Electronic behaviors of the gap states in amorphous semiconductors

Solid State Communications, Vol. 24, PP. 23—27, 1977.

Pergamon Press

Printed in Great Britain

ELECTRONIC BEHAVIORS OF THE GAP STATES IN AMORPHOUS SEMICONDUCTORS H. Okamoto and Y. Hamakawa Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan (Received 11 April 1977; in revised form 26 May 1977 by Y. Toyozawa) An extention of the Adler—Yoffa’s calculation on the localized gap states in amorphous semiconductors has been made with a more realistic model which takes into account an influence of the diffused gap states and impurity states. A considerable large difference in the electron occupation probability of the gap states with sign of the correlation energy Uhas been examined on the tetrahedrally bonded and chalcogenide glasses. Variations of the Fermi level as a function of doped impurity concentration and gap state density have been studied. IT HAS LONG been believed on the electronic property that amorphous semiconductors usually show an intrinsic type conduction due to the presence ofhigh density localized gap states. A striking experimental fact for the

0(E) Dl 02

field of amorphous semiconductor physics has been recently released, that is, substitutional doping of impurity atoms into a tetrahedrally bonded amorphous material has been accomplished by Spear and his group [1] This fact implies that it is possible to control not only carrier concentration but also conductivity type in the amorphous semiconductor. Some attempts [2,3] for the device applications have already been initiated on p—n and hetero-junction sollar cells. On the other hand, a considerable amount of effort for conductivity type control in chalcogenide glasses has also been done in various ways, e.g., ion implantation and thermal diffusion [4] But there has been no clear experimental evidence on the controllability of electrical properties reported so far for the chalcogenide glasses. Besides it has been found experimentally that there are some differences between tetrahedrally bonded amorphous materials and chalcogenide glasses in the electronic processes with respect to EPR signal and temperature dependence of the d.c. conductivity, etc. To explain these slight but clear differences in both materials, Street and Mott [5] have proposed a new model for the localized gap states, and statistical calculations of the gap state electrons have been demonstrated by Adler and Yoffa [61 in terms of this model. We have made an extended calculation of Adler and Yoffa’s work for the realistic cases in which the effects of diffused gap states, band edges and impurity states are taken into consideration in order to make detailed discussions of the actual problems in amorphous semiconductors. Consider a semiconductor having localized defect states Dl and D2 at energy e~and e~+ U in the energy gap between e~,and e~,as shown in Fig. 1. The

D2 Dl

(U)O)

w
ND

.

_________

E~

_____

E~

_________

E~

_______

E~ E

__________

~Obl(lt~

gap

Fig. 1. A simple model of theDldensity ofare states amorphous semiconductors. and D2 theinlocalized states originated in a single defect at energy e~,and assumed to locate at energy e~, and eç~+ U. Here U is the effective electronic intrasite correlation energy proposed by Anderson. D~and D~are diffused band tail states induced by deformation potential fluctuation.

.

assumption is made that these gap states are origmated in a single defect at energy C~each of which is available to be occupied by up to two electrons, and there exists the effective intrasite electronic correlation energy U proposed first by Anderson [7]. This correlation energy is considered to be the sum of the repulsive coulomb interaction and the attractive interaction mediated by the lattice distortion between upspin and down-spin electrons in a defect site, and the positive sign of the correlation energy U is corresponding to the case of tetrahedrally bonded amorphous materials and negative U to that of chalcogenide glasses. The energy position of Dl states has to be determined through experimental and theoretical considerations as had been done by Adler and Yoffa [6]. To discuss the actual problems on the electronic processes in 23

24

GAP STATES IN AMORPHOUS SEMICONDUCTORS

amorphous semiconductors, we have to know the distribution functions F, F°and F~F is defined as the probability that a defect site is doubly occupied (named as D center after Mott [5]), F°as that of singly

defect 0, as shown in equation (4) of reference [61 The distribution functions can thus be obtained from equations (1), (2) and (3) as follows, F(e0)

occupied (D°center) and F~as that of unoccupied (D~center). However these distribution functions can not be determined from simple Fermi—Dirac distribution function because of the presence of the intrasite electronic correlation in the gap states. Suitable distribution functions in this situation might be determined basically in a similar way as had been applied to the problem of multi-level impurity states system [8] Here we introduce, however, a more simple derivation of these functions. The average number of electrons n(e0) in a particular defect site at energy Co is expressed with the aid of the probabilities F, F°and F~as, =

2F(e0) + F°(e0).

=

(2~+ U)F(0)

+ exp [(2fF

0F°(0).

—

2e~ U)/kT] F~(e0),

(4)

e0)/kT] F~(e0),

(5)

—

+

2exp [(CF —e0)/kT]

—

2e~ U)/kTl —

explanation of the experimental fact on the lack of EPR signal based on dangling bonds [9] in chalcogenide glasses, and support strongly the concept of the Street— Mott [5] . of Onthe thedefect otherstates hand,would in the widely realisticspread cases model the energy

(2)

over the gap, therefore the densities of charged centers such as D and D~are relatively high even in the case

(3)

of positive U~needless to say for the case of negative U. These charged centers might act as the considerably strong microfield in amorphous semiconductors, and

While by means of the grand partition function of ~ system, n(eo) and E(eo) can easily be calculated as6F, a function of the temperature T, the Fermi energy the correlation energy U and the energy of a single

consequantly give rise to the Urbach tail optical absorption spectrumofnear the band of these available the edge electron transition materials density [101. The states more for intuitive diagrams for the in connection with D, D°and D~centers are drawn in u>0

0.2

E

~0.1 w

~~U>0 U<0

KT=0.026eV ILJ=0.2eY

Cc

PI

~0—

.~

~-

o~j- -

. —....

~?

/

\

-0.1

~ W

I

D-~

E~, ~-

5-

F

._.—~

~-.

0

DD~ Ec!~/

•-

E~~

T

.—

y

I

I

~~io 0.5 Distribution Function (a)

-

CF

- .—

.

-

ri~.D°

~

~

-

. -

I

Ev~

-

~

—

~—~-~::

I __~5~

_-~~‘

EF~D° —‘—-~——-

F° ~‘

—S.

L

-,

I~

.—

—0.2

U<0

-—

—-

0

(6)

}.

energy are shown in Fig. 2(a). As can be seen in the figure, the existence probability of D°paramagnetic center for the negative Uis always small in comparison with that of positive U. This might work well as an

Moreover F, F°and F~satisfy the relation; F(e0) + F°(e0)+ F~(e0)= 1.

[(CF

—

The calculated results of these functions as a function

(1)

+

exp [(2eF

F~(e0)= l/{l

The average total energy E(e0) of this site can be written, E(0)

=

F°(eo) = 2 exp

.

n(e0)

Vol. 24, No. 1

~

F(E)D(E) (b)

F(E>D(E) (c)

Fig. 2. (a) The distribution functions F, F°and F~which give the probabilities that a defect site is doubly occupied, singly occupied and unoccupied. (b) and (c) The left (right) side diagrams of (b) and (c) for each sign of U show the available density of states F(e)D(e) for the electron emission (capture) processes in connection with D, D°and D~center, and the energy position of these states are corresponding to that of the initial (fmal) state of electron transition. Here F(e) denotes F(e), F°(e)and F~(e).The main parts of the optical transitions (indicated by arrows with solid lines), and electron and hole detrapping processes and excess electron and hole trapping processes (broken lines) are also shown.

Vol. 24, No. 1

GAP STATES IN AMORPHOUS SEMICONDUCTORS

Fig. 2(b) and (c). The rate of electron emission from D° center both in optical and thermal processes, for example, is simply proportional to the available density of states defined as F°() x D(e) which is seen easily as the oblique lined area indicated by D°inthe left diagrams of Fig. 2(b) and (c). In the same way, the available density of states for the electron emission from D centerareillustratedintheleftsidediagramsofFig. 2(b) and (c), and furthermore that of electron capture by D’ and D°center are given in the right side diagrams of Fig. 2(b) and (c). From these diagrams, some clear discussions can be carried out on the optical transitions, trapping or detrapping processes of electrons and holes, -

o

-

+

and the hopping processes related to D D and D centers in tetrahedrally bonded amorphous materials and chalcogenide glasses. One of the most remarkable differences observed in the basic properties between tetrahedrally bonded amorphous materials and chalcogenide glasses is the temperature dependence of d.c. conductivity at low temperature. The d.c. conductivity of a-Si and a-Ge varies with T”4 law which is explained by the model of variable range hopping [11] except for amorphous Si prepared by glow discharge decomposition of SiH 4 [12], while that of chalcogenide glasses shows the thermal activation type temperature dependence [11, 13] An explanation which had been given so far is that there exists a very small hopping probability due to almost negligible density of states near the Fermi level in chalcogenide glasses. However there are some contradictional experimental facts. For example the experimental data on a.c. conductivity [14] and photoluminescence [15] imply rather high density of states near the Fermi level even in such materials. Here we can give more adequate explanation on this problem from the result of calculations as shown in Fig. 3. The main hopping processes at low temperature are known to be D to D°process and D°to D~process, and the probability of other hopping processes (iT to D~and D°to D°)are so small as to be neglected as is implied in Fig. 2(b) and (c). Figure 3 shows F x F° and F°x F~which correspond to the statistical factors of hopping probability for the processes iT to D°and D°to D~at sufficiently low temperature. It can be seen from the figure that there is a remarkable difference in these functions with the sign of the correlation energy U. The most probable hopping stage is found to be in the vicinity of the Fermi level for positive U. For negative U, the stage is located near around the Fermi level ranged with a half of the absolute value of U, in addition to this fact, the probability is about four orders smaller than the former case. Namely the density of states at the Fermi level is not solely responsible for the absence of variable range hopping in chalcogenide

I

I

0.2

25 I —

4

~

cf-.D

u>o 11<0

(X10 0.1

Z~-_.~

--

LW2

.5-.-—-— ‘-

Z.

-.—-.

0 U.)

i U.)

~_.

..

~

-0.1

I

.—---. ~

~

—

——

(X 10k) D~D° —0.2

KT~0.01eV Iul= 0.2 #/

,

-

I

.

4

~,

10

10

I_

10

~

10

F X F and r ~r Fig. 3. The statistical factor of hopping probability F x F°(D to D°)and F°x F~(D°to D~)as a function of energy at sufficiently low temperature.

glasses but this very small statistical factor of the hopping probability might be the basic reason affecting to the difference observed in experimental results. To step into further analysis on the electronic properties of amorphous semiconductors, it is necessary to take into account the density of states scattered around band edges and gap states. We have calculated the position of Fermi level as a function of temperature for several combinations of the density of states profiles including D1 and D2 gap states having the Gaussian distribution, parabolic bands with small exponential tails and impurity states. The calculations are carried out from a conventional charge neutrality condition. One can easily imagine that for the most cases the Fermi level is practically pinned at the center of the gap states Dl and D2 without impurity except for the case that either Dl or D2 overlaps with band edge, and the density of gap states is considerably small in comparison with that of the band edges. The effect of substitutional doping of impurity atoms on the position of the Fermi level has been examined with simple model as shown in Fig. 4(a). The density of states used in the Fermi level calculations is probable values for the practical cases taken from the experimental results [12, 131 in amorphous semiconductors. Figure 4(b) shows the calculated Fermi energy as a function of impurity concentration with parameters of density of gap states and sign of the correlation energy U. As can be seen from the figure, the shift of Fermi level is larger in the case of positive U than that of negative U. In the case the absolute value of U is

26

GAP STATES IN AMORPHOUS SEMICONDUCTORS ~

Donor

level

4

~ S__i

0

—

11>0

ND~lO~

U<0

_—~/~

/1

W W

Defect level

0’

fl type

~0.8

D2

Dl ~

N~ Dl

/ •‘

-

~

.,

~

i~~9 ,‘/ /

/1

/

~2O /

~

/

/

~‘

/

.-.

..

D2~!~~

—.-..---

.5 _S~S_.~S.

-

~S•

‘S

-

i020

~ type

02Acceptor level ~~21

Ii

—

0.6

04

//

‘i

‘I

~

UI

U>0 11<0

Lv

Vol. 24, No. 1

12i

.

300K

(eI~cr,~3)1~16

i018 i~8

1~17

Density of State 0(E)

Impurity Concentration

N

3)

1

(cm

(b)

(a)

Fig. 4. (a) A model of density states in the gap used for calculation. (b) Fermi energy as a function of impurity concentration with parameters of the density of gap states and sign of the correlation energy U determined by charge neutrality condition. 0.2 eV as shown in Fig. 4(b), for instance, the maximum Fermi energy seperation es,, of 0.08 eV is observed. A noticeable result found in the figure is that this Fermi energy seperation with sign of U prevails rather in the lower impurity concentration side. And the critical concentration for the Fermi energy seperation lies at the impurity concentration ofN1 = ND/lU. The larger the absolute value of the correlation energy Uis, the more striking this seperation of Fermi energy becomes in the lower impurity concentration region. The abovementioned result implies that there are some possibiities ofp—n control even in chalcogenide glasses, [16—18] particularly for the case of low density of localized gap states. However, it is an undoubted conclusion that the electrical properties of tetrahedrally bonded amorphous materials can be more effectively controlled by impurity atoms than chalcogenide glasses even if the other conditions are the same. In fact, this result is fully supported by the experimental evidences

realized by amorphous Si prepared by glow discharge decomposition of SiH 4 [1]. In conclusion the electronic properties of amorphous semiconductors have been explained more clearly with the aid of the suitable distribution functions proposed, and the model calculation has led to the consistent results with a series of experimental facts observed both on tetrahedrally bonded amorphous materials and chalcogenide glasses. By applying this model calculation, it is expected, in addition, that more precise analysis for the experimental results such as EPR, d.c. and a.c. conductivity, photo conductivity and field effect measurement could become possible if the more realistic informations on the basic parameters for the calculation, that is, the density of localized gap states and their energy distribution are given from experiments on the electrical and optical properties of amorphous semiconductors.

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2.

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3. 4.

CARLSON D.E. & WRONSKI C.R.,Appl. Phys. Lett. 28,671(1976). OKAMOTO H. & HAMAKAWA Y. (unpublished).

5.

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Vol. 24, No. 1

GAP STATES IN AMORPHOUS SEMICONDUCTORS

6.

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7.

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8.

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9.

AGARWALS.C.,Phys.Rev. B7, 685 (1973).

10.

TAUC J.,Amorphous and Liquid Semiconductors (Edited by TAUC J.), Ch. 4. Plenum, New York (1974).

11.

MOTT N.F. & DAVIS E.A., Electronic Processes in Non-CrystallineMaterials. Oxford Univ. Press, England (1971).

12. 13.

SPEAR W.E.,Proc. Fifth mt. Con. Amorph. Liq. Semicond., 1. Garmisch-Partenkirchen (1973). NUNOSHITA M., ARAI H., TANEKJ 1. & HAMAKAWA Y.,J. Non-C,yst. Solids 12,339(1973).

14.

FRITZSHE H.,Amorphous and Liquid Semiconductors (Edited by TAUC J.), Ch. 5. Plenum, New York (1974).

15.

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16.

KUMEDA M., JINNO Y., SUZUKI T. & SHIMIZU T.,Japan. J. Appl. Phys. 15,201(1976).

17.

MOTTN.F.,Phil.Mag.34,llOl(l976).

18.

KNIGHTS J.C.,PhiI. Mag. 34,663 (1976).

27