Polarization dependences of terahertz radiation emitted by hot charge carriers in p-Te
aa r X i v : . [ c ond - m a t . m e s - h a ll ] F e b Polarization Dependences of Terahertz Radiation
P.M. TOMCHUK, V.M. BONDAR, L.S. SOLONCHUK
Institute of Physics, Nat. Acad. of Sci. of Ukraine (46, Nauky Ave., Kyiv 03680, Ukraine; e-mail: [email protected])
POLARIZATION DEPENDENCES OF TERAHERTZRADIATION EMITTED BY HOT CHARGECARRIERS IN p -Te PACS 42.72. Ai, 72.20.Ht,61.72.uf, 72.20
Polarization dependences of the terahertz radiation emitted by hot charge carriers in p -Tehave been studied both theoretically and experimentally. The angular dependences of the spon-taneous radiation emission by hot carriers is shown to originate from the anisotropy of theirdispersion law and the anisotropy of the dielectric permittivity of a tellurium crystal. We haveshown that the polarization dependences of radiation are determined by the angle between thecrystallographic axis C in p -Te and the polarization vector; they are found to have a periodiccharacter.K e y w o r d s: terahertz radiation, hot carriers, polarization dependences
1. Introduction
Free charge carriers can neither absorb nor emitlight, because the laws of energy and momentumconservation cannot be satisfied simultaneously insuch processes. These processes become possible if“a third body” participates in them. Various im-purities, lattice vibrations, or a boundary can playthis role. Which phenomenon (absorption or radia-tion emission) dominates at that depends on externalconditions.If charge carriers are in the thermodynamic equi-librium state, and if the semiconductor is irradiatedwith an external electromagnetic flux, the processesof light absorption by free carriers dominate. On theother hand, if no external radiation is present, and ifcarriers are heated up by an electric field applied tothe semiconductor, then the processes of light emis-sion by free carriers prevail. This radiation emissionbelongs mainly to the terahertz frequency range.In semiconductors, the dispersion law for chargecarriers and the mechanisms of their scattering areanisotropic, so that the spontaneous emission by hotcarriers depends on the polarization. Earlier, wehave studied similar polarization dependences withthe use of n -Ge as an example [1–3]. However, de-spite the fact that the dispersion law of electrons inthe minima (valleys) of the Brillouin zone in mul-tivalley semiconductors of the n -Ge type has a pro-nounced anisotropic character, the valleys themselves c (cid:13) P.M. TOMCHUK, V.M. BONDAR,L.S. SOLONCHUK, 2013 are arranged symmetrically in this zone. As a result,the angular dependences of the spontaneous radia-tion emission by hot electrons arise only at certainorientations of a heating electric field. Namely, incrystals with the cubic symmetry of the n -Ge and n -Si type, the polarization dependences of the spon-taneous radiation emission by hot electrons appearonly at such orientations of a heating electric field,at which the temperatures of electrons in differentvalleys is also different. One can also break the cu-bic symmetry and, hence, induce the polarization de-pendences by applying a unidirectional pressure to asemiconductor [1].An absolutely different situation takes place in p -Te, to which this work is devoted. Tellurium is a con-siderably anisotropic semiconductor, although, pro-vided that certain restrictions are imposed upon thehole concentration [4], the isoenergetic hole surfacesin tellurium can be accepted with a sufficient accu-racy in the form of ellipsoids of revolution, similarlyto what takes place for electrons in n -Ge and n -Si.However, there is a basic difference. Namely, the ro-tation axes of ellipsoids for the electron mass tensorin p -Te (there are six ellipsoids) are parallel to oneanother and to the axis C . At the same time, in n -Ge and n -Si, the ellipsoids of the electron mass tensorare oriented differently, but so that the symmetry ofa crystal as a whole remains cubic. Therefore, thepolarization dependences caused by the presence ofthe mass tensor of charge carriers can be observed intellurium in their bare form, i.e. without any modi-fication related to different contributions of different ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 .M. Tomchuk, V.M. Bondar, L.S. Solonchuk valleys to the radiation process, as it takes place in n -Ge and n -Si.The processes of radiation absorption and emissionby free carriers can be studied in the framework ofvarious mathematical methods. In works [1, 6], wesuggested a method to study such processes, whichhas definite advantages in comparison with the avail-able methods. Those advantages consist in that acommon approach can be used to analyze absorp-tion and emission of light by free carriers, in boththe classical (when the light quantum energy, ~ ω , ismuch lower than the thermal energy of carriers, kT e )and quantum-mechanical (when ~ ω > kT e ) frequencyranges. In this approach, the results can be obtainedin the analytical form even if the anisotropy of boththe dispersion law and the scattering mechanisms istaken into account. Just this method was used inthis work.
