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Liquid phase electroepitaxy of semiconductor compounds
Prog. Crysta/Growth and Charact. 1986,Vol. 12, pp. 29-43
0146-3535/86$0.00 + .50
Printed in Great Britain.All rights reserved.
Copyright~) 1986 PergamonJournalsLtd.
LIQUID PHASE ELECTROEPITAXY OF SEMICONDUCTOR COMPOUNDS T. Bryskiewicz Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
1.
INTRODUCTION
The liquid phase electroepitaxiai growth method has been developed in recent years [i-68]. This technique utilizes essentially the same equipment as that used in standard liquid phase epitaxy but modified to permit the passage of an electric current through the substrate/ solution interface (Fig. i) [i]. Two stainless steel or molybdenum electrodes are threaded into the slider and the solution holder, respectively, and both parts of the graphite boat are electrically isolated with boron nitride. Thus, electric current can flow only when the substrate is brought into contact with the solution. A uniform, low resistance electrical contact between the bottom part of the substrate and graphite slider is essential for satisfactory growth [2-8]. In a typical growth experiment the solution is heated at the growth temperature for several hours, in order to insure its saturation with source material. Finally, the substrate is brought into contact with the solution and electric current is passed across the substrate/solution interface as the sole driving force of the epitaxial growth. Deposition of the material is terminated by switching the current off and moving the slider. Liquid phase eletroepitaxy (LPEE) has since been employed for the growth of InSb [i], GaAs [3-5, 9-21], GaP [22, 23], GaSb [24-26], InAs [27], InP [6,28], SiC [29], as well as GaAIAs [2,7,8, 30-38], GalnP [39,40], GaAsSb [41], GaAISb [24-26], InGaAs [42,43], InAsSb [44], HgCdTe [45,46], and InGaAsP [47].
Fig. I - Schematic diagram of the electroepitaxial growth system. (Ref. [i]).
The idea of crystallization induced by the passage of an electric current is not new. Electrodeposition of electrically conducting materials from aqueous solutions or molten salts, a closely related technique, has been studied extensively for many years. This growth process is based on ionic transport in the bulk solution driven by the electric field. The current is a measure of both the rate of flow of ions through the solution and the rate at which the ions are deposited on the crystal surface of the electrode. However, in electroepitaxy the metallic electrode is molten while the epitaxial layer, which can be treated as the solution with
29
30
T. Bryskiewicz
ionized impurities and free charges, is solid. This configuration means that many of the physical phenomena occurring in electrodeposition are inherently different from those in liquid phase electroepitaxial growth. The aim of this paper is to show how the achievements in improved surface morphology and homogeneity as well as improved electrical parameters of the layers depend on better and more detailed understanding and control of physical phenomena occurring in liquid phase electroepitaxy. The details of results obtained during the early developmental stages of this growth technique can be found in previous review papers [48,49]. 2.
GROWTH KINETICS VS. MASS TRANSPORT MECHANISMS
The observed growth rate-current density relationship is linear in most cases of electroepltaxy [2,3,6,10,12,15,22,27,29,30,33,42,43, 46,47] but sometimes tends to be superlinear [3,10,28,41] (Fig. 2). It was originally proposed that Peltier cooling at the growth interface was solely responsible for supersaturation of the solution and epitaxial growth [i-3]. Subsequently, it was demonstrated that migration of solute species due to electrotransport constitutes the essential contribution to supersaturation [9,12 ,23]. However, in experiments using both 2 mm thick p- and n-type substrates it was shown that el ~ctroepitaxial growth kinetic is dominated by the Peltier cooling and convection [32]. Thus, quantitative analysis of the growth kinetics in LPEE requires taking into consideration all the above transport mechanisms of crystallizing material towards the interface.
Average GrowthRote (#m/rnin)
AveroQe Growth Rote
(/zm/rnin) 0.5
hO
0.4
/ /
0,8
o,,
• 800°C
/760°C
O.3
/ /
•
760°C
Z /
L Current Density [A/cm2) n~ Substrates
o ~ f - - " - ' - ~ 0 5
,
IO 15 Current Density(A/cm2) Semi-Insulating Substrates
Fig. 2 - Average growth rate versus current density for electroepitaxial growth of tin doped GaAs on n + and semi-insulating substrates at 680°C, 720°C, and 800°C (Ref. [i0]). 2.1.
Peltier Cooling
Since the substrate used in electroepitaxy is a semiconductor, and the solution is a metal, they have different thermoelectric coefficients. Thus, the flow of electric current across their interface is accompanied by the absorption or evolution of heat, depending on the current direction. The magnitude of heat (Q) produced per unit time and surface is directly proportional to the current density (J) and Peltler coefficient (Q = ~J) resulting in a stationary temperature gradient at the solution/substrate interface. The interface temperature change (ATp) is roughly directly proportional to the current density (J) and its magnitude is controlled by the growth temperature (To) , solution height (L) as well as by the substrate thickness, conductivity type, and carrier concentration [2,15,30,38,50-57] (Fig. 3). In electroepitaxy the interface temperature decrease AT due to the Peltier effect, typically P • of the order of i o C, induces supersaturation of the solutzon providing solute diffusion towards the substrate, and thus, epitaxial growth.
Liquid phase electroepitaxy
-3
31
n= 2 xl0J? crn-5 n= 2 x1018 c m " 3 p = 2 x I018 cm"5 o semi- insulating
• •
-I.5
rl/s
• IO00#.m
• 350~m o
,,A
-I,0
~'50~n
<3
O s •S O
s
pJ
/
-0,5 I
,
I
-40-30
~ I
,
I
,
-20 _o.~'~
/
""
•
40 Current density, (A/crn 2) MO
212j I
20
30
E
-~ 0
I
I(X~
I
1500
"~.. Subslrate thickness,(/.Lm ) c +1 .S
A'.%% %
c "~2
o
%%% %'%%~ +3
Fig. 3 - Changes in temperature ATp at the GaAs solution interface due to the Peltier effect at 800°C versus current density and substrate thickness (Ref. [15]). 2.2.
Solute Electrotransport
The solutions used in the electroepitaxy of semiconducting compounds are metallic conductors; essentially they exhibit no ionic contribution to the current. This fact means that solute electromigration due to the direct interaction of the electrostatic field with ionized particles is negligible. However, in these solutions as in other liquid metals, migration takes place due to momentum exchange between electrons in the conduction band and solute particles. Under the electric field E induced by the current flow, species in the solution migrate towards the anode with a velocity v = uE, where u is their effective mobility. The efficiency of electrotransport is characterized by the effective charge Zeff=U/Uo, where u o is the real solute mobility. In most metallic solutions the Zef f parameter is negative and its absolute value is much larger than one [12,54,58]. 2.3.
Convection
The primary cause of convection during liquid phase electroepitaxial growth has been identified with the horizontal temperature gradients resulting from pronounced Joule heating at the contacts of the current carrying rods and the graphite segments of the boat [13]. As a criterion of convective flow the magnitude of the thermal Grashof number has to be considered L4 Gr = ~g • - - A T (i) 2 W v where ~, v and g are the coefficient of the thermal expansion, the kinematic viscosity, and the gravitational constant, respectively; L and W are the height and diameter of the solution; AT is the horizontal temperature difference across the solution. On the basis of the experimental data obtained for electroepitaxially grown GaAs [13] it appears that the growth ~rocess is not affected by the convective flow until Gr exceeds a value of the order of i0 . It is not understood, at this time, why such a relatively high value of Gr is necessary before significant convective flow is present in the solution to affect the growth process. However, no quantitative data are available at this time to determine the thickness of such a stabilizing solute layer. It is important to note that in numerical calculations of the growth velocity including convection, a static boundary diffusion layer in a moving solution immediately adjacent to the growth interface, has been assumed (the Nernst's approximation) [15,52,59].
