ISSN 1063-7826, Semiconductors, 2008, Vol. 42, No. 11, pp. 1282–1285. © Pleiades Publishing, Ltd., 2008.Original Russian Text © A.P. Belyaev, V.P. Rubets, V.V. Antipov, V.V. Grishin, 2008, published in Fizika i Tekhnika Poluprovodnikov, 2008, Vol. 42, No. 11, pp. 1309–1313.

1282

Electrical properties reflect the features of the sub-stance thereby limiting the prospects of its practicalapplication. However, a few scientific publications aredevoted to electrical properties of the films synthesizedunder highly nonequilibrium conditions. In order tofill the existing gap as much as possible, we report fur-ther on the electrical and galvanomagnetic propertiesof CdTe films, whose mechanisms of formation underhighly nonequilibrium conditions were reported ear-lier [1–3].

The films were synthesized in vacuum via evapora-tion and vapor condensation on the substrate. Highlynonequilibrium conditions were provided by coolingthe substrate with liquid nitrogen. As the substrates, weused pieces of artificial fluoroflogopite mica. Specificsynthesis modes were selected to provide the highestcrystalline quality of the films. Their structure isdepicted in Figs. 1 and 2, where a typical RHEED pat-tern of the film and microphotograph of the surface areshown. We grew the films of the cubic modification

with orientation (111) CdTe

||

(0001)mica. The films were intentionally not doped orannealed. The thickness of the films under study wasseveral micrometers.

Conductivity was measured using a V7-30 elec-trometer in a current mode. The minimal currentdetected was 10

–15

A. The Hall effect was studied usingan ac 8-Hz current, which allowed us to detect a mini-mal Hall mobility of 0.5 cm

2

V

–1

s

–1

. All measurementswere performed at a residual pressure of ~10

–3

Pa. The

110[ ] 1120[ ]

temperature was maintained using a temperature con-troller accurate to 0.1 K.

For measurements in the planar geometry, gold con-tacts were deposited on the films. The distance betweenthe current contacts was 0.6 cm, and that between theHall contacts was 0.3 cm. Contacts were formed byvacuum deposition.

To measure conductivity in the sandwich geometry,we prepared special samples synthesized on the epitax-ial gold film [4]. After synthesis, a gold contact wasformed on these samples by vacuum deposition.

The samples were illuminated with scattered lightfrom a 100-W incandescent lamp.

Electrical and Galvanomagnetic Properties of Cadmium Telluride Films Synthesized under Highly

Nonequilibrium Conditions

A. P. Belyaev^, V. P. Rubets, V. V. Antipov, and V. V. Grishin

St. Petersburg Technological Institute (Technical University), Moskovskii pr. 26, St. Petersburg, 198013 Russia^e-mail: Belyaev@lti-gti.ru; Belyaev@tu.spb.ru

Submitted March 17, 2008; accepted for publication March 27, 2008

Abstract

—The results of experimental studies of electrical and galvanomagnetic properties of CdTe films syn-thesized under highly nonequilibrium conditions via vapor condensation on a substrate cooled with liquid nitro-gen are reported. The temperature dependences of dark conductivity, current–voltage characteristics with andwithout illumination, temperature dependences of the Hall coefficient

R

H

and effective Hall mobility

µ

H

in theplanar geometry, and dark current–voltage characteristics in the sandwich geometry are reported. Anisotropyof conductivity is revealed. It is shown that the electrical and galvanomagnetic properties of the films are con-sistently described by a percolation model of charge transport, according to which, at high temperatures, thecharge transport takes place over the percolation level of the valence band, and at low temperatures, over thepercolation level of the impurity band.

PACS numbers: 73.50.Jt, 72.20.My, 73.50.-h

DOI:

10.1134/S1063782608110067

ELECTRONIC AND OPTICAL PROPERTIESOF SEMICONDUCTORS

Fig. 1.

Typical electron diffraction pattern of the CdTe filmsynthesized under highly nonequilibrium conditions.

SEMICONDUCTORS

Vol. 42

No. 11

2008

ELECTRICAL AND GALVANOMAGNETIC PROPERTIES 1283

The samples were of

p-

type conduction, which wasdetermined from the sign of the thermopower.

