Calculation of exciton energy levels in (ZnxCd1-x)3p2 alloy system Текст научной статьи по специальности «Физика»

ФУНДАМЕНТАЛЬН1 НАУКИ

УДК 548.76+621.315

DM. STEPANCHIKOV

Kherson National Technical University

CALCULATION OF EXCITON ENERGY LEVELS IN (ZnxCd1-x№ ALLOY SYSTEM

The energy levels of free excitons and exciton-impurity complexes in (ZnxCd1-x)3P2 alloy system are calculated by variational method taking into account twofold degenerate valence band. The band structure of (ZnxCd1-x)3P2 alloy system is considered within the framework of Kildal's band model. Analytical dependencies of band parameters on a composition x are gained. A theoretical analysis is developed for ascertaining the influence of exciton states on edge absorption and luminescence spectra. Screening effects have been taken into account using the modified Coulomb potential with dielectric function depended on electron-hole distance.

Keywords: excitons, zinc (cadmium) phosphide, Kildal's band model.

Д.М. СТЕПАНЧИКОВ

Херсонський нацюнальний техшчний ушверситет

РОЗРАХУНОК ЕНЕРГЕТИЧНИХ Р1ВН1В ЕКСИТОН1В В СИСТЕМ1 (ZnxCd1.x)3P2

Енергетичш pieni вшьних eKcumoHie та екситон-домшкових комплекав в cucmeMi (ZnxCd1-x)3P2 розраховаш eapia^muM методом, який враховуе подвшне виродження валентног зони. Зонна структура системи (ZnxCd1-x)3P2 розглянута у межах зонног модeлi Юлдал. Отримано аналтичш залeжноcmi зонних паpамempiв вiд композицИ х. Теоретичний анализ розвинуто для того, щоб встановити вплив екситонних cmанiв на спектри крайового поглинання i люмтесценци. Ефекти екранування враховано з використанням модифжованого потенщалу Кулона з дieлeкmpuчною функ^ею, яка залежить вiд вiдcmанi мiж частинками.

Ключовi слова: екситони, фоcфiд цинку (кадмт), зонна модель Юлдал.

Д.М. СТЕПАНЧИКОВ

Херсонский национальный технический университет

РАСЧЕТ ЭНЕРГЕТИЧЕСКИХ УРОВНЕЙ ЭКСИТОНОВ В СИСТЕМЕ (ZnxCd1-x)3P2

Энергетические уровни свободных экситонов и экситон-примесных комплексов в системе (ZnxCd1-x)3P2 рассчитаны вариационным методом, принимающим во внимание двукратное вырождение валентной зоны. Зонная структура системы (ZnxCd1-x)3P2 рассмотрена в рамках зонной модели Килдал. Аналитические зависимости зонных параметров от композиции х получены. Теоретический анализ развит для того, чтобы установить влияние экситонных состояний на спектры краевого поглощения и люминесценции. Эффекты экранирования приняты во внимание с использованием модифицированного потенциала Кулона с диэлектрической функцией, зависящей от расстояния между частицами.

Ключевые слова: экситоны, фосфид цинка (кадмия), зонная модель Килдал.

Formulation of the problem

Zn^2 and Cd3P2 form a continuous series of substitution (ZnxCd1-x)3P2 solid solutions, which possess to the tetragonal unit cell described by P42/nmc symmetry (space symmetry group D\h) and belong to the group of A3nB2V compounds. The

(ZnxCd1-x)3P2 solid solutions are characterized by a direct fundamental energy gap in the range from 0,53 eV (for Cd3P2) to 1,51 eV (for Zn3P2) with 300 K [1,2]. Therefore, they are drawing particularly strong attention as materials, which will make it possible to produce highly efficient solar cells, sensors, IR lasers, energy converters, ultrasonic multipliers, Li-ion batteries and the like at low cost [3-9].

Therefore, theoretical considering new characteristics of A3nB2V semiconductors such as exciton effects in optical spectra are requisite because of fast progress of nanotechnologies [4,6]. Some unsolved problems should be mentioned thereupon. Absence of theoretical band model for intermediate compositions of (ZnxCd1-x)3P2 solid solutions, firstly. The investigations of free excitons and exciton-impurity complexes in binary and ternary II-V phosphides has been lingering far behind compared with the significant progress in II-VI and III-V semiconductors, secondly. Ordinarily in excitonic problem the screening effects in Coulomb potential are not considered. The dielectric function (г) is calculated as constant on this

understanding. Although naturally, the dielectric properties are depend on electron-hole distance (r). So, the dielectric function s(f) is not constant in the excitonic Hamiltonian Besides, the dielectric function values powerfully influences upon values of the exciton binding energy. Because of analytical complexity the solutions of the Schrodinger equation with the dielectric function s(r) are not gained today. It is the third and main problem on our way.

