A method for controlling specific resistance of single crystal

Abstract: A method for controlling a specific resistance of a single crystal in a Czochralski-method type single crystal pulling apparatus having a hermetical chamber in which the single crystal is pulled up from a polycrystal melt and an inert gas supply and exhaust system by means of which an inert gas is supplied to the hermetical chamber and exhausted therefrom; the method being characterized in that the pneumatic pressure in the hermetical chamber and the supply rate of the inert gas are controlled in accordance with a prepared control pattern with respect to the passage of pulling time.

Description: This invention relates to a method for controlling a specific resistance of a single crystal ingot (rod) pulled up from a polycrystal melt of a semiconductor substance in a Czochralski (CZ) method. In a CZ method-type single crystal pulling apparatus for growing and raising a single crystal silicon ingot from a polycrystal silicon melt , a silicon seed crystal fixed at the lower end of a pull wire (or, alternatively, supported by a pull shaft) is dipped slightly in the silicon melt contained in a quartz crucible provided in a hermetical chamber , and is pulled up at a given rate while being turned about its axis by means of the pull wire, whereby a growing silicon single crystal rod is raised. When a material having a high volatility and a small segregation coefficient, such as Sb, is added to the polycrystal melt in the crucible as a dopant, or an impurity, for the purpose of obtaining a doped or impure semiconductor, e.g. Sb-doped single crystal, an inconvenience is experienced as the single crystal is pulled up and the liquid level of the polycrystal melt lowers in the crucible: that is, since the segregation coefficient of the dopant (Sb) is small, its tendency of entering the growing single crystal is small, and consequently the dopant concentration of the polycrystal melt in the crucible gradually increases as the pulling operation proceeds, so long as the pressure in the chamber is maintained at a constant value (e.g., 30 millibar, as shown by the broken straight line A in Fig. 2 of the accompanying drawings) so as to fix the evaporation rate of the dopant throughout the pulling operation. There exists a relation between the specific resistance of a single crystal and the Sb concentration thereof which is typically represented by the graph of Fig. 4 of the accompanying drawings. As the Sb concentration increases, the specific resistance of the single crystal decreases along a curve resembling a hyperbolic curve. Therefore, as described above, as the single crystal grows longer causing the dopant concentration to increase, that is, as the proportion of the length of the grown crystal to the aimed final length thereof increases (abscissa, %), the specific resistance drops along the broken line a of Fig. 3 of the accompanying drawings, and eventually may become lower than the minimum allowable value. In Fig. 3, plotted with a symbol ⋄ is the actually measured specific resistance. FR-A-2038156 discloses a method for preparing a semiconductor single crystal such as Si or Ge doped with P, As or Sb having a uniform specific resistance across the entire drawn crystal. This is achieved by controlling the pressure of the inert gas atmosphere, such as Ar or He, according to a predetermined pattern during the pulling of the crystal. JP-A-61,117191 discloses a device for preparing a silicon single crystal having a carbon heater and a controller for controlling the degree of opening of a first flow rate control valve so as to feed always a fixed amount of gaseous Ar into a chamber and for controlling a second flow rate control valve so as to adjust the pressure in the chamber to an always fixed value or to an optional value by changing the conductance in a duct. When pulling of an Si single crystal proceeds, generation of a reaction product tends to increase. At this stage, an output signal from a manometer is inputted into the controller (or regulator) and the degree of opening of the second flow rate control valve is increased by the controller or regulator. Thus the pressure in the chamber is held at an almost fixed value. FR-E-94593 discloses an apparatus and a method of growing Sb-doped Si single crystals in which the pressure is reduced controllably so that the dopant concentration in the drawn crystal is homogeneous (page 1, lines 27-37). The present invention aims to provide a method for controlling the axial specific resistance of a single crystal ingot pulled up from a polycrystal melt of a semiconductor substance in a Czochralski (CZ) method with high precision. More particularly, the invention aims to provide a method which enables arbitrary controlling of axial distribution of the specific