We studied the temperature dependences of darkconductivity, current–voltage (

I–V

) characteristics withand without illumination, temperature dependences ofthe Hall coefficient

R

H

and effective Hall mobility

µ

H

inthe planar geometry, and dark

I–V

characteristics in thesandwich geometry. The main results are shown inFigs. 3 and 4.

Figure 3 shows the temperature dependence of darkconductivity (curve

3

), the temperature dependence ofthe Hall effect

R

H

(curve

1

), and the temperature depen-dence of the effective Hall mobility

µ

H

(curve

2

). Thefirst curve is characterized by the presence of two por-tions, each of which can be described by a simple expo-nential function. In the higher-temperature region, theactivation energy of conductivity was

E

σ

1

= 0.65 eV,and in the lower-temperature region,

E

σ

2

= 0.4 eV. Atroom temperature, conductivity of the samples corre-sponded to

σ

≈

10

–7

Ω

–1

cm

–1

.The Hall coefficient was positive, and its tempera-

ture dependence peaked. The location of the peak coin-cided with the transition region in the temperaturedependence of conductivity. The effective Hall mobil-ity was low (no higher than 20 cm

2

V

–1

s

–1

). At highertemperatures, the mobility was almost independent oftemperature and decreased abruptly after the peak inthe temperature dependence of the Hall coefficient.

Figure 4 shows the results of the study of how elec-tric field affects the conductivity of CdTe films.Curve

3

is the dark

I–V

characteristic. It is evident that,starting from fields of ~200 V/cm, the characteristic isessentially nonlinear. The character of nonlinearity isdescribed satisfactorily by the Pool–Frenkel type equation

(1)

with the parameter

β

= 0.008 (V/cm)

–1/2

, which is largerthan prescribed by the Pool–Frenkel effect by almostan order of magnitude. Fulfillment of dependence (1)is demonstrated by curve

4

, which corresponds to the

E

i i0 β E( )exp=

I–V

characteristic reconstructed in coordinates of

. Curve

1

shows weakening in the nonohmicbehavior as caused by illumination with visible light.This is the

I–V

characteristic with illumination in coor-

dinates of and, if we compare its slope withrespect to the abscissa with the dark

I–V

characteristicin the same coordinates (curve

4

), we can see a substan-tial decrease in the slope. According to relation (1), thisindicates a decrease in the parameter of the nonohmicbehavior

β

.

Curve

2

corresponds to the dark

I–V

characteristicmeasured at a distance between the measuring electrodesthat is larger by a factor of 6 than for other

I–V

character-istics. It indicates a decrease in the nonohmic behaviorwith a total increase in the sample conductivity.

ivs Elog

ivs Elog

50

µ

m

Fig. 2.

Microphotograph of the surface of the CdTe filmsynthesized under highly nonequilibrium conditions.

10

–4

10

–6

10

–8

10

–10

10

–12

3.42.92.410

3

/

T

, K

–1

10

7

10

6

R

H

, cm

3

/C

σ

,

Ω

–1

cm

–1

10

3

/

T

, K

–1

2.4 3.4 4.4 5.4 6.4

1

2

3

10

2

10

1

10

0

µ

H

, cm

2

V

–1

s

–1

Fig. 3.

Temperature dependences of the Hall coefficient

R

H

(curve

1

), effective Hall mobility

µ

H

(curve

2

), and conduc-tivity

σ

(curve

3

).

10

–6

10

–8

10

–9

E

, V cm

–1

i

, A

1

2

3

10

–6

i

, A

4

5

10

–8

10

–10

10

–12

10

–1

10

0

10

1 102 103

10–7

E V1/2 cm 1/2–,

Fig. 4. Current–voltage characteristics of the CdTe film synthe-sized under highly nonequilibrium conditions. Curves 1–4 cor-respond to planar measurements; curve 5 is obtained with theuse of the sandwich geometry. Curve 1 is recorded under illu-mination with visible light, and curves 2–5 is recorded in dark.

1284

SEMICONDUCTORS Vol. 42 No. 11 2008

BELYAEV et al.

Finally, curve 5 corresponds to the I–V characteris-tic of the CdTe film in the sandwich geometry. It is evi-dent that, in the region of studied fields, this curve islinear. Conductivity of the film in the sandwich geome-try was lower than that measured in the planar geome-try by several orders of magnitude.

