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Transition regions in epitaxially grown semiconductor films and devices
Thin Solid Films, 50 (1978) 13-24 © Elsevier Sequoia S.A., Lausanne--Printed in the Netherlands
13
TRANSITION REGIONS IN EPITAXIALLY GROWN SEMICONDUCTOR FILMS AND DEVICES L. N. ALEKSANDROV Institute of Semiconductor Physics, Siberian Branch of the U.S.S.R. Academy of Sciences, 630090 Novosibirsk (U.S.S.R.)
Consideration is given to the principal physical factors in the formation of transition regions between a substrate and an epitaxial film. The transition region indicates a thickness inhomogeneity of the film structure, and this has an influence on size effects. From analysis of experimental data on the nature and form of transition regions and from theoretical descriptions of the mechanisms of epitaxial film growth, methods of reducing the thickness of film-substrate transitions are demonstrated. It is possible to produce multilayer film structures for devices in optoelectronics and microelectronics with no noticeable film-film transition regions by using small inertia vacuum methods and molecular beam epitaxy.
1. INTRODUCTION The speed of response and the packing density of elements in electronic and optoelectronic computing systems have been increased by widespread use of devices and apparatus with three-dimensional multilayer active regions. Unlike diffusion methods and ion doping, epitaxial deposition permits the production of an unlimited number of single-crystal layers of different conductivities in any sequence. Epitaxial methods are successfully used in the production of multilayer structures for devices with Gunn diodes (the n + - n - n - - n ÷ ÷ type of gallium arsenide), in the production of double-laser heterostructures, in the formation of waveguide structures in integrated optics and in the production of multilayer structures on silicon and germanium for avalanche photoreceivers. Epitaxial deposition requires certain conditions that depend on the crystalline lattice structure of the deposited substance, the temperature, oversaturation, the state of the substrate surface, the action of external fields and radiation. However, epitaxial formation and the further growth of semiconductor films in the substrate-film interface are accompanied by the formation of a transition region (TR) whose features differ from those of both the substrate and the film. These TRs have a thickness of from several interatomic spacings to tens of microns, and manifest themselves in all film structures of semiconductor electronics, in laser and opto-acoustoelectronic devices, in film detectors of nuclear radiation, in diode transistor charge-coupled device matrices, in integrated circuits and in waveguide heterostructures. For the discrete devices of semiconductor electronics produced in the 1960s, with a film about 10-20 ~tm thick, it was possible in most cases to consider the TR to be a geometrical two-dimensional
14
L. N. ALEKSANDROV
interface and to neglect its thickness, but in the devices of microelectronics with their dramatic reduction in the thickness of the active region of the films the TR must be carefully studied. The problem arose of determining the physical processes that cause the development of the TR in epitaxial film growth and that prevent an abrupt change in the concentration of doping impurities, in the concentration of charge carriers and in their mobility at the film-substrate interface. Over the last decade numerous theoretical and experimental investigations on the nature of TRs, on their structure and on ways of reducing them were carried out. The first surveys of this problem, published in 1969-72, promoted systematization of the data obtained, made the conventional concepts ofepitaxial film growth more complete and precise. and speeded up the use of new methods in film production ~-s. The improvements of the technique of capacitance-voltage measurements of the concentration distribution of charge carriers through the film thickness, of electron microscope methods for studying film structures and interfaces and of optical diffraction methods for studying film growth, and the use of optical and current-voltage measurements and instrumental parameters of the structures obtained to describe a film-substrate interface promoted a better understanding of the causes of formation ofTRs9-11. The removal of the T R is part of the general problem of producing films of homogeneous thickness. The criterion of homogeneity became the constancy of local values of the parameters of the film through its thickness. A careful consideration of the T R in semiconductor films necessitates the elimination of the influence of a size effect. Thus the current state of the problem of TRs in epitaxial films is closely associated with the development of the theory of size effects. To make the treatment of and the identification of the reasons for TR formation more convenient, the major factors are divided into three groups: the influence of the substrate, the influence of growth processes, and the influence of changes in an initial phase. Phenomenologically TRs can be considered to be regions of a near-boundary phase of the solid solution type in the substrate and the film. In accordance with the limits of solubility of the film and substrate substances, phases of intermediate composition can be formed, and the mismatch of lattice parameters in heteroepitaxy leads to misfit dislocations and stress fields 2" 12. The formation and properties of TRs have been studied in more detail in epitaxial films of silicon, germanium and binary compounds (gallium arsenide, gallium phosphide, indium arsenide) grown on semiconductor or insulating (sapphire, spinel) substrates. In most practical problems, the TR thickness is determined as the film thickness over which the charge carrier concentration changes by a factor of ten compared with that at the boundary with the substrate (or another film), if further change of the concentration may be neglected. In theoretical calculations we used the following relation for the change in the concentration gradient 13 :
dn/dx <~0.01t~*(d)
(1)
where ~* is the established value of the gradient at a distance d. The T R thickness is determined by the whole spectrum of structure-sensitive film properties, but for applications in devices the ones of great importance are the type and concentration
15
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
of the charge carriers, their mobility, the diffusion lengths, the lifetimes, the refractive indices and other optical and electrical grating parameters. 2.
THE TRANSITION REGION AS A MANIFESTATION OF FILM THICKNESS INHOMOGENEITY OR OF A SIZE EFFECT
The properties of a film are determined by its surface and its volume. The thinner the film, the more is the surface contribution. The thin film state of a solid is characterized by a change in properties with thickness. The physical measure of "'thinness" is the relation of the film thickness to the range of action of characteristic parameters, e.g. the Debye radius ~b of charge shielding, the mean free path 2 s of the charge carriers, the distance between dislocations. In semiconductor films the resistivity p increases for d < 2s owing to an increase in the scattering of charge carriers over the surface (Fig. 1, curve 1), although from the constancy of p for d >> 2s the film itself is homogeneous through its thickness. However, the change o f p with thickness for d > 2~ (Fig. 1, curve 2) is not connected with a size effect but is caused by the inhomogeneity of the film structure through the thickness, The quantitative separation of the influence ofinhomogeneity from that of a size effect is not difficult. 10-~
-~
A
• ....... 10-2
I
I0 2
d (~.ml
fit,.
_e
., 7_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A, ,i
"1
1i"
Fig. 1. The change in film resistivity with thickness for homogeneous (curve 1) and inhomogeneous (curve 2) films. Fig. 2. An epitaxial film considered as a sequence of layers d i thick with conductivity tr~ on the substrate (do, ao).
