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10Journal of Siberian Federal University. Engineering & Technologies 2015 8. Issue 7. 835-850
УДК 004.7
Area Measurement Crystals Grown from the Liquid Melