LEC method for growing a single crystal of compound semiconductors

If the distribution coefficient of an impurity in a compound melt is less than 1, the impurity concentration in the compound melt doped with the impurity increased during a crystal growth in an LEC method. A supplying device replenishes an undoped crystal into the melt in order to keep the impurity concentration constant. The undoped crystal is covered with a liquid encapsulant which is contained in an encapsulant-supporting-cylinder or double-cylinder. Replenishing rate (dQ/dt) of the undoped crystal and the growing rate (dS/dt) should satisfy the equation EQU dQ/dt=(1-k)dS/dt The impurity concentration of a grown single crystal is uniform. Whole of the crystal is a single crystal. Electronic properties of the single crystal is uniform from seed end to tail end.

BACKGROUND OF THE INVENTION 
This invention relates to an improvement of a liquid encapsulated 
Czockralski method (LEC method) for growing a single crystal of compound 
semiconductors. 
In growing a single crystal of compound semiconductors, various kinds of 
elements are usually doped in order to change electronic characteristics 
or to reduce the dislocation density of the single crystal. 
For example, some elements which have a different valence number from that 
of matrix elements of the semiconductor crystal are doped as impurity in 
order to make the grown crystal into an n-type semiconductor or a p-type 
semiconductor. 
In this invention compound semiconductors mean semiconductors of groups 
III-V and groups II-VI in the periodic table. 
For example GaAs, GaP, InP, GaSb, etc are semiconductors of groups III-V. 
CdS, CdSe, CdTe, etc are semiconductors of groups II-VI. 
For example in the case of growing a single crystal of GaAs, isoelectronic 
impurities--B, In, Sb, etc--are doped in order to reduce the dislocation 
density in the single crystal. Isoelectronic impurity is defined as an 
impurity whose valence number is the same with one of the matrix elements 
of semiconductor crystals. 
Besides, S, Te, Si, etc which are not isoelectronic impurities are doped 
into GaAs single crystals to change electronic characteristics. 
A liquid encapsulated Czockralski method (LEC method) is one of the 
prevailing methods used to grow a single crystal of semiconductor. 
An LEC method comprises: melting encapsulant material and compound material 
into a compound melt covered with a liquid encapsulant in a crucible by 
heating, dipping a seed crystal into the compound melt, growing a single 
crystal from the compound melt by pulling up and rotating the seed crystal 
and cooling the grown crystal in a cooling zone above the crucible. 
In the case of doping some impurities, the impurities ae added into the 
compound material as elements or compound which comprise the impurity 
elements. 
When a single crystal is grown from a compound melt which includes an 
impurity element, the impurity concentration C.sub.s in a solidified 
single crystal pulled up is not equal to the impurity concentration 
C.sub.L in the compound melt in general. 
The boundary between a compound melt and a solidified single crystal is 
called a liquid-solid interface. Generally the ratio of the impurity 
concentrations of a solidified part to that of a melt is a constant value, 
which is called a distribution coefficient. 
The distribution coefficient depends upon a pressure acting on the melt and 
a ratio of elements of matrix compound in the melt. But if the pressure is 
kept constant, the distribution coefficient is constant in the crystal 
growth. 
The distribution coefficient k is defined by 
EQU k=C.sub.s /C.sub.L ( 1) 
If the impurity concentration is 1 in a melt, the impurity concentration of 
the solidified part at the liquid-solid interface is k. 
Distribution coefficients are defined by determining an impurity element 
and a matrix melt. They obtain various values according to the impurity 
element and the matrix melt. When the impurity element and the matrix melt 
are identified, the distribution coefficient changes as a function of 
pressure. 
But in many cases the distribution coefficient is smaller than 1. If the 
impurity has a distribution coefficient smaller than 1, impurity atoms do 
not easily penetrate into the solidified part. When a single crystal is 
pulled up from a compound melt including an impurity element by an LEC 
method, the compound elements of the matrix of the crystal are removed 
from the crucible more rapidly than the impurity element. Then the 
impurity concentration in the melt gradually increases during the crystal 
growth. 
The impurity concentration C in a crystal grown by an LEC method is given 
by 
EQU C=C.sub.0 k(1-g).sup.k-1 ( 2) 
Where C.sub.0 is an initial impurity concentration in the compound melt and 
g is a ratio of solidified part to the initial compound melt by weight. 
This ratio is called solidification ratio from now for simplicity. 