32 2.4.
T. Bryskiewicz Growth Velocity Calculations
In order to calculate the electroepitaxial growth velocity let us assume that at a temperature To a substrate is placed horizontally under a saturated solution of concentration CL(TO) and thickness L (see Fig. 4). Let a source wafer be in turn situated on the surface of the solution. As we know, epitaxial growth at constant temperature can be achieved by passing an electric current across the substrate-solution interface. Since Peltier cooling at the interface produced by the current causes a lowering of the temperature and concentration of the solute down to T 1 and CL(TI) , respectively, the solute concentration and temperature gradients (diffusion and convection) as well as the electric field E (electrotransport) are the driving forces of growth. The equation for the growth velocity V can be carried out from the balance of streams of crystallizing material at the growing interface [12,15,56]
D ~
x=R - UECL(TI) Cs -
V(t) =
CL(TI)
(2)
where D is the diffusion coefficient, x is the distance from the interface, C(x,t) and C are s solute concentrations in the solution and epilayers, and t is growth time.
solid
IC(x,t) source
Cs melt
Fig. 4 - Distribution of the solute
CL(T O)
concentration C(x,t) in the melt and solid: CL and C s are equilibrium solute concentrations in the melt and solid (Ref. [12]).
0 R(t)
L
x ,L
As we see, the growth velocity calculations require estimation of the solute concentration gradient at the growth interface, which in turn can be carried out by solving the mass transport equation with the proper initial and boundary conditions [12,15,33,52,55,56,59-61]. The analytical expression for the growth velocity V, calculated by assuming the semi-infinite solution thickness, is of the form [15]
fDlj2 AT v(t)
=
m\~l
-
u ECL(TI)
P
Cs _ CL(TI)
(3)
in the absence of convection, and D ATp.m" ~ - u ECL(TI) V(t) =
Cs _ CL(TI)
(4)
in the presence of convection, where m = dCL/dT is the liquidus slope defined by the phase diagram, and 6 is the Nernst diffusion layer. The first term in the above equations represents the contribution of the Peltier effect, whereas the second one represents the contribution of electrotransport to the growth velocity, both these terms being linearly dependent on the current density through AT and E, respectively. Consequently,,the calculated growth rate is directly proportional to t~e current density, in accordance with experimental results. The superlinear growth rate-current density relationship observed in some cases is apparently related to the increasing convective flow as the
Liquid phase electroepitaxy
33
current density becomes higher. Equation (3) suggests appreciable contribution of the Peltier effect to the growth kinetics merely at the initial stage of the electroepitaxial growth. However, more precise growth velocity calculations including the limited thickness of the solution have proved that the diffusion term does not tend to zero with time but rather takes ss its finite steady-state value Vdiff [52,55,56,59,60] equal to AT ss = p Vdiff Cs - CL
m u E exp(uEL/D) - 1
(5)
The transient time required for the steady-state growth conditions depends upon the solution thickness L and varies from a few seconds for L = 0.05 cm to several minutes for L = 1 cm [56] (Fig. 5).
t(min)
t(s)
? ,,o,5 !~,5
o,
L = Icm J = I0 A l c m z T =850°C
A r-
IC o )o 5 I ~,5 0.40 L= 0 . 0 5 cm j = IOA/cm z -T=850°C
0,18 =44 3,14
E
"~:
o,I
/
/
0~07 .=E
-
E
,
0,4
3aO .~E
=L t,
> Vu
.
3~D6 >'o
t
> Vu
~ ' V _Vdl ff :,~'t--" - r - - - - . r - . -~. ---.-~-.-- ),02 2 4 6 8 I0 12
Iz
OX>9
,,'_
(m in-V;~
~
I°
sppp
_._~v-v=.~ ....
0~05 E =L
i 2
= 4
~ 6 ,z
...... i 8
,I I0
o=3 >~' 12
3.01
(s-,/2)
Fig. 5 - Time dependence of the growth velocity V and its diffusion contribution V .... in the liquid phase electroepitaxy of GaAs calculated for the solution thickness L = ~ cm and L = 0.05 cm (Ref. [56]). 3.
SURFACE MORPHOLOGY
In the earlier studies of growth by liquid phase electroepitaxy two types of epilayer thickness variations were observed: random fluctuations and systematic variations [6,10,13]. Random fluctuations were typically about ~ 15% for GaAs layers grown with typical current densities of 5 or i0 A/cm 2, and often ~ 20% for layers grown with 15 or 20 A/cm 2, neglecting excess edge growtn which sometimes was equal to the average layer thickness [I0]. Moreover, the formation of several terraces and cusps was favored when one attempted to force growth directly upon the substrates with a current density of 15 or 20 A/cm 2. For current density of 5 or I0 A/cm 2 the terracing was milder and in several cases large areas of the layer were nearly featureless. In addition, the terracing was less severe when growth at 15 or 20 A/cm 2 was carried out upon growth with 5 or i0 A/cm 2 rather than directly upon the substrate. These observations, together with the long-range thickness variations observed in epitaxial layers grown with higher current densities, suggest that all these features depend largely upon the non-uniformity of the current density across the substrate. It was found that non-uniformity of the electrical contact to the back side of the substrate yielded those regions of nonuniform layer thickness [6,10,13]. In the earlier studies of growth by liquid phase electroepitaxy, the back contact for electric current flow between the substrate and graphite was achieved by either using a thin film of Ga or In metal, depending on the substrate material, or by using the liquid metal film separated with a tantalum foil to promote wetting [3,4,6,10]. In either case, some non-uniformity in the contact was observed which was attributed to nonuniform wetting of the back surface of the substrate by the metallic film and to crumbling of the tantalum foil as a result of reaction with the hydrogen ambient in the reaction tube. Poor electrical contacts cause undesirable localized Joule heating, particularly at high current densities. Finally, local variations in the contact resistance lead to variations in the thickness of the epitaxial layers. This disadvantage of growth by liquid phase electroepitaxy has been entirely overcome in recent years. A new electroepitaxial configuration has been developed in which the back side electrical contact to the substrate is formed at the
34
T. Bryskiewicz
growth temperature under high purity hydrogen flow [5,8] (see Fig. 6).
Solution (~/
SS Electrode ,,-TC Fig. 6 - A novel construction of
Slider
J
~-".-b
=
~
~-"
electroepitaxial growth apparatus without back-contact (Ref. [5]).
Substrate/
~.. - .'J
i
"
" -~-TC
Solution
Systematic variations of the epilayer thickness were in turn found to be associated with temperature gradients in the solution [13]. In the presence of convection in the solution the thickness profile of the layers reflects the convective flow pattern. As previously mentioned, the primary cause of convection has been identified with the horizontal t e m p e r ~ u r e gradients resulting from Joule heating at the contact of the current carrying rods and the graphite segments of the boat. It can be eliminated by minimizing the temperature gradient across the solution through reduction of the system's resistance and by positioning the solution well in the furnace so that the horizontal gradient in the solution, prior to current flow, is of the same magnitude but opposite in sign to that induced by Joule heating [13]. Epilayers grown by electrotransport-controlled electroepitaxy in which random as well as systematic thickness variations have been eliminated are flat and exhibit no terracing or other morphological defects typically found in layers grown by thermal LPE [7,14,18,26,43]. The occasional appearance of defects such as dishes or hillocks are invariably related to defects in the electrical contact of the substrate [14]. The pronounced difference in the surface morphology of the layers grown by electroepitaxy and those grown by thermal LPE can be explained with fundamental differences in the growth mechanisms involved in these two growth methods. In electroepitaxy, supersaturation takes place in the immediate vicinity of the growth interface and growth is controlled by the rate of transfer of solute, under an electric field, towards the interface. It means that growth takes place at near equilibrium (isothermal) conditions and interface instabilities due to constitutional supercooling do not occur. The unusual features of liquid phase electroepitaxy with regard to interface stability can be justified on the basis of the interface stability model of Mullins and Sekerka [63]. The temperature gradient (G) at the interface required to overcome the onset of constitutional supercooling is
G > ~
1 -
(6)
From Eq. (6) it is apparent that the value of G required to prevent constitutional supercooling decreases with increasing contribution of electrotransport (VE) to the overall growth velocity V, and thus it is always smaller than in thermal LPE [63]. 4.
