Low-Temperature Dependences of the Polarization of Terahertz Emission from $n$-Germanium in Heating Electric Fields

Abstract

As was noted in [3], in order to verify the assumption that the behavior of the polarization dependences of the terahertz emission by hot electrons from $n$-Ge is determined by the type of carrier scattering, it is necessary to perform temperature measurements of this dependence in the range between the temperatures, where the scattering is determined by impurities and by acoustic lattice vibrations, respectively. The given work presents the results of such investigations.

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V.M. BONDAR, P.M. TOMCHUK
LOW-TEMPERATURE DEPENDENCES
OF THE POLARIZATION OF TERAHERTZ EMISSION
FROM n-GERMANIUM IN HEATING ELECTRIC FIELDS
V.M. BONDAR, P.M. TOMCHUK
Institute of Physics, Nat. Acad. of Sci. of Ukraine
(46, Nauky Ave., Kyiv 03680, Ukraine; e-mail: ptomchuk@iop.kiev.ua)
PACS 78.20.Jq, 78.67.De
c
○2010
As was noted in [3], in order to verify the assumption that the
behavior of the polarization dependences of the terahertz emission
by hot electrons from n-Ge is determined by the type of carrier
scattering, it is necessary to perform temperature measurements
of this dependence in the range between the temperatures, where
the scattering is determined by impurities and by acoustic lattice
vibrations, respectively. The given work presents the results of
such investigations.
1. Introduction
As was noted in [1–3], the terahertz emission by hot
carriers from n-Ge has a specific feature – it is polar-
ized. Its polarization dependences as functions of the
angle between the polarization vector and the heating
field direction are periodic. The positions of maxima
and minima of these dependences can change due to
variations of the impurity concentration and the lat-
tice temperature. In addition, the polarization depends
on the intensity of a heating electric field and its di-
rection relative to the crystallographic axes, as well as
on the degree of intervalley repopulation.
sons for a behavior of the polarization of this emis-
sion were studied in a number of works [3–5].
known that the main mechanisms of carrier scatter-
ing in n-Ge that determine its electric characteristics
are the impurity scattering at low temperatures and
the scattering by acoustic lattice vibrations at high
ones.
It was noted in [3] that, in order to verify the assump-
tion that different polarizations of the terahertz emission
by hot carriers in n-Ge in pure and doped materials are
caused by different prevailing scattering mechanisms, it
is necessary to perform temperature measurements of
this phenomenon.
The idea of the method was to obtain the mentioned
polarization characteristics at temperatures, at which
each of these mechanisms is determinative, and to fol-
low the variation of these characteristics under tran-
The rea-
It is
sition from one temperature region to the other.
the case of low temperatures (impurity scattering), the
mobility of carriers in n-Ge changes with the temper-
ature as µ ∼ T3/2, whereas it varies as µ ∼ T−3/2
at high temperatures (scattering by lattice vibrations).
The maximum point of the mobility, where the impu-
rity scattering is replaced by the scattering by acous-
tic phonons lies in the region ∼20 K for pure n-Ge.
One could expect that the polarization characteristic
will change its pattern passing through zero somewhere
in this temperature region.
behavior of the polarization dependence of the emis-
sion is determined by the type of scattering of hot
carriers. The experiments proposed and performed in
this work were to demonstrate whether it is true or
not.
In
This will mean that the
2. Experiments
All measurements were carried out with the use of stan-
dard samples produced by the typical technology [3].
Rectangular pulses of a heating electric field had a length
of 0.8 mus, whereas their amplitude could change in
wide ranges. The detecting part of the experimental
set-up differed from the previous versions in the ar-
rangement of the filter, polarizer, detector, and emit-
ting sample. The main experimental difficulty of these
measurements consists in the fact that the n-Ge emit-
ting sample, whose temperature should be increased by
an additional heating to 50 ÷70 K, is located near the
Ge(Ga) semiconductor detector requiring helium tem-
perature. Such a temperature gradient at a distance
of 8÷12 mm induces very strong temperature insta-
bilities and noise signals in the detecting part, which
makes measurements practically inadequate [3].
problem was solved in the following way: the Ge(Ga)
detector immersed in helium and the emitting sam-
ple, whose temperature must be changed from the he-
lium one to 70÷80 K, were located at the different
ends of a vertical light guide. Locating the sample at
The
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arXiv:1011.2170v1 [cond-mat.mtrl-sci] 9 Nov 2010

