Low-Temperature Dependences of the Polarization of Terahertz Emission from n -Germanium in Heating Electric Fields
VV.M. BONDAR, P.M. TOMCHUK
LOW-TEMPERATURE DEPENDENCESOF THE POLARIZATION OF TERAHERTZ EMISSIONFROM 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: [email protected])
PACS 78.20.Jq, 78.67.Dec ○ As was noted in [3], in order to verify the assumption that thebehavior of the polarization dependences of the terahertz emissionby hot electrons from 𝑛 -Ge is determined by the type of carrierscattering, it is necessary to perform temperature measurementsof this dependence in the range between the temperatures, wherethe scattering is determined by impurities and by acoustic latticevibrations, respectively. The given work presents the results ofsuch investigations.
1. Introduction
As was noted in [1–3], the terahertz emission by hotcarriers from 𝑛 -Ge has a specific feature – it is polar-ized. Its polarization dependences as functions of theangle between the polarization vector and the heatingfield direction are periodic. The positions of maximaand minima of these dependences can change due tovariations of the impurity concentration and the lat-tice temperature. In addition, the polarization dependson the intensity of a heating electric field and its di-rection relative to the crystallographic axes, as well ason the degree of intervalley repopulation. The rea-sons for a behavior of the polarization of this emis-sion were studied in a number of works [3–5]. It isknown that the main mechanisms of carrier scatter-ing in 𝑛 -Ge that determine its electric characteristicsare the impurity scattering at low temperatures andthe scattering by acoustic lattice vibrations at highones.It was noted in [3] that, in order to verify the assump-tion that different polarizations of the terahertz emissionby hot carriers in 𝑛 -Ge in pure and doped materials arecaused by different prevailing scattering mechanisms, itis necessary to perform temperature measurements ofthis phenomenon.The idea of the method was to obtain the mentionedpolarization characteristics at temperatures, at whicheach of these mechanisms is determinative, and to fol-low the variation of these characteristics under tran- sition from one temperature region to the other. Inthe case of low temperatures (impurity scattering), themobility of carriers in 𝑛 -Ge changes with the temper-ature as 𝜇 ∼ 𝑇 / , whereas it varies as 𝜇 ∼ 𝑇 − / 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 characteristicwill change its pattern passing through zero somewherein this temperature region. This will mean that thebehavior of the polarization dependence of the emis-sion is determined by the type of scattering of hotcarriers. The experiments proposed and performed inthis work were to demonstrate whether it is true ornot.
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 lengthof 0.8 𝑚𝑢 s, whereas their amplitude could change inwide ranges. The detecting part of the experimentalset-up differed from the previous versions in the ar-rangement of the filter, polarizer, detector, and emit-ting sample. The main experimental difficulty of thesemeasurements consists in the fact that the 𝑛 -Ge emit-ting sample, whose temperature should be increased byan additional heating to 50 ÷
70 K, is located near theGe(Ga) semiconductor detector requiring helium tem-perature. Such a temperature gradient at a distanceof 8 ÷
12 mm induces very strong temperature insta-bilities and noise signals in the detecting part, whichmakes measurements practically inadequate [3]. Theproblem 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 differentends of a vertical light guide. Locating the sample at