DOPANT SEGREGATION
One of the most important features of liquid phase electroepitaxy is its potential for the growth of very homogeneous wafers when the current density is fixed [24,28,30,33,34, 40,44,64]. As an example, doping profiles typical for InP epilayers grown at constant temperature and current are shown in Fig. 7 [28]. However, modulation of the dopant concentration can be achieved in the growing epilayer by a corresponding variation of the current density [3,4,10,ii,17,28,64-66]. The dependence of the carrier concentration in Sn- and Te-doped GaAs layers on the current density is seen in Fig. 8 [4]. The electron concentration in the epilayer increases about 40% as the current density changes from 0.5 to 40 A/cm 2, while no significant c~ange of the carrier concentration is evident in the thermally grown layers for various growth velocities. It is important to note that changes in the concentration caused by the electric current are very similar for both impurities despite a large difference in the values of their segregation coefficient (kTe = 0.7 at ~50°C, ksn = 0.01 at 950°C) [4].
Liquid phase /
---e._--~
n Icm,3F
35
electroepitaxy
cmZ/V-sec
!
= . t:_ ~r_ O
~
C C O--IpO--~k g ....4J-....
Fig. 7 - Typical doping and mobility profiles in InP
10 4
epilayers grown by thermal LPE (tg) and electroepitaxy (ccg) (Ref. [28]).
10'51
0
t
20
xlO~7
I
i
40
60
I
I
80
I00 p.m
iO ~
Current~ensity (A cm~) xlO 18
'E o
A2 i I
Growth
~,
i 2 rote(~m
Fig. 8 - Electron concentration at room temperature in Te-doped GaAs layers grown at 850°C (&) and Sn-doped GaAs layers grown at 950°C (e) as a function of growth velocity in electroepitaxially and thermally grown layers (Ref. [4]).
~s n
| 5 Te rain-')
Unusual segregation characteristics are seen during growth of GaAs epilayers from Sidoped solutions [ii]. For a constant current density, the Si distribution coefficient increases by two orders of magnitude in going from temperature of 825°C to 975°C, a phenomenon not observed in LPE by thermal growth. The Si distribution coefficient increase with current density is much more pronounced than in the case of Sn or Te. Finally, Si-doped layers grown at 900°C exhibit p- or n-type conduction depending on the current density, in addition to the conductivity type change as a function of the growth temperature observed in conventional LPE. The uniformity of dopant concentration distribution in electroepitaxially grown layers and the doping level changes with current density have been theoretically explained by taking into consideration the contribution of the growth rate (V), electric field (E) in the solution, and Peltier cooling (ATp) [17] as well as the limited solution thickness (L) to the effective segregation coefficient kef f [64,66]. The relative changes of the kef f parameter can be calculated by starting with the following series [64]
m=O
k=m
m
where a = (uE-V)/2~, b = a + Vk / ~ , and ia-b[<
36
T. Bryskiewicz
Fig. 9 - Relative changes of the effective
dKiff Ko
distribution coefficienCAkeff/k ° versus
Ko-O,OI
0,:~
Ko= t
growth time in electroepitaxially grown GaAs calculated for different values of the inter-
Ko=5
face segregation coefficient k ° (Ref. [64]).
0,1 -~= -24
Ko=I0
0,4OA(cmZ ,6
20 3o ;o sO 65 Growth time (rain)
means that dopant transport in the solution constitutes the dominant contribution to the observed segregation phenomena. In many cases Akeff/k o can be estimated immediately from a simplified formula, which is stringly justified only for ko -~ O [64]
Ake~fiko :
f:;
k=O
e-~(~+l)~L
(~e t ~
-e-
a -e t ~
) + [i - (2k+l)aL+ 2~2Dt]erfc
-[0.5 - 2(k+l)~L + 2~2Dt]erfc (,,,_(k+l) I~ ~ L
x e r f c \ D d ~t
+ a DC~t
(2k+l)L 2 D#~t
~D#~ t
+ ~L
)
~--]~ e2k°~L I (0.5 + 2kaL + 2a2Dt) + k=0
- [1 + (2k + 1)aL + 2 a 2 D t ] e r f c
I where
01~)]
(
~
(2k+l)L2 DC~t + c~DCD-tt
+
~ = (uE-V)/2D.
The Ak ~ / k o parameter versus growth time (t) relationship calculated for different values e of the solution thickness (L) is shown in Fig. I0 [64]. It can clearly be seen from this figure that dopant segregation quickly approaches near steady-state growth conditions when the solution thickness is 0.5 cm or less. For larger solution thickness, convection induced
Keff 0,8 0,6 0,4
T= 800=C J=4OA/cm
J
L.5cm L Icm Fig. i0 - Relative changes of the effective
Ko=Oy
~
distribution coefficient Akeff/k ° versus
L=O 5era
growth time in electroepitaxially grown GaAs calculated for different values of the
0.2
L=O,2cm
2'0 ~o ~o 5~ ~o
Growth time (min)
solution thickness L [Ref. [64]).
Liquid phase electroepitaxy
37
by the electric current becomes unavoidable. It is evident from Fig. i0 that even in the case of light convection (a boundary diffusion layer thickness less than 0.5 cm), the dopant is expected to be distributed homogeneously. The relative dopant concentration change versus current density calculated from Eq. (7) can be seen in Fig. Ii [64]. Doping level variations for current densities of 0-40 A/cm 2 do not exceed 40% in accordance with experimental data.
6Kef.__f [ Ko
0 , 6 [_
/
Fig. ii - Relative changes of the effective To = 8 0 0 ° C
uE=-,e V
L =O,Scm
distribution coefficient Akeff/k ° versus cur-
L=o,,cm
rent density in electroepitaxially grown GaAs
o,41- Ko=o,o, / j
L=O,Scm
0 , 2 ~
L=02.cm
calculated for different values of the solution thickness L (Ref. [64]).
L = O , I cm
I0
20
SO
40 50
Current density (A/cm 2)
In the above theoretical treatment of the dopant segregation a constant value for the interface distribution coefficient (ko) is assumed. Such an assumption is justified only when incorporation of t h e v a r i o u s species into the solid occurs under near equilibrium conditions. In this case the law of mass action is applied to calculate values of the ko parameter [65]. When the growth rate is extremely low, an equilibrium distribution of dopant concentration in the solid is expected, and the application of the law of mass action to the bulk incorporation reaction is justified. In this case the k o parameter is independent of dopant concentration in the low doping region, while for heavily doped materials it varies as the square root of concentration. Conversely, at extremely high growth rates the impurities at the interface are frozen in and the k parameter, derived from the law of mass action applied • o to the surface incorporation reaction, is independent of dopant concentration in the whole doping region. In general, a state of local equilibrium at the metallic solution/semiconductor interface is established and the transport of impurities in a strong electric field existing at the growth interface within the depletion region of the semiconductor cannot be neglected. In accordance with the Boltzman equation, Nv=Nsexp(- Ub/kT), the equilibrium dopant concentration in the bulk semiconductor (Nv) differs considerably from the surface impurity concentration (Ns) , depending on the potential drop (Ub) in the depletion region of the semiconductor (Fig. 12). However, at extremely high growth rates the impurities at the interface are frozen in and their bulk and surface concentrations are equal (Nv=Ns). A similar effect
N(x) Ns
2
Fig. 12 - Distribution of the impurity
S~mico~ Metal
concentration N(x) and the potential ~(x) in epitaxial layers grown at a very low (1) and extremely high (2) growth velocity
Nv
I f I
II0
~ i. . j. .(. . x
(Ref. [65]).
