DISLOCATION ELECTRON SPECTRUM AND THE MECHANISM OF DISLOCATION MICROWAVE CONDUCTION IN SEMICONDUCTORS

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DISLOCATION ELECTRON SPECTRUM AND THE MECHANISM OF DISLOCATION MICROWAVE

CONDUCTION IN SEMICONDUCTORS

Yu. Ossipyan

To cite this version:

Yu. Ossipyan. DISLOCATION ELECTRON SPECTRUM AND THE MECHANISM OF DISLO- CATION MICROWAVE CONDUCTION IN SEMICONDUCTORS. Journal de Physique Colloques, 1983, 44 (C4), pp.C4-103-C4-111. �10.1051/jphyscol:1983412�. �jpa-00222852�

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JOURNAL DE PHYSIQUE

Colloque C4, supplément au n°9, Tome 44, septembre 1983 page C4-103

DISLOCATION ELECTRON SPECTRUM AND THE MECHANISM OF DISLOCATION MICROWAVE CONDUCTION IN SEMICONDUCTORS

Vu.A. Ossipyan

Institute of Solid State Physics of the U.S.S.R. Academy of Sciences, 14'24.->2 Chevnoaolovka, U.S.S.R.

Résumé - Un modèle du spectre d'énergie introduit par les clislocations est décrit. Ce modèle résulte des études expéri- mentales d'effet des dislocations sur la conduction et la photo-ESR. Une méthode de dopage par irradiation aux neutrons a

été utilisée pour étudier le mécanisme de conduction par les dislocations.

Abstract - The model of the dislocation energy spectrum of electrons in germanium and silicon has been treated. The model follows from the results of the experimental study of the dislocation conduction and the photo-ESR. The method of doping with neutron irradiation is employed to investigate the dislocation conduction mechanism.

Previously, the analysis of the data on the dislocation microwave conduction of dislocated Si and Ge crystals as well as on the photo- -hbK enabled us to advance a general scheme of the dislocation energy electron spectrum of elemental semiconductors /1/.

conduction band

V///////////////////////M

mWMMW/s

valence band

Fig. 1 - Scheme of the dislocations bands following from the experi- mental data on the dislocation conduction in n- and p-Ge. The mobi- lity is high in the upper (electron) and lower (hole) bands. The mobility is small in the middle band.

It has turned out that the experimental results on the dislocation conduction of n- and p-type crystals can be explained by assuming tnat there are at least three different dislocation bands for elect-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983412

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C4-104 JOURNAL DE PHYSIQUE

rons in the forbidden gap. In this case, we have to assume that the carriers mobility is rather high in the upper and the lower bands but in the middle band it is very low /3/ Fig. 1.

The photo-ESR data has suggested the conclusion that at plastic deformation, together with the principal dislocation electron states, there originate simultaneously certain acceptor states, filled in darkness by electrons. Under illumination the electrons transfer f m these states to the fundamental dislocation band increasing thereby the ESR dislocation signal /2/. It has given rise to the scheme of the spectrum, that we present in Pig. 3. Before explaining the speci- fic spectrum structure we shall dwell on some features of the dislocation chains model Pig. 2.

As previously / I / , we assume that the electrons of the dangling bonds of the atoms, making up the dislocation core, form a narrow one-dimensional donor band El. The width of the band depends on the amount

of overlaping of the wave functions of the dangling-bond electrons along the dislocation chain. The dislocation dangling bonds can capture the extra electrons contained in the crystal either in the presence of chemical donors and other defects, or in the case when the electrons are excited for instance, by light or by a strong electric field. These extra electrons can be captured by dislocation acceptor levels forming the narrow acceptor dislocation band E2. Due to the Coulomb interaction of the two electrons on one site, the gap appears between the aforementioned one-dimensional bands. The presence of this gap implies that the dislocation chain with the dangling bonds can be described as a Mott-Hubbard dielectric.

Fig. 2

-

The electronic states associated with the dislocation chain. Designations are the same as in Fig. 3.

It has been well known from the dislocation structure studies in real crystals that the length of the regular sections of the dislocation line is rather small (some tens or hundreds of interatomic distances). The regular sections in the dislocations alternate with local defects on them, such as jogs, points of intersection with other dislocations, splitted sections and etc.. In addition to, some other defects may appear as impurity a t o m ~ ~ s a y , oqgen, located near the core. These local defects neq,er on the dislocation lines can form additional acceptor and donor states for the electrons and

e2.