Analysis of last investigations and publications

Possibility of producing of the simple and reliable blue light emitting diodes, electromagnetic radiation amplifiers in optical fiber communication systems, devices with use nonlinear optical effects in the region of absorption edges are perspective practical applications of Cd3P2 nanocrystals. Nanoparticles of Cd3P2 which are estimated to be -1,5^4 nm in diameter, are characterized by a very strong quantum size effects. It is due to the large excitonic diameter of Cd3P2 (360 A) in comparison with GaAs (233 A), InP (216 A), CdSe (60 A), CdS (47 A), and therefore fluorescence of Cd3P2 nanoparticles are stronger [5,6,9].

Zinc phosphide is used at direct fabrication of hierarchical nanotube/nanowire heterostructures with controlled morphologies, crystallography, and surface architectures. The hierarchical Zn3P2/ZnS one-dimensional nanotube/nanowire heterostructure may be considered as example. Zn3P2 nanotubes with outer diameters of 100^200 nm and wall thickness of 10, 20 and 45 nm, show emissions centered at about 491, 711 and 796 nm respectively. Optoelectronic devices fabricated using single crystalline branched zinc phosphide nanowires demonstrate a high sensitivity and rapid response to impinging light and it offers a great potential for a high efficient spatial resolved photon detector. Study and practical application of the bicrystalline Zn3P2 and Cd3P2 nanobelts, which were synthesized at recent time, is a new perspective way [5,7,8].

The purpose of the investigation The purpose of the investigation is a theoretical study of the energy levels of free excitons and exciton-impurity complexes in absorption and luminescence spectra of (ZnxCdi-x)3P2 alloy systems with different values x in the region of direct optical transitions. The generalized Kildal's band model [5,8,10] is used for calculations. Excitonic Hamiltonian with modified Coulomb potential is solved by variational method. The received results are analyzed with famous experimental data.

Statement of the basic material of the investigation The effective Hamiltonian for D\l space modifications of A3eB2v semiconductors nearby the point k0=0 and within quasicubic approximation of Kildal's band model may be written as [10]:

r Hii Hi:

Hk =

H,+0 H„

(1)

here

r

H,

E„

H

0

ir)-1 Pk. 0

(-2A/3 0 0

0 E

ir-Pkz 0

0

irPkz

(2)

iPk 0 iPk+ л

0 iPk 0

0 0 0

0 -¿-A/3 0 - iT]-2 Pk2 0 -S -A/3j 0 0 0| ( 0 -2A/3 0 0 _ -iPk+

0 0 0' 12 = V2A/3 v 0 0 0 0J [ 0 42A/3 0 0 y

Thereto: (Eg, A, P) - are three well-known Kane's parameters, i.e. the energy gap, the spin-splitting parameter and the matrix element of impulse respectively; S - is the parameter of the crystal field; ] - is the scalar factor taking into account the tetragonal deformation of the lattice; k+ = (1/V2)k + ik ).

By diagonalization of Hamiltonian (1) we get a following secular equation:

(k2 + k^ Pf (E) + klP>/2 (E)-y(E) = 0, (3)

where energy polynomials y(E), f1(E), f2(E) are given by relations:

2AY„ „ A

r(E) = E

(E - E. He + E + , + A j-0

2 ДЛ

A

Aj A2

2A

(4)

(5)

ME) = ^ E + - E + S + - j- — f2(E) = E + T j^.

Dispersion equation (3) has four non-identical solutions, each with double spin degeneration. These solutions are describing the conductivity band (c), the heavy holes band (hh), the light holes (Ih) and the spinorbital split bands (50), respectively (see fig. 1). In addition, the equation (3) is a particular case of second order equation, describing a surface of the rotation around polar z- axis in the k- space. Therefore, transversal and longitudinal effective masses associate themselves with two semi-axes of this surface [11]:

h 2r(E) Eh2 (e - Eg )((э(£ + S) + а)(3Е + 2a)r2 - 2а2 ) ' 2 (Е-E0)P f(E) " 2P2(E-E0)((3E + а)(з(Е + S) + a)^2 -а2) h V(E) hГ2 (E - Eg )(3(E + S) + a)(3E + 2a)r2 - 2a2 )

2(E - Eo )P f (E )"

6P2 (E - E )(3E + 2 a)

(6) (7)

E, eV 1.6

1.5

-0.1

-0.2

\ /ç

£f

hh ' \ мГ"

E, eV

2.0

1.0

-0.2

5/

EP

■Ï %

гГч

E, eV

0.9

0.7

0.5

-0.2

-0.4

r;/

8

0

8

к 10e 1/m к , Ю1

8

к, 10! 1/m

8

0

10s

К 10® I'm kw,

10!

