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Conductivity and Photoconductivity at DislocationsR. Labusch

To cite this version:R. Labusch. Conductivity and Photoconductivity at Dislocations. Journal de Physique III, EDPSciences, 1997, 7 (7), pp.1411-1424. �10.1051/jp3:1997196�. �jpa-00249654�

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J Phys. III IYance 7 (1997) 1411-1424 JULY1997, PAGE 1411

Overview Article

Conductivity and Photoconductivity at Dislocations

R. Labu8ch

Clausthal, 38678 Clausthal-Zellerfeld, Germany

(Received 25 November1996, accepted 11 April 1997)

PACS.71.55.-I Impurity and defect level

PACS 72 20.-I Conductivity phenomena in semiconductors and insulators

PACS 72.20.-I General theory, scattering mechanisms

PACS.72.40.+w Photoconduction and photovoltaic effects

Abstract. The general features of one-dimensional states at dislocations, including those

that are bound in the electrostatic field of trapped charges, are discussed An overview of the

available evidence for the existence or nonexistence of one-dimensional conduction in these states

is given Photoconductivity measurements along dislocations and from the dislocation core to

the bulk are presented and discussed in some detail. The analysis of the results leads to a

revision of some old concepts indislocation modelling.

1. Introduction

Investijations of dislocations in semiconductors are frequently motivated by their potentiallydestructive effect on microelectronic devices. Thus, a dislocation piercing a depletion region

in a p-n-junction or a Schottky diode or crossing the active surface layer of a field effect

transistor could provide a conductive channel through the depletion zone and corrupt the

intended function of a microelectronic device, provided the dislocation core exhibits in fact a

conductivity. This aspect 18 of particular interest in GaAs because dislocations in the substrates

can not be avoided while Si can be grown virtually dislocation free, so that the problem is of

minor importance from a practical point of view. Dislocation conduction can also be a handicapfor polycrystalline solar cell material.

Another aspect of destructive dislocation effects in devices is the trapping and recombina-

tion of carriers at dislocations. This is not strictly the topic of the present contribution but

nevertheless plays a role in this context because our understanding of the transitions between

dislocation states and band states in the bulk can be improved considerably by conductivityexperiments at dislocations and their proper analysis (see later on).

From a less practical but more basic point of view, the structure of electron levels asiociated

with dislocations and their behaviour as single one-dimensional conductors or "quantum wires",

are of course interesting in themselves.

© Les #ditions de Physique 1997

1412 JOURNAL DE PHYSIQUE III N°7

1

f~~~0

~~2

-1

-1

0 0 5 0kb/~

Fig. 1. Dislocation states of the 90°-partial in Ge according to Veth and Teichler [1]

2. Overview of Dislocation States

In theoretical papers the object of the investigation is usually a straight, neutral dislocation

and, because of the translational symmetry along the line, the dislocation states are described

as one-dimensional Bloch waves, i.e. they are localised perpendicular to the dislocation and

delocalised along its line direction. As a result of the calculation of these "core states", the

theory will also yield fully delocalised states which are equal to the unperturbed band states

of the bulk far away from the dislocation.

All states are appropriately represented in an E(kz )-diagrams where kz is the wave number

in the line direction. An example is given in Figure I which is originated from a paper on

dislocation states in Ge by Veth and Teichler iii.The fully delocalised states in this representation are given as two continua, one for the

valence and one for the conduction band. For a given value of kz the upper edge of the valence

band continuum and the lower edge of the conduction band continuum are approximately equal

to the highest valence band state and to the lowest conduction band state of the same kz-value,respectively.

In real life, the dislocation is not neutral in most cases of interest but has trapped carriers

flom point defects in the bulk and carries a positive or negative line charge. Suppose, for

instance, that the line charge is negative (which corresponds to our favorite example, n-typeGe). Then the potential around the dislocation line is attractive for holes and, in addition to

the "primary" bound dislocation states calculated by theoreticians, there will be secondary,bound hole states that are localised in this potential.