2. Theory and Adopted Model
In accordance with works [5, 7], the dispersion law forholes in p -Te is taken in the form ε ( p ) = p ⊥ m ⊥ + p k m k , (1)where p k and p ⊥ = ( p x + p y ) are the longitudinal andtransverse, respectively, components of the momen-tum vector p with respect to the direction of the axis C in the crystal. For p -Te, according to work [8], wehave m k = 0 . m and m ⊥ = 0 . m , where m isthe free electron mass.Let an external constant electric field be appliedto a p -Te specimen, and let this field heat up holes.On the basis of our experimental conditions (the lat-tice temperature T = 4 K and the concentration ofionized impurities n i ≈ × cm − ), we may sup-pose [9, 10] that the relaxation of hole momenta isdriven by the hole scattering at ionized impurities,and the relaxation of the hole energy is determinedby the inelastic hole scattering at acoustic and opticallattice vibrations. In the framework of this model, ifthe temperature is low, the contribution to the en-ergy exchange between holes and the lattice can begiven by the interaction between holes and only thoseoptical vibrations of the lattice, whose Debye temper-ature is the lowest. In particular, for p -Te, it is the A optical mode, for which the Debye temperatureequals 138 K [11]. Below, we describe a scheme of the construction ofthe theory of spontaneous radiation emission by hotcarriers in brief, readdressing the reader to work [6]for details.Hence, in order to obtain the collision integral thatinvolves the influence of the electromagnetic wavefield on the scattering processes of free carriers, letus do it as follows. While deriving the collision inte-gral, we use the wave functions of free carriers in theelectromagnetic wave field Ψ p = 1 V exp (cid:18) i ~ p r (cid:19) × exp − i ~ t Z dt ′ X j m j (cid:16) p j − ec A j ( t ′ ) (cid:17) , (2)instead of their basic wave functions. Here, V is thevolume, t ′ the time, e the carrier charge, c the ve-locity of light, and A ( t ) the vector-potential in thedipole approximation, A ( t ) = A (0) cos ωt. Note thatthe inclusion of the electromagnetic wave field intothe collision integral, rather than into the left-handside of the kinetic equation as an external force, isvalid if the inequality ωτ > , where τ is the relax-ation time, is satisfied.As was shown in work [6], the collision integral forthe scattering of carriers by ionized impurities can beobtained with the use of basis (2) in the form ˆ If = 4 e N i ×× ∞ X l = −∞ Z d p ′ f ( p ′ ) − f ( p ) n χ ⊥ ( p ⊥ − p ′⊥ ) + χ k ( p k − p ′k ) +( ~ /r (0) D ) o ××ℑ l ec ~ ω X j =1 A (0) j p j − p ′ j m j δ ( ε ( p ) − ε ( p ′ ) − l ~ ω ) , (3)Here, f ( p ) is the distribution function of charge car-riers over their momenta p ’s, N i the concentration ofionized impurities, and ℑ l ( x ) the Bessel function ofthe l -th order. Moreover, we have additionally con-sidered the tensor character of the dielectric permit-tivity of tellurium in formula (3) in contrast to work[6]. In particular, in the coordinate system with theaxis z directed along the axis C in tellurium, we ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 olarization Dependences of Terahertz Radiation have χ xx = χ yy ≡ χ ⊥ and χ zz ≡ χ k . Expression (3)includes low-frequency values of χ ii . The parameter r (0) D is the radius of charge screening by free carriers.In particular, in the case of non-degenerate statistics, (cid:18) r D (cid:19) = 4 π e nkT p , (4)where n is the concentration of free carriers, and T p is their temperature.If we are not interested in a special action of power-ful laser pulses, the argument of the Bessel functionin Eq. (3) is, as a rule, less than 1. Therefore, themultiplier ℑ l ( . . . ) in formula (3) can be expanded ina series, and only the first term of the series can beretained. In addition, in what follows, we will confinethe consideration to one-quantum