At the initial state the solidification ratio g is zero. During the crystal 
growth the solidification rate g increases. 
If the distribution coefficient k is smaller than 1, the impurity 
concentration C is lowest at the beginning of the crystal growth, because 
the solidification rate g is zero. And the impurity concentration C raises 
as the crystal growth proceeds. When the solidification rate g comes near 
to 1, the impurity concentration diverges. 
Accordingly if the impurity having a distribution coefficient k less than 1 
is doped in a compound melt, the impurity concentration C is lowest at a 
seed end of a single crystal grown from the melt and is highest at a tail 
end of the crystal. 
A single crystal ingot grown by the LEC method is sliced in the planes 
which are perpendicular to the growth axis. Sliced crystals are called 
wafers. According to the explanation abovementioned, the impurity 
concentration is different with regard to each wafer sliced from the same 
crystal ingot. Therefore it is difficult to make many wafers having the 
same characteristics by the LEC method. 
Furthermore when the impurity concentration in the initial melt is very 
high, the impurity concentration in the melt raises higher than a limit of 
single-crystallization. Separating of impurity atoms on the surface of the 
pulled crystal happens. After the separating occurs, the solidified part 
does not become a single crystal. Therefore, only a small upper portion of 
the ingot is available, because a semiconductor wafer must be a single 
crystal. 
It is desirable that the grown ingot should be a single crystal from seed 
end to tail end and the impurity concentration should be uniform in the 
single crystal. 
If a great amount of compound melt which is many times larger than the 
crystal to be grown are contained in a big crucible, the change of the 
impurity concentration during the crystal growth might be trivial. 
But in the practical case the diameter of a crucible is determined to be 
twice as big as the diameter of the single crystal grown from the 
crucible, and the depth of the crucible is nearly equal to the diameter of 
the crystal. Thus it is impossible to use excessively much compound melt. 
SUMMARY OF THE INVENTION 
An object of the invention is to provide an LEC method and apparatus for 
growing a single crystal of compound semiconductors wherein the whole of 
the grown crystal is single and the impurity concentration is uniform from 
seed end to tail end of the single crystal. 
The LEC apparatus of this invention has a device for supplying compound 
material into the melt to keep the impurity concentration constant in the 
melt during the crystal growth. The supplying device holds an undoped 
polycrystal or single crystal of compound material and dips little by 
little the compound material into the melt. The replenished material 
compensates for the decrease of the material removed by the grown crystal. 
Mathematical consideration will clarify the features of the invention. 
"L" denotes a weight of compound melt. "S" denotes a weight of the single 
crystal grown from the compound melt. "Q" denotes a weight of a 
polycrystal or single crystal replenished into the melt by the supplying 
device. And "m" denotes a weight of an impurity in the compound melt. 
The following equations hold. When the single crystal is pulled more by an 
infinitesimal weight dS and the impurity in the compound melt decreases by 
an infinitesimal weight (-dm), the decrement (-dm) is given by 
EQU -dm=kCdS (3) 
because CdS is the weight of impurity included in the infinitesimal part dS 
of the melt and kCdS is the weight of impurity included in the 
infinitesimal part dS of the crystal pulled from the melt. 
The sum of the increment of the weight of the crystal and the increment of 
the weight of the melt must be zero, if the compound material is not 
replenished like conventional LEC methods. However, the apparatus of the 
invention replenishes compound material into the melt. Then the sum of the 
increments of the weights of the melt and the crystal must be the 
replenished amount of the compound material. Thus we obtain 
EQU dS+dL=dQ (4) 
The impurity weight m in the melt must be equal to the product of the melt 
weight L and the impurity concentration C in the melt. Hence, 
EQU CL=m (5) 
Eq.(3), Eq.(4), and Eq. (5) are fundamental equations. 
If we assume the impurity concentration C should be constant during a 
crystal growth, the infinitesimal increment dC is zero. By differentiating 
Eq.(5) and substituting Eq.(3) and Eq.(4) into the differential equation, 
we obtain 
EQU dQ=(1-k)dS (6) 
EQU dL=-kdS (7) 
EQU dm=-kCdS (8) 
Eq.(6) is an important equation for this invention. From Eq.(6) when the 
crystal is pulled more by dS, the replenishment of polycrystal or single 
crystal by (1-k) dS will keep the impurity concentration constant. 