According to Read [2] the potential of the charged line is in very good approximation

(e~ f/27rEEob)[In(R/r) 1/2], where ef16 is the charge per unit length, R the radius of the

screening cylinder of positive shallow donors by which the negative dislocation line is sur-

rounded, andr the distance to the dislocation in cylindrical coordinates (here and throughout

N°7 CONDUCTIVITY AND PHOTOCONDUCTIVITY AT DISLOCATIONS 1413

the paper we neglect a third term, (1/2)(r/R)~, in the square brackets which is negligible in

the regime r/R « I in which we areinterested).

In an effective mass approximation the Schr6dinger equation of the bound hole states is:

~~~*'~ i~E~ob~~~~~~~~ ~~~~'~ ~~ ~~~'~

where Ee=

Ee(kz) is the edge of the delocalised band states at kz and m*=

m*(kz) is the

effective mass perpendicular to the dislocation. For kz=

0, I-e- at the upper edge of the one

dimensional hole band, m* is equal to the normal bulk effective mass and Ee equal to the

upper edge of the valence band.

~i

We now introduce the characteristic radius rc =

(@W)~, the reduced energy

e =(27rEEoble~f)(E Ee) + In(R/rc) -1/2 and the reduced radius (

=r/rc. Then we

obtain by elementary algebra the dimensionless Schr6dinger equation

v2-j~fi(f) 'n(I/f)~fi(f)= E~fi(f)

which can be solved numerically with the result e =-0.18 for the lowest eigenstate. The

characteristic radius of the wave function is (c"

1.08. The energy of the bound hole states

according to this calculation is

E(kz)"

Ee(kz) (~~i12~TEE0b)J~(R/~C) l/2 + °.18i

This result shows that the so called "rigid band" approximation in which it is assumed that all

bound dislocation states are shifted by the electrostatic potential in the same way and which

is frequently used in the literature is well justified.Since rc is proportional to /~, E(kz) depends logarithmically on the tran8verse effective

mass of the holes. In the special case of Ge which will be of interest later on there are two

subbands of Heavy (HH) and Light Holes (LH) which are degenerate at k=

0. Consequentlythere will be two one-dimensional bound hole bands and the difference between their upper

edges is simply AE= (e~ f) /(27rEEob)(1/2) In(mHH/mLH).

This looks like a nice and easy result which in fact it is, but one should bear in mind that

the electrostatic potential of the line charge, although it is certainly the most important one, is

not the only contribution to the total potential (see below ). Therefore the quantitative results

given in the equations above can be modified to some extent in reality.

3. Evidence for Conduction Along Dislocations

In principle the core of a straight dislocation is expected to behave like a one-dimensional

quantum system and to exhibit quasi-metallic properties if its one-dimensional bands are partlyfilled with electrons or holes. A necessary (not sufficient!) condition for the latter is that

there are extended dislocation states in the gap of the semiconductor. For the associated

quasi-metallic conduction along the core to be detectable, it is furthermore necessary that the

parallel conductivity of the bulk material can be frozen out or suppressed by other means.

Since one-dimensional quasi-metallic conduction is thermally activated at low temperaturesand decreases exponentially, due to a Peierls transition by which a gap at the Fermi level is

introduced, this requirement can make its experimental demonstration difficult.

So far we have only few examples of conduction along the dislocation core. The best of these

is the 60°-dislocation in Germanium on which I shall report in detail later on. A high one-

dimensional conductivity along screw dislo'cations was also found in CdS [3,4].


3. I. SiLicoN. For Silicon positive evidence has been provided only by AC-measurements [5]in which the difficult procedure of contacting the dislocations is avoided. The experiments

on p- as well as n-type material with dislocation densities of the order of107 cm~~ show

an AC conductivity in the MHz range which is several orders of magnitude above the DC

bulk conductivity. The AC conductivity is considerably enhanced (bj~ more than two orders

of magnitude) if the specimens are exposed to atomic hydrogen which is supposed to diffuse

rapidly in Si and to render defects that are associated with dangling bonds electrically inactive.

These results have been interpreted in terms of the following hypothetical model:

Dislocation core states as well as point defects, introduced during deformation, trap electrons

from shallow impurities and pull the Fermi level towards the middle of the gap. The dislocation

core states are more or less localised and, by themselves, provide only a very low conductance