processes, i.e. onlythe terms in expression (3) corresponding to l = ± will be taken into account. Then, by multiplying ex-pression (3) by ε ( p ) and integrating the product over d p , we obtain the variation of the electron system en-ergy per unit time, which is related to the processesof absorption and emission of light quanta, ~ ω : p = Z d p ˆ If = P (+) + P ( − ) ,P ( ± ) = ± e c ~ ω ×× Z d p d ¯ p ′ f ( p ′ ) δ { ε ( p ) − ε ( p ′ ) ± ~ ω }{ χ ⊥ ( p ⊥ − p ′⊥ ) + χ k ( p k − p ′k ) + ( ~ /r D ) } ×× (cid:18)X A (0) j p j − p ′ j m j (cid:19) . (5)While calculating integral (5), let the Maxwell func-tion with the effective hole temperature θ p ≡ kT p beused as a distribution function for hot holes, f ( p ) = n (2 πθ p ) / m ⊥ √ m k exp( − ε ( p ) /θ p ) . (6)The sign “ + ” in Eq. (5) describes the process of ~ ω -quantum absorption (i.e. the energy of charge car-riers increases), and the sign “ − ” corresponds to theemission of a quantum ~ ω (i.e. the energy of chargecarriers decreases).The quantity P ( − ) describes the variation of thehot hole energy per unit time, which is related to the emission of a quantum ~ ω . To obtain the total energychange induced by the emission of all quanta in a unitfrequency interval into the space angle d Ω , we haveto multiply P ( − ) by the density of final field statesin a solid angle d Ω , i.e. by dρ ( ω ) = V (2 πc ) ω d Ω . (7)Then, the product P ( − ) dρ ( ω ) describes the radiationemission of charge carriers induced by the electromag-netic wave field. However, we are interested in thespontaneous radiation emission by hot carriers. Tofind this quantity, we use the Einstein ratio betweenthe probabilities of induced and spontaneous emis-sions (see, e.g., work [12]). For this purpose, we mustfirst normalize the vector-potential A (0) (see Eq. (5))in such a way that the volume V would contain N ph photons, i.e. we have to use the condition V N ph ~ ω = E π = 18 π (cid:16) ωc (cid:17) A (0)2 . (8)Whence, A (0) = 2 c (cid:18) π ~ V ω N ph (cid:19) / . (9)After substituting Eq. (9) in Eq. (5), the quantity W ( − ) ≡ [ P ( − ) dρ ( ω )] N ph =1 is the power of sponta-neous radiation emission by hot carriers in a unitspectral interval into the solid angle d Ω .As was shown in work [6], after the transition inEq. (5) to a deformed coordinate system, in whichthe elliptic isoenergetic surfaces (1) transform intospherical ones, the integrals in expression (5) can becalculated, and we obtain W ( − ) = e n N i √ m k (2 π ) / c Ψ( ∞ ) d Ω( m k χ k − m ⊥ χ ⊥ ) ×× √ π √ θ p ln (cid:16) C ~ m ⊥ χ ⊥ θ p (cid:17) − for ~ ω ≪ θ p , √ ~ ω exp (cid:16) − ~ ωθ p (cid:17) for ~ ω ≫ θ p , (10)where ln C = 0 . ... is the Euler constant.According to the results of work [6], the quantity Ψ( ∞ ) equals Ψ( ∞ ) = 1 b (cid:20) b + (1 − b ) arctg 1 b (cid:21) sin ϕ + ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 .M. Tomchuk, V.M. Bondar, L.S. Solonchuk +2 m ⊥ m k (cid:20) −
11 + b + 1 b arctg 1 b (cid:21) cos ϕ, (11)where ϕ is the angle between the polarization vectorand the axis C (the latter is parallel to the axis ofrevolution of ellipsoids of the effective-mass tensor),and b = m ⊥ χ ⊥ m k χ k − m ⊥ χ ⊥ . (12)At χ k = χ ⊥ , the quantity b coincides with the cor-responding quantity obtained in work [6].Substituting expression (11) in Eq. (10), we obtain W ( − ) = (cid:8) a ⊥ sin ϕ + a k cos ϕ (cid:9) d Ω . (13)The coefficients a ⊥ and a k can be easily obtained bycomparing expressions (10) and (13). It is not difficultto get convinced that if m ⊥ = m k and χ ⊥ = χ k , wehave a ⊥ = a k , and the angular dependence disappearsfrom expression (13).Hence, we have obtained the explicit expression forthe angular dependence of the spontaneous radiationemission by hot holes in the form (13). The coef-ficients that characterize this angular dependence –these are a ⊥ and a k – are known functions of themass tensor components ( m ⊥ and m k ), the dielec-tric permittivity tensor components ( χ ⊥ and χ k ), thelight frequency ω , and the hot electron temperature θ p . All those parameters, but θ p , are known.To obtain the simplest expression for the hot-holetemperature, we confine the consideration to low tem-peratures ( ≤ T ≤