Let us analyze the results starting with conductivity.The large value of its activation energy (0.65 eV) unam-biguously indicates that the Fermi level is fixed deep inthe band gap. This situation can only be caused by twofactors. The first is that the semiconductor is intrinsic,and the second is that the semiconductor is highly com-pensated. For the studied samples, the first cause isscarcely possible since according to experimental stud-ies of the Hall effect, even at high temperatures, theHall mobility is no higher than 20 cm2 V–1 s–1. A highdegree of compensation remains, which can be realizedin CdTe owing to self-compensation of intrinsic defects[5] emerging in the course of synthesis. For example,owing to the displacement of the cadmium atom to theinterstices, a lattice cadmium vacancy and interstitialcadmium atom are formed. They possess acceptor anddonor properties, respectively. The electron from thedonor is captured by the acceptor, and self-compensa-tion with the formation of the charged donor andcharged acceptor takes place.

A random arrangement of defects leads to violationof the long-range order in the crystal lattice and varia-tion in the potential energy of the carrier in the latticefield. If the variation in energy caused by the violationof the long-range order ∆ is small compared with theaverage carrier energy kT, the random field only leadsto the additional carrier scattering. Otherwise, the ran-dom field spatially modulates the bands of semiconduc-tor (Fig. 5), and its conductivity is realized only by afraction of carriers activated into the band over whichthe charge transport is performed. The question of cal-culation of the current-involved particles (effectiveconcentration ρσ) in the theory of semiconductors issolved differently depending on the spatial scale of therandom field L. Two extreme cases are considered. In

the first case, tunneling cannot be neglected, and in thesecond case, tunneling can be disregarded. If tunnelingis taken into account, the Hall coefficient RH is alwaysnegative irrespective of the conductivity type of semi-conductor [6]. Therefore, to describe conductivity ofthe CdTe films, for which RH > 0, this coefficient isinapplicable. In the case tunneling is disregarded, it isassumed that the random field induces a large-scalepotential profile, in which the random potential isalready not the main mechanism of carrier scattering.They are scattered owing to some other factors existingin the absence of a random potential, for example,phonons. Due to this fact, the carrier mobility at allpoints of the sample is identical and equal to its valuein the absence of nonuniformities of µ. Conductivity ofthe semiconductor is described by the expression σ =epσµ, in which the effective concentration pσ is calcu-lated using percolation theory [7]. Therefore, it isreferred to as the carrier concentration at the percola-tion level EP, and conductivity σ is referred to as thepercolation conductivity.

Percolation conductivity, similarly to the experi-ment under consideration (see Fig. 3), is related to thetemperature by the equation

(2)

In this equation, the role of the activation energy isplayed by the energy gap from the Fermi level EF to thepercolation level EP, which agrees quite well with Eσ1 =0.65 eV, corresponding to highly compensated CdTe.

The nonohmic behavior revealed by us, which man-ifests itself in relatively low electric fields (~200 V/cm),can be interpreted using the percolation conductivitymodel. In semiconductors with a large-scale potentialprofile, the main part of the external voltage drops onthe profile portions with the energy close to the perco-lation level. Such portions are remote from one anotherconsiderably farther than the spatial scale of nonunifor-mities L. Therefore, substantially higher voltages drop onthem and nonohmic behavior of such semiconductors issubstantially more pronounced [8]. The I–V characteristicwith percolation conductivity is described by the Pool–Frenkel-type equation with the exponent depending onthe value of the random potential ∆:

(3)

Here, e is the elementary charge, σ is the ohmic con-ductivity, is the electric field strength, and c is a con-stant with an unknown exact value. If we set c equal tounity and set the spatial size of inhomogeneities equalto the size of growth patterns on the surface of the CdTefilms (60 nm), then, at ∆ = 0.006 eV, we obtain

= 0.008 (V/cm)–1/2, which agrees with the

σ σ0EP EF–

kT------------------–⎝ ⎠

⎛ ⎞ .exp=

j σEceL∆( )1/2 E( )1/2

kT------------------------------------- .exp=

E

ceL∆( )1/2

kT-----------------------

L

Eσ l

∆ EF

Ei

EP

EV

Fig. 5. Schematic energy diagram of the CdTe film. EF is theFermi level, Ei is the ionization energy of the defect, Eσ1 isthe activation energy of conductivity over the valence band,EP is the percolation level in the valence band, EV is thevalence band top, ∆ is the random potential, and L is the spa-tial scale of nonuniformity of the potential profile in thebands.