ISSN 2071-0186. Ukr. J. Phys. 2010. Vol. 55, No. 6 a r X i v : . [ c ond - m a t . m t r l - s c i ] N ov OW-TEMPERATURE DEPENDENCES OF THE POLARIZATION
Fig. 1. Diagram of the set-up used for temperature measurementsof the polarization of the terahertz emission from 𝑛 -Ge: — heliumcryostat; – Ge(Ga) detector; – filter; -– polarizer rotating inthe horizontal plane; – emitting sample; – mobile light guide different distances from the detector (and the liquid-helium surface), we can vary the temperature of theemitting 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 inFig. 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 thecrystallographic orientation along the large sample size ⟨ ⟩ . One can see that, at the lowest temperatures(6.6 ÷ ∼
10K [6]. Additional experiments performed for a numberof samples with a different concentration yielded similarresults (Fig. 3). As it turned out later on, the differ-ence in the temperature measurements was due to the
Fig. 2. Polarization dependence of the terahertz emission from 𝑛 -Ge (GES-2.5, ⟨ ⟩ ) for different temperatures (the curves areshifted in amplitude): –76 K; – 57 K; – 26 K; – 14 K ; –8.8 K; – 7.7 K; – 7.2 K; – 6.6 K fact that the semiconductor thermometer measured thetemperature of the environment surrounding the emit-ting sample, whereas the sample itself was heated bypulses of the strong electric field ( 𝜏 𝑖 = 0 . 𝜇 s, 𝜐 = ℑ = 2 . A, 𝐸 rep = 6 Hz). Our calculations demon-strate that, at these temperatures (taking into accountthe rapid decrease of the heat capacity), the quantityof heat released in the sample (Fig. 2) increases itstemperature by 10 ÷
15 K, i.e. its real temperaturewill be higher than that fixed by the thermometer by ∼ ÷
15 K, which completely agrees with literaturedata.Hence, the refined position of the point of tempera-ture change of the dominant scattering mechanism andthe form of the curves given in Figs. 2 and 3 allowus to make an unambiguous conclusion about the rela-tion between the angular polarization dependence andthe scattering mechanism. There took place a shift ofthe 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 acousticone.Thus, the presented experimental results (Figs. 2 and3) confirm the proposed explanation of the behavior ofthe polarization characteristic of the terahertz emission
ISSN 2071-0186. Ukr. J. Phys. 2010. Vol. 55, No. 6 .M. BONDAR, P.M. TOMCHUK
Fig. 3. Polarization dependence of the terahertz emission from 𝑛 -Ge (GES-0.3, ⟨ ⟩ ) for different temperatures (the curves areshifted in amplitude): – 70 K; – 57 K; – 26 K; – 14 K; –7.2 K; – 6.4 K; – 5.7 K by hot electrons from 𝑛 -Ge depending on the type ofcarrier scattering.We thank O.G. Sarbey for the detailed discussion ofthe results of this work and O.K. Florova for the givenpolarizers.
1. V.M. Bondar, O.G. Sarbey, and P.M. Tomchuk, Fiz.Tverd. Tela , 1540 (2002).2. P.M. Tomchuk, Ukr. Fiz. Zh. , 681 (2004).3. V.M. Bondar and N.F. Chornomorets, Ukr. Fiz. Zh. ,51 (2003).4. P.M. Tomchuk and V.M. Bondar, Ukr. J. Phys. , 668(2008).5. V.M. Bondar, B.O. Danilchenko, and A.M. Kraichins’kyi,Ukr. J. Phys. , 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. KalyuzhnaТЕМПЕРАТУРНI ЗАЛЕЖНОСТI ПОЛЯРИЗАЦIЇТЕРАГЕРЦОВОГО ВИПРОМIНЮВАННЯ ГЕРМАНIЮ 𝑛 -ТИПУ У ГРIЮЧИХ ЕЛЕКТРИЧНИХ ПОЛЯХВ ОБЛАСТI НИЗЬКИХ ТЕМПЕРАТУР В.М. Бондар, П.М. Томчук
Р е з ю м еЯк було вiдзначено в роботi [3] для правомiрностi припущен-ня про те, що хiд поляризацiйних залежностей терагерцовоговипромiнювання гарячими електронами з 𝑛 -Ge визначаєтьсятипом розсiювання носiїв, необхiдно провести температурнi ви-мiри цiєї залежностi вiд температур, де превалює розсiюванняна домiшках, до температур, де превалює розсiювання на аку-стичних коливаннях ґратки. У данiй роботi наведено резуль-тати таких дослiджень.724