possibly of the hoping type and/or only for very short segments. If, on the other hand,the core states and point defects are neutralised because dangling bonds are saturated with

atomic hydrogen, electrons become available to occupy one-dimensionally extended levels that

are not associated with the core but with the deformation potential of the strain field of the

dislocation. This potential is less localised than the core potential and its one-dimensional

bands are closer to the conduction and the valence band, respectively, than the core states

but still deeper in the gap than the typical shallow donor levels. The observed conduction is

attributed to electrons in these states in the deformation potential.The disadvantage of the AC measurements is that the specimens contain a network of dis-

locations as well as many point defects so that the observed conduction can not be attributed

to a specific dislocation type and, since an RF-conductivity can be produced by any polariz-able defect, it is not even absolutely certain that the observed conductivity is associated with

dislocations at all (nevertheless it is very likely that 60° dislocations are responsible for the

observed effects. The dislocations were introduced by uniaxial compression of (123)-orientedspecimens which yields a majority of this type).

Recently [6], we have tried to improve the experimental situation by DC-measurements on

groups of straight parallel 60°-dislocations that had been introduced in Si by loop expansionunder an applied load after scratching the surface with a diamond needle. After generation of

the loops a thin slice was cut from the scratched surface and ground and polished down to a

thickness at which some of the dislocations extend through the specimen from one surface to

the other. Both sides were then contacted with alloyed AL-contacts and the conductivity was

measured down to about 10 K.

So far, we have not found positive evidence for dislocation conduction and could only confirm

that the conductance of untreated dislocations, if it exists at all, is smaller than a lower limit.

A continuation of this experiment with different starting material, alternative contacts and

also dangling bond-saturation by hydrogen is under way.

3.2. GALLIUM ARSENIDE. For GaAs the experimental situation is somewhat better al-

though rather disappointing if we consider one-dimensional conduction at dislocations as sci-

entifically exciting and satisfactory:Misawa et al. iii have investigated screw dislocations that penetrated a thin wafer (thickness

18 ~m). The specimens were contacted with In on both sides and compared with dislocation

free wafers. No evidence for dislocation conduction was found.

Recently we have done a similar investigation of 60° dislocations in semi-insulating GaAs [8].The dislocations were introduced by micro-indentations on a (001) surface. The loops are

arranged in a rosette whose arms extend from the indentation in the (i10)- and (l10)-directions.Dislocations in the different arms are Ga and As dislocations (a and fl according to the Huenfeld

convention [9]), respectively.


In GaAs the mobility of screw dislocations is much lower than that of 60°-dislocations. The

loops under the surface are therefore extended parallel to the surface and comparatively shallow

compared with Ge and Si where they are semi-hexagonal. The depth to which the dislocations

extend below the surface was checked in test specimens by grinding and polishing the indented

surface until the etch pits in the rosette disappeared. This was typically the case at a depthof about 30 ~m.

For the conduction measurements, ohmic contacts were applied by alloying a thin In-film

(thickness 750 nm) into the surface. This contact was found to have superior properties com-

pared with others that have been described in the literature. The contact area covers a- as

well as fl-dislocations. After application of thin Au wires to the contacts, the specimens were

embedded in expoxy, together with the contact wires, and ground and polished to the desired

thickness of about 20 ~m. This is a rather difficult process because a small misorientation

yields a poorly controlled wedge shape and complete failure quite easily. Details are given byJ. Korallus in his thesis.

Unfortunately there is no practical way to apply another ohmic contact to the free surface

because this would require another alloying process at elevated temperatures and destroy the

epoxy as well as the specimen. We therefore used a Gold film which forms a Schottky diode on

GaAs. If there is dislocation conduction, it should be apparent in the I-V-characteristic of the

diode. Actuallyour experiment simulates directly a situation of practical interest: dislocations