resistance of the single crystal ingot and thus enables growing of the single crystal ingot in which the specific resistance is within an allowable range throughout the whole length of the ingot. The present invention provides a method for controlling a specific resistance of a single crystal which is grown in a Czochralski-method type single crystal pulling apparatus having a hermetical chamber in which the single crystal is pulled up from a polycrystal melt and an inert gas supply and exhaust system by means of which an inert gas is supplied to said hermetical chamber and exhausted therefrom; said method being characterized in that the pneumatic pressure in said hermetical chamber and the supply rate of said inert gas are controlled in accordance with a prepared control pattern with respect to the passage of pulling time, (i) wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δP/δt) F and (δF/δt) P such that K Sb is not equal to 1: K Sb =aP o +b(δP/δt) F +cF o +d(δF/δt) P +e wherein a, b, c, d, e are empirically obtained coefficients, P is the pressure in said chamber, F the inert gas flow rate, t the time passage of the pulling operation, K Sb an apparent segregation coefficient of Sb dopant in the silicon melt, P o the initial value of said chamber pressure P, F o the initial value of said inert gas flow rate F, and then programming the values of the pneumatic pressure P in said chamber and the inert gas flow rate F with respect to the time passage t of the pulling operation; or (ii) wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δP/δt) F such that K Sb is not equal to 1: K Sb = aP o + b(δP/δt) F + cF o + e wherein a, b, c, e, P, F, t, K Sb , P o , and F o are as defined above, and then programming the value of the pneumatic pressure P in said chamber with respect to the time passage t of the pulling operation; or (iii) wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δF/δt) P such that K Sb is not equal to 1: K Sb = aP o + cF o + d(δF/δt) P + e wherein a, c, d, e, P, F, t, K Sb , P o , and F o are as defined above, and then programming the value of the inert gas flow rate F with respect to the time passage t of the pulling operation. The method of the invention is preferably characterized by further determining a solute concentration C within the solidification region in the vicinity of the solid-liquid interface in the silicon melt, by means of the following equation: C = C o · K Sb (1-G) KSb - 1 wherein C o is the initial solute concentration of the melt, G the proportion of the weight of the grown crystal to the initial weight of the silicon melt, K Sb the apparent segregation coefficient, and Sb the solute. The evaporation rate of a dopant such as Sb in a polycrystal melt depends on the ambient pressure and time such that the evaporation rate of the dopant increases as the pressure decreases with time, and the dopant concentration of the polycrystal melt is caused to decrease. According to the invention, it is now possible 6o regulate the growth of a single crystal rod in a manner such that the specific resistance of the single crystal rod throughout its entire length becomes within a desired range. This regulation is attained by employing a central processing unit to reduce the gas pressure in the chamber of a single crystal pulling apparatus as the pulling operation proceeds, whereby the evaporation rate of the dopant is increased and the dopant concentration of the polycrystal melt is reduced, which in turn checks or moderates the drop in specific resistance of the single crystal, as is clear from Fig. 3 of the accompanying drawings; consequently, it is now possible to regulate the specific resistance of the single crystal rod within a desired range throughout its entire length. Also, by increasing the inert gas flow rate to the chamber by employing a flow rate control means, as the pulling operation proceeds, the evaporation rate of the dopant increases and the dopant concentration of the polycrystal melt decreases, whereby the dropping of the specific resistance of the single crystal is checked or moderated, as is clear from Fig. 3; consequently it is also possible to regulate the specific resistance within a tolerable range throughout the whole length of the single crystal. The invention will be further described, by way of example only, with reference to the accompanying drawings, in which: Fig. 1 is a block diagram showing the construction of a specific resistance control apparatus for carrying out the method of the invention; Fig. 2 is a graph showing a variation of pressure in a chamber with respect to the passage of time; Fig. 3 is a graph where the measured result of the specific resistance of a single crystal is plotted with respect to the proportion of the length of the grown crystal to the aimed final length thereof; and