In general cases a film with a substrate is a multilayer structure d 1 + d o thick (Fig. 2), where the thickness dofall film layers is ~ d r If the electrical conductivity of the substrate is % and that of each layer d; thick is tri, then the effective electrical conductivity of the film is at = d l - t ~ trid i
(2)
i=1
With a high resistance or insulating substrate, measurements give an effective value of a t for the film when trod o ,~ trld r By measuring the electrical conductivity of the film as it grows or during layer-by-layer etching, we obtain a sequence of effective values of o'(~ii = 1dl). The relevant local values are determined by the relation ~ ( Z i + t d~)d~ + ~ - ~ ( ~ i dl)dl ai ~ dl + 1
(3)
16
L . N . ALEKSANDROV
The difference in the nature of the change o f a i and a ( ~ i d i ) with thickness allows the degree of film thickness inhomogeneity and the contribution of surface (boundary) charges to be estimated. The purer and the thinner the film, the more noticeable the influence of surface properties on the effective values of its parameters. The effective concentration neff of charge carriers in a film of thickness d is determined by their concentration n o in the volume and ns on the surfaces from the summation relation n o V + 2nsS
ne" -
V
2n s
- no + d -
(4)
where V and S are, respectively, the volume and the surface of the film. For 3, ns = 101o c m - 2 and d ~ 10 -3 cm, nef~ decreases monotonically with an increase in film thickness from microns to tens of microns, even though the film is homogeneous in thickness, i.e. n o = constant. An apparent film inhomogeneity is also manifested for thicknesses d > rD. The real local values of the carrier concentration n~ and of the mobility #~ in the layers can be determined by calculation for the specific type of multilayer film using an expression similar to eqn. (3). Note that although in some work the usual size effects are wrongly assigned to the influence of the TR, in other experimental work the changes in film properties caused by the interface inhomogeneity, i.e. the TR, are assigned to a size effect ! n o <~ 2 n s / d , e . g . in pure germanium films with n o = 10 ~3 cm
3.
EXPERIMENTAL STUDIES OF TRANSITION REGIONS
Table I summarizes the results of experimental studies 8-11.14 of defects and charge carriers in the TR. Most attention is given to the fit of the crystallographic structures of the epitaxially conjugated substances of film and substrate, to the preparation of the substrate surface before epitaxy, to impurity evaporation and diffusion and to the growth processes, the properties and the influence of environmental conditions on the properties. It has been shown that improvement in cleaning carbide particles and oxide impurities from the substrate surface has a direct influence on the epitaxy mechanism: step motion occurs instead of the development of three-dimensional growth centres. On an atomically pure stepped silicon surface obtained by high temperature annealing (1300°C, 20 min) in an ultrahigh vacuum, epitaxial film growth by ion sputtering or from a molecular beam follows the steady state surface relief ~5 A system of growth steps made as in ref. 13 accelerates the approach to a steady state relief and reduces the TR to less than 0.5 iam over the film structure. Heteroepitaxial germanium growth on this surface begins with the formation of a pseudomorphic film, and the appearance of misfit dislocations is followed by the stage of steady state growth 16. However, the reduction of an impurity TR also necessitates suppression of diffusion processes by a decrease in the epitaxy temperature. In the gas transport methods for the epitaxial deposition of germanium, silicon and gallium arsenide films, a reduction in the TR of the charge carrier concentration was observed when deep polishing and purifying-gas etching of the substrate surface was carried out before epitaxy I L ~4. It was found that atoms of doping impurities and of the principal substance were evaporated in the substrate surface cleaning. Complicated profiles of the charge carrier distribution were formed in the epitaxial
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
17
TABLE I P R I N C I P A L CAUSES OF T R A N S I T I O N R E G I O N F O R M A T I O N I N E P I T A X I A L L Y
GROWN FILMS
Influence of the substances and the substrate Stale
Growth processes
Changes in the initial phase
Misfit of the crystalline lattices of the film and substrate
Three-dimensional nucleation in the initial epitaxy stage
The time of the start of stationary conditions of growth
Difference in the elastic moduli of the film and substrate
Changes in growth surface microrelief
Changes in the temperature of the sources and the substrate
Initial orientation and treatment and cleaning of the substrate surface
"'Evolutionary selection" of grains and blocks and recrystallization
Changes in impurity concentration
Impurity diffusion from the substrate
Dynamics and relaxation of defects
Self-doping through the surrounding phase
Changes in the substrate by thermal treatment and etching
Impurity diffusion from the film
Changes in external fields
structures d e p e n d i n g on the relative velocity o f e v a p o r a t i o n o f d o n o r a n d a c c c p t o r impurities and, in b i n a r y c o m p o u n d s , o f a t o m s o f the m a j o r c o m p o n e n t s . F i g u r e 3 shows the possible d i s t r i b u t i o n s o f electrons in a h o m o e p i t a x i a l G a A s film on a d o p e d substrate d u r i n g growth o f an n ÷ - n structure for a G u n n diode. O n t e l l u r i u m - d o p e d substrates direct film d o p i n g was o b s e r v e d (curve 1); by reducing the d o p i n g it was possible practically to r e m o v e the T R (curve 2). A high resistance region which d e g r a d e d the d i o d e p a r a m e t e r s (curve 3) was f o r m e d due to silicon d o p i n g o f the film, because o f the u n s t e a d y c a p t u r e b e h a v i o u r that is c o m m o n in the initial stages o f e p i t a x y ; this was m o s t l y d e t e r m i n e d by the s u b s t r a t e surface p r e p a r a t i o n . A change in the AsC13 c o n c e n t r a t i o n in the v a p o u r phase a n d tin d o p i n g f a v o u r e d the r e m o v a l o f the TR.
Film
'~
$~lrale
1015
I 'o
J
__z
10I/'
I
I
I
I
I
I
2
3
~
S
d ll~ml
Fig. 3. The distribution of charge carriers (electrons) in a homoepitaxial GaAs film on a doped substrate: curve 1, doping of the film from the substrate; curve 2, the ideal case of no TR; curve 3, formation of a high resistance region.
18
L. N. ALEKSANDROV
On tin-doped GaAs films it was found that the total concentration of donors and acceptors decreased markedly from 1018 to l0 ts c m - 3 with an increase in the growth rate from 0.06 to 0.47 p.m min l; this is associated with a change in the capture coefficient and with the suppression of diffusion processes near the film substrate interface 17. The dependence of the film doping level on growth rate has been used in theoretical estimations of the TR thickness under varying environmental conditions. Long relaxation times in complicated gas transport systems slow down the commencement of steady state growth, and every change in growth rate, cessation, slowing down or acceleration, results in a change in film conductivity. Slow changes of the environmental conditions result in monotonic changes in conductivity; fast ones give rise to unsteadiness and abrupt changes in properties t 8. A change in the ratio of the partial pressures of the components during G a A s film growth gave rise to a shift of the maximum dislocation density into the substrate for growth on the (111) A face and into the film for growth on the (111) B face. Thus excess arsenic widened the structural T R in the first case but narrowed it in the second t9 because the total film non-stoichiometry was reduced and the film thickness homogeneity was increased. The complication of stabilizing a vapour phase state in order to obtain solid solutions in systems o f l l I V or I I - V I elements usually results, in view of the variety' of associated reactions, in an extension of the thickness of the T R to tt 20-40 p.m. Nevertheless, Sugano and his collaborators 2° have succeeded in obtaining films of solid solutions of indium-gallium arsenides with an inhomogeneity region of hole mobility and electrical resistance of about 3 p.m in an overall film thickness of 5 p.m. The suitability of vacuum deposition methods for obtaining homogeneous films of solid solutions is evident. Even the first work on GaAs film epitaxy from molecular beams showed the possibility of using their short time lag to reduce the T R in n + n structures down to hundredths of a micron 21 . The production of supertattices based on solid solutions of gallium-aluminium arsenides with a period of several interatomic spacings also confirmed the possibility of a sharp change in concentration at the film-film interface in epitaxial deposition. However, the action of other factors, say, the substrate surface treatment and cleaning, and diffusion or self-doping from the substrate, was still evident.