The number of these states is related to the number of the local defects, We shall assume that both types of these local levels

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lie below the fundamental dislocation donor band Fig.

3.

Let us con- sider the pure semiconductor with dislocations, but not doped with shallow impurities. In this case some portion of the electrons from the dangling bands will transfer to the acceptor levels formed by these local defects, and the holes appear in the dislocation donor band. These holes are mobile and a r e bound to move towards the electrons captured by the local defects, because of a Coulomb interaction with them. 'Ilhey locate close to these defects and lose the mobilit

.

Since the gap Atl between El and E;, does nqt exceed 0.05eV (Fig. 3q, the average distance between the hole in El and the electron in El should approximately be of five lattice constants. This "dislocation

Fig. 3

-

Dislocation energy spectrum of Ge and Si.

4 -

the distance from the valence band top to the donor dislocation band El, for germanium

-

^0,07ev, for silicon

-

^0,42 ^ev.

A2 -

the distance from the conduction band bottom to the acceptor dislocation band E2, for germanium

-

O,5 ev, for silicon

-

^{0,52 ev.}

A12-

the Mott-Hubbaxd gap between the donor and acceptor dislocation bands El and E2, for germanium

-

0,18 ev, for silicon

-

^0,20^ev.

&-the gap -between the donor dislocation band and the split-off states for holes, for germanium and silicon less than 0.03 ev.

No direct experimental data to characterize the positions of the bands and

E2

are yet available.

exciton" may be stable, e.g., due to the energy barrier on the dislocation or due to the spatial separation, if the local defect is not located entirely in the dislocation core. Thus, a small hole band El is separated from the fundamental dislocation donor band. There is a Coulomb interaction between the holes and the electrons captured by the acceptor levels of the local defects on the dislocations. It is clear that these holes have low mobility in contrast to the ordinary

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C4-106 JOURNAL DE PHYSIQUE

holes occuring in the donor dislocation band when the electrons from the dangling bonds are captured by chemical acceptors. In the case of an undoped semiconductor or in the presence of a small number of acceptor or donor impurities, both bands and

E 2

are always filled indarkness.

The phdo-ESR data analysis on the base of the proposed spectrum is given in our paper / 2 / . Let us come back to the dislocation conduction (DC),

Despite a considerable progress in investigation of the DC, the experimental results /3-6/ are, nevertheless, insufficient to arrive to the conclusion on the M: mechanism. The dislocation mechanism proper seems most probable: the microwave conduction is due to the motion of the carriers (electrons or holes), captured by the dislocations,along the dislocation cores. In this case, the dislocations can be treated as one-dimensional conductors distributed within the crystal volume.

However the data of /3-6/ do not permit to exclude another DC mecha- nism, According to this mechanism the role played by dislocations is different from the aforementioned. In the course of the plastic deformation of crystal and subsequent annealing (for Ge the temperatures are 460 and 700°C, respectively) diffusion of the shallow doping impurities can proceed due to dislocation elastic fields. Thus, it is not out of question that in the vicinity of the dislocations in principal, at least, the region might be formed in which the impurity concentration is of some orders more than the average one. We have employed Ge n- and p-type crystals having a shallow impurities concentration 1013cm-3. If the impurities have concentrated in the vicinity of the dislocations, the strongly doped regions might form. In this regions the carriers might be degenerate, what in its turn, might give rise to the microwave conduction.

The aforesaid suggests that if one succeeded in preparing the samples with the dislocations and with deliberately homogeneous distribution of shallow impurities, one might choose between these alternative D.C.mechanisms.

We have attempted to solve the problem by neutrons doping method of Ge /7,8/. In irradiating with thermal neutrons some Ge isotopes capturing the neutrons, became unstable. Then, having decayed they transform to 111-and V-group elements.

Natural Ge consists of the following isotopes Table 1

Isotopes Ge70 ~e~~ ~e~~ ~e~~ ~e~~

76 content in 21 ,2

natural Ge 2793 799 3791 6,5

The following reactions occur under the irradiation with thernal neutrons :

Ge70 (",* ) Ge7I K-ca~ture+

Ga71

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~ e ~ ~ ( n , a Ge 75 ~3 -decay A,75 ( 2 )

~e~~ ( n , ~ ) ~e~~ j3 -decay+ J3 -decay_Se 77

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The rest of the isotopes remain stable after capturing a neutron.