Fig. 1. Energy band structure of (ZnxCdi_x)3P2 alloy system for x= 1; 0,5; 0 near the k0=0 point at T = 300K

In our calculations the low anisotropy of band structure of (ZnxCdi_x)3P2 alloy systems was not considered and consequently the effective mass of density of states is used further:

m = ^m* (m )2

(8)

h2 (e - Eg )(3(E + S) + A)(3E + 2A)r2 - 2A2 ) 2(E - Eo )P2

E У

3(3E + 2A)(A2 - (3E + A)(3(E + S) + A)r2 )

where E0 - is the energy of bands extremum in k0 = 0 point [11]:

ec - e ■ ehh - 0- eih-so E0 Eg - E0 0' Eo

3r(S + a) + 49S2r2 - 6Sar2 + a2(8 + r2 )

(9)

6r

In last equation the sign "-" and "+" correspond to Ih-band and so -band respectively. The top of the hh-band is selected as the zero of energy coordinates.

The average effective mass of hole is used below. It is an arithmetical mean mh=(mhh+mlh)/2 of effective masses of heavy mhh and light mh holes calculated by equation (8). The reduce effective mass of an exciton is spotted as /j=me mh/(me+mh). Here me is the effective electron mass of conduction band calculated by equation (8).

The band parameters and effective masses value depending on composition x of (ZnxCdi-x)3P2 alloy systems are shown in Table 1. Regrettably, in literary sources the values of full set of band parameters are available for Zn3P2 and Cd3P2 only. Using values of band gap for Cd3P2, Zn3P2 at T = 300 K and (ZnxCd1-x)3P2 with x = 0,2; 0,4; 0,5; 0,8 at T = 100 K [5,12] we have got a following exponential equation for function of Eg(x) at T = 300 K:

(x) = 0,53 + 0,70x + 0,69x2 -1,42x3 + 3,38x4 - 2,36x5 , (10)

here values of band gap Eg at T = 100 K have been recounted for T = 300 K with using temperature coefficient dEg/dT = -1,810-4 eV/K.

Scalar factor ^ = c /(«V2) (a,c - are the lattice parameters) for Cd3P2 and Zn3P2 has nearly equal values (7 = 0,99) and so it was considered as constant for (ZnxCd1-x)3P2 alloy systems. The composition dependencies for other band parameters i.e. A, P and S were accepted as linear, similar to following function:

A(x) = A(Znp )x + A(Cdp )(1 - x), (11)

here v4={A, P, S}.

Linear relation of band parameters from a composition i.e. Vegard's law is feature of band spectrums of solid solutions. The Vegard's law is fulfilled better if components of solid solutions have equal physicochemical structure. It is completely achieved for explored semiconductors.

1

Undoped Zn3P2 displays p- type conductivity with characteristic charge concentration about 10 ^10 cm-3, while at another end of series Cd3P2 is the degenerated n- type semiconductor with characteristic charge concentration about 1017-^1018 cm- . The data about type of conductivity in the intermediate solutions of the (ZnxCdi-x)3P2 system are not available. Therefore, we suppose that the crossover p- to n- type occur at x=0,5. Until x>0,5 prevail the p- type conductivity, and with x<0,5 prevail the n- type conductivity. Using such assumptions we have got a following nonlinear equation for composition dependence of Fermi level sF(x):

eF(x)=eF(Cd3P2) + Bx -Cx2, (12)

where B = 0,15 eV, C = 0,54 eV. The Fermi level values for different compositions x of (ZnxCd1-x)3P2 solid solutions are shown in Table 1.