E
0.5
06
1
0.8
10 X (~m)
1.2
Fig. 4. The spectral characteristic of Mo-p-Si-n-Si photodiodes at 296 K obtained by high temperature treatment of n-Si with resistivity 0.3 f2 cm (curve 1) and 7.5 f~ cm (curve 2).
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
19
In investigations of phosphorus-doped silicon substrates which were cleaned by high temperature annealing in an ultrahigh vacuum before epitaxy, it was shown that a layer of hole-type conductivity of up to 1 ~tm was formed in the near-surface region 16. P ÷ - p - n structures with good photoelectric properties were formed by epitaxial deposition on the substrate surface. The maximum spectral sensitivity of the diodes was at a wavelength of about l lam (Fig. 4), the detectability (maximum) exceeded 1013 cm Hz 1/2 W-1 and the integrated sensitivity was 9 m A I m - 1. The formation o f a p layer during annealing was ascribed to phosphorus diffusion to the surface and its evaporation with other doping elements and silicon. The stationary profile of the phosphorus concentration and the depth of the p-n junction that is limiting for a given temperature were established from the ratio of the evaporation rates for phosphorus and silicon. Layer-by-layer etching and capacitance-voltage measurements have indicated the possibility of obtaining the concentration profile of the electrons from the diffusion curve for the accelerated diffusion in the nearsurface region due both to the participation of vacancies and to the possible displacement of other donor and acceptor impurities.
4.
THEORETICAL DESCRIPTION OF THE PROCESSES OF TRANSITION REGION FORMATION
In quantitative studies of the TR most attention has been paid to misfit dislocations and elastic stresses, to film growth kinetics and to the impurity distribution dependence on the growth-limiting mechanism. Estimations of the critical thickness of a coherent conjugation region for the film and substrate before misfit dislocation formation were made by van der Merwe 22, who in further work took into consideration the energy of interaction of dislocations with the film or substrate surface 23,12. The following relation is used in estimating the lattice parameter misfit: -
as - at a~
~
2 as - at a~ -t-af
(5)
where af is the lattice parameter of the film and a s that of the substrate. The quantity e is determined by the concentration dependence coi and the temperature dependence Ki of the lattice parameters, because film deposition is carried out at some temperature T and doping additions are present in both the substrate and the film. At concentrations C i of n different impurities the lattice parameter of, say, the film in eqn. (5) is determined from a r = aor ~ (1 + toiCi)(1 q- KfT)
(6)
i=1
By making use of the difference in size of the atoms introduced and by combined doping we can obtain a junction with small lattice misfit. From the equation e(C~s, C~f, T) = 0 we can find the impurity concentrations in the film and substrate and the epitaxy temperature that minimize stresses in the junction a' 24. Consideration of the elastic properties in the substrate-transition region-film system for coherent and incoherent interfaces (Fig. 5) allowed us to estimate the interaction force of
20
L. N. ALEKSANDROV
dislocations with phase interfaces and the influence of the misfit dislocations. The image stresses that influence the dislocations were determined using the analogy between the electrostatics of a point charge and the elastic statics of dislocations. The forces that draw a dislocation out of the film to the film surface or the substrate interface were determined for different relations between the moduli of elasticity of the layers and their thicknesses a 1, a - a l . An increase in the coherent TR length favoured an increase in the forces. At the incoherent interface and for x o > 0.2 (Fig. 5(b)) the area of action of the stresses was extended. The longer the TR, the more intensive was the concentration of misfit dislocations in the TR ~2. The impurity TR thickness was calculated by solving eqn. (1) and using ~3
Nim nim - Np + Nim
Nim -- ~ Np
t'~ 1
(7)
which gives the relation between the concentration n~mof impurities captured during growth and the effective film growth rate ven; Nim and Np are the atomic fluxes of the impurity and of the principal substance to the growth surface. An assumption concerning the constant flow of impurity from the gas phase is valid if the flow is limited by mass transfer but not by surface reactions. The effective film growth rate was determined from the formation of three-dimensional clusters and from the motion of surface steps: nucleation prevails on single-crystal faces and growth step motion on vicinal ones. Since a change with time of ve~ in the initial growth stage takes place only in the first case, it is possible to reduce the TR by enhancing the contribution of layer growth by step motion 8. The calculated results were in good agreement with experimental data for GaAs and germanium films. A statistical probability description of the process of film formation in the case
2
xo
Fi[rn
Transition ayer
Substrate I 1
(a)
(b)
I 2
I 3
1 /,
1 5
I 6
I 7
~3d~2t
Fig. 5. The film-substrate transition region for (a) coherent conjugationofthecrystallinelatticesand (b) incoherent conjugation of the crystalline lattices with the formation o f misfit dislocations. Fig. 6. The change with time of the relative rate of filling of all simultaneously grown layers: curve 1, homoepitaxy on a perfectly smooth substrate; curve 2, homoepitaxy at poisoned initial steps; curve 3, homoepitaxy at active initial steps. L is the step length, C2. t is their growth rate; fld is a kinetic coefficient.
of the development of three-dimensional growth centres permitted us to estimate the minimum TR thickness as the limiting thickness of a continuous epitaxial film 25. For a constant grain growth rate c determined by surface reactions and a nucleation rate I, we used the following relation to estimate dm:
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
dm = K , ( c / l ) '/3
21 (8)
For diffusion-limited growth d m = K2(D/1)'/"
(9)
where D is the diffusion coefficient. The coefficients K, and K 2 (approximately unity) are determined by the geometry of the growth centres. With I ~ 1016 cm-2 s -1 andc ~ 10-6 cm s-l, dm ~, 1 pm. For layer-by-layer growth the TR was estimated as the thickness of a nonsteadily formed film with simultaneous overgrowth of several layers on the substrate and with impurity atoms captured by roughnesses and at steps 26. In the calculations we used the relations between the fraction Pm of filling of the ruth layer and an "extended" fraction P,,xx of filling of the same layer at time t: P,,,ex =
I2s(t - r)P m_ l(z) dr
0o)
where 12 is the two-dimensional nucleation rate and s ( t - r ) is the area of growth centres. This relation corresponds to the kinetic equation dP, J d P ~ , x
=
1-P,~
(II)
An expected impurity profile calculated from the change ifi the area of an active film growth surface is given in Fig. 6. Calculations for germanium homoepitaxy gave 5-20 nm for the TR depending on the growth-limiting mechanisms and on the substrate surface state. Monte Carlo calculations of film growth are promising for a detailed description of TR formation.
5.
WAYS OF REDUCING THE TR THICKNESS IN FILMS AND DEVICES
This progress in our understanding of the causes of .TR formation and in the removal of TRs in epitaxial structures does not reduce the topicality of the problem. The use of film materials in technology is increasing; new instruments are being produced, and requirements for the interface structure of homojunctions and heterojunctions are becoming more and more strict. We have already mentioned the deterioration of the parameters ofa p--njunction in GaAs devices due to the TR: the breakdown voltage is decreased and the leakage current increasedXo. In devices with n-n + structures, reduction of the electron concentration in the TR results in deterioration of the frequency properties, in an increase of the threshold voltage of Gunn generators and in generation suppression; a concentration increase reduces the breakdown voltage and the power of the devices. The removal of a high resistance region increased the efficiency of generators by 20 ~o27. In silicon epitaxial p-n junctions, when the TR was reduced from 3-4 to 1-2 lam by a decrease in the epitaxy temperature during growth by 100 °C, the breakdown voltage was increased by 60 ~2a.