piercing a Schottky diode.

A rough overview of typical results is given in Figure 2 which shows I-V-characteristics

between 228 K and 299 K of a Schottky diode with dislocations (V) and of a dislocation free

reference diode (R) on the same specimen. Unfortunately, the specimens were destroyed bycooling down to lower temperatures due to different expansion coefficients of GaAs and the

epoxy. Therefore the temperature range of our measurements is rather limited but nevertheless

we can draw some firm conclusions from the results:

The only obvious difference between the dislocation-(V) and the reference contact (R) is a

different factor in the exponential increase of I in the forward direction, but this is only due to

a difference in the reverse currents which can be the consequence of a very small difference in

height of the Schottky barrier. In one case the factor was higher for the dislocation contact, in

another case for the reference contact. In fact some scatter in the contacts must be expecteddue to surface contamination between the last cleaning step and the beginning of Au deposition.We therefore consider this effect as insignificant.

A detailed analysis of the data was done in terms of the circuit diagrams in Figure 3. The

bulk and the dislocation are represented by parallel resistors R and Rp respectively. The

possibility that the dislocation could be connected to the Au contact by another diode, Dp,

was also taken into consideration but turned out to be not necessary for a good fit.

The diode is described by the relation

1=

Irevexp (~)

lj (I)nkT

with Irev=

IO exp(-USB/kT) where USB is the height of the Schottky barrier.The bulk resis-

tance is assumed to be thermally activated:

R=

Ro exp(-UR/kt).

A least square fit with llo, UR, IO, USB, n and Rv as parameters yields the following parametervalues:

n =4 Rv > 10~~ Q at all temperatures Ro

=5 x

10~~ Q.


imio~ exit,T=299K T=297K

4D,2 Q-o Q~ QA Q& o-a lo 4D~ Q,Q o 2 4 o 6 as I

a) U/V ~) U/V

T=283K T=265K

~~ a,~ a ~ o,, ~,~ a a i o ~~ o a u o,~ o,~ as i,o

c) u/vd) u/v

T=253K T=241K

~ z an o~ o.4 ~6 as i o ~,z o,a o z a 4 o 6 Da i,o

~) U/V0 U/V

Fig. 2. I-V-curves for dislocation and reference contacts (R) in a thin GaAs wafer

specmn UR dislocation UR reference USB dislocation USB reference

06 (0.41+ 0.02) eV (0.42 + 0.02) eV (0.63 + 0.02) eV (0.69 + 0.02) eV

07 (0.39 + 0.02) eV (0.37 + 0.02) eV (0.55 + 0.02) eV (0.54 + 0.02) eV

We notice that in both specimens and at all temperatures Rv > 10~~ Q for about 30 par-allel dislocations of about 25 ~m length. Furthermore the barrier height with and without

dislocations is the same within the experimental uncertainty but we can not exclude a small

systematic difference of the order of 50 mev between dislocation and reference contact because


~ ~~_~P RP

a) D R

~IwB-

~b) ij

R

Fig 3. Circuit diagrams for modelling of a dislocation and a reference contact pairs.

the barrier height could not be determined with high accuracy because of the limited tempera-

ture range and is subject to some scatter anyway, as mentioned before. Otherwise the accuracy

is excellent: the mean square deviation between the fitted curves and the experimental data

was less than I% for all I-I'-curves.

From our results we conclude that conduction along 60° dislocations of both types (Ga and

As dislocations) is not detectable and would not play a role in practical applications. This

result seems to be at odds with some theoretical investigations of dislocation states which,apart from differences in details, show one-dimensional band states in the gap [10-12]. In some

cases the prediction is a combination of full and empty bands with a gap inbetween so that a

neutral dislocation would nevertheless not be expected to show quasi metallic conduction but

rather behave like a one-dimensional semiconductor, as long as the Fermi level of the bulk is in

the gap between the full and empty dislocation bands. Conductivity would then be observable

only in suitably doped materials (but still not in a depletion zone where the Fermi level crosses

a major part of the gap). Our experiments should therefore be repeated using samples with

different types and concentrations of doping. On the other hand, it is also possible that the

core structure of the dislocations is not as regular as it has been assumed in the theoretical

description. One possibility is a repetitive change of the core from the glide set to the shuffle

set configuration, another possibility would be an association of point defects with the core

at small intervalls. In both cases one-dimensional conduction which is extremely sensitive to