) x ]-u b
should be expected in electroepitaxy by changing the U b parameter with an exteTnal voltage supplied to the metallic solutlon/semlconductor junction. It has been proven that the interface segregation coefficient (ko) is approximately proportional to the Nv/N s ratio [65]. Thus, the k parameter may vary through several orders of magnitude as the growth rate and voltage are c~anged. By choosing the proper growth conditions, even the solubility limit may be
38
T. Bryskiewicz
increased. The detailed quantitative treatment of the above problem in the case of electroepitaxy must take into account that both the potential drop U b and the growth velocity V depend on the electric current. Further theoretical and experimental studies are required in this area. 5.
ELECTROEPITAXY OF SOLID SOLUTIONS
A distinctive feature of the electroepitaxial growth of AxCI_xByD 1 v multicomponent systems (0 < x,y < i) is the strong stabilizing influence of the electric - burrent over the'ir composition [24,30,33,34,40,44]. Gal_xAlxAS wafers as thick as 600 ~n [34], GaASl_xSb x [41], Inl_xGaxP [40], and HgxCdl_dTe [45] epilayers up to 200 nm, 120 um, and 500 um, respectively, can be grown with a remarkable uniformity of composition, varying by Ax = 0.01-0.03 over their entire thickness (Fig. 13). The electroepitaxial growth of highly homogeneous InAsl_ Sb~ has also been reported [44]. Moreover, current density fluctuations on the order of i0 A~cm ~ do not introduce any measurable changes in composition [30]. The ability for the composition changes &x and Ay in the solid solutions during electroepitaxial growth is also important from the point of view of possible applications. As we see later, the magnitude of such changes introduced solely by corresponding variation of the current density is very small [33] (see Fig. 14), and only the combination of electroepitaxy with programmed cooling [36] or the growth from a limited solution volume [35,37] allow structures with graded composition.
0.10
8000
7900 7800 A 7700 ~ ~=Ax=O,Oi ~" 7600 :E _1 7500 0
0,15
'~,,, ~
~J
8
z 6700 13. 6600 650q
Fig. 13 - Plots of peak photoluminescence wavelength as a function of distance from
x
c"-.-L._
the substrate interface for three different Gal_xAlxAS layers grown by electroepitaxy (Ref. [31]).
)~.O
'
8
0,35 I
I
I
1
I
I
8~
I
90O
DISTANCE FROM INTERFACE (/.L)
The growth conditions in which the composition of multicomponent systems is either stabilized or changed by the current can be quantitatively analyzed by taking into consideration the following derivative [33] 3 Ax AT
i=l 3 P
Ki x
Yil
~ Yil/mi i=l
3 ~ Ki Ay = i=l y Yil ATp 3
(9)
~ Yil/mi i=l
u.E i i D(~.) p Cis - (i - --7) e L (i0) = u.E Yij C j " ( i - - i - - ) C~ s v i i . . where Kx ) , = 8 x ( y ) / S C L i s t h e s o l z d u s s l o p e o f t h e z e l e m e n t d e f i n e d b y t h e p h a s e d i a g r a m and Yij ~ ) t h e growth path function for components i and j (p = 1/2 or i in the absence and in the presence of c o n v e c t i o n , respectively). The d e p e n d e n c e o f Ax/ATp o n t h e i n i t i a l growth conditions of Ga~ Al.~s epilayers calculated from Eq. (9) is shown in Fig. 14 [33]. It can ~-x easily be seen from Fig. 14 that the magnitude of the current controlled changes in the solid composition is2very small. I t e x p l a i n s why i n e p i l a y e r s grown with typical current densities (J = 0-20 A/cm ) the composition changes could not be consistently resolved.
Liquid phase electroepitaxy
39
xlO-z 0,6
t
0,4
<3
0.2
X
<3
Fig. 14 - Ax/JT versus solid composition x of Ca l_xAlxAs, lavers calculated for electroepitaxial and thermal step cooling
0
-0.2
growth (Ref. [33]).
. . . .
I I I~ I _ O,I 0.2 0,3 " ~ Solid Composition, x, ~
I~" U.~ A¢~oC
-0.4 6.
CONCLUSIONS
It has been proven that Peltier cooling as well as electrotransport are dominant drivin~ forces of electroepitaxy, and the epilayer growth velocity is directly proportional to the current density. The growth process is not affected by convection until the thermal Grashof number exceeds a value of the order of 104 . Epilayers grown by electrotransport-controlled epitaxy are flat and exhibit no terracing or other morphological defects typically found in layers grown by thermal LPE. The pronounced difference in their surface morphology is related to fundamental differences in the growth mechanisms involved in these two growth methods. The electric current has a strong stabilizing influence over the composition of mixed crystals, however, the doping level of the layers depends on the current density. These important features of liquid phase electroepitaxy allow the growth of semiconductor layers with excellent electrical and structural properties comparable to or, in many cases, superior to those grown by thermal LPE [4,18,26,31,40,42,43]. Although few discrete optoelectronic devices have been made with this technique [31], the usefulness of liquid phase electroepitaxy in the preparation of high-radiance LED's, dome lenses, and other related structures, is apparent [34]. There are also other advantages of the electroepitaxial technique which have not been emphasized in this paper. Constant growth temperature and continuous saturation of the solution with source material enables the growth of crystals several millimeters thick with the quality of epitaxial layers. Only recently, very promising results in this area of "bulk" electroepitaxial crystal growth have been obtained in Professor Harry C. Gates' group at M.I.T. [67,68]. The author is very grateful to Mr. Charles Brandt for reviewing this paper and his valuable remarks as well as to Ms. Phyllis Merrick for typing the manuscript. REFERENCES
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[49]
T. Bryskiewicz, Electroepitaxy of Semiconductor Compounds, in Physi~ Compounds, Ed. J. M. Langer, p. 47 (Ossolineum 1982).
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Phys. L ~ .
42
T. Bryskiewicz
Appl. Phys.
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[66]
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52, 1347 (1981).
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Liquid phase electroepitaxy
43
THE AUTHOR
T. BRYSKIEWlCZ
BIBLIOGRAPHICAL NOTE Tadeusz Bryskiewicz received his M. Sc. degree (1971) in Solid State Physics from Warsaw University, and his Ph.D. degree (1976) from the Institute of Physics of the Polish Academy of Sciences in Warsaw. His principal research activities are in the study of physical phenomena occurring in liquid phase epitaxial (LPE) and electroepitaxial (LPEE) growth. He has recognized the electrotransport as a dominating mechanism of the solute transport in LPEE, and has developed the electroepitaxy from a limited solution volume, a suitable technique for preparation of multilayer laser structures especially operating in the visible range of wavelengths. He has also created, in cooperation with his co-worker, a fundamental theory of dopant incorporation in LPE and LPEE. This theory predicts an exciting possibility of increasing the solubility limit of some dopants during electroepitaxy, a very useful phenomenon in producing hig h quality semi-insulatlng material by LPEE. His discovery of the considerable growth velocity increase by applying microsecond current pulses instead of dc current, commonly used in LPEE, may be crucial in adopting electroepitaxy for the growth of large diameter bulk crystals. Only recently, in Electronic Materials Group at MIT, he has developed electroepitaxial growth of bulk GaAs crystals comparable in quality with epitaxial layers. Dr. T. Bryskiewicz is a member of the American Association for Crystal GrowthJ
0146-3535/86$0.00 + .50
Printed in Great Britain.All rights reserved.