20 K ) and weak enough electricfields, at which T p ≪
138 K , i.e. when the value of kT p is much lower than the energy of optical phonons.In those ranges of temperatures and fields, it is pos-sible to consider that the relaxation of the momen-tum of holes takes place predominately at their scat-tering by ionized impurities, and the energy relax-ation occurs at their quasielastic scattering by acous-tic phonons. The energy given by hot carriers to thelattice per unit time at the quasielastic scattering byacoustic vibrations, according to the results of work[13], equals Z d ¯ p ε ( p ) ˆ I ak f = g n θ / p (cid:18) − θθ p (cid:19) , (14) where g = 8 √ m ⊥ √ m k π / ρ ~ m + ⊥ m k ! X d , (15)and Σ d is the constant of the deformation potential(we confine the consideration to the one-constant ap-proximation).In the stationary case, the scattering power (14)must be equal to that obtained by carriers from theheating field F , i.e. jF = e n n µ ⊥ ( θ p ) F ⊥ + µ k ( θ p ) F k o , (16)where j is the current-density vector, µ ⊥ ( θ p ) and µ k ( θ p ) are the transverse and longitudinal, respec-tively, components of the mobility tensor arising ow-ing to the scattering of charge carriers by ionized im-purities [6], µ ⊥ ( θ p ) = 8 √ π e τ ⊥ ( θ p ) m ⊥ ; µ k ( θ p ) = 8 √ π e τ k ( θ p ) m k , (17)and τ ⊥ ( θ p ) and τ k ( θ p ) are the transverse and lon-gitudinal, respectively, components of the relaxationtensor at the impurity-driven scattering, given by theexpressions τ ⊥ ( θ p ) = 83 e p m k χ ⊥ m ⊥ θ / p ×× N i b (cid:20) b + (1 − b ) arctg 1 b (cid:21) ln (cid:18) C ~ m ⊥ χ ⊥ θ p (cid:19) − , (18)and τ k ( θ p ) = 83 e p m k χ ⊥ m k θ / p ×× N i b (cid:20) − b + (1 + b ) arctg 1 b (cid:21) ln (cid:18) C ~ m ⊥ χ ⊥ θ p (cid:19) − . (19)At χ ⊥ = χ k , expressions (18) and (19) transform intothe corresponding formulas obtained in work [6] (Un-fortunately, the notations τ ⊥ and τ k in formula (54)in work [6] were transposed!) ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 olarization Dependences of Terahertz Radiation
If the weak dependence on θ p in the logarithm informulas (18) and (19) is neglected, then Eqs. (17)–(19) yield µ ⊥ , k ( θ p ) ≈ (cid:18) θ p θ (cid:19) / µ ⊥ , k ( θ ) . (20)Now, let us make expressions (14) and (16) equal toeach other and use relation (20). Then, from thisbalance equation, we easily obtain the temperatureof hot holes, θ p = θ (cid:26) − eg θ / h µ ⊥ ( θ ) F ⊥ + µ k ( θ ) F k i(cid:27) − . (21)The validity of this formula is restricted to fields, atwhich θ p < ~ ω , where ω is the frequency of thelowest optical mode (it corresponds to a tempera-ture of 138 K). If θ p approaches the energy of opticalphonons, the scattering of holes by the latter has tobe taken into consideration.Hence, we obtained an expression for the angulardependence of the spontaneous radiation emission byhot holes in tellurium in the form of formula (13)in the case where the dominating mechanism of mo-mentum scattering is the scattering by ionized impu-rities. In so doing, we made allowance for the ten-sor character of the effective mass and the dielectricpermittivity in p -Te. In work [1], we obtained anexpression for the spontaneous radiation emission byhot carriers with the dispersion law (1) in the casewhere the acoustic scattering plays the dominatingrole. The angular dependence of the spontaneous ra-diation emission by hot carriers looks like Eq. (13) atboth acoustic- and impurity-driven scattering. Theonly difference consists in the different dependencesof the coefficients a ⊥ and a k on the hot-carrier tem-perature.