The first expression describes the appearance of acceptor, the second and the third ones of donors. On ca turing neutron, Ge70isotope tran-

P

sforms to unstable Ge71isotope. Ge' due to the K-capture transforms to Can. The time dependence of Gan acceptors concentration is des-

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cribed by the equations of Ge7lisotope radioactive decay:

where No is the concentration of ~e~~ which have captured neutrons;

t

is the time elapsed since the irradiation; 7 is the half-decay period (12 days).

The plot of this dependence is shown in F i g . 4 c m e (a). The transformation of ~e'4 to As 75 occurs in the following m e r : on capturing neutron, ~ e ~ 4 i s o t o p e transf o m s to Ge75 radioactive isotope which in its turn, due to

p -

decay (with a period of 82 min) transforms to As75. As for Ge76, it, on capturing neutron, transforms to unstable Ge77isotope which decaying transforms to unstable A ~ ~ ~ i s o t o p e . In its turn, As77 decaying with a half-decay period of 38.8h transforms to stable selenium isotope Se

The eqn to describe the kinetics of the ~e~~ appearing looks more complicated than the similar eqns for Ga7l and A s 7 5 . It is associated with the fact that the concentration of A ~ ~ ~ i s o t o p e (that "yields"

Se7') is itself time-dependent.

Pig. 4

-

Ge-isotopes transformations kinetics after the neutron irradiation of natural Ge. (calculated)

Fig 4 presents the curves a,c,d,e,. They describe the transformation kinetics for all. aforementioned isotopes, i.e. the kinetics of accu- mulating of the donor and acceptor centers. Pig.

4

(b) shown the differential concentration of donor and acceptor centers as a function of time (taking into consideration the fact that se7' is a double donor). The c.ompensation degree is the donor-to-acceptor concentra- tions ratio:

K=- t Nd

2 Na

Since donor and acceptor impurities appear under irradiation, and their concentration time dependence is different, it is natural that the compensation degree, will change too. At the instant when the acceptor impurity concentration becomes equal to the gross concentration of donor impurities, the compensation degree will equal unity.

This occurs in 5.85 days and nights after the irradiation.

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Pig. 5

-

Left hand section of Fig. 4. Enlarged scale.

By this time Ge isotopes which transform to donor centers have practically completely decayed (Fig. 4,5). That means that the compensation change is determined by the generation of acceptor impurities.

When, virterally, all the decays have been completed the compensation degree attains a steady-state level and is subsequently invariable.

The final compensation value can be found as:

The selenium concentration enters the eqn with the factor 2, bacause

Se77 gives up two electrons to the conduction band. The quantity of K is independent of the irradiation dose and is only determined by the Ge70~74,X isotopes concentration in natural Ge and by the proba- bilities of capturing of thermal neutron by these isotopes.

THE PREPARATION 03''l?HE SAMPLES

The samples to be d formed were cut in the sha e of parallelepi ed

5

measuring 3x6~30 mm along the directions [ I T O ~ , [001] and [I ?Of, respect~vely, from a high purity n-Ge single crysta) ( t y differential concentration of donors and acceptors being 2.10 cm' ). The bending a x i s was directed along 170]. The samples were deformed by a four- point bending at 4600C.

k

ter the deformation high purity tin was vacuum-sputtered on the samples. The samples were subsequently annealed for 10 rnin at 7000C in high purity argon atmosphere. The crystals prepared thereby were cut along the neutral plane, a parallelepiped was cut from each half across the bending axis. The density of dislocations was derived from etc h pit count on gaces (110~.

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the samples tested the dislocation density was 3.10 and 6.10 cm-

.

^{No mic-}

rowave dislocation conduction was exhibited after the deformation.

W s can be attributed to an extremely small donor concentration in the original samples. The samples were then coated with a protective tin layer and irradiated in the nuclear reactor (thermal-to-fast neutrons ratio being 300:l). The irradiation time was eight minutes.

This time has been chosen to the final concentration of the introduced acceptors as 4.101

3r:$3.