In the case of the compound semiconductor of group III-V, the elements of 
group V are apt to escape from the polycrystal or single crystal to be 
replenished in the melt. To prevent this phenomenon, a liquid 
encapsulation should be required. 
The liquid encapsulant should be B.sub.2 O.sub.3 in the case of the crystal 
growth of GaAs. The density of the B.sub.2 O.sub.3 is considerably smaller 
than that of GaAs. Then the liquid encapsulant B.sub.2 O.sub.3 can cover a 
polycrystal or single crystal of GaAs up to a definite level much higher 
than the liquid-solid interface in the crucible.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In FIG. 1 a heater (1) is a cylindrical resistance heater. A lower shaft 
(2) is a vertical shaft which can rotate and move upward or downward. A 
susceptor (3) is supported at the top end of the lower shaft (2). A 
crucible (4) is inserted into the susceptor (3). The crucible (4) is made 
from quartz, PBN (pyrolytic boron nitride), etc. 
There is a compound melt (5) in the crucible (4). The compound melt (5) 
keeps a liquid state, because it is heated by the heater (1). The compound 
melt (5) consists of pure material of matrix compound and some impurities. 
A liquid encapsulant (6) covers on the upper surface of the compound melt 
(5). The liquid encapsulant (6) prevents an element of group V with a high 
dissolution pressure from escaping out of the crystal. 
If the compound melt is GaAs, a most preferable liquid encapsulant is 
B.sub.2 O.sub.3. If the compound melt is GaSb, a most preferable liquid 
encapsulant is an eutectic of KCl and NaCl. 
These members are contained in a pressurized chamber in which nitrogen gas 
or inert gas (Ar, He, etc) is filled at a high pressure. The pressurized 
chamber is not shown in the figures for simplicity. 
From an upper region of the pressurized chamber an upper shaft (13) is 
retained along a vertical line. 
A seed crystal (7) is fixed to the bottom end of the upper shaft (13). The 
upper shaft (13) can rotate and move upward or downward arbitrarily. 
By dipping the seed crystal (7) into the compound melt (5) and pulling up 
the seed crystal (7) with a certain rotation speed, a single crystal (8) 
is pulling up, succeeding to the seed crystal (7). 
The structure mentioned so far is the same with that of the conventional 
LEC apparatus. 
Besides these members the LEC apparatus of this invention has a device for 
supplying compound material little by little into the melt (5) to keep the 
impurity concentration constant. This is an important characteristic of 
the invention. 
The compound material to be replenished is either an undoped polycrystal or 
single crystal of the compound semiconductor to be grown. Then the 
material to be replenished is called an "undoped crystal" in common. 
In the embodiment shown in FIG. 1 an undoped crystal (9) is formed in a 
long, round stick. The upper end of the undoped crystal (9) is supported 
by a supplying shaft (10) which can rotate and move upward or downward. 
Bottom end (17) of the undoped crystal (9) contacts with the compound melt 
(5) and is melted little by little by the heat transmitted from the melt 
(5). Molten material dissolves in and mixes with the melt (5). 
Because compound material is replenished into the melt (5), the impurity is 
diluted by the newly-replenished material of matrix compound. To dilute 
the impurity uniformly, the crucible (4) and the single crystal (8) are 
rotated. The rotational motion helps the impurity mix with the matrix 
material. 
By controlling the speed of dipping of the undoped crystal (9) into the 
melt (5), we can suppress the increase of the impurity concentration, keep 
the impurity concentration constant or reduce it also. 
The undoped crystal must be covered by a pertinent liquid encapsulant to 
prevent the element of group V from escaping out of the undoped crystal. A 
cylinder (12) is suspended from a sustaining device (not shown in the 
figures) above the crucible. The cylinder (12) encloses the undoped 
crystal (9). Between the pillared undoped crystal (9) and the inner 
surface of the cylinder (12) a liquid encapsulant (16) is filled. 
The liquid encapsulant (16) covers greater part of the undoped crystal (9) 
from the bottom end. Thus the cylinder (12) is called an 
encapsulant-supporting cylinder. 
The element of group V is apt to escape from the compound crystal of groups 
III-V only when the crystal is heated up to a high temperature. The 
pillared undoped crystal (9) is hottest at the bottom end. Thus the liquid 
encapsulant (16) must cover the lower half of the pillared undoped crystal 
(9). 