SEMICONDUCTORS Vol. 42 No. 11 2008

ELECTRICAL AND GALVANOMAGNETIC PROPERTIES 1285

parameter β = 0.008 (V/cm)–1/2 of the experimentaldark I–V characteristic (1).

Under illumination of the sample with visible light,the average energy of carriers becomes higher than kT;conditions used in derivation of relation (3) are vio-lated; and the parameter β of the I–V characteristicunder illumination becomes smaller than that pre-scribed by relation (3).

The temperature dependence of the Hall coefficientof the CdTe films synthesized under highly nonequilib-rium conditions (curve 1 in Fig. 3) qualitatively corre-sponds to the so-called two-band conductivity model[7, 9]. According to this model, the charge transport isrealized by carriers of two bands, namely, by holes acti-vated at the percolation level of the valence band andholes activated at the percolation level of the impurityband. The impurity band is located in the band gap andis the result of overlap of the wave functions of defects(impurities). At higher temperatures, the charge trans-port over the valence band is dominant, and at lowertemperatures, that over the impurity band is dominant.As the temperature increases, the carrier concentrationat the percolation level of the valence band decreasesexponentially. Therefore, although the charge transportover the impurity band is characterized by lower mobil-ity, it is more favorable owing to the high concentrationof carriers that contribute to the charge transport.

The temperature dependence of conductivity ofsemiconductor with the charge transport over twobands is characterized by two activation energies, Eσ1for the high temperature region and Eσ2 for the low-temperature region, which agrees quite well with thediscussed experiment. The activation energy Eσ1 =0.65 eV corresponds to activation at the percolationlevel of the valence band, and Eσ2 = 0.4 eV correspondsto activation at the percolation level of the impurity band.

In conclusion, we call attention to an unusual anisot-ropy of conductivity of the CdTe films synthesizedunder highly nonequilibrium conditions, where con-ductivity in the planar geometry exceeds conductivityin the direction normal to the film surface. In order tointerpret this, let us recall the mechanism of film orien-tation during growth under highly nonequilibrium con-ditions [3]. The azimuthal orientation of dispersed par-ticles of a new phase under highly nonequilibrium con-ditions is performed owing to the elasticity waves(solitons) induced by misfit dislocations [2, 3, 10]. Cor-relation in the direction normal to the film surface isachieved owing to minimization of the isobaric poten-tial in the direction of the densely packed face [11]. Thefirst cause of minimization requires almost no energyconsumption and proceeds fairly rapidly; the secondcause is apparently associated with certain diffusionprocesses. Therefore, it requires certain time, whichcan be insufficient to complete correlation to the pointin time of coalescence of dispersed particles into a con-tinuous layer at lower temperatures. At higher synthesistemperatures, orientation in both directions is associ-ated with diffusion [12]. Therefore, as a rule, no conduc-tivity anisotropy is observed, and even if this is the case,this anisotropy is inverse to that found by us in the CdTe

films, which is associated with longer duration of orienta-tion diffusion processes in the azimuthal direction.

The results presented in this study allow us to makethe following conclusions.

(i) Electrical and galvanomagnetic properties of ori-ented CdTe films synthesized under highly nonequilib-rium conditions are described consistently by the per-colation charge transport model, according to which, athigher temperatures, the charge transport is performedat the percolation level of the valence band, and atlower temperatures, at the percolation level of theimpurity band.

(ii) Unannealed highly oriented CdTe films synthe-sized under highly nonequilibrium conditions possesshigh degree of compensation of native defects.

(iii) Well-oriented CdTe films synthesized underhighly nonequilibrium conditions possess increasedconductivity in the planar geometry, which is caused bythe features of the mechanism of the azimuthal orienta-tion during synthesis, so-called soliton epitaxy.

ACKNOWLEDGMENTS

This study was supported by the Russian Founda-tion for Basic Research, project no. 07-03-00366.

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Translated by N. Korovin