22
L. N. ALEKSANDROV
Reduction of the TR and improvements in device parameters have been obtained by better levels of substrate surface perfection and purity and purity of the starting materials, by stationary deposition conditions, by suppression of selfdoping as well as by special methods. Table II summarizes the possible ways of reducing the TR. TABLE II WAYSOFREDUCINGTHETRANSITIONREGION Action on the substrate state and surface
Changes in growth processes
Action on the initial phase
Substrate surface cleaning
Decrease in deposition temperature and oversaturation
Stabilization of the sourcesof dopingof the main substance
Production of a systemof growth steps
Combined film doping
Conservation of vacuum purity or gas mixture composition
Deposition of bufferepitaxial layers
Conservation of vicinalityof the growth surface
Constancyof deposition temperature, mixing
Protection of the reverse side of the substrate
Two-stepconditions of film deposition
Stabilization and homogeneity of external fields
Reduction of the temperature and time of substrate treatment
Reduction of the period of non-steadygrowth
Production of the liquid phase on the growth surface
Worthy of special attention are the methods of production of intermediate (buffer) epitaxial layers between the substrate and the deposited film. The introduction into devices of a buffer layer that repeated the film properties allowed us to replace the substrate-film transition with an active film-film transition. The T R indicated only the time lag from the introduction of the doping addition, and the profile of the other impurities and the general deposition conditions were kept constant; a new substrate had no undesirable influence 29. Using buffer layers in epitaxial structures for Gunn diodes we achieved a difference in electron concentration of more than 100 times in a distance of 0.1-i.5 p,m. Figure 7 shows the influence of a buffer layer on the T R thickness for tellurium doping. In this case 3° with a reduction of the n ÷ layer to 3 lain the TR was extended to 10 Ixm. In germanium doping of GaAs the T R between the buffer and the doped film was decreased to 0.1 lam when the flow velocity of the gas mixture was changed to give a fourfold change of the composition of the mixture in the reactor 31. In the liquid phase epitaxy method the T R was decreased considerably by rapid transfer of the substrate to solutions with different amounts of doping elements. Epitaxial p + - p - n - n + structures for high power Gunn diodes at a frequency of 20-30 G H z and with sharp (less than 0.1 lam) junctions between films were obtained in one growth cycle 32. Successful use of the methods of reducing the TR in silicon p ÷ - n - n + planar structures in integrated circuits for microelectronics has resulted 33 in a change in resistivity from 0.01 ~ cm (in the substrate) to 0.7 fl cm (in the film) over a distance of less than 0.2 lam.
T R A N S I T I O N R E G I O N S IN S E M I C O N D U C T O R FILMS A N D DEVICES
2
10~
10 t5
Buffer layer
fi
I
23
I
I ~,
I
Fig. 7. T h e e l e c t r o n d i s t r i b u t i o n in a t h r e e - l a y e r epitaxial n ÷ + n - n + s t r u c t u r e o f g a l l i u m a r s e n i d e with a thick buffer l a y e r o n a t e l l u r i u m - d o p e d s u b s t r a t e .
It should be noted that the methods for the study and reduction of the TR that have been developed for epitaxial structures are beginning to be used in MOS, MNOS devices, in dielectric films and in polycrystalline and amorphous semiconductor films for which thickness homogeneity is important. However, an abrupt junction in device heterostructures with a large lattice misfit can result in considerable mechanical stresses and even in destruction; this is avoided by the formation of a TR of the solid solution type. Thus in laser heteroepitaxial structures of binary compounds of the III-V elements, stresses arising at the film interfaces are more dangerous than an extended electrical TR; by extending the T R over the structure an improved conjugation of successive layers is achieved. Liquid phase epitaxy permits 34 effective control of the composition and elastic stresses in multilayer structures of Ga 1 _xAlxAsl _rPy and of changes in TR thickness within the required limits. The main gas transport methods for obtaining device structures are controllable, but at present molecular beam epitaxy in a vacuum is the most promising technique 35 ; the use of this method is impeded by technological difficulties.
6. CONCLUSIONS The present paper and the surveys in refs 3, 8, 9-11, 14 and 36 indicate the marked progress that has been made in solving the problem of TRs in epitaxial structures. The principal factors causing TR broadening have been identified, and many ways of reducing the TRs have been successfully carried out. However, the necessity of producing new instrumental epitaxial structures, e.g. for optoelectronic devices, for avalanche diodes 37 and other devices, presents new problems which require further investigation. It should be borne in mind that the criterion for the presence or absence o f a TR is the level of engineering and measurement precision, and requirements on the T R nature are determined by those on the instrumental parameters. Further improvement of the methods for finding inhomogeneities in films will favour a more complete understanding of the proeesses of formation of TRs and their removal. However, even the controllable deposition of monolayers of the required composition in molecular beam epitaxy does not exclude the influence of the substrate--does not remove the TR problem.
24
L. N. ALEKSANDROV
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2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
L.N. Aleksandrov, Report at the All-Union Symp. on Electronic Processes on the Surface and in Single-crystalline Layers of Semiconductors, Novosibirsk, November, 1967. In Semiconductor Physics, U.S.S.R. Academy of Sciences and the Institute of Electrical Engineering, Novosibirsk, 1968, p. 3. Yu. D. Cistjakov, H. C. Schneider and C. Weinhold, in Epitaxie Endotaxie, VEB Deutscher Verlag fiir Grundstoflindustrie, Leipzig, 1969, p. 15. L.N. Aleksandrov, Vortrags, Mikroelektronik 4, Oldenbourg, Munich, Vienna, 1970, p. 13. H. Mayer, in Advances in Epitaxy and Endotaxy, VEB Deutscher Verlag fiJr Grundstoflindustrie, Leipzig, 1971, p. 63. L. Hollan, J. Hallais and C. Schiller, J. Cryst. Growth, 9 (1971) 165. B.S. Lisenker, I. Ye. Maronchuk, Yu. Ye. Maronchuk and A. P. Sherstyakov, l:v. Akad. Nauk SSSR, Neorg. Mater., 7 (1971) 741. F. Hasegawa, J. Electrochem. Soc., 119 (1972) 929. L.N. Aleksandrov, Phys. Status Solidi A, 9 (1972) 11. L.N. Aleksandrov, J. Cryst. Growth, 31 (1975) 102. L.G. Lavrentyeva and M. D. Vilisova, Izv. Sib. Otd. Akad. Nauk SSSR, Set. Khim. Nauk, 2 (1975) 58. L. N. Aleksandrov, in Growth and Doping o f Semiconductor Crystals and Films, Nauka, Novosibirsk, 1977, Part 2, p. 5. L.N. Aleksandrov and 1. A. Entin, Phys. Status Solidi A, 27 (1975) 665. L.N. Aleksandrov and R. V. Loginova, Kristallografiya, 17 (1972) 1031. L.G. Lavrentyeva, in Gallium Arsenide, Vol. 6, Izd. Tomsk University, Tomsk, 1975, p. 95. L.N. Aleksandrov and R. N. Lovyagin, Vacuum, 26 (1977) 8. L.N. Aleksandrov and R. N. Lovyagin, Thin Solid Films, 20 (1974) 1. Yu. V. Agrafenin, L. P. Bashukova, I. Miotkovsky and A. P. Sherstyakov, in Generation of SHF Vibrations by using the Gunn Effect, Sibirskogo Odteleniya Akademie Nauk SSSR, Novosibirsk, 1974, p. 344. T. Saito and F. Hasegawa, Jpn. J. AppL Phys., 10 (1971) 197. V.F. Dorfman, B. N. Pypkin and A. L. Ochertyansky, Kristallografiya, 17(1972) 1225. T. Katoda, F. Osaka and T. Sugano, Jpn. J. Appl. Phys., 13 (1973) 561. A . V . ChoandF. K. Reinhart, J. Appl. Phys.,45(1974) lO12. T.N. van der Merwe, Surf. Sci., 31 (1972) 198. C . A . S . BallandC. Baird, ThinSolidFilms, 41(1977)9. M.G. Milvidsky and V. B. Osvensky, Kristallografiya, 22 (1977) 431. L.N. Aleksandrov, Formation Kinetics and Solid Layer Structures, Nauka, Novosibirsk, 1972. L.N. Aleksandrov and I. A. Entin, Kristallografiya, 20 (1975) 1140. F. Hasegawa and M. Suga, IEEE Trans. Electron Devices, 19 (1972) 26. P. Wang and R. Bracken, Proc. 3rdlnt. ConJ~on Chemical Vapour Deposition, Utah, 1972, American Nuclear Society, Hinsdale, Illinois, p. 755. E.D. Bullimore, R. R. Bradley, J. P. McCechan and F. A. Myers, Electron. Lett., 8 (26) (1972) 629. Yu. V. Agrafenin, Mikroelektronika, 4 (1975) 161. A.I. Frolov, P. B. Boldyrevsky, B. V. Kozeikin and Ye. B. Sokolov, Izv. Akad. Nauk SSSR, Neorg. Mater., 13 (1977) 726. A. Doi, T. Toyabe and M. Migitaka, J. Jpn. Soc. Appl. Phys., Suppl., 43 (1974) 217. A.P. Petrov, V. P. Demyanenko and L. A. Khomenko, Elektron. Tekh., Set. Poluprovodn. Pribory. 