Copyright~) 1986 PergamonJournalsLtd.
LIQUID PHASE ELECTROEPITAXY OF SEMICONDUCTOR COMPOUNDS T. Bryskiewicz Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
1.
INTRODUCTION
The liquid phase electroepitaxiai growth method has been developed in recent years [i-68]. This technique utilizes essentially the same equipment as that used in standard liquid phase epitaxy but modified to permit the passage of an electric current through the substrate/ solution interface (Fig. i) [i]. Two stainless steel or molybdenum electrodes are threaded into the slider and the solution holder, respectively, and both parts of the graphite boat are electrically isolated with boron nitride. Thus, electric current can flow only when the substrate is brought into contact with the solution. A uniform, low resistance electrical contact between the bottom part of the substrate and graphite slider is essential for satisfactory growth [2-8]. In a typical growth experiment the solution is heated at the growth temperature for several hours, in order to insure its saturation with source material. Finally, the substrate is brought into contact with the solution and electric current is passed across the substrate/solution interface as the sole driving force of the epitaxial growth. Deposition of the material is terminated by switching the current off and moving the slider. Liquid phase eletroepitaxy (LPEE) has since been employed for the growth of InSb [i], GaAs [3-5, 9-21], GaP [22, 23], GaSb [24-26], InAs [27], InP [6,28], SiC [29], as well as GaAIAs [2,7,8, 30-38], GalnP [39,40], GaAsSb [41], GaAISb [24-26], InGaAs [42,43], InAsSb [44], HgCdTe [45,46], and InGaAsP [47].
Fig. I - Schematic diagram of the electroepitaxial growth system. (Ref. [i]).
The idea of crystallization induced by the passage of an electric current is not new. Electrodeposition of electrically conducting materials from aqueous solutions or molten salts, a closely related technique, has been studied extensively for many years. This growth process is based on ionic transport in the bulk solution driven by the electric field. The current is a measure of both the rate of flow of ions through the solution and the rate at which the ions are deposited on the crystal surface of the electrode. However, in electroepitaxy the metallic electrode is molten while the epitaxial layer, which can be treated as the solution with
29
30
T. Bryskiewicz
ionized impurities and free charges, is solid. This configuration means that many of the physical phenomena occurring in electrodeposition are inherently different from those in liquid phase electroepitaxial growth. The aim of this paper is to show how the achievements in improved surface morphology and homogeneity as well as improved electrical parameters of the layers depend on better and more detailed understanding and control of physical phenomena occurring in liquid phase electroepitaxy. The details of results obtained during the early developmental stages of this growth technique can be found in previous review papers [48,49]. 2.
GROWTH KINETICS VS. MASS TRANSPORT MECHANISMS
The observed growth rate-current density relationship is linear in most cases of electroepltaxy [2,3,6,10,12,15,22,27,29,30,33,42,43, 46,47] but sometimes tends to be superlinear [3,10,28,41] (Fig. 2). It was originally proposed that Peltier cooling at the growth interface was solely responsible for supersaturation of the solution and epitaxial growth [i-3]. Subsequently, it was demonstrated that migration of solute species due to electrotransport constitutes the essential contribution to supersaturation [9,12 ,23]. However, in experiments using both 2 mm thick p- and n-type substrates it was shown that el ~ctroepitaxial growth kinetic is dominated by the Peltier cooling and convection [32]. Thus, quantitative analysis of the growth kinetics in LPEE requires taking into consideration all the above transport mechanisms of crystallizing material towards the interface.
Average GrowthRote (#m/rnin)
AveroQe Growth Rote
(/zm/rnin) 0.5
hO
0.4
/ /
0,8
o,,
• 800°C
/760°C
O.3
/ /
•
760°C
Z /
L Current Density [A/cm2) n~ Substrates
o ~ f - - " - ' - ~ 0 5
,
IO 15 Current Density(A/cm2) Semi-Insulating Substrates
Fig. 2 - Average growth rate versus current density for electroepitaxial growth of tin doped GaAs on n + and semi-insulating substrates at 680°C, 720°C, and 800°C (Ref. [i0]). 2.1.
Peltier Cooling
Since the substrate used in electroepitaxy is a semiconductor, and the solution is a metal, they have different thermoelectric coefficients. Thus, the flow of electric current across their interface is accompanied by the absorption or evolution of heat, depending on the current direction. The magnitude of heat (Q) produced per unit time and surface is directly proportional to the current density (J) and Peltler coefficient (Q = ~J) resulting in a stationary temperature gradient at the solution/substrate interface. The interface temperature change (ATp) is roughly directly proportional to the current density (J) and its magnitude is controlled by the growth temperature (To) , solution height (L) as well as by the substrate thickness, conductivity type, and carrier concentration [2,15,30,38,50-57] (Fig. 3). In electroepitaxy the interface temperature decrease AT due to the Peltier effect, typically P • of the order of i o C, induces supersaturation of the solutzon providing solute diffusion towards the substrate, and thus, epitaxial growth.
Liquid phase electroepitaxy
-3
31
n= 2 xl0J? crn-5 n= 2 x1018 c m " 3 p = 2 x I018 cm"5 o semi- insulating
• •
-I.5
rl/s
• IO00#.m
• 350~m o
,,A
-I,0
~'50~n
<3
O s •S O
s
pJ
/
-0,5 I
,
I
-40-30
~ I
,
I
,
-20 _o.~'~
/
""
•
40 Current density, (A/crn 2) MO
212j I
20
30
E
-~ 0
I
I(X~
I
1500
"~.. Subslrate thickness,(/.Lm ) c +1 .S
A'.%% %
c "~2
o
%%% %'%%~ +3
Fig. 3 - Changes in temperature ATp at the GaAs solution interface due to the Peltier effect at 800°C versus current density and substrate thickness (Ref. [15]). 2.2.
Solute Electrotransport
The solutions used in the electroepitaxy of semiconducting compounds are metallic conductors; essentially they exhibit no ionic contribution to the current. This fact means that solute electromigration due to the direct interaction of the electrostatic field with ionized particles is negligible. However, in these solutions as in other liquid metals, migration takes place due to momentum exchange between electrons in the conduction band and solute particles. Under the electric field E induced by the current flow, species in the solution migrate towards the anode with a velocity v = uE, where u is their effective mobility. The efficiency of electrotransport is characterized by the effective charge Zeff=U/Uo, where u o is the real solute mobility. In most metallic solutions the Zef f parameter is negative and its absolute value is much larger than one [12,54,58]. 2.3.
Convection
The primary cause of convection during liquid phase electroepitaxial growth has been identified with the horizontal temperature gradients resulting from pronounced Joule heating at the contacts of the current carrying rods and the graphite segments of the boat [13]. As a criterion of convective flow the magnitude of the thermal Grashof number has to be considered L4 Gr = ~g • - - A T (i) 2 W v where ~, v and g are the coefficient of the thermal expansion, the kinematic viscosity, and the gravitational constant, respectively; L and W are the height and diameter of the solution; AT is the horizontal temperature difference across the solution. On the basis of the experimental data obtained for electroepitaxially grown GaAs [13] it appears that the growth ~rocess is not affected by the convective flow until Gr exceeds a value of the order of i0 . It is not understood, at this time, why such a relatively high value of Gr is necessary before significant convective flow is present in the solution to affect the growth process. However, no quantitative data are available at this time to determine the thickness of such a stabilizing solute layer. It is important to note that in numerical calculations of the growth velocity including convection, a static boundary diffusion layer in a moving solution immediately adjacent to the growth interface, has been assumed (the Nernst's approximation) [15,52,59].