Fig. 4 is a graph showing a relation between the specific resistance of the single crystal and the Sb concentration thereof. An embodiment of the invention will now be described with reference to the drawings. Reference numeral 1 designates a single crystal pulling apparatus based on CZ method, in which a pull chamber 3 is provided above and in coaxial alignment with a heat chamber 2, both made of a stainless steel. A quartz crucible 4 for containing a semiconductor substance 10 is supported by a support shaft 5 in the chamber 2. The support shaft 5 is adapted to rotate about its axis and shift in the axial direction. If the quartz crucible 4 were always held at the original level, the melt level in the quartz crucible 4 would gradually shift downwards relative to a heater 6 with the growth of a single crystal 9, thus resulting in an instability of the thermal field around the crystal and the melt 10. Therefore, the support shaft 5 is adapted to axially displace the crucible such that the displacement of the melt level (solid-liquid interface) downwards is compensated for by continuous rise of the crucible 4 so that the interface level is stationary relative to the heater 6 during the growing. Around the heater 6 is provided a cylindrical thermal insulator 7, both made of carbon. In the upper part of the chamber 2 a purge tube 8 for supplying Ar gas is provided vertically and in coaxial alignment with the growing single crystal 9, which is raised into the purge tube 8. During the single crystal pulling operation, the height of the crucible is controlled such that the lower end of the purge tube 8 is always in the upward vicinity of the surface of the melt of the polycrystal Si melt 10. A seed crystal 12 is fixed at the lower end of a pull wire 11, which hangs within the purge tube 8. The wire 11 is rotated and vertically moved at various rates by means of a drive mechanism, not shown, provided in the upper part of the pull chamber 3. Argon gas is supplied to the pull chamber 3 and the heat chamber 2 from an argon gas supply source 13, e.g. an gas cylinder, by way of a supply line 14, across which are provided a mass flow controller (MFC) 15 and a valve 16. The MFC 15 is capable of controlling the Ar gas flow rate to a set value. In this kind of single crystal pulling apparatus, a chemical reaction takes place between the quartz crucible and the Si melt to generate SiO, which is dissolved in the Si melt. A part of the SiO evaporates from the melt and mixes in the atmosphere within the heat chamber, and the other part stays in the Si melt. The Ar gas supplied from the supply source 13 and the SiO gas evaporating from the melt are drawn from the chamber 2 by means of a vacuum pump 18. In an exhaust line 19 connecting the chamber 2 with the vacuum pump 18 is provided a conductance valve 20, which consists of an electrically operated butterfly valve 21 and an electrically operated needle valve 22, the valves 21 and 22 being arranged in parallel. The needle valve 22 is driven by a pulse motor 23 such that its opening is precisely controlled. It is possible to replace the conductance valve 20 with a single electrically controlled butterfly valve or an electrically controlled ball valve. A pressure sensor 24 is affixed to the chamber 2 for detecting the internal pressure (lower than the atmospheric pressure) of the chamber 2. In Fig. 1, reference numeral 25 designates a central processing unit (CPU) 25 which constitutes control means adapted to control the internal pressure of the chamber 2 and/or the Ar gas flow rate by controlling the opening of the MFC 15 and the opening of the needle valve 22 in response to the pressure value detected by the pressure sensor 24 in accordance with a control pattern corresponding to the passage of crystal pulling time. When it is intended to control the pressure in the chamber 2, the pressure value (analog value) detected by the pressure sensor 24 is digitized through an A/D converter 26, and inputted to the CPU 25, which CPU 25 outputs a control signal responsive to the detected pressure value. This control signal is amplified through a pulse amplifier 27, and inputted to the pulse motor 23, which, thereupon, drives the needle valve 22 to control the opening thereof based on the control signal received. As a result, the internal pressure of the chamber 2 is controlled in accordance with the control pattern. When the opening of the needle valve 22 is decreased, the pressure in the chamber 2 increases, and the flow rate of the Ar gas is lowered. When it is not possible to control the pressure of the chamber 2 by only adjusting the opening degree of the needle valve 22, the opening of the MFC 15 is adjusted to change the Ar flow rate to thereby control the pressure in the chamber 2. The flow rate of Ar gas (analog value) detected by