The control samples were irradiated simultaneously with the deformed ones. After the irradiation the samples have been annealed at 5000C for 7-8 h with a subsequent slow cooling to eliminate the irradiation-induced structural defects. !L%e latter arose mainly due to the presence of the fast neutrons in the

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reactor beam. At first sight this unavoidable annealing offsets the advantage of the neutrons doping method because one can appretend that during the annealing the shallow impurities draw to the dislocations. 'Phese apprehensions are, however, justified only with respect to donors. As far as acceptor are concerned they, actually, have had no time to occur by the moment of the annealing termination. So, by the beginning of he m asurements we had the samples with the donor

3 3

concentration 101 cm'

.

As to homogeneity of their distribution, we are unable to ascertain qgt;hing definite due to the annealing per- formed. F@weve?j, as to the acceptors, we can state that each day and night 10 cm- acceptors originate in the samples with the entirely homogeneous distribution.

The sample was placed into a passthrough cylindrical cavity, TEll oscillation was excited at a frequency 9500 MH

.

^In^{the upper} ^of

the cavity there were slots coupling it with

tee

microwave oscillator and with the detector. m e detector signal was fed to the oscillnswpe.

!Fhe oscillator operated in the frequency modulation regime. A resonance curve was observed on the oscilloscope screen. A thin metallic platelet was soldered to the cavity bottom i n parallel to the coupling slots. The platelet removed the oscillation degeneration and fixed the electric field direction in the cavity. The sample in the shape of a disc was passed through an opening in the upper part of the cavity and placed on a thin Teflon insert i n the cavity center.

The insert with the sample can be turned relatively to the cavity.

In this case, the direction of the electric field in the cavity re- mained unchanged, it was only the angle between the field and the dislocations that changed. By rotating the sample, we find the orien- tation with the least Q-quality of the resonator. It always turned out that a minimal Q-quality (maximal conductivity) corresponded to that position when the electric field is directed along the dislocations (i.e. along [ I 101 / 6 / ) . The resonance frequency was practically invariable at the rotatings. The temperature of the cavity and of the sample was maintained at 4.2K. To check the doping-impurity concentration change we have measured the Hall effect by a usual direct current technique at 77K in the samples irradiated with the same dose of neutrons as those employed for the microwave conductivity measurements.

THE RESULTS AND DISCUSSION

Fig. 6 presents the results of the measlyrements of the carriers concentration change versus the time inpost-irradiated samples. Curve (a) corresponds to the control sample, curve (b) to the sam le

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subjected to the preliminary plastic deformation (ND = 3.10 cm'2). It is seen that in accordance with the given above graphs illustra- ting the kinetics of the Ge isotopes transformations, the irradiated sample continues to be n-type for the first several days and nights, but its conduction-electron concentration decreases. In 5,85 days the compensation degree in the sample amounted to unity and, thereafter, the hole concentration started increasing. The dislocated s m p l e exhibited no noticeable concentration of conduction electrons even in the first days after the irradiation. This is related to the fact that at this temperature all the donor electrons that are being ge- nerated are captured by the dislocations and escape from the conduction band /9/. Subsequently, in the course of the compensation, when the conduction has been transformed to the hole-type, the both samples behave practical1 in the same manner except that the free-holes

concentration is somew%at higher in the control sample.

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JOURNAL DE PHYSIQUE

Pig. 6 i r r a d i a t i o n

-

Change of t h e f r e e - c a r r i e r c o n c e n t r a t i n i n Ge a f t e r t h e a

-

c o n t r o l sample, b

-

^ND⁼^3.10

g

cm-*

Fig.7 shows t h e r e s u l t s of t h e measurements of t h e microwave d i s l o - c a t i o n c o n d u c t i v i t y ~ v e r s u s t h e t i m e a f t e r t h e i r r a d i a t i o n . It i s seen ( c u r v e 1, = 3.106 cm-2) t h a t , i t i n i t i a l l y d r o p s , r e a c h i n g a minimum a f t e ; ~ d a y s , t h e n i t s t a r t s i n c r e a s i n g and comes t o s a t u r a - t i o n by, a p p r o x i m a t e l y , t h e 12-th d a y of t h e measurements.

Fig. 7

-

l.licrowave d i s l o c a t i o n conduction of p l a s t i c a l l y def o m e d germanium-af e r t h e n e u t r o n

E

irra

8'

l a t i ^!^!n. The d i s l o c a t i o n d e n s i t y : 1) ND = 3.10 cm-2, 2) ND = 6.10 om'

.