In the case of the crystal growth of GaAs, the liquid encapsulant (16) is 
B.sub.2 O.sub.3. B.sub.2 O.sub.3 is solid at a room temperature. B.sub.2 
O.sub.3 is melted into liquid by heating it at about 500.degree. C. to 
600.degree. C. Fortunately at 500.degree. C. to 600.degree. C. As dose not 
escape from a GaAs crystal. 
Then a local heater (14) is installed n the middle region of the 
encapsulant-supporting-cylinder (12) in order to heat the upper portion of 
the liquid encapsulant (16). The heater (14) melts the encapsulant 
material into a liquid state. Whole encapsulant material keeps a liquid 
state by the heat generated at the main heater (1) and the local heater 
(14). Thus the local heater (14) is called an encapsulant-heater. 
Because the encapsulant is liquid throughout the full length, and because 
the upper surface of the liquid encapsulant is pressurized by nitrogen gas 
at a high pressure, the liquid encapsulant effectively prevents As from 
escaping out of the strongly-heated bottom region of the undoped GaAs 
crystal. 
The speed for supplying the undoped crystal (9) into the compound melt (5) 
determines the variation of the impurity concentration in the compound 
melt (5). 
In order to keep the impurity concentration constant, the supplying speed 
of the undoped crystal is given by 
EQU dQ/dt=(1-k)dS/dt (9) 
according to Eq.(6). Here dQ/dt means the supplying speed. It is a weight 
of undoped crystal which is supplied into the melt in a unit time. dS/dt 
means a speed of the crystal growth. It is a weight increment of the 
growing crystal in a unit time. 
Now more specialized case is considered to use more measurable parameters. 
We assume the single crystal (8) has a round section with a radius E and 
the undoped crystal (9) has a round section with a radius F. "U*" denotes 
a relative line velocity for pulling the single crystal (8) with regard to 
a liquid-solid interface (15). "V*" denotes a relative line velocity for 
dipping the undoped crystal (9) with regard to a liquid-solid interface 
(17). The ascending velocity U* and the descending velocity V* must 
satisfy the equation 
EQU F.sup.2 V*=(1-k)E.sup.2 U* (10) 
in order to keep the impurity concentration constant. 
Strictly speaking the liquid-solid interfaces (15) and (17) move upward or 
downward by vertical displacements of the lower shaft (2) and the upper 
shaft (13). "W" is an ascending velocity of the lower shaft. Because W is 
the ascending velocity, W is negative when the lower shaft is descending. 
"U" is an ascending velocity of the upper shaft (13). This is not a 
relative velocity but an absolute velocity. U is not identical to U* in 
Eq.(10). "V" is a descending velocity of the supporting shaft (10). This 
is not a relative velocity. V is not identical to V* in Eq.(10). "A" is an 
area of the liquid-solid interface (15). "B" is a sectional area of the 
single crystal (8). "C" is a sectional area of the undoped crystal (9) to 
be replenished. 
The condition for keeping the impurity concentration constant in the 
compound melt (5) is given by 
##EQU1## 
When Eq.(9) is not rigorously satisfied, the impurity concentration will 
vary. The rate of variation is calculated from 
EQU dC/CL=(1-k)dS-dQ (12) 
In Eq.(12) dS and dQ are independent variables. From Eq.(12) when the melt 
weight L is large enough, even if the variables dS and dQ deviate a little 
from Eq.(9), the variation of the impurity concentration C is very small. 
An example which satisfies the special equation (10) is now explained. 
In this example the relative pulling velocity of the single crystal (8) is 
5 mm/H, the diameter of the single crystal (8) is 50 mm, and the diameter 
of the undoped crystal (9) to be replenished is 15 mm. Then from Eq.(10) 
the most pertinent relative velocity of the undoped crystal dipping into 
the melt should be 
EQU (1-k).times.55.6 (mm/H) 
In the example shown in FIG. 1 the undoped crystal (9) is a pillar. And it 
is enclosed by the encapsulant-supporting-cylinder (12). The supplying 
device comprises the supplying shaft (10), the cylinder (12) and the 
supporting device (not shown in FIG. 1) which rotates and suspends the 
supplying shaft (10). In the disposition the cylinder (12) dips into the 
melt (5) at the peripheral region of the crucible (4). 
This disposition of the cylinder breaks a rotational-symmetry of the melt. 
The crucible (4), the susceptor (3), the lower shaft (2) and the melt (5) 
rotate in the crystal growth. The non-symmetric disposition of the 
cylinder may make a perturbation on the liquid-solid interface (15). The 
perturbation may hinder the cylindrical growth of a crystal. 