the mass flow controller 15 is digitized through an A/D converter 29, and supplied to the CPU 25 as a feedback. The CPU 25 compares this detected Ar gas flow rate with a reference value for Ar gas flow rate, and generates a control signal (digital signal) based on the result of the comparison. Then, this digital control signal is converted into an analog signal through a D/A converter 30 and inputted to the MFC 15 as a setting input to renew the set value to which the Ar gas flow rate is controlled. When the Ar gas supply rate to the MFC 15 is decreased, the pressure in the chamber 2 is reduced. The Ar gas flow rate detected by the MFC 15 and the internal pressure of the chamber 2 detected by the pressure sensor 24 are alternatively displayed digitally on the display device 32 by alternating the switch 31. To pull up the Si single crystal 9 based on the CZ method in the single crystal pulling apparatus 1, lumps of polycrystal silicon having appropriate sizes are charged into the crucible 4, and melted by the heater 6; then the seed crystal 12 connected to the lower end of the wire 11 is lowered until it comes in contact with the Si melt 10 contained in the crucible 4. After the lower end face of the seed crystal 12 is partially melted, the melt temperature is lowered to such an extent that the seed crystal would not be melted any more. Then, the wire carrying the seed crystal is pulled up at a given rate, and a single crystal grows on the seed crystal, while the crystal and the melt are counter-rotated with respect to each other. During this operation, Ar gas is supplied to the chamber 2 through the purge tube 8, and this Ar gas and the SiO gas evaporating from the melt are drawn out of the chamber 2 by the vacuum pump 18. As the single crystal pulling operation proceeds, the melt level shifts downwards relative to the crucible wall, and if the evaporation rate of the dopant Sb is maintained unchanged by keeping the pressure in the chamber 2 at a constant value, as is the case with the conventional procedure, the Sb concentration in the Si melt 10 increases and, as a result, the specific resistance of the as-grown single crystal 9 decreases with the progress of the pulling operation, as shown in Fig. 4 (ref. broken straight line a in Fig. 3, also). With a view to preventing this phenomenon of gradual decrease in the specific resistance of the single crystal ingot with the growth of the single crystal, experiments were conducted and it was found that when the opening degrees of the needle valve 22 and the mass flow controller 15 were adjusted in accordance with a control pattern which was designed such that the pressure in the chamber 2 was caused to decrease along a curve B in Fig. 2, which was a broken line, as the single crystal pulling operation proceeded, the evaporation rate of Sb increased with time so that the Sb concentration of the melt was reduced and, consequently, due to the relation shown in Fig. 4, the lowering in specific resistance of the single crystal 9 was restrained. In Fig. 3, the result of the actual measurement of the specific resistance is plotted with a symbol X with respect to the proportion of the length of the as-grown crystal to the aimed final length thereof. Compared with the result plotted with the symbol ⋄ (which corresponds to the specific resistance measured when the pressure in the chamber 2 was kept constant), the result of the method of the present invention shows a clear improvement in that the lowering of the specific resistance with the lengthening of the single crystal is greatly moderated, if not completely checked. As described above, it is possible to control the pressure in the chamber 2 in accordance with a control pattern, like that of Fig. 2, stored in the CPU 25, so that it is possible to arbitrarily control the specific resistance of the single crystal ingot 9 after conducting extensive trial operations. Consequently, the specific resistance throughout the whole length of the single crystal 9 can be controlled to be within a tolerable range. In the above description of the invention, the pressure in the chamber 2 is varied in accordance with a predetermined control pattern by adjusting the opening degrees of the needle valve 22 and the mass flow controller 15; but if a conductance valve is used which has a sufficient sensitivity for covering the region across which the pressure control pattern extends, it is not always necessary to employ the mass flow controller 15 to control the Ar gas flow rate. In the procedure described above, only the pressure in the chamber 2 is controlled; but it is also possible to regulate the value of the specific resistance within a range throughout the whole length of the single crystal 9 by fixing the pressure in the chamber 2 at a constant value, and increasing under control the