Table 1

The main band parameters of (ZnxCd1-x)3P2 alloy system at T = 300K

X Eg, eV Д, eV Р, 10-10 eVm 8, eV ef, eV* me mh M

0 0,53 0,150 7,2 0,023 0,59 0,047 0,244 0,039

0,2 0,69 0,142 6,7 0,024 0,60 0,062 0,333 0,052

0,4 0,85 0,134 6,2 0,025 0,56 0,092 0,456 0,076

0,5 1,01 0,130 5,95 0,026 0,53 0,113 0,536 0,093

0,6 1,11 0,126 5,7 0,027 0,49 0,139 0,639 0,114

0,8 1,41 0,118 5,2 0,029 0,36 0,204 0,861 0,165

1 1,51 0,110 4,7 0,03 0,2 0,268 1,069 0,214

the top of the heavy holes band is selected as the zero counting of Fermi level value.

The potential energy of electron-hole interaction depends on how much strongly an electron polarizes a lattice at the moving. If the rotation frequency of an electron around the hole a « hl(paB) (p - is the reduce effective mass of exciton, aB = 4ns0h2ej(pe2) - is the Bohr radius) exceeds an effective resonance frequency of valence electrons a0 « Eglh the interaction potential is not Coulomb. The model of Wannier-Mott exciton is not correct in this case. On the other hand, the relative motion of an exciton becomes slow, if a<a0. Valence electrons move together with an exciton. Electron-hole interaction is described by a Coulomb potential and the Wannier-Mott exciton model is valid in this case. Hence, the canon of performance of Wannier-Mott exciton model will be noted by an inequality [13]:

^ (13)

ab >Pe =

and values of the dielectric constant in the Coulomb potential correspond to a high-frequency optical constant sm.

As a result of the further increase of radius of an exciton the electron rotation frequency is decreasing so, that all electrons are follow an exciton move. Thus frequency is comparable with frequency of optical oscillations o&oLO and the static dielectric constant ss is necessary for using in the Coulomb potential. Hence, the condition of replacement sx on ss in the Coulomb potential can be noted in such form [13]:

(14)

ab > Pl

h

M®lo

Accordingly for radiuses aB > pE the Coulomb potential can be written as function of radius r of an

exciton:

with dielectric function described as [5,13]

V {r )=-

4ле0Е(г )r

1 1

exp

1 --

r

pe

+ expI -

(15)

(16)

here pe h /(2ot*®lo); ph h /(2m*haLO); e - is the elementary charge; £b - is the electric constant; me, mh -

are the effective mass of electron and hole respectively. Frequencies of optical oscillations a>LO for Zn3P2 and Cd3P2 in the equations (14,16) are spotted from far-infrared reflectivity by making a choice of a LO -phonon with the greatest oscillator strength. For the intermediate solutions of the (ZnxCd1-x)3P2 alloy system the composition dependency of a>LO is accepted linear like to equation (11). Bohr radius of an exciton aB, characteristic distances Pe, PL, frequencies of optical oscillations a>LO and dielectric constant s(r=aB) are shown in Table 2.

2

e

r

1

1

2

e

e

e

In our calculations of the dielectric function (16) high-frequency optical constant sf associated with a maximum of a real part of permittivity in the region of direct optical transitions (see Table 2). When the relaxations frequency of the carriers in comparison with photon frequency is negligible quantity, the interband contribution to real part of permittivity with spherical coordinates (k, в, q>) has a such form [14]:

(\ i . 2e2 v f2ff f " fc У*Ы2k2з1пв (17)

where j - is the number of valence band, Ec, Ev - are the energies of conduction and valence bands respectively, fc,v, vcv, Fcv are the Fermi-Dirac function, velocity of charges and the oscillator strength of interband transitions which are defined as follows

1 . y p 2\(c\ep\v)\2 (18)

c,v f Ec,v -eF ^ ' " 8k die ' c Vcv (Ec - Ev)'

eXP I KT

where |(c\ep\v)| - is the dipole matrix element, kB - is the Boltzmann constant.

The main dielectric parameters, Bohr exciton radius and characteristic distances for (ZnxCdi_x)3P2 alloy system at T = 300K

Table 2

X km, 1010 m-1 ®LO, 1013s-1 PE, Ä PL Ä üß, Ä £co ss s(ctß)

0 2,40 3,68 19,20 89,81 153,41 11,35 22,85 22,03

0,2 2,06 3,99 14,04 74,52 119,32 11,76 23,65 22,64

0,4 1,72 4,30 10,30 59,32 87,01 12,56 24,46 23,26

0,5 1,55 4,46 8,78 52,75 74,33 13,08 24,86 23,58

0,6 1,38 4,61 7,49 46,91 63,36 13,64 25,26 23,91

0,8 1,04 4,93 5,63 37,74 44,21 13,75 26,07 24,11

1 0,70 5,24 4,86 32,12 34,20 13,82 26,87 24,34

The integral on wave vector k for real part of dielectric function (17) has a logarithmic break up on top limit. However, the main contribution to integral derives from Eg < E < Eat energy region. So, with logarithmic accuracy the integral must be truncate on km value, which corresponds to atomic energy Eat [14]. In our calculations there was accepted Eat « 4 eV for Zn3P2 and Eat « 17 eV for Cd3P2. The values of wave vector km, corresponding to Eat are presented in Table 2. The composition dependency of the wave vector km is accepted linear like to equation (11).