3. Experiment and Its Discussion
The experimental setup is shown in Fig. 1. We usedspecimens of single-crystalline tellurium grown by theCzochralski method. The specimens were either cutout of single-crystalline ingots along the axis C orcarefully sawn out of those ingots across it. Then, thespecimens were annealed in the hydrogen atmosphereat a temperature of 380 ◦ C for 200 h and treated witha chromic etching solution HF + CrO + H O (1:1:3).After annealing and etching, the mobility and the Fig. 1.
Experimental setup: p -Te specimen with either paral-lel ( k ) or normal ( ⊥ ) C -axis orientation ( ), black polyethylenefilter ( ), polarizer (analyzer) ( ), and Ge(Ga) detector ( ) concentration of charge carriers fell within the inter-vals 5200–6000 cm / V / s and (1 . ÷ . × cm − ,respectively. The cross-section dimensions of speci-mens were × . , and their length varied from3.2 to 7 mm. Ohmic contacts were soldered with theuse of the solder 50% St + 47% Bi + 3% Sb.To heat up holes in Te specimens, a generator ofelectric pulses with a low input resistance of about20 Ω was used, which enabled us to carry out mea-surements for low-resistance specimens. The pulseduration was 0.8 µ s and the repetition frequency was6 Hz. As a 3-THz radiation detector ( λ ≈ µ m ),we used a Ge(Ga) detector × × . in size.A signal registered by the detector was ampli-fied with the use of a broadband amplifier, inte-grated, converted into a constant voltage, and sup-plied to a two-coordinate recorder. The short-wavesection of the radiation spectrum emitted by hot holes( λ < µ m ) was cut off by applying a filter fabricatedof black polyethylene. The polarizer (analyzer, Fig. 1)was rotated at a low speed of one rotation per 2 min,and its axis was rigidly connected with the long-axisdirection of the emitting specimen (and, hence, withthe direction of the electric field applied to the spec-imen). As the “zero” rotation angle of a polarizer,its such orientation was selected, when the directionof polarizer grooves coincided with the direction ofspecimen’s long axis and the electric field applied tothe specimen. We recall that the polarizer transmitsthe electromagnetic wave only in the case where theelectric component of the wave is perpendicular to itsgrooves.The polarization dependences of the terahertz ra-diation emission by hot carriers in p -Te were stud-ied using the specimens cut out along the crystallo-graphic axis C and perpendicularly to it (below, werefer to them as the specimens of the first and secondtypes). Figures 4, a and b exhibit one of six (parallel) ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 .M. Tomchuk, V.M. Bondar, L.S. Solonchuk
Fig. 2.
Dependences of the specimen radiation emission inten-sity on the polarizer rotation angle for various heating fields (in-dicated in the figure) in the ( p -Te k C )-geometry of experiment Fig. 3.
The same as in Fig. 2, but for the ( p -Te ⊥ C )-geometryof experiment ellipsoids, which describe the dispersion law for holesin p -Te (1), and demonstrate the orientation of thelong axis of this ellipsoid with respect to the crystal-lographic axis C and the direction of electric fieldapplied to the specimen. In both cases, the electricfield is applied along the long axis of the specimen.While studying the polarization dependence of theradiation emission by specimens of both the first andsecond types, the polarizer was rotated in the plane zy around the axis x . In Figs. 2 and 3, the de-pendences of the radiation intensity emitted by hotholes on the angle between the direction of polarizergrooves and the direction of electric field that heatsup charge carriers are depicted. It will be recalledthat the zero value of this angle corresponds to the ab Fig. 4.