Ar gas flow rate alone with the progress of single crystal pulling operation, whereby the evaporation rate of Sb increases with the progress of single crystal pulling operation and, consequently, the lowering of the specific resistance of the single crystal 9 is checked due to the relation shown in Fig. 4. If, as described in the embodiment above, the Ar gas flow rate in addition to the opening degree of the needle valve 22 is controlled in order to obtain improved controlling of the pressure in the chamber 2, a correction to the control pattern (B in Fig. 2) used in the embodiment for the chamber pressure is required because the control pattern is effective only when the Ar gas flow rate is constant. The control pattern, according to which the changes in the pressure in the chamber 2 and/or the Ar gas flow rate are determined, is programmed in advance in a storage of the CPU. So far has been described a procedure for regulating the specific resistance of an as-grown single crystal to a roughly constant value throughout the whole length of the crystal, particularly in the case of a Sb-doped single crystal, by controlling the pressure in the chamber and/or the Ar gas flow rate with respect to the passage of single crystal pulling time. Next, a manner for determining such a control pattern for the chamber pressure and/or the inert gas flow rate will be described in detail. Let C be the solute concentration within the solidification region in the vicinity of the solid-liquid interface in the silicon melt, C O the initial solute concentration of the melt, G the proportion of the weight of the grown crystal to the initial weight of the silicon melt, and K Sb the apparent segregation coefficient, Sb being the solute; then the following relation holds: C = C O · K Sb (1-G) KSb - 1 (1) In the case of Sb, which has a relatively high volatility, the concentration of the solute Sb in the silicon melt decreases as the chamber pressure is reduced and/or as the inert gas flow rate in the chamber is increased; and the present inventors confirmed by experiments that the solute concentration decreased more sharply than was expected from the fact that the segregation coefficient is far smaller than 1, and that the apparent segregation coefficient K Sb was greatly affected. Also, they confirmed after quite a few difficult experiments that it is possible to approximate the segregation coefficient K Sb to 1. Let P represent the pressure in the chamber 2, and F the inert gas flow rate. Through repetition of various mathematical methods as well as experiments, the present inventors discovered that the segregation coefficient K Sb can be given as a function of certain variables, which are the initial value P O of the chamber pressure P, the initial value F O of the inert gas flow rate F, the partial differential of the pressure P by the time t, i.e., (∂ P/∂ t) F and/or the partial differential of the flow rate F by the time t, i.e., (∂ F/∂ t) P : K Sb = aP O + b(∂ P/∂ t) F + cF O + d(∂ F/∂ t) P + e (2) wherein a, b, c, d and e are empirically obtained coefficients. Now, by solving the partial differential equation (2) to obtain the partial differential (∂ P/∂ t) F and/or the partial differential (∂ F/∂ t) P such that K Sb is not equal to 1, and programming the pressure P and/or the flow rate F with time t, and storing the same in the memory storage of the CPU 25 shown in Fig. 1, then since C is not equal to C O , it becomes possible to regulate the specific resistance of the single crystal to a roughly constant value throughout the whole length of the single crystal. It has been empirically confirmed that the empirical coefficients a, b, c, d, and e of equation (2) are independent from each other, so that it is possible to obtain them respectively by means of the known least square approximation method. For example, in the case where the inert gas flow rate F is fixed at a constant value, then, since (∂ F/∂ t) P = 0 , equation (2) is rewritten as follows: K Sb = -7.5× 10⁻⁶P O 1.7 - (∂ P/∂ t) F - 1.1 × 10⁻⁴F O + 1.00 (3) If P O = 50 millibar, (∂ P/∂ t) F = 0.015 , and F O = 70Nl/min, then, according to equation (3), K Sb = 0.97, which is approximately one. As is clear from the above description, according to the invention, the pressure in the chamber of a single crystal pulling apparatus and/or the inert gas flow rate is controlled in accordance with a pattern with respect to the passage of single crystal pulling time, so that it is possible to control the evaporation rate of the dopant to thereby prevent thickening of the dopant in the polycrystal melt, and consequently the lowering in the specific resistance with progress of the crystal growing is checked such that the specific resistance is regulated to be within a tolerable range throughout the whole length of the single crystal.