32 2.4.
T. Bryskiewicz Growth Velocity Calculations
In order to calculate the electroepitaxial growth velocity let us assume that at a temperature To a substrate is placed horizontally under a saturated solution of concentration CL(TO) and thickness L (see Fig. 4). Let a source wafer be in turn situated on the surface of the solution. As we know, epitaxial growth at constant temperature can be achieved by passing an electric current across the substrate-solution interface. Since Peltier cooling at the interface produced by the current causes a lowering of the temperature and concentration of the solute down to T 1 and CL(TI) , respectively, the solute concentration and temperature gradients (diffusion and convection) as well as the electric field E (electrotransport) are the driving forces of growth. The equation for the growth velocity V can be carried out from the balance of streams of crystallizing material at the growing interface [12,15,56]
D ~
x=R - UECL(TI) Cs -
V(t) =
CL(TI)
(2)
where D is the diffusion coefficient, x is the distance from the interface, C(x,t) and C are s solute concentrations in the solution and epilayers, and t is growth time.
solid
IC(x,t) source
Cs melt
Fig. 4 - Distribution of the solute
CL(T O)
concentration C(x,t) in the melt and solid: CL and C s are equilibrium solute concentrations in the melt and solid (Ref. [12]).
0 R(t)
L
x ,L
As we see, the growth velocity calculations require estimation of the solute concentration gradient at the growth interface, which in turn can be carried out by solving the mass transport equation with the proper initial and boundary conditions [12,15,33,52,55,56,59-61]. The analytical expression for the growth velocity V, calculated by assuming the semi-infinite solution thickness, is of the form [15]
fDlj2 AT v(t)
=
m\~l
-
u ECL(TI)
P
Cs _ CL(TI)
(3)
in the absence of convection, and D ATp.m" ~ - u ECL(TI) V(t) =
Cs _ CL(TI)
(4)
in the presence of convection, where m = dCL/dT is the liquidus slope defined by the phase diagram, and 6 is the Nernst diffusion layer. The first term in the above equations represents the contribution of the Peltier effect, whereas the second one represents the contribution of electrotransport to the growth velocity, both these terms being linearly dependent on the current density through AT and E, respectively. Consequently,,the calculated growth rate is directly proportional to t~e current density, in accordance with experimental results. The superlinear growth rate-current density relationship observed in some cases is apparently related to the increasing convective flow as the
Liquid phase electroepitaxy
33
current density becomes higher. Equation (3) suggests appreciable contribution of the Peltier effect to the growth kinetics merely at the initial stage of the electroepitaxial growth. However, more precise growth velocity calculations including the limited thickness of the solution have proved that the diffusion term does not tend to zero with time but rather takes ss its finite steady-state value Vdiff [52,55,56,59,60] equal to AT ss = p Vdiff Cs - CL
m u E exp(uEL/D) - 1
(5)
The transient time required for the steady-state growth conditions depends upon the solution thickness L and varies from a few seconds for L = 0.05 cm to several minutes for L = 1 cm [56] (Fig. 5).
t(min)
t(s)
? ,,o,5 !~,5
o,
L = Icm J = I0 A l c m z T =850°C
A r-
IC o )o 5 I ~,5 0.40 L= 0 . 0 5 cm j = IOA/cm z -T=850°C
0,18 =44 3,14
E
"~:
o,I
/
/
0~07 .=E
-
E
,
0,4
3aO .~E
=L t,
> Vu
.
3~D6 >'o
t
> Vu
~ ' V _Vdl ff :,~'t--" - r - - - - . r - . -~. ---.-~-.-- ),02 2 4 6 8 I0 12
Iz
OX>9
,,'_
(m in-V;~
~
I°
sppp
_._~v-v=.~ ....
0~05 E =L
i 2
= 4
~ 6 ,z
...... i 8
,I I0
o=3 >~' 12
3.01
(s-,/2)
Fig. 5 - Time dependence of the growth velocity V and its diffusion contribution V .... in the liquid phase electroepitaxy of GaAs calculated for the solution thickness L = ~ cm and L = 0.05 cm (Ref. [56]). 3.
SURFACE MORPHOLOGY
In the earlier studies of growth by liquid phase electroepitaxy two types of epilayer thickness variations were observed: random fluctuations and systematic variations [6,10,13]. Random fluctuations were typically about ~ 15% for GaAs layers grown with typical current densities of 5 or i0 A/cm 2, and often ~ 20% for layers grown with 15 or 20 A/cm 2, neglecting excess edge growtn which sometimes was equal to the average layer thickness [I0]. Moreover, the formation of several terraces and cusps was favored when one attempted to force growth directly upon the substrates with a current density of 15 or 20 A/cm 2. For current density of 5 or I0 A/cm 2 the terracing was milder and in several cases large areas of the layer were nearly featureless. In addition, the terracing was less severe when growth at 15 or 20 A/cm 2 was carried out upon growth with 5 or i0 A/cm 2 rather than directly upon the substrate. These observations, together with the long-range thickness variations observed in epitaxial layers grown with higher current densities, suggest that all these features depend largely upon the non-uniformity of the current density across the substrate. It was found that non-uniformity of the electrical contact to the back side of the substrate yielded those regions of nonuniform layer thickness [6,10,13]. In the earlier studies of growth by liquid phase electroepitaxy, the back contact for electric current flow between the substrate and graphite was achieved by either using a thin film of Ga or In metal, depending on the substrate material, or by using the liquid metal film separated with a tantalum foil to promote wetting [3,4,6,10]. In either case, some non-uniformity in the contact was observed which was attributed to nonuniform wetting of the back surface of the substrate by the metallic film and to crumbling of the tantalum foil as a result of reaction with the hydrogen ambient in the reaction tube. Poor electrical contacts cause undesirable localized Joule heating, particularly at high current densities. Finally, local variations in the contact resistance lead to variations in the thickness of the epitaxial layers. This disadvantage of growth by liquid phase electroepitaxy has been entirely overcome in recent years. A new electroepitaxial configuration has been developed in which the back side electrical contact to the substrate is formed at the
34
T. Bryskiewicz
growth temperature under high purity hydrogen flow [5,8] (see Fig. 6).
Solution (~/
SS Electrode ,,-TC Fig. 6 - A novel construction of
Slider
J
~-".-b
=
~
~-"
electroepitaxial growth apparatus without back-contact (Ref. [5]).
Substrate/
~.. - .'J
i
"
" -~-TC
Solution
Systematic variations of the epilayer thickness were in turn found to be associated with temperature gradients in the solution [13]. In the presence of convection in the solution the thickness profile of the layers reflects the convective flow pattern. As previously mentioned, the primary cause of convection has been identified with the horizontal t e m p e r ~ u r e gradients resulting from Joule heating at the contact of the current carrying rods and the graphite segments of the boat. It can be eliminated by minimizing the temperature gradient across the solution through reduction of the system's resistance and by positioning the solution well in the furnace so that the horizontal gradient in the solution, prior to current flow, is of the same magnitude but opposite in sign to that induced by Joule heating [13]. Epilayers grown by electrotransport-controlled electroepitaxy in which random as well as systematic thickness variations have been eliminated are flat and exhibit no terracing or other morphological defects typically found in layers grown by thermal LPE [7,14,18,26,43]. The occasional appearance of defects such as dishes or hillocks are invariably related to defects in the electrical contact of the substrate [14]. The pronounced difference in the surface morphology of the layers grown by electroepitaxy and those grown by thermal LPE can be explained with fundamental differences in the growth mechanisms involved in these two growth methods. In electroepitaxy, supersaturation takes place in the immediate vicinity of the growth interface and growth is controlled by the rate of transfer of solute, under an electric field, towards the interface. It means that growth takes place at near equilibrium (isothermal) conditions and interface instabilities due to constitutional supercooling do not occur. The unusual features of liquid phase electroepitaxy with regard to interface stability can be justified on the basis of the interface stability model of Mullins and Sekerka [63]. The temperature gradient (G) at the interface required to overcome the onset of constitutional supercooling is
G > ~
1 -
(6)
From Eq. (6) it is apparent that the value of G required to prevent constitutional supercooling decreases with increasing contribution of electrotransport (VE) to the overall growth velocity V, and thus it is always smaller than in thermal LPE [63]. 4.