5 (1974) 93. G.A. Rozgonyi, P. M. Petroff and M. B. Panish, Appl. Phys., 24 (I 974) 251. A.G. Cossard, P. M. Petroff, W. Weigrnann, R. Dingle and A. Savage, Appl. Phys. Lett., 29 (1976) 323. L.N. Aleksandrov, in Semiconductor Films for Microelectronics, Nauka, Novosibirsk, 1977, p. 48. 1. A. Fomin, G. G. Akimov and V. V. Lebedev, Elektron. Tekh., Ser. Mater., 12 (1975) 25.
13
TRANSITION REGIONS IN EPITAXIALLY GROWN SEMICONDUCTOR FILMS AND DEVICES L. N. ALEKSANDROV Institute of Semiconductor Physics, Siberian Branch of the U.S.S.R. Academy of Sciences, 630090 Novosibirsk (U.S.S.R.)
Consideration is given to the principal physical factors in the formation of transition regions between a substrate and an epitaxial film. The transition region indicates a thickness inhomogeneity of the film structure, and this has an influence on size effects. From analysis of experimental data on the nature and form of transition regions and from theoretical descriptions of the mechanisms of epitaxial film growth, methods of reducing the thickness of film-substrate transitions are demonstrated. It is possible to produce multilayer film structures for devices in optoelectronics and microelectronics with no noticeable film-film transition regions by using small inertia vacuum methods and molecular beam epitaxy.
1. INTRODUCTION The speed of response and the packing density of elements in electronic and optoelectronic computing systems have been increased by widespread use of devices and apparatus with three-dimensional multilayer active regions. Unlike diffusion methods and ion doping, epitaxial deposition permits the production of an unlimited number of single-crystal layers of different conductivities in any sequence. Epitaxial methods are successfully used in the production of multilayer structures for devices with Gunn diodes (the n + - n - n - - n ÷ ÷ type of gallium arsenide), in the production of double-laser heterostructures, in the formation of waveguide structures in integrated optics and in the production of multilayer structures on silicon and germanium for avalanche photoreceivers. Epitaxial deposition requires certain conditions that depend on the crystalline lattice structure of the deposited substance, the temperature, oversaturation, the state of the substrate surface, the action of external fields and radiation. However, epitaxial formation and the further growth of semiconductor films in the substrate-film interface are accompanied by the formation of a transition region (TR) whose features differ from those of both the substrate and the film. These TRs have a thickness of from several interatomic spacings to tens of microns, and manifest themselves in all film structures of semiconductor electronics, in laser and opto-acoustoelectronic devices, in film detectors of nuclear radiation, in diode transistor charge-coupled device matrices, in integrated circuits and in waveguide heterostructures. For the discrete devices of semiconductor electronics produced in the 1960s, with a film about 10-20 ~tm thick, it was possible in most cases to consider the TR to be a geometrical two-dimensional
14
L. N. ALEKSANDROV
interface and to neglect its thickness, but in the devices of microelectronics with their dramatic reduction in the thickness of the active region of the films the TR must be carefully studied. The problem arose of determining the physical processes that cause the development of the TR in epitaxial film growth and that prevent an abrupt change in the concentration of doping impurities, in the concentration of charge carriers and in their mobility at the film-substrate interface. Over the last decade numerous theoretical and experimental investigations on the nature of TRs, on their structure and on ways of reducing them were carried out. The first surveys of this problem, published in 1969-72, promoted systematization of the data obtained, made the conventional concepts ofepitaxial film growth more complete and precise. and speeded up the use of new methods in film production ~-s. The improvements of the technique of capacitance-voltage measurements of the concentration distribution of charge carriers through the film thickness, of electron microscope methods for studying film structures and interfaces and of optical diffraction methods for studying film growth, and the use of optical and current-voltage measurements and instrumental parameters of the structures obtained to describe a film-substrate interface promoted a better understanding of the causes of formation ofTRs9-11. The removal of the T R is part of the general problem of producing films of homogeneous thickness. The criterion of homogeneity became the constancy of local values of the parameters of the film through its thickness. A careful consideration of the T R in semiconductor films necessitates the elimination of the influence of a size effect. Thus the current state of the problem of TRs in epitaxial films is closely associated with the development of the theory of size effects. To make the treatment of and the identification of the reasons for TR formation more convenient, the major factors are divided into three groups: the influence of the substrate, the influence of growth processes, and the influence of changes in an initial phase. Phenomenologically TRs can be considered to be regions of a near-boundary phase of the solid solution type in the substrate and the film. In accordance with the limits of solubility of the film and substrate substances, phases of intermediate composition can be formed, and the mismatch of lattice parameters in heteroepitaxy leads to misfit dislocations and stress fields 2" 12. The formation and properties of TRs have been studied in more detail in epitaxial films of silicon, germanium and binary compounds (gallium arsenide, gallium phosphide, indium arsenide) grown on semiconductor or insulating (sapphire, spinel) substrates. In most practical problems, the TR thickness is determined as the film thickness over which the charge carrier concentration changes by a factor of ten compared with that at the boundary with the substrate (or another film), if further change of the concentration may be neglected. In theoretical calculations we used the following relation for the change in the concentration gradient 13 :
dn/dx <~0.01t~*(d)
(1)
where ~* is the established value of the gradient at a distance d. The T R thickness is determined by the whole spectrum of structure-sensitive film properties, but for applications in devices the ones of great importance are the type and concentration
15
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
of the charge carriers, their mobility, the diffusion lengths, the lifetimes, the refractive indices and other optical and electrical grating parameters. 2.
