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Conductivity and Photoconductivity at Dislocations
R. Labusch
To cite this version:
R. Labusch. Conductivity and Photoconductivity at Dislocations. Journal de Physique III, EDP Sciences, 1997, 7 (7), pp.1411-1424. �10.1051/jp3:1997196�. �jpa-00249654�
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 in dislocation modelling.
1. Introduction
Investijations of dislocations in semiconductors are frequently motivated by their potentially
destructive 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 handicap for 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 conductivity experiments 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
1
f~
~
~0
~ ~2
-1
-1
0 0 5 0
kb/~
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-type
Ge). 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, and r the distance to the dislocation in cylindrical coordinates (here and throughout
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 are interested).
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
-j~fi(f)v2 '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. Consequently there 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 partly
filled 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 temperatures and 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)-oriented
specimens 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 expansion under 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 depth of 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 by
J. 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. Actually our 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 by cooling 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 expected due 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 = Irev exp
(~)
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 parameter values:
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/v d) u/v
T=253K T=241K
~ z an o~ o.4 ~6 as io ~,z o,a o z a 4 o 6 Da i,o
~) U/V 0 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 along 60° 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.