DOPANT SEGREGATION
One of the most important features of liquid phase electroepitaxy is its potential for the growth of very homogeneous wafers when the current density is fixed [24,28,30,33,34, 40,44,64]. As an example, doping profiles typical for InP epilayers grown at constant temperature and current are shown in Fig. 7 [28]. However, modulation of the dopant concentration can be achieved in the growing epilayer by a corresponding variation of the current density [3,4,10,ii,17,28,64-66]. The dependence of the carrier concentration in Sn- and Te-doped GaAs layers on the current density is seen in Fig. 8 [4]. The electron concentration in the epilayer increases about 40% as the current density changes from 0.5 to 40 A/cm 2, while no significant c~ange of the carrier concentration is evident in the thermally grown layers for various growth velocities. It is important to note that changes in the concentration caused by the electric current are very similar for both impurities despite a large difference in the values of their segregation coefficient (kTe = 0.7 at ~50°C, ksn = 0.01 at 950°C) [4].
Liquid phase /
---e._--~
n Icm,3F
35
electroepitaxy
cmZ/V-sec
!
= . t:_ ~r_ O
~
C C O--IpO--~k g ....4J-....
Fig. 7 - Typical doping and mobility profiles in InP
10 4
epilayers grown by thermal LPE (tg) and electroepitaxy (ccg) (Ref. [28]).
10'51
0
t
20
xlO~7
I
i
40
60
I
I
80
I00 p.m
iO ~
Current~ensity (A cm~) xlO 18
'E o
A2 i I
Growth
~,
i 2 rote(~m
Fig. 8 - Electron concentration at room temperature in Te-doped GaAs layers grown at 850°C (&) and Sn-doped GaAs layers grown at 950°C (e) as a function of growth velocity in electroepitaxially and thermally grown layers (Ref. [4]).
~s n
| 5 Te rain-')
Unusual segregation characteristics are seen during growth of GaAs epilayers from Sidoped solutions [ii]. For a constant current density, the Si distribution coefficient increases by two orders of magnitude in going from temperature of 825°C to 975°C, a phenomenon not observed in LPE by thermal growth. The Si distribution coefficient increase with current density is much more pronounced than in the case of Sn or Te. Finally, Si-doped layers grown at 900°C exhibit p- or n-type conduction depending on the current density, in addition to the conductivity type change as a function of the growth temperature observed in conventional LPE. The uniformity of dopant concentration distribution in electroepitaxially grown layers and the doping level changes with current density have been theoretically explained by taking into consideration the contribution of the growth rate (V), electric field (E) in the solution, and Peltier cooling (ATp) [17] as well as the limited solution thickness (L) to the effective segregation coefficient kef f [64,66]. The relative changes of the kef f parameter can be calculated by starting with the following series [64]
m=O
k=m
m
where a = (uE-V)/2~, b = a + Vk / ~ , and ia-b[<
36
T. Bryskiewicz
Fig. 9 - Relative changes of the effective
dKiff Ko
distribution coefficienCAkeff/k ° versus
Ko-O,OI
0,:~
Ko= t
growth time in electroepitaxially grown GaAs calculated for different values of the inter-
Ko=5
face segregation coefficient k ° (Ref. [64]).
0,1 -~= -24
Ko=I0
0,4OA(cmZ ,6
20 3o ;o sO 65 Growth time (rain)
means that dopant transport in the solution constitutes the dominant contribution to the observed segregation phenomena. In many cases Akeff/k o can be estimated immediately from a simplified formula, which is stringly justified only for ko -~ O [64]
Ake~fiko :
f:;
k=O
e-~(~+l)~L
(~e t ~
-e-
a -e t ~
) + [i - (2k+l)aL+ 2~2Dt]erfc
-[0.5 - 2(k+l)~L + 2~2Dt]erfc (,,,_(k+l) I~ ~ L
x e r f c \ D d ~t
+ a DC~t
(2k+l)L 2 D#~t
~D#~ t
+ ~L
)
~--]~ e2k°~L I (0.5 + 2kaL + 2a2Dt) + k=0
- [1 + (2k + 1)aL + 2 a 2 D t ] e r f c
I where
01~)]
(
~
(2k+l)L2 DC~t + c~DCD-tt
+
~ = (uE-V)/2D.
The Ak ~ / k o parameter versus growth time (t) relationship calculated for different values e of the solution thickness (L) is shown in Fig. I0 [64]. It can clearly be seen from this figure that dopant segregation quickly approaches near steady-state growth conditions when the solution thickness is 0.5 cm or less. For larger solution thickness, convection induced
Keff 0,8 0,6 0,4
T= 800=C J=4OA/cm
J
L.5cm L Icm Fig. i0 - Relative changes of the effective
Ko=Oy
~
distribution coefficient Akeff/k ° versus
L=O 5era
growth time in electroepitaxially grown GaAs calculated for different values of the
0.2
L=O,2cm
2'0 ~o ~o 5~ ~o
Growth time (min)
solution thickness L [Ref. [64]).
Liquid phase electroepitaxy
37
by the electric current becomes unavoidable. It is evident from Fig. i0 that even in the case of light convection (a boundary diffusion layer thickness less than 0.5 cm), the dopant is expected to be distributed homogeneously. The relative dopant concentration change versus current density calculated from Eq. (7) can be seen in Fig. Ii [64]. Doping level variations for current densities of 0-40 A/cm 2 do not exceed 40% in accordance with experimental data.
6Kef.__f [ Ko
0 , 6 [_
/
Fig. ii - Relative changes of the effective To = 8 0 0 ° C
uE=-,e V
L =O,Scm
distribution coefficient Akeff/k ° versus cur-
L=o,,cm
rent density in electroepitaxially grown GaAs
o,41- Ko=o,o, / j
L=O,Scm
0 , 2 ~
L=02.cm
calculated for different values of the solution thickness L (Ref. [64]).
L = O , I cm
I0
20
SO
40 50
Current density (A/cm 2)
In the above theoretical treatment of the dopant segregation a constant value for the interface distribution coefficient (ko) is assumed. Such an assumption is justified only when incorporation of t h e v a r i o u s species into the solid occurs under near equilibrium conditions. In this case the law of mass action is applied to calculate values of the ko parameter [65]. When the growth rate is extremely low, an equilibrium distribution of dopant concentration in the solid is expected, and the application of the law of mass action to the bulk incorporation reaction is justified. In this case the k o parameter is independent of dopant concentration in the low doping region, while for heavily doped materials it varies as the square root of concentration. Conversely, at extremely high growth rates the impurities at the interface are frozen in and the k parameter, derived from the law of mass action applied • o to the surface incorporation reaction, is independent of dopant concentration in the whole doping region. In general, a state of local equilibrium at the metallic solution/semiconductor interface is established and the transport of impurities in a strong electric field existing at the growth interface within the depletion region of the semiconductor cannot be neglected. In accordance with the Boltzman equation, Nv=Nsexp(- Ub/kT), the equilibrium dopant concentration in the bulk semiconductor (Nv) differs considerably from the surface impurity concentration (Ns) , depending on the potential drop (Ub) in the depletion region of the semiconductor (Fig. 12). However, at extremely high growth rates the impurities at the interface are frozen in and their bulk and surface concentrations are equal (Nv=Ns). A similar effect
N(x) Ns
2
Fig. 12 - Distribution of the impurity
S~mico~ Metal
concentration N(x) and the potential ~(x) in epitaxial layers grown at a very low (1) and extremely high (2) growth velocity
Nv
I f I
II0
~ i. . j. .(. . x
(Ref. [65]).
