery of the solid solution, i.e., the charge carrier
concentration will increase due to the additional
transition of the part of dopant into the solid solution.

Study of decomposition of the solid solution of
germanium and its influence on the kinetic effects is of
great scientific and practical interest. It should be noted
that the crystal lattice of the basic substance is
significantly deformed at the decomposition of the solid
solution of impurity. The impurity that is not included in
the substitutional solid solution and forms (as noted
above) the various kinds of defects creates local
disturbances in the crystal. These disturbances can be
investigated using the structural methods based on X-ray
diffraction (for example, the Lang method or the method
of anomalous transmission of X-rays) [12].

In recent years, germanium doped with arsenic
attracts greater interest. This interest is due to the fact
that in heavily doped _n_ -Ge  As  crystals the phenomena
of decomposition of solid solution occur relatively
easily. The arsenic atoms have significant diffusion
mobility in the germanium lattice, which allows
observing the decomposition of impurity solid solution
in a wide temperature range.

_Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 53-56._

doi: 10.15407/ spqeo18.01.053

The thermoannealing of semiconductor crystals is
studied in [6, 13]. The authors compared the data
obtained, which were the result of the annealings carried
out at different temperatures ( _Tann_ ) and various durations
( _t_ ), when the initial crystals were characterized by the
usual level of the impurity content.

The aim of this study was to carry out a series of
sequential thermoannealings of equal duration in a wide
temperature range of heavily doped _n_ -Ge  As  single
crystals and to investigate changes in their electrophysical parameters that arise under the influence of
these thermoannealings.

3. Results and discussion

In this paper, the research of changes in the
concentration of charge carriers _ne_ and their mobility 
as a result of thermoannealings of the heavily doped
_n_ -Ge  As  single crystals at different temperatures within
the range from 540 to 900 °C was performed. The
concentration of the arsenic dopant for all the
germanium samples was approximately equal to

9.3  1019cm  3 . The samples were studied in the initial
state (the concentration and mobility of charge carriers
in their bulk were calculated), and then were subjected to
the thermal treatment in a vacuum furnace at
temperatures of 540, 600, 640, 725, 800, 830 and
900 °C. The annealing time of crystals at each
temperature was 0.5 h. After the thermal treatment, the
study of the same parameters as in the initial state, using
standard methods of measuring the Hall effect and
conductivity, was carried out.

The results of these experiments are presented in
Figs 1 and 2. The reasons of changes that occur in the
dependences of _ne_ and  on the annealing temperatures,
probably, boil down to the manifestation of the factors
described below, which inevitably accompany these
annealings.

1.3

1.2

1.1

1.0

0.9

0.8

500 550 600 650 700 750 800 850 900 950

_Tann_, оС

Fig. 1. Dependences of the charge carrier concentration after
annealing _n_ _eT_ normalized by the corresponding values in the

initial state _n_ _e_ 0 on the annealing temperatures _Тann_ = 540, 600, 640,

725, 800, 830, 900 °C in the heavily doped _n_ -Ge  As  samples.

1.10

1.05

1.00

0.95

0.90

0.85

0.80
500 550 600 650 700 750 800 850 900 950

_Tann_, оС

Fig. 2. Dependences of the charge carrier mobility after
annealing  _Т_ normalized by the corresponding values in the
initial state  0 on the annealing temperatures _Тann_ = 540, 600,
640, 725, 800, 830, 900 °C in the heavily doped _n_ -Ge  As 
samples.

At the annealing temperature 540 °C, the charge
carrier concentration _ne_ is not changed as compared with
its value in the initial state (Fig. 1).

Within the range from 600 to 725 °C, the
performed electrical measurements showed that
intensive decomposition of arsenic solution in
germanium occurs. As shown in Fig. 1, decomposition
of supersaturated solid solution of arsenic in germanium
is accompanied by a decrease in the charge carrier
concentration, because part of impurities under
decomposition becomes electrically inactive. The carrier
mobility at the same time, respectively, increases,
because the number of the effective electrically-active
scatterers decreases.