With axial symmetry the equations (17) may be a simplified to following forms:

*»=iH jjE^^ (19)

'( ^ ^ r I Jo (Ec -Ej%EC -Ej)) ' here the spin degeneration of each band is taken into account (the degeneration factor is 2).

The real part of permittivity calculated by equation (19) for different compositions x of (ZnxCdi_x)3P2 alloy systems is shown in fig.2.

The static dielectric constant ss is calculated from the experimental spectrums of infrared reflectivity with use of well-known Lyddane-Sachs-Teller relation for a multiphonon system:

n

_ n ^QJ (20)

Ss n ■

n^O, j=1

The eigenfrequencies of the transverse aTO and longitudinal a>LO coupled modes of Cd3P2 and Zn3P2 semiconductors are spotted from far-infrared reflectivity [15]. For the intermediate solutions of the (ZnxCd1-x)3P2 alloy system the composition dependencies of aTO and a>LO are accepted linear like to equation (11). The values of static dielectric constant ss are presented in Table 2.

Screening of Coulomb interaction is the fatal reason destroying all exciton effects in volume crystals. It occurs owing to magnification of concentration of charged particles when the exciton radius aB exceeds of Debye screening radius rD. Therefore the requirement of existence of excitons in volume crystals can be noted in the form [13]:

rn > a„. (21)

Let's control validity of an inequality (21) for binary terms of (ZnxCdi-x)3P2 alloy system. Cadmium phosphide Cd3P2 is a degenerate semiconductor. The Debye screening radius for degenerate semiconductors is spotted by a relation:

2se 0Sf

'D "il 2 ■

e n

(22)

Zinc phosphide Zn3P2 is a nondegenerate semiconductor and Debye screening radius is spotted by a relation:

eeokoT 'D -i| 2 , e n

(23)

where n is the carriers concentration.

hv, relative units

Fig.2. The real part of dielectric function in region of optical transitions for (ZnxCd1-x)3P2 alloy system vs photon energy (in units of the band gap Eg) at T = 300K. Maximum of er(a) is connected with high-frequency optical constant s

Calculation by equations (22,23) give an following results: rD=378,93 A for Cd3P2 (n=1018 cm-3) and rD=1866,43 A for Zn3P2 (n=1015 cm-3, 7=300 K). Thus the requirement (21) for binary phosphides AII3BV2 is carried out. Obviously for the intermediate compositions of (ZnxCdi-x)3P2 alloy system the requirement (21) is carried out too.

We use a variational method for calculating the free exciton binding energy. The exciton Hamiltonian is given by [5,8]:

h ' )--14--À-.

2 dr e(r)r

(24)

where dielectric function s(r) is determined by equation (16). Hamiltonian (24) is written in the non-dimensional atomic units of length a0=4ns0h /(u e ) and energy E0=u e /(32# 7ts0).

To calculate the s-exciton ground state we choose the trial wavefunction in the form:

Wis (r )- C exp r j

(25)

where a is variational parameter, C is the normalization constant. The energy of the s-exciton ground state is obtained by minimizing the following equation:

Es = V (r )H (r\Vu (r) = ¡Vs (r )H (r V (r )dr. (26)

For an allowed interband transition the oscillator strength of free exciton may be determined as [5]:

2a 1 i/ , , \i2 (27)

F„

ep|v

where Q0 is the volume of unit cell, m0 is the free electron mass, hwex=Eg - EXs - Ev is the resonance photon energy, Ev is the top valence band energy, n is the main quantum number.

Free excitons are the electronic excitations of ideal crystals without impurities and defects. However, impurities and defects always are present at real crystals. So, presence of many vacant sites is a "logo" of An3BV2 crystalline structures. One or several energy levels (donor or acceptor) in the band gap associate with these vacancies. Exciton localization on the charged or neutral impurities is possible. Such complexes will be stable if

n

exciton-impurity binding energy more than electron-hole binding energy. Exciton localization on a singly charged impurity is most probable in the ionic An3BV2 semiconductors.