perturbations would be suppressed or restricted to very short segments of the order of a few

nanometers.

Nevertheless the dislocations can act as traps and recombination centres which seem to play

an important role, for instance in the degradation of GaAs laser diodes.

3.3. GERMANIUM. As mentioned before, one-dimensional quasi-metallic conduction along60° dislocations in Germanium is well established. It has been demonstrated in three ways.

I) AC-measurements in the MHz range [5] wllich demonstrate the existence of dislocation

conduction but cannot identify the dislocation type or types to which it is attributed.

ii) DC-measurements in thin plates with contacts which are rectifying with respect to the

bulk but ohmic with respect to dislocations [13,14]. An example is shown in Figure 4, which

shows I- V-curves for a group of about 20 parallel dislocations in n-Ge between 82 and 109 K.

Notice that in the same temperature range the currents through identical reference contacts

(alloyed Auln) in a dislocation free area are less then 10~~ A. The nonlinearity of the curves

is not yet fully understood. As a tentative explanation we suggest a small tunneling barrier

between the contacts and the dislocation core.


Qf~'

(a) T=

108.6K (b) ~ ~(a) T

=71.6K

( (b) T=

96.4K 7 (b) T=

60.9K

cS (c) T=

82.1K ] (c) T=

52.5KQ Q

o,~

_~,2.

,I. o. 1. ,J. o. I.

lf/V lf/V

Fig. 4. I- V-curves of the conduction along a group of 20 dislocations in Ge For a dislocation free

reference contact pair of the same kind the currents are below 10~~ A.

EBIC signal~~~~~~°~ ~~~~'

ohmiccontact

i iiY

n,p-Ge

Schoflky contact d=

100 ~m

Fig. 5. Configuration for EBIC measurements at 60°-dislocations in Ge [15].

iii) EBIC measurements in a special configuration which is shown in Figure 5 [15]. In this

setup the Schottky contact which in other EBIC experiments separates the electron hole pairsand thereby yields the observed current, is 100 ~m away from the surface where the pairs are

generated, so that the EBIC signal is quite weak if no dislocations are present.If, on the other hand, the electron beam impinges near a dislocation, two things can happen:

a) In n-type material, where the dislocation acts as an acceptor and carries a negative line

charge, excess minority carriers (holes)are rapidly trapped by the dislocation and carried

along its core to the contact on the other side. This gives rise to a bright contrast. Thus,the dislocation can be considered as a linear extension of the Schottky contact into the

plate. This is in fact observed.

b) In p-type material, the dislocation acts as a donor and carries a positive line chargebut, due to the position of the neutral dislocation levels in the gap, only a weak one.

Consequently, the trapping rate of minority carriers (electrons) is much lower than in

n-type material and has to compete with recombination at the dislocation which, byitself, would lead to a weak, extended dark contrast.


~ ~

EBIC contrast profile n-Ge

O.09

D-Da

O-O?

O.06line

Q O.05 scan

JO.04

O.03 fi

O.02

~ ~~

O.Ol

O.OO

-O.Ol

-O.02

-O.03

~o 4 8 12 6 20 24

a) X '~m

EBIC contrast profile p-Geo,12

O.08

0.04

Io.oo

------------------------d

-O.04

-O.08

-0.125 5 20 25 30 35

b) Xl ~m

Fig. 6 Profiles through EBIC dislocation profiles in n-Ge (a) and p-Ge (b) [15].

The observed contrast profiles through dislocation images show in fact both effects verynicely (see Figs. 6a and 6b): in n-type material we obtain essentially only a bright contrast

while in p-type material we observe a wide dark contrast (due to pair recombination along the

way from one side to the other) superimposed by a narrow bright contrast (due to trapping of

electrons and conduction along the dislocation).

4. Photoconductivity at Dislocations

More recently we have also done photoconductivity measurements on groups of 60° dislocations

in Ge [16]. These provide additional information on the dislocation levels but are also of broader

interest because in the course of their analysis we are forced to reconsider some old concepts


.6'@

ee~

ed ~pd e

~ ~p$A m

~

e

onon

e J£~e

e

ea

.2 qi~

~e~

~

~'~'

.0

.3 ,4 .5 .6

Awlev

Fig 7. Spectral photoconductivity along a group of 20 parallel 60°-dislocations in n-Ge [16].

and models related to dislocations in semiconductors in general. Thus, the following discussion

may provide some new insight beyond the special case of Ge.

All photoconductivity signals depend very weakly on temperature. As far as noise is con-

cerned, the best results were obtained between 60 and 90 K. Our measurements were done in

this range in two different modes:

I) The spectral response of the conductivity along dislocations to incident light was measured