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LOW-TEMPERATURE DEPENDENCES OF THE POLARIZATION
Fig. 1. Diagram of the set-up used for temperature measurements
of the polarization of the terahertz emission from n-Ge: 1 — helium
cryostat; 2 – Ge(Ga) detector; 3 – filter; 4 -– polarizer rotating in
the horizontal plane; 5 – emitting sample; 6 – mobile light guide
different distances from the detector (and the liquid-
helium surface), we can vary the temperature of the
emitting sample within the required limits. The neces-
sity of an additional heating of the sample disappeared,
and temperature gradients were reduced to a minimum.
A diagram of the experimental set-up is presented in
Fig. 1.
3. Experimental Results and Their Discussion
Figure 2 shows the results of measuring the tempera-
ture dependence of the terahertz emission of hot ger-
manium carriers for a typical GES-2.5 sample with the
crystallographic orientation along the large sample size
⟨111⟩.
(6.6÷6.9) K, the behavior of the polarization dependence
is typical of doped samples. With increase in the sample
temperature, this dependence becomes straight, passes
through zero at 7.7 K, and then takes the form typical
of a pure material. This form does not change with the
further increase of the temperature up to 77 K. Thus,
we observed an inflection point of the polarization de-
pendence close to 8 K. Relating this point to the tran-
sition from the impurity scattering to the acoustic one
(where the electron mobility reaches a maximum), one
can see that it differs from the literature data by ∼10
K [6]. Additional experiments performed for a number
of samples with a different concentration yielded similar
results (Fig. 3). As it turned out later on, the differ-
ence in the temperature measurements was due to the
One can see that, at the lowest temperatures
Fig. 2. Polarization dependence of the terahertz emission from
n-Ge (GES-2.5, ⟨111⟩) for different temperatures (the curves are
shifted in amplitude): 1 –76 K; 2 – 57 K; 3 – 26 K; 4 – 14 K ; 5 –
8.8 K; 6 – 7.7 K; 7 – 7.2 K; 8 – 6.6 K
fact that the semiconductor thermometer measured the
temperature of the environment surrounding the emit-
ting sample, whereas the sample itself was heated by
pulses of the strong electric field (τi= 0.8 µs, υ =140
V, ℑ = 2.6 A, Erep= 6 Hz). Our calculations demon-
strate that, at these temperatures (taking into account
the rapid decrease of the heat capacity), the quantity
of heat released in the sample (Fig.
temperature by 10 ÷15 K, i.e.
will be higher than that fixed by the thermometer by
∼ 10÷15 K, which completely agrees with literature
data.
Hence, the refined position of the point of tempera-
ture change of the dominant scattering mechanism and
the form of the curves given in Figs.
us to make an unambiguous conclusion about the rela-
tion between the angular polarization dependence and
the scattering mechanism. There took place a shift of
the maxima (minima): the regions of maxima in the po-
larization dependence in the case of the impurity scat-
tering changed to minima in the case of the acoustic
one.
Thus, the presented experimental results (Figs. 2 and
3) confirm the proposed explanation of the behavior of
the polarization characteristic of the terahertz emission
2) increases its
its real temperature
2 and 3 allow
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V.M. BONDAR, P.M. TOMCHUK
Fig. 3. Polarization dependence of the terahertz emission from
n-Ge (GES-0.3, ⟨111⟩) for different temperatures (the curves are
shifted in amplitude): 1 – 70 K; 2 – 57 K; 3 – 26 K; 4 – 14 K; 5 –
7.2 K; 6 – 6.4 K; 7 – 5.7 K
by hot electrons from n-Ge depending on the type of
carrier scattering.
We thank O.G. Sarbey for the detailed discussion of
the results of this work and O.K. Florova for the given
polarizers.
1. V.M. Bondar, O.G. Sarbey, and P.M. Tomchuk, Fiz.
Tverd. Tela 44, 1540 (2002).
2. P.M. Tomchuk, Ukr. Fiz. Zh. 49, 681 (2004).
3. V.M. Bondar and N.F. Chornomorets, Ukr. Fiz. Zh. 48,
51 (2003).
4. P.M. Tomchuk and V.M. Bondar, Ukr. J. Phys. 53, 668
(2008).
5. V.M. Bondar, B.O. Danilchenko, and A.M. Kraichins’kyi,
Ukr. J. Phys. 54, 491 (2009).
6. L.P. Pavlov, Methods of Determination of the Basic Pa-
rameters of Semiconductor Materials (Vysshaya Shkola,
Moscow, 1975) (in Russian).
Received 16.12.09.
Translated from Ukrainian by H.G. Kalyuzhna
ТЕМПЕРАТУРНI
ТЕРАГЕРЦОВОГО ВИПРОМIНЮВАННЯ ГЕРМАНIЮ
n-ТИПУ У ГРIЮЧИХ ЕЛЕКТРИЧНИХ ПОЛЯХ
В ОБЛАСТI НИЗЬКИХ ТЕМПЕРАТУР
ЗАЛЕЖНОСТIПОЛЯРИЗАЦIЇ
В.М. Бондар, П.М. Томчук
Р е з ю м е
Як було вiдзначено в роботi [3] для правомiрностi припущен-
ня про те, що хiд поляризацiйних залежностей терагерцового
випромiнювання гарячими електронами з n-Ge визначається
типом розсiювання носiїв, необхiдно провести температурнi ви-
мiри цiєї залежностi вiд температур, де превалює розсiювання
на домiшках, до температур, де превалює розсiювання на аку-
стичних коливаннях ґратки. У данiй роботi наведено резуль-
тати таких дослiджень.
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