Let us consider the exciton-impurity complex (EIC) formed with positively ionized atom (donor impurity). The charged ion is accounted as a dot structure with the perpetual mass. The EIC Hamiltonian is given by [5]:

H{n, r, r12)=-1 (il+m ill__L_+_J___(28)

1 2 12 21^2 mh Sri) £(rl2)ri £(rl2)r2 e(rl2)rl2

where rb r2 are coordinates of electron and hole respectively, rl2 = -r2|, the dielectric function s(r12) is

determined by equation (16). Results for an acceptor center may be gained by replacements r1 ^ r2 and

me mh.

To calculate the EIC ground state we choose five-parameters trial wavefunction written in the form [5]: Yeic (l, r2, ri2 ) = C[exp (-a(r + Pr))+b exp (-«fa + Pr ))}■/, (29)

where a, p, P, b, q are variational parameters, C is the normalization constant.

The energy of the EIC ground state is obtained by minimizing the following equation:

eeic = {wec (ri> ^ ri2 )H(1> r2> ri2\yec (ri > r2> ri2 )) = (3Q)

= j j j ¥ec (ri. ^ rn)h(ri. r2, ri2 vec (ri. ^ ri2dr2dri2• In dipole approach for direct allowed transitions the oscillator strength ratio of the exciton-impurity complex Feic and free exciton Fex is given by [5]:

F re _ 71 ' 2h

Fex ^G V mG BEC

(31)

The values of binding energy E1s and free exciton oscillator strength Fex, values of binding energy Eeic and oscillator strength ratio FEICIFex are presented in Table 3.

Table 3

The binding energy and oscillator strength of excitons in (ZnxCdi_x)3P2 alloy system

3/2

X free excitons exciton-impurity complexes

E1s, meV F 1 ex Eeic, meV Feic / Fex

exciton+D+ exciton+Л" exciton+D+ exciton+Л"

0 1,52 3,19T0-4 1,29 6,76 4317,38 358,39

0,2 1,97 3,54-10-4 1,61 8,77 3225,83 253,84

0,4 2,76 5,60-10-4 2,25 11,31 2037,60 181,23

0,5 3,27 7,38-10-4 2,69 12,90 1600,69 152,32

0,6 3,85 9,95T0-4 3,21 14,94 1254,51 125,03

0,8 5,62 17,70T0-4 4,62 19,75 762,16 86,18

1 7,29 25,90T0-4 6,06 24,04 532,32 67,33

Conclusions

The aim of the present theoretical study was to investigate the energy levels of free excitons and exciton-impurity complexes in (ZnxCdi_x)3P2 alloy system. The band structure of (ZnxCdi_x)3P2 alloy system is considered within the framework of generalized Kildal's band model and the simple analytical equations for effective masses of carriers are written. Analytical dependencies of band parameters on a composition x are gained. As a first, approximation, the temperature dependence of band structure is determined by temperature modification of a band gap only. The criterion of implementation of Wannier-Mott exciton model is viewed and the dependence of the dielectric function vs exciton radius is gained on its ground. As a result it was possible to consider more correctly a Coulomb interaction in exciton Hamiltonian.

The energy levels of free excitons and exciton-impurity complexes in (ZnxCd1-x)3P2 alloy system are calculated by variational method taking into account twofold degenerate valence band. In our calculations the low anisotropy of band structure of (ZnxCd1-x)3P2 alloy systems was not considered. The big oscillator strength for exciton-impurity complexes in comparison with free excitons is observed. The binding energy of excitons and exciton-impurity complexes increases in a direction from Cd3P2 to Zn3P2 because the band gap grows. Values of a binding energy of the free excitons and exciton+D+ complexes are approximately equal for the same compositions x and much less than medial thermal energy kBT at room temperatures. Therefore, the strong developing process of discrete states of free excitons and exciton+D+ complexes should be expected at low temperatures. The binding energy of exciton+^_ complexes in 3,5^4 times exceeds a binding energy of the free excitons and for compositions x>0,8 becomes comparable with medial thermal energy at room temperatures.

Should be noted, that the exciton is born the "cold" and for it's warming up to temperatures kBT>Eb some time is necessary (exciton lifetime). In narrow spectroscopic region of a discrete absorption of excitons the big oscillator strength of optical transitions is present. Therefore absorption of excitons is essential even at kBT>>Eb when a thermal degradation hides a discrete states of an excitons against the background of continuum.

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