THE TRANSITION REGION AS A MANIFESTATION OF FILM THICKNESS INHOMOGENEITY OR OF A SIZE EFFECT
The properties of a film are determined by its surface and its volume. The thinner the film, the more is the surface contribution. The thin film state of a solid is characterized by a change in properties with thickness. The physical measure of "'thinness" is the relation of the film thickness to the range of action of characteristic parameters, e.g. the Debye radius ~b of charge shielding, the mean free path 2 s of the charge carriers, the distance between dislocations. In semiconductor films the resistivity p increases for d < 2s owing to an increase in the scattering of charge carriers over the surface (Fig. 1, curve 1), although from the constancy of p for d >> 2s the film itself is homogeneous through its thickness. However, the change o f p with thickness for d > 2~ (Fig. 1, curve 2) is not connected with a size effect but is caused by the inhomogeneity of the film structure through the thickness, The quantitative separation of the influence ofinhomogeneity from that of a size effect is not difficult. 10-~
-~
A
• ....... 10-2
I
I0 2
d (~.ml
fit,.
_e
., 7_ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A, ,i
"1
1i"
Fig. 1. The change in film resistivity with thickness for homogeneous (curve 1) and inhomogeneous (curve 2) films. Fig. 2. An epitaxial film considered as a sequence of layers d i thick with conductivity tr~ on the substrate (do, ao).
In general cases a film with a substrate is a multilayer structure d 1 + d o thick (Fig. 2), where the thickness dofall film layers is ~ d r If the electrical conductivity of the substrate is % and that of each layer d; thick is tri, then the effective electrical conductivity of the film is at = d l - t ~ trid i
(2)
i=1
With a high resistance or insulating substrate, measurements give an effective value of a t for the film when trod o ,~ trld r By measuring the electrical conductivity of the film as it grows or during layer-by-layer etching, we obtain a sequence of effective values of o'(~ii = 1dl). The relevant local values are determined by the relation ~ ( Z i + t d~)d~ + ~ - ~ ( ~ i dl)dl ai ~ dl + 1
(3)
16
L . N . ALEKSANDROV
The difference in the nature of the change o f a i and a ( ~ i d i ) with thickness allows the degree of film thickness inhomogeneity and the contribution of surface (boundary) charges to be estimated. The purer and the thinner the film, the more noticeable the influence of surface properties on the effective values of its parameters. The effective concentration neff of charge carriers in a film of thickness d is determined by their concentration n o in the volume and ns on the surfaces from the summation relation n o V + 2nsS
ne" -
V
2n s
- no + d -
(4)
where V and S are, respectively, the volume and the surface of the film. For 3, ns = 101o c m - 2 and d ~ 10 -3 cm, nef~ decreases monotonically with an increase in film thickness from microns to tens of microns, even though the film is homogeneous in thickness, i.e. n o = constant. An apparent film inhomogeneity is also manifested for thicknesses d > rD. The real local values of the carrier concentration n~ and of the mobility #~ in the layers can be determined by calculation for the specific type of multilayer film using an expression similar to eqn. (3). Note that although in some work the usual size effects are wrongly assigned to the influence of the TR, in other experimental work the changes in film properties caused by the interface inhomogeneity, i.e. the TR, are assigned to a size effect ! n o <~ 2 n s / d , e . g . in pure germanium films with n o = 10 ~3 cm
3.
EXPERIMENTAL STUDIES OF TRANSITION REGIONS
Table I summarizes the results of experimental studies 8-11.14 of defects and charge carriers in the TR. Most attention is given to the fit of the crystallographic structures of the epitaxially conjugated substances of film and substrate, to the preparation of the substrate surface before epitaxy, to impurity evaporation and diffusion and to the growth processes, the properties and the influence of environmental conditions on the properties. It has been shown that improvement in cleaning carbide particles and oxide impurities from the substrate surface has a direct influence on the epitaxy mechanism: step motion occurs instead of the development of three-dimensional growth centres. On an atomically pure stepped silicon surface obtained by high temperature annealing (1300°C, 20 min) in an ultrahigh vacuum, epitaxial film growth by ion sputtering or from a molecular beam follows the steady state surface relief ~5 A system of growth steps made as in ref. 13 accelerates the approach to a steady state relief and reduces the TR to less than 0.5 iam over the film structure. Heteroepitaxial germanium growth on this surface begins with the formation of a pseudomorphic film, and the appearance of misfit dislocations is followed by the stage of steady state growth 16. However, the reduction of an impurity TR also necessitates suppression of diffusion processes by a decrease in the epitaxy temperature. In the gas transport methods for the epitaxial deposition of germanium, silicon and gallium arsenide films, a reduction in the TR of the charge carrier concentration was observed when deep polishing and purifying-gas etching of the substrate surface was carried out before epitaxy I L ~4. It was found that atoms of doping impurities and of the principal substance were evaporated in the substrate surface cleaning. Complicated profiles of the charge carrier distribution were formed in the epitaxial
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
17
TABLE I P R I N C I P A L CAUSES OF T R A N S I T I O N R E G I O N F O R M A T I O N I N E P I T A X I A L L Y
GROWN FILMS
Influence of the substances and the substrate Stale
Growth processes
Changes in the initial phase
Misfit of the crystalline lattices of the film and substrate
Three-dimensional nucleation in the initial epitaxy stage
The time of the start of stationary conditions of growth
Difference in the elastic moduli of the film and substrate
Changes in growth surface microrelief
Changes in the temperature of the sources and the substrate
Initial orientation and treatment and cleaning of the substrate surface
"'Evolutionary selection" of grains and blocks and recrystallization
Changes in impurity concentration
Impurity diffusion from the substrate
Dynamics and relaxation of defects
Self-doping through the surrounding phase
Changes in the substrate by thermal treatment and etching
Impurity diffusion from the film
Changes in external fields
structures d e p e n d i n g on the relative velocity o f e v a p o r a t i o n o f d o n o r a n d a c c c p t o r impurities and, in b i n a r y c o m p o u n d s , o f a t o m s o f the m a j o r c o m p o n e n t s . F i g u r e 3 shows the possible d i s t r i b u t i o n s o f electrons in a h o m o e p i t a x i a l G a A s film on a d o p e d substrate d u r i n g growth o f an n ÷ - n structure for a G u n n diode. O n t e l l u r i u m - d o p e d substrates direct film d o p i n g was o b s e r v e d (curve 1); by reducing the d o p i n g it was possible practically to r e m o v e the T R (curve 2). A high resistance region which d e g r a d e d the d i o d e p a r a m e t e r s (curve 3) was f o r m e d due to silicon d o p i n g o f the film, because o f the u n s t e a d y c a p t u r e b e h a v i o u r that is c o m m o n in the initial stages o f e p i t a x y ; this was m o s t l y d e t e r m i n e d by the s u b s t r a t e surface p r e p a r a t i o n . A change in the AsC13 c o n c e n t r a t i o n in the v a p o u r phase a n d tin d o p i n g f a v o u r e d the r e m o v a l o f the TR.