It should be noted that the measurement of the
electrical parameters was carried out at the temperature
of liquid nitrogen. At this temperature, taking into
account the very high charge carrier concentration, the
system approaches to the degeneracy and the Hall factor
approaches to the unity. Consequently, the obtained
values of the carrier concentration will be more accurate
than those measured at room temperature.

Investigation of the samples after the thermal
treatment at the annealing temperatures _Тann_ - 725 °C
showed that the carrier concentration _ne_ is not reduced
but increased relative to the values in the initial state
(Fig. 1), although probably the phenomenon of
decomposition of solid solution at these temperatures to
a certain extent takes place. This discrepancy is likely
related to the fact that at these annealing temperatures,
taking into account the high concentration of impurities,
the electrically-active complexes (up to the annealing
temperature of _Тann_  830 °C) are formed. This process
causes an increase in the carrier concentration.

The annealing even at higher temperature
( _Тann_  830 °C) causes the electrically-active complexes
to be decomposed, therefore, the carrier concentration is
decreased, while the mobility is increased. At these

_Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 1. P. 53-56._

doi: 10.15407/ spqeo18.01.053

annealing temperatures, perhaps, another process may
take place: the impurities precipitated earlier will be
returned to the crystal lattice, which can be accompanied
by the recovery of its structural perfection. As a result of
this process, the charge carrier concentration will
increase and their mobility will decrease.

As can be seen from comparison of Figs 2 and 1,
the change in the charge carrier mobility is correlated in
the opposite phase with changes in the concentration of
the electrically-active complexes (scattering centers)
both in the area of _ne_ growth (and, therefore, of the
concentration of scattering centers), and in the initial
area of their thermal dissociation.

It was also experimentally found that the changes
in the concentrations and mobilities of charge carriers
that occur at each annealing, after cooling the samples to
the room temperature, are very stable and can remain
unchanged for six months, i.e. the diffusion processes in
the annealed crystals at the high temperatures ( _Тann_ 500…600 °C) do not subjected to the appreciable
influence of the room temperatures for a long time. It
opens practical possibilities to change the physical
parameters of germanium (such as _ne_ and  ) in the
desired direction (within the changes provided by the
thermoannealings at the elevated temperatures) and to
use the achieved changes at lower temperatures (for
example, at room temperatures). At the same time,
surely, you must take into account the changes (in the
values of the charge carrier mobility, lifetime of the
minority carrier and other parameters), which inevitably
accompany annealings of the crystals at various
temperatures. After all, these changes can be not only
useful but also quite undesirable. For example, if you
want to increase the carrier concentration in the crystal
due to annealings, then in _n_ -Ge  As  the charge carrier
mobility will only decrease within the region of the
annealing temperatures 500…850 °C (which is urgent
for practice).

4. Conclusions

Features of changing in the electrophysical parameters
(concentrations of charge carriers _ne_ and their mobilities
 ) in heavily doped _n_ -Ge  As  single crystals, grown
using the Czochralski method, that occurred as a result
of the series of thermoannealings (each for 0.5 h) over a
wide temperature range, were investigated and
explained. It has been ascertained that a change in the
basic parameters of the samples under conditions of
using the thermoannealing regimes that are commonly
used in manufacturing the semiconductor devices occur
non-monotonic. As a result of the analysis of carried out
thermal treatments of samples, it has been found that the
dependences of concentrations and mobilities of charge
carriers (normalized by the corresponding values in the

initial state) on the values of the annealing temperatures
possess two extrema corresponding to the values
approximately 640 and 830 °C. Information allows
understanding the physical meaning of the above
changes has been adduced.

_References_

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Changes in electrophysical properties of heavily doped n-Ge &lt;As&gt; single crystals under the influence of thermoannealings

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Changes in electrophysical properties of heavily doped n-Ge <As> single crystals under the influence of thermoannealings