T h i s can be e x p l a i n e d as f o l l o w s . I n i t i a l l y , a s t h e number of d o n o r s d e c r e a s e s and t h e d e g r e e of compensation i n c r e a s e s , t h e number of e l e c t r o n s c a p t u r e d by a d i s l o c a t i o n and, c o n s e q u e n t l y , t h e d i s l o c a t - i o n c o n d u c t i o n , d e c r e a s e s . The conduction i s minimal, when t h e com- p e n s a t i o n d e g r e e i s c l o s e t o u n i t y . Then i t s t a r t s i n c r e a s i n g now as t h e hole-type whereas t h e number of a c c e p t o r i s i n c r e a s i n g too. Af- t e r t h e d i s l o c a t i o n s , a l l o w i n g f o r t h e magnitude of t h e f i l l i n g f a c - t o r , h a s c a p t u r e d as many h o l e s as i f i s a b l e t o , and t h e h o l e con- c e n t r a t i o n on t h e d i s l o c a t i o n s no l o n g e r changes, t h e d i s l o c a t i o n

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c o n d u c t i o n a l s o comes t o s a t u r a t i o n . It s h o u l d be n o t e d t h a t t h e t o t a l h o l e c o n c e n t r a t i o n i n t h e sample a t t h i s t i m e i s s t i l l i n c r e a - s i n g - ( F i g . 6 ) . I f t h e d i s l o a t i o n c o n c e n t r a t i o n i s somewhat g r e a t e r

z l

( F i g . ? , c u r v e 2, N = 6.10 cm-2) t h e n , i n a c c o r d w i t h t h e spectrum s t r u c t u r e ( F i g . 1 aRd 2) we, a t once a f t e r t h e i r r a d i a t i o n , w i t n e s s t h e s i t u a t i o n when t h e c a r r i e r s ( h o l e s ) a r e l o c a t e d i n t h e low-mobi- l i t y band ( F i g . l ) , t h a t i s i n t h e E ~ ' - band ( F i g . 3 ) , and no conduc- t i o n a l o n g t h e d i s l o c a t i o n s can be observed. S u b s e q u e n t l y , as t h e number of t h e a c c e p t o r i n c r e a s e s , t h e h o l e s t r a n s f e r t o t h e El-band and t h e c o n d u c t i v i t y i n c r e a s e s . A f t e r t h e compensation h a s been a c c o m p l i s h e d , c u r v e s 1 and 2 ( ~ i g . 7) p r a c t i c a l l y c o i n c i d e . Thus, t h e g i v e n e x p e r i m e n t a l r e s u l t s s u g g e s t t h e c o n c l u s i o n t h a t we have managed t o o b s e r v e t h e d i s l o c a t i o n microwave c o n d u c t i o n u n d e r t h e c o n d i t i o n s of d e l i b e r a t e l y homogeneous d i s t r i b u t i o n of t h e d o p a n t (Ga7f ).

T h i s , i n t u r n , p r o v i d e s a d e c i s i v e argument f o r t h e mechanism of t h e e l e c t r i c c o n d u c t i o n a l o n g t h e d i s l o c a t i o n c o r e s .

I n c o n c l u s i o n , I should l i k e t o p r e s e n t one more e x p e r i m e n t a l r e s u l t t h a t s u p p o r t s t h e advanced d i s l o c a t i o n s p e c t r u m model. "The D i s l o - c a t i o n H a l l e f f e c t " measurements have shown

/lo/

t h a t i n n-type Ge c r y s t a l s , when t h e d i s l o c a t i o n s c a p t u r e e l e c t r o n s from t h e d o n o r s and g e t n e g a t i v e l y c h a r g e d , t h e c o n d u c t i o n a l o n g t h e d i s l o c a t i o n s i s r e a l i z e d by h o l e s .

The a u t h o r e x p r e s s e s h i s g r a t i t u d e t o V.V.Kveder, V.RI.Prokopenko, V. I.Ta19yansky and S.A.Shevchenko f o r t h e i r a s s i s t a n c e i n o b t a i n i n g

t h e main r e s u l t s s t a t e d i n t h e p a p e r . REFERENCES

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