Film
'~
$~lrale
1015
I 'o
J
__z
10I/'
I
I
I
I
I
I
2
3
~
S
d ll~ml
Fig. 3. The distribution of charge carriers (electrons) in a homoepitaxial GaAs film on a doped substrate: curve 1, doping of the film from the substrate; curve 2, the ideal case of no TR; curve 3, formation of a high resistance region.
18
L. N. ALEKSANDROV
On tin-doped GaAs films it was found that the total concentration of donors and acceptors decreased markedly from 1018 to l0 ts c m - 3 with an increase in the growth rate from 0.06 to 0.47 p.m min l; this is associated with a change in the capture coefficient and with the suppression of diffusion processes near the film substrate interface 17. The dependence of the film doping level on growth rate has been used in theoretical estimations of the TR thickness under varying environmental conditions. Long relaxation times in complicated gas transport systems slow down the commencement of steady state growth, and every change in growth rate, cessation, slowing down or acceleration, results in a change in film conductivity. Slow changes of the environmental conditions result in monotonic changes in conductivity; fast ones give rise to unsteadiness and abrupt changes in properties t 8. A change in the ratio of the partial pressures of the components during G a A s film growth gave rise to a shift of the maximum dislocation density into the substrate for growth on the (111) A face and into the film for growth on the (111) B face. Thus excess arsenic widened the structural T R in the first case but narrowed it in the second t9 because the total film non-stoichiometry was reduced and the film thickness homogeneity was increased. The complication of stabilizing a vapour phase state in order to obtain solid solutions in systems o f l l I V or I I - V I elements usually results, in view of the variety' of associated reactions, in an extension of the thickness of the T R to tt 20-40 p.m. Nevertheless, Sugano and his collaborators 2° have succeeded in obtaining films of solid solutions of indium-gallium arsenides with an inhomogeneity region of hole mobility and electrical resistance of about 3 p.m in an overall film thickness of 5 p.m. The suitability of vacuum deposition methods for obtaining homogeneous films of solid solutions is evident. Even the first work on GaAs film epitaxy from molecular beams showed the possibility of using their short time lag to reduce the T R in n + n structures down to hundredths of a micron 21 . The production of supertattices based on solid solutions of gallium-aluminium arsenides with a period of several interatomic spacings also confirmed the possibility of a sharp change in concentration at the film-film interface in epitaxial deposition. However, the action of other factors, say, the substrate surface treatment and cleaning, and diffusion or self-doping from the substrate, was still evident.
E
0.5
06
1
0.8
10 X (~m)
1.2
Fig. 4. The spectral characteristic of Mo-p-Si-n-Si photodiodes at 296 K obtained by high temperature treatment of n-Si with resistivity 0.3 f2 cm (curve 1) and 7.5 f~ cm (curve 2).
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
19
In investigations of phosphorus-doped silicon substrates which were cleaned by high temperature annealing in an ultrahigh vacuum before epitaxy, it was shown that a layer of hole-type conductivity of up to 1 ~tm was formed in the near-surface region 16. P ÷ - p - n structures with good photoelectric properties were formed by epitaxial deposition on the substrate surface. The maximum spectral sensitivity of the diodes was at a wavelength of about l lam (Fig. 4), the detectability (maximum) exceeded 1013 cm Hz 1/2 W-1 and the integrated sensitivity was 9 m A I m - 1. The formation o f a p layer during annealing was ascribed to phosphorus diffusion to the surface and its evaporation with other doping elements and silicon. The stationary profile of the phosphorus concentration and the depth of the p-n junction that is limiting for a given temperature were established from the ratio of the evaporation rates for phosphorus and silicon. Layer-by-layer etching and capacitance-voltage measurements have indicated the possibility of obtaining the concentration profile of the electrons from the diffusion curve for the accelerated diffusion in the nearsurface region due both to the participation of vacancies and to the possible displacement of other donor and acceptor impurities.
4.
THEORETICAL DESCRIPTION OF THE PROCESSES OF TRANSITION REGION FORMATION
In quantitative studies of the TR most attention has been paid to misfit dislocations and elastic stresses, to film growth kinetics and to the impurity distribution dependence on the growth-limiting mechanism. Estimations of the critical thickness of a coherent conjugation region for the film and substrate before misfit dislocation formation were made by van der Merwe 22, who in further work took into consideration the energy of interaction of dislocations with the film or substrate surface 23,12. The following relation is used in estimating the lattice parameter misfit: -
as - at a~
~
2 as - at a~ -t-af
(5)
where af is the lattice parameter of the film and a s that of the substrate. The quantity e is determined by the concentration dependence coi and the temperature dependence Ki of the lattice parameters, because film deposition is carried out at some temperature T and doping additions are present in both the substrate and the film. At concentrations C i of n different impurities the lattice parameter of, say, the film in eqn. (5) is determined from a r = aor ~ (1 + toiCi)(1 q- KfT)
(6)
i=1
By making use of the difference in size of the atoms introduced and by combined doping we can obtain a junction with small lattice misfit. From the equation e(C~s, C~f, T) = 0 we can find the impurity concentrations in the film and substrate and the epitaxy temperature that minimize stresses in the junction a' 24. Consideration of the elastic properties in the substrate-transition region-film system for coherent and incoherent interfaces (Fig. 5) allowed us to estimate the interaction force of
20
L. N. ALEKSANDROV
dislocations with phase interfaces and the influence of the misfit dislocations. The image stresses that influence the dislocations were determined using the analogy between the electrostatics of a point charge and the elastic statics of dislocations. The forces that draw a dislocation out of the film to the film surface or the substrate interface were determined for different relations between the moduli of elasticity of the layers and their thicknesses a 1, a - a l . An increase in the coherent TR length favoured an increase in the forces. At the incoherent interface and for x o > 0.2 (Fig. 5(b)) the area of action of the stresses was extended. The longer the TR, the more intensive was the concentration of misfit dislocations in the TR ~2. The impurity TR thickness was calculated by solving eqn. (1) and using ~3
Nim nim - Np + Nim
Nim -- ~ Np
t'~ 1
(7)
which gives the relation between the concentration n~mof impurities captured during growth and the effective film growth rate ven; Nim and Np are the atomic fluxes of the impurity and of the principal substance to the growth surface. An assumption concerning the constant flow of impurity from the gas phase is valid if the flow is limited by mass transfer but not by surface reactions. The effective film growth rate was determined from the formation of three-dimensional clusters and from the motion of surface steps: nucleation prevails on single-crystal faces and growth step motion on vicinal ones. Since a change with time of ve~ in the initial growth stage takes place only in the first case, it is possible to reduce the TR by enhancing the contribution of layer growth by step motion 8. The calculated results were in good agreement with experimental data for GaAs and germanium films. A statistical probability description of the process of film formation in the case
2
xo
Fi[rn
Transition ayer
Substrate I 1
(a)
(b)
I 2
I 3
1 /,
1 5
I 6
I 7
~3d~2t
Fig. 5. The film-substrate transition region for (a) coherent conjugationofthecrystallinelatticesand (b) incoherent conjugation of the crystalline lattices with the formation o f misfit dislocations. Fig. 6. The change with time of the relative rate of filling of all simultaneously grown layers: curve 1, homoepitaxy on a perfectly smooth substrate; curve 2, homoepitaxy at poisoned initial steps; curve 3, homoepitaxy at active initial steps. L is the step length, C2. t is their growth rate; fld is a kinetic coefficient.