) x ]-u b
should be expected in electroepitaxy by changing the U b parameter with an exteTnal voltage supplied to the metallic solutlon/semlconductor junction. It has been proven that the interface segregation coefficient (ko) is approximately proportional to the Nv/N s ratio [65]. Thus, the k parameter may vary through several orders of magnitude as the growth rate and voltage are c~anged. By choosing the proper growth conditions, even the solubility limit may be
38
T. Bryskiewicz
increased. The detailed quantitative treatment of the above problem in the case of electroepitaxy must take into account that both the potential drop U b and the growth velocity V depend on the electric current. Further theoretical and experimental studies are required in this area. 5.
ELECTROEPITAXY OF SOLID SOLUTIONS
A distinctive feature of the electroepitaxial growth of AxCI_xByD 1 v multicomponent systems (0 < x,y < i) is the strong stabilizing influence of the electric - burrent over the'ir composition [24,30,33,34,40,44]. Gal_xAlxAS wafers as thick as 600 ~n [34], GaASl_xSb x [41], Inl_xGaxP [40], and HgxCdl_dTe [45] epilayers up to 200 nm, 120 um, and 500 um, respectively, can be grown with a remarkable uniformity of composition, varying by Ax = 0.01-0.03 over their entire thickness (Fig. 13). The electroepitaxial growth of highly homogeneous InAsl_ Sb~ has also been reported [44]. Moreover, current density fluctuations on the order of i0 A~cm ~ do not introduce any measurable changes in composition [30]. The ability for the composition changes &x and Ay in the solid solutions during electroepitaxial growth is also important from the point of view of possible applications. As we see later, the magnitude of such changes introduced solely by corresponding variation of the current density is very small [33] (see Fig. 14), and only the combination of electroepitaxy with programmed cooling [36] or the growth from a limited solution volume [35,37] allow structures with graded composition.
0.10
8000
7900 7800 A 7700 ~ ~=Ax=O,Oi ~" 7600 :E _1 7500 0
0,15
'~,,, ~
~J
8
z 6700 13. 6600 650q
Fig. 13 - Plots of peak photoluminescence wavelength as a function of distance from
x
c"-.-L._
the substrate interface for three different Gal_xAlxAS layers grown by electroepitaxy (Ref. [31]).
)~.O
'
8
0,35 I
I
I
1
I
I
8~
I
90O
DISTANCE FROM INTERFACE (/.L)
The growth conditions in which the composition of multicomponent systems is either stabilized or changed by the current can be quantitatively analyzed by taking into consideration the following derivative [33] 3 Ax AT
i=l 3 P
Ki x
Yil
~ Yil/mi i=l
3 ~ Ki Ay = i=l y Yil ATp 3
(9)
~ Yil/mi i=l
u.E i i D(~.) p Cis - (i - --7) e L (i0) = u.E Yij C j " ( i - - i - - ) C~ s v i i . . where Kx ) , = 8 x ( y ) / S C L i s t h e s o l z d u s s l o p e o f t h e z e l e m e n t d e f i n e d b y t h e p h a s e d i a g r a m and Yij ~ ) t h e growth path function for components i and j (p = 1/2 or i in the absence and in the presence of c o n v e c t i o n , respectively). The d e p e n d e n c e o f Ax/ATp o n t h e i n i t i a l growth conditions of Ga~ Al.~s epilayers calculated from Eq. (9) is shown in Fig. 14 [33]. It can ~-x easily be seen from Fig. 14 that the magnitude of the current controlled changes in the solid composition is2very small. I t e x p l a i n s why i n e p i l a y e r s grown with typical current densities (J = 0-20 A/cm ) the composition changes could not be consistently resolved.
Liquid phase electroepitaxy
39
xlO-z 0,6
t
0,4
<3
0.2
X
<3
Fig. 14 - Ax/JT versus solid composition x of Ca l_xAlxAs, lavers calculated for electroepitaxial and thermal step cooling
0
-0.2
growth (Ref. [33]).
. . . .
I I I~ I _ O,I 0.2 0,3 " ~ Solid Composition, x, ~
I~" U.~ A¢~oC
-0.4 6.
CONCLUSIONS
It has been proven that Peltier cooling as well as electrotransport are dominant drivin~ forces of electroepitaxy, and the epilayer growth velocity is directly proportional to the current density. The growth process is not affected by convection until the thermal Grashof number exceeds a value of the order of 104 . Epilayers grown by electrotransport-controlled epitaxy are flat and exhibit no terracing or other morphological defects typically found in layers grown by thermal LPE. The pronounced difference in their surface morphology is related to fundamental differences in the growth mechanisms involved in these two growth methods. The electric current has a strong stabilizing influence over the composition of mixed crystals, however, the doping level of the layers depends on the current density. These important features of liquid phase electroepitaxy allow the growth of semiconductor layers with excellent electrical and structural properties comparable to or, in many cases, superior to those grown by thermal LPE [4,18,26,31,40,42,43]. Although few discrete optoelectronic devices have been made with this technique [31], the usefulness of liquid phase electroepitaxy in the preparation of high-radiance LED's, dome lenses, and other related structures, is apparent [34]. There are also other advantages of the electroepitaxial technique which have not been emphasized in this paper. Constant growth temperature and continuous saturation of the solution with source material enables the growth of crystals several millimeters thick with the quality of epitaxial layers. Only recently, very promising results in this area of "bulk" electroepitaxial crystal growth have been obtained in Professor Harry C. Gates' group at M.I.T. [67,68]. The author is very grateful to Mr. Charles Brandt for reviewing this paper and his valuable remarks as well as to Ms. Phyllis Merrick for typing the manuscript. REFERENCES
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Liquid phase electroepitaxy
43
THE AUTHOR
T. BRYSKIEWlCZ
BIBLIOGRAPHICAL NOTE Tadeusz Bryskiewicz received his M. Sc. degree (1971) in Solid State Physics from Warsaw University, and his Ph.D. degree (1976) from the Institute of Physics of the Polish Academy of Sciences in Warsaw. His principal research activities are in the study of physical phenomena occurring in liquid phase epitaxial (LPE) and electroepitaxial (LPEE) growth. He has recognized the electrotransport as a dominating mechanism of the solute transport in LPEE, and has developed the electroepitaxy from a limited solution volume, a suitable technique for preparation of multilayer laser structures especially operating in the visible range of wavelengths. He has also created, in cooperation with his co-worker, a fundamental theory of dopant incorporation in LPE and LPEE. This theory predicts an exciting possibility of increasing the solubility limit of some dopants during electroepitaxy, a very useful phenomenon in producing hig h quality semi-insulatlng material by LPEE. His discovery of the considerable growth velocity increase by applying microsecond current pulses instead of dc current, commonly used in LPEE, may be crucial in adopting electroepitaxy for the growth of large diameter bulk crystals. Only recently, in Electronic Materials Group at MIT, he has developed electroepitaxial growth of bulk GaAs crystals comparable in quality with epitaxial layers. Dr. T. Bryskiewicz is a member of the American Association for Crystal GrowthJ