Claims: A method for controlling a specific resistance of a single crystal which is grown in a Czochralski-method type single crystal pulling apparatus having a hermetical chamber in which the single crystal is pulled up from a polycrystal melt and an inert gas supply and exhaust system by means of which an inert gas is supplied to said hermetical chamber and exhausted therefrom; said method being characterized in that the pneumatic pressure in said hermetical chamber and the supply rate of said inert gas are controlled in accordance with a prepared control pattern with respect to the passage of pulling time, wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δP/δt) F and (δF/δt) P such that K Sb is not equal to 1: K Sb = aP o + b(δP/δt) F + cF o + d(δF/δt) P + e wherein a, b, c, d, e are empirically obtained coefficients, P is the pressure in said chamber, F the inert gas flow rate, t the time passage of the pulling operation, K Sb an apparent segregation coefficient of Sb dopant in the silicon melt, P o the initial value of said chamber pressure P, F o the initial value of said inert gas flow rate F; and then programming the values of the pneumatic pressure P in said chamber and the inert gas flow rate F with respect to the time passage t of the pulling operation. A method for controlling a specific resistance of a single crystal which is grown in a Czochralski-method type single crystal pulling apparatus having a hermetical chamber in which the single crystal is pulled up from a polycrystal melt and an inert gas supply and exhaust system by means of which an inert gas is supplied to said hermetical chamber and exhausted therefrom; said method being characterized in that the pneumatic pressure in said hermetical chamber and the supply rate of said inert gas are controlled in accordance with a prepared control pattern with respect to the passage of pulling time, wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δP/δt) F such that K Sb is not equal to 1: K Sb = aP o + b(δP/δt) F + cF o + e wherein a, b, c, e are empirically obtained coefficients, P is the pressure in said chamber, F the inert gas flow rate, t the time passage of the pulling operation, K Sb an apparent segregation coefficient of Sb dopant in the silicon melt, P o the initial value of said chamber pressure P, F o the initial value of said inert gas flow rate F; and then programming the value of the pneumatic pressure P in said chamber with respect to the time passage t of the pulling operation. A method for controlling a specific resistance of a single crystal which is grown in a Czochralski-method type single crystal pulling apparatus having a hermetical chamber in which the single crystal is pulled up from a polycrystal melt and an inert gas supply and exhaust system by means of which an inert gas is supplied to said hermetical chamber and exhausted therefrom; said method being characterized in that the pneumatic pressure in said hermetical chamber and the supply rate of said inert gas are controlled in accordance with a prepared control pattern with respect to the passage of pulling time, wherein said prepared control pattern is obtained by first solving the following partial differential equation for (δF/δt) P such that K Sb is not equal to 1: K Sb = aP o + cF o + d(δF/δt) P + e wherein a, c, d, e are empirically obtained coefficients, P is the pressure in said chamber, F the inert gas flow rate, t the time passage of the pulling operation, K Sb an apparent segregation coefficient of Sb dopant in the silicon melt, P o the initial value of said chamber pressure P, F o the initial value of said inert gas flow rate F; and then programming the value of the inert gas flow rate F with respect to the time passage t of the pulling operation. A method as claimed in any of claims 1 to 3, characterized by further determining a solute concentration C within the solidification region in the vicinity of the solid-liquid interface in the silicon melt, by means of the following equation: C = C o · K Sb (1-G) KSb - 1 wherein C o is the initial solute concentration of the melt, G the proportion of the weight of the grown crystal to the initial weight of the silicon melt, K Sb the apparent segregation coefficient, and Sb the solute.

Inventors: BABA MASAHIKO, OHTSUKA SEIICHIRO, SEKI HIDETOSHI, BABA, MASAHIKO, OHTSUKA, SEIICHIRO, SEKI, HIDETOSHI
Applicants: SHINETSU HANDOTAI KK, SHIN-ETSU HANDOTAI COMPANY LIMITED
Application year: 1990
Main classification: C30B15
IPC codes: C30B15, C30B29