of the development of three-dimensional growth centres permitted us to estimate the minimum TR thickness as the limiting thickness of a continuous epitaxial film 25. For a constant grain growth rate c determined by surface reactions and a nucleation rate I, we used the following relation to estimate dm:
TRANSITION REGIONS IN SEMICONDUCTOR FILMS AND DEVICES
dm = K , ( c / l ) '/3
21 (8)
For diffusion-limited growth d m = K2(D/1)'/"
(9)
where D is the diffusion coefficient. The coefficients K, and K 2 (approximately unity) are determined by the geometry of the growth centres. With I ~ 1016 cm-2 s -1 andc ~ 10-6 cm s-l, dm ~, 1 pm. For layer-by-layer growth the TR was estimated as the thickness of a nonsteadily formed film with simultaneous overgrowth of several layers on the substrate and with impurity atoms captured by roughnesses and at steps 26. In the calculations we used the relations between the fraction Pm of filling of the ruth layer and an "extended" fraction P,,xx of filling of the same layer at time t: P,,,ex =
I2s(t - r)P m_ l(z) dr
0o)
where 12 is the two-dimensional nucleation rate and s ( t - r ) is the area of growth centres. This relation corresponds to the kinetic equation dP, J d P ~ , x
=
1-P,~
(II)
An expected impurity profile calculated from the change ifi the area of an active film growth surface is given in Fig. 6. Calculations for germanium homoepitaxy gave 5-20 nm for the TR depending on the growth-limiting mechanisms and on the substrate surface state. Monte Carlo calculations of film growth are promising for a detailed description of TR formation.
5.
WAYS OF REDUCING THE TR THICKNESS IN FILMS AND DEVICES
This progress in our understanding of the causes of .TR formation and in the removal of TRs in epitaxial structures does not reduce the topicality of the problem. The use of film materials in technology is increasing; new instruments are being produced, and requirements for the interface structure of homojunctions and heterojunctions are becoming more and more strict. We have already mentioned the deterioration of the parameters ofa p--njunction in GaAs devices due to the TR: the breakdown voltage is decreased and the leakage current increasedXo. In devices with n-n + structures, reduction of the electron concentration in the TR results in deterioration of the frequency properties, in an increase of the threshold voltage of Gunn generators and in generation suppression; a concentration increase reduces the breakdown voltage and the power of the devices. The removal of a high resistance region increased the efficiency of generators by 20 ~o27. In silicon epitaxial p-n junctions, when the TR was reduced from 3-4 to 1-2 lam by a decrease in the epitaxy temperature during growth by 100 °C, the breakdown voltage was increased by 60 ~2a.
22
L. N. ALEKSANDROV
Reduction of the TR and improvements in device parameters have been obtained by better levels of substrate surface perfection and purity and purity of the starting materials, by stationary deposition conditions, by suppression of selfdoping as well as by special methods. Table II summarizes the possible ways of reducing the TR. TABLE II WAYSOFREDUCINGTHETRANSITIONREGION Action on the substrate state and surface
Changes in growth processes
Action on the initial phase
Substrate surface cleaning
Decrease in deposition temperature and oversaturation
Stabilization of the sourcesof dopingof the main substance
Production of a systemof growth steps
Combined film doping
Conservation of vacuum purity or gas mixture composition
Deposition of bufferepitaxial layers
Conservation of vicinalityof the growth surface
Constancyof deposition temperature, mixing
Protection of the reverse side of the substrate
Two-stepconditions of film deposition
Stabilization and homogeneity of external fields
Reduction of the temperature and time of substrate treatment
Reduction of the period of non-steadygrowth
Production of the liquid phase on the growth surface
Worthy of special attention are the methods of production of intermediate (buffer) epitaxial layers between the substrate and the deposited film. The introduction into devices of a buffer layer that repeated the film properties allowed us to replace the substrate-film transition with an active film-film transition. The T R indicated only the time lag from the introduction of the doping addition, and the profile of the other impurities and the general deposition conditions were kept constant; a new substrate had no undesirable influence 29. Using buffer layers in epitaxial structures for Gunn diodes we achieved a difference in electron concentration of more than 100 times in a distance of 0.1-i.5 p,m. Figure 7 shows the influence of a buffer layer on the T R thickness for tellurium doping. In this case 3° with a reduction of the n ÷ layer to 3 lain the TR was extended to 10 Ixm. In germanium doping of GaAs the T R between the buffer and the doped film was decreased to 0.1 lam when the flow velocity of the gas mixture was changed to give a fourfold change of the composition of the mixture in the reactor 31. In the liquid phase epitaxy method the T R was decreased considerably by rapid transfer of the substrate to solutions with different amounts of doping elements. Epitaxial p + - p - n - n + structures for high power Gunn diodes at a frequency of 20-30 G H z and with sharp (less than 0.1 lam) junctions between films were obtained in one growth cycle 32. Successful use of the methods of reducing the TR in silicon p ÷ - n - n + planar structures in integrated circuits for microelectronics has resulted 33 in a change in resistivity from 0.01 ~ cm (in the substrate) to 0.7 fl cm (in the film) over a distance of less than 0.2 lam.
T R A N S I T I O N R E G I O N S IN S E M I C O N D U C T O R FILMS A N D DEVICES
2
10~
10 t5
Buffer layer
fi
I
23
I
I ~,
I
Fig. 7. T h e e l e c t r o n d i s t r i b u t i o n in a t h r e e - l a y e r epitaxial n ÷ + n - n + s t r u c t u r e o f g a l l i u m a r s e n i d e with a thick buffer l a y e r o n a t e l l u r i u m - d o p e d s u b s t r a t e .
It should be noted that the methods for the study and reduction of the TR that have been developed for epitaxial structures are beginning to be used in MOS, MNOS devices, in dielectric films and in polycrystalline and amorphous semiconductor films for which thickness homogeneity is important. However, an abrupt junction in device heterostructures with a large lattice misfit can result in considerable mechanical stresses and even in destruction; this is avoided by the formation of a TR of the solid solution type. Thus in laser heteroepitaxial structures of binary compounds of the III-V elements, stresses arising at the film interfaces are more dangerous than an extended electrical TR; by extending the T R over the structure an improved conjugation of successive layers is achieved. Liquid phase epitaxy permits 34 effective control of the composition and elastic stresses in multilayer structures of Ga 1 _xAlxAsl _rPy and of changes in TR thickness within the required limits. The main gas transport methods for obtaining device structures are controllable, but at present molecular beam epitaxy in a vacuum is the most promising technique 35 ; the use of this method is impeded by technological difficulties.
6. CONCLUSIONS The present paper and the surveys in refs 3, 8, 9-11, 14 and 36 indicate the marked progress that has been made in solving the problem of TRs in epitaxial structures. The principal factors causing TR broadening have been identified, and many ways of reducing the TRs have been successfully carried out. However, the necessity of producing new instrumental epitaxial structures, e.g. for optoelectronic devices, for avalanche diodes 37 and other devices, presents new problems which require further investigation. It should be borne in mind that the criterion for the presence or absence o f a TR is the level of engineering and measurement precision, and requirements on the T R nature are determined by those on the instrumental parameters. Further improvement of the methods for finding inhomogeneities in films will favour a more complete understanding of the proeesses of formation of TRs and their removal. However, even the controllable deposition of monolayers of the required composition in molecular beam epitaxy does not exclude the influence of the substrate--does not remove the TR problem.
24
L. N. ALEKSANDROV
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