FIG. 2 shows another embodiment of the invention. This embodiment is immune 
from the perturbation of the non-symmetric disposition of the supplying 
device. 
In this embodiment a non-doped crystal (9) to be replenished is shaped in a 
large cylinder whose diameter is a little smaller than that of the 
crucible (4). And the cylinder of the non-doped crystal (9) is enclosed by 
a double cylinder (12'). In a gap between the double cylinder (12') and 
the cylindrical non-doped crystal (9) a liquid encapsulant (16) is filled. 
Then the double cylinder (12') is called an 
encapsulant-supporting-double-cylinder. 
The disposition and the shape of the encapsulant-supporting-double-cylinder 
(12') has a perfect rotational symmetry. The existence of the cylinder 
(12') does not disturb the rotation of the melt (5). No perturbation would 
occur on the liquid-solid interface (15). 
In this case an encapsulant-heater (14) is a double coiled heater installed 
at a pertinent height of the double cylinder (12'). An alternative of an 
encapsulant-heater (14) is an assembly of several small heaters which are 
disposed with several fold symmetry. And two or three identical supporting 
shafts (10) should be installed. 
Now we consider the height of the liquid encapsulant (16) for covering the 
undoped crystal (9). 
What is important is a height H which is defined as a distance from the 
surface of the lower liquid encapsulant (6) to the surface of the upper 
liquid encapsulant (16). 
"h" denotes a distance from the liquid-solid interface (15) to the bottom 
end of the encapsulant-supporting-cylinder (12) or double cylinder (12'). 
"h.sub.1 " denotes a distance from the normal liquid-solid interface (15) 
to the suppressed liquid-solid interface (17) in the 
encapsulant-supporting-cylinder (12) or double cylinder (12'). 
".rho..sub.0" is a density of the compound melt (5). ".rho..sub.1" is a 
density of the liquid encapsulant (6) or (16). The height H is a function 
of the interface difference h.sub.1. Simple calculations lead to 
EQU H=(.rho..sub.0 /.rho..sub.1 -1)h.sub.1 (13) 
It is desirable that H is higher, because the greater part of the undoped 
crystal (9) is covered with the liquid encapsulant (16). 
The height H is in proportion to h.sub.1 from Eq.(13). The suppressed 
liquid-solid interface (17) is kept by the encapsulant-supporting-cylinder 
(12) or double cylinder (12'). Thus the maximum of the variable h.sub.1 is 
equal to h. Then the maximum of the height H is obtained from Eq.(13) by 
replacing h.sub.1 by h. 
Accordingly it is important that the bottom end of the 
encapsulant-supporting-cylinder (12) or double cylinder (12') is dipped 
deep into the compound melt (5) and much encapsulant material is filled in 
the cylinder (12) or double cylinder (12'). 
In the case of the crystal growth of GaAs the density .rho..sub.0 of the 
melt is 5.7 g/cm.sup.3 and the density .rho..sub.1 of liquid B.sub.2 
O.sub.3 is 1.6 g/cm.sup.3. The ratio of H to h.sub.1 is about 2.6. 
Advantages of this invention are now explained. 
(1) The impurity concentration of a single crystal grown by the invention 
is uniform from seed end to tail end. 
This is because the impurity concentration of the melt is kept to be 
constant by replenishing an undoped poly-crystal or single crystal into 
the melt. 
(2) The separating of impurity near the tail end of a crystal does not 
occur, because the impurity concentration is uniform in the grown crystal. 
Therefore whole of a crystal is available for making various electronic 
devices. Waste portion of the crystal is very little. 
(3) There happens no deviation from stoichiometry of compounds of groups 
III-V or groups II-VI. 
Heated portion of an undoped crystal to be replenished is covered with a 
liquid encapsulant which is pressed by N.sub.2 gas or inert gas with a 
high pressure. Volatile elements of group V do not escape from the undoped 
crystal. 
This invention has a wide scope of applicability. This is fully applicable 
for all kinds of crystal growth by an LEC method. The examples of the 
matrix crystals are GaAs, GaP, InP, InAs, GaSb, PbTe, PbSe, etc. 
Impurities doped into the matrix compound are one or more than one elements 
among S, B, Te, Sn, Sb, In, Si, Cr, Fe, As, and so on which have a 
distribution coefficient less than 1 in the matrix compound melt.