in the configuration of the previous conductivity measurements. The results are shown in

Figure 7.

ii) As mentioned before, the dislocation in n-Ge carries a negative charge and is surrounded

by a potential. Givena quasimetallic core, this configuration is equivalent to a linear Schottky

diode between the dislocation core and the bulk. In the setup shown in Figure 8 we can

measure the I-V-curve of this diode which has in fact the expected shape. A second set

of photoconductivity measurements was done in this configuration under reverse bias. This

means that electrons which are excited to a level above the edge of the conduction band at the

dislocation can escape into free states and contribute to the measured current.

The spectral dependence of the signal (see Fig. 9) is qualitatively similar to the photocon-ductivity along the dislocation. However, the sharp double peak near 0.38 eV is a factor of

30 smaller than in Figure 7 (not evident from the figures where the photocurrent is given in

arbitrary units) while at higher photon energies the signals become comparable.

We consider this as convincing evidence that the sharp peak in Figure 7 corresponds to

internal transitions between bound dislocation states for which the excited electrons can not,

or only with a small probability, escape into the volume while above 0.42 eV the excited carriers

contribute to both currents, along the dislocation as well as from the core to the volume. In

fact the structure of the double peak in Figure 7 fits very nicely a model calculation of the


galvanometer

voltage source

contacteddislocations

Fig. 8. Experimental setup for measuring I-V-characteristic of the dislocation-bulk diode [16].

1.

d .8 ~

dj w

~, w

e

.6 ~

e

ee

e

.4

.2

.0

.3 ,4 .5 .6

-hwlev

Fig, g. Spectral photoconductivity from the dislocation cores to the bulk (dislocation-bulk diode

under reverse voltage) [16].

probalities for direct optical transitions between the edges of one-dimensional energy bands:

the transition probabilities are essentially proportional to the combined density of states of

the two bands between which the transitions take place. For transitions between the edges of


two one dimensional bands this combined density of states has a square root singularity which

is folded with the spectral output of the illuminating monochromator to obtain the curve in

Figure 10.

Although it is always difficult to attribute optical transitions to a specific pair of levels

unambiguously, we find that the best agreement with all known experimental and theoretical

data is obtained if we assume that one of the peaks is due to transitions between the heavyhole band and one of the primary dislocation bands at k

=0 while the other one corresponds

to transitions between the two primary band8 [17].As mentioned before, our experiments indicate that electrons can escape from the dislocation

core if they are excited more than 0.42 eV above the level of the highest occupied core states

which is identical with the Fermi level. This seems to be in contradiction to the classical

model of a charged dislocation in n-Ge: in thermal equilibrium the dislocation traps electrons

and builds up an electrostatic potential until it highest occupied core states are at the level

of the Fermi energy. The distance of these core states from the valence band is known from

independent experiments. Therefore we can evaluate the height of the potential barrier for the

escape of electrons from core states at the Fermi level with reasonable accuracy and find it

to be 0.6 eV. Consequently an excitation energy of the same magnitude rather than 0.42 eV

should be necessary for an escape to the bulk. According to Schr0ter [18] a small reduction can

be expected due to tunneling through the tip of the barrier but this would not be sufficient to

explain the observed discrepancy. There is however another reduction of the potential barrier

due to the deformation potential of the stress field of the dislocation:

According to Winter [19] the main contribution of this potential at a 60°-dislocation comes

from the 90°-partial and has the form -Dobp /(27rr)g(@ Ho where is the angle in a planeperpendicular to the hnedirection and Ho corresponds approximately to the direction of the

extra half plane. For isotropic elasticity g is simply a cosine bp is the Burgers vector of the

partial d1810cation and Do * 10 eV in Ge (in other semiconductors Do is of the same order of

magnitude). This potential is added to the electrostatic potential of the charged dislocation

line which is essentially logarithmic in r.

The total potential is now

~ ~

~E~ob~~~~~~~~ ~~~~~

~~~~)i~~

'~

Obviously the potential has a saddle point in the plane perpendicular to the dislocation at

= Ho and, by elementary algebra, we obtain for its radial position

rs "DobpbEEo/(e~ f)

and for it height

Us"

(e~ f/27rEEob)[In(R/rS) 3/2)].

Typically rS is about 50 Angstroms,i.e.

considerably bigger than the lattice constant so that

the use of the deformation potential which is a macroscopic concept for the description of a

microscopic situation is justified.Adding the third dimension we obtain in fact a saddle line at Ho and rS. In our particular

example we find that the saddle line potential is only m 0.42 eV above the Fermi level which is a

8ignificant reduction (m 0.18 eV) compared with the electrostatic potential alone, in agreementwith the experimental ob8ervations.

We can go even one step further and convince ourselves that the saddle point energy is not

a 8harp threshold but that electrons can e8cape from the dislocation, although with decreasing


0.25 0.30 0.35 0.40 0.45&w(eV)-

Fig. 10. Model calculation of the photoresponse for transitions between one-dimensional bands

edges. The effective masses and the energy differences between the band were adjusted to fit the data

in Figure 10.

>w~ ,05

o~

u~~

04

L

L@

IL ,03

fl

02

,oi

oo

5 6 .7 8 9 0 2 3 4 5

r-0efect/r-Saddle

Fig 11. Reduction of the potential barrier at a dislocation due to a charged impurity at distance

rDefect from the dislocation core.


probability, at even lower excitation energie8: actually the screening cloud around the dislo-

cation 18 not homogeneou8 but con818ts of local18ed donor8. Let u8 con8ider a 8ingle chargeddonor in the vicinity of the 8addle line. Th18 add8 another term -e~/47rEEo(r rD( to the

potential where the two-dimen8ional vector rD is the position of the donor atom in the planeperpendicular to the dislocation. This lowers the saddle point energy. The strongest effect is

expected along a line connecting the dislocation line and the donor atom.

Figure II shows, as a result of a numerical calculation, the reduction of the saddle point

energy as a function of the distance of the donor atom from the dislocation. The maximum

reduction of the saddle point energy is about 40 mev, depending weakly on doping concentra-

tion and temperature which influence the parameters of the logarithmic potential of the line

charge. This kind of local barrier reduction can explain why a weak signal below 0,4 eV is

seen in Figure 9 although the corresponding transitions are intrinsic to the dislocation and the

excited electron8 can not e8cape through the average barrier.

The two eflect8 of barrier reduction that we have pointed out here are of course equallysignificant in any experiments in which transitions between dislocation 8tates and bulk states

play a role but have frequently not been taken into consideration in the analysis of EBIC,DLTS and other experiments in the past.

References

[1] Veth H. and Teichler H., Philos. Mag. B 49 (1984) 379.

[2] Read T.W., Philos. Mag. 45(1954) 775.

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