Specimens and their orientation with respect to thecrystallographic axis: specimen cut out ( a ) along the axis and( b ) perpendicularly to it situation where the polarizer grooves are parallel tothe applied electric field.In the theory developed above, the angular depen-dence of the radiation intensity was described by theangle between the axis C , which is parallel to thelong axis of the ellipsoid, and the polarization direc-tion, i.e. the direction of the electric component ofan emitted electromagnetic wave. Since the polarizertransmits only the electric wave component which isperpendicular to its grooves, then, as is seen fromFig. 4, a corresponding to the case of first-type speci-mens, when the heating electric field, the axis C , andthe grooves are parallel to one another, the angles inFig. 2 and in the theoretical formula (13) are shiftedwith respect to one another by π/ . At the same time,for specimens of the second type, for which the heat-ing field and the axis C are mutually perpendicular,the angles in Fig. 3 and in the theory (formula (13))coincide (see Fig. 4, b ). In this case, there is a mini-mum at the angle ϕ = 0 . This fact agrees with for-mula (13). Passing in this formula to the doubled ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 olarization Dependences of Terahertz Radiation angle, we obtain W ( − ) = 12 { a ⊥ + a k + ( a −k a ⊥ ) cos 2 ϕ } d Ω . (22)Whence, one can see that the presence of theminimum at ϕ = 0 corresponds to the condition a ⊥ /a k > .From Eqs. (10) and (11), we obtain a ⊥ a k = b h b + (1 − b ) arctg b i m ⊥ m k h − b + b arctg b i . (23)For p -Te, m k = 0 . m , m ⊥ = 0 . m , χ k = 56 ,and χ ⊥ = 33 . Hence, b ≡ m ⊥ χ ⊥ m k χ k − m ⊥ χ ⊥ ≈ . and a ⊥ a k ≈ . Thus, in both the theory and the experi-ment, we obtain a minimum at ϕ = 0 . Therefore,the positions of minima and maxima in the theoryand the experiment coincide. Hence, our theory ad-equately predicts a periodic character of polarizationdependences of the spontaneous radiation emission byhot holes in p -Te and correctly evaluates the positionsof maxima and minima for this radiation.It would be of interest to have not only a quali-tative, but also a quantitative comparison betweenthe theory and the experiment. However, unfortu-nately, it cannot be done now. First, expression(13) gives the spectral distribution of the radiationintensity, whereas experimentally the integrated ra-diation power in the given frequency range is mea-sured. Therefore, for the quantitative comparison tobe made, expression (10) should be integrated overa frequency interval given in the experiment. Thisprocedure renormalizes the coefficients a ⊥ and a k inexpression (13). While integrating over the frequency,we would have to determine the temperature of hotcarriers, θ p , for every heating field, which is a separatelarge problem.Second, the very expression for θ p can change withthe growth of the electric field owing to the engagingof new relaxation mechanisms. However, the angulardependence of the spontaneous radiation emission byhot carriers in form (13) has a more universal charac-ter, which is governed, first of all, by the dispersionlaw (1). Provide that the dispersion law is fixed, onlythe specific values of parameters a ⊥ and a k in formula(13) depend on the scattering mechanism.
4. Conclusions
The dependences of the terahertz radiation emissionintensity by hot charge carriers in p -Te on the anglebetween the crystallographic axis C and the polar-ization vector, as well as their periodic character, havebeen studied both theoretically and experimentally.The periodic character of the dependence concernedand the positions of radiation intensity minima andmaxima were demonstrated to coincide in the theoryand the experiment. The polarization dependencesof the radiation emission by hot charge carriers werefound to be associated with the anisotropy of thecharge carrier dispersion law and the anisotropy ofthe dielectric permittivity.
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Received 27.06.12.Translated from Ukrainian by O.I. Voitenko
П.М. Томчук, В.М. Бондар, Л.С. Солончук
ПОЛЯРИЗАЦIЙНI ЗАЛЕЖНОСТI ТЕРАГЕРЦОВОГОВИПРОМIНЮВАННЯ ГАРЯЧИМИ НОСIЯМИ
ISSN 2071-0186. Ukr. J. Phys. 2013. Vol. 58, No. 2 .M. Tomchuk, V.M. Bondar, L.S. Solonchuk
ЗАРЯДУ в p -TeР е з ю м еВ роботi теоретично i експериментально вивчено поляри-зацiйнi залежностi терагерцового випромiнювання гарячи-ми носiями заряду в p -Te. Показано, що кутовi залежно- стi спонтанного випромiнювання гарячих носiїв зумовленiанiзотропiєю їх закону дисперсiї i анiзотропiєю дiелектри-чної проникностi. Встановлено, що поляризацiйнi залежно-стi випромiнювання визначаються кутом мiж кристалогра-фiчною вiссю C в p -Te та ортом поляризацiї i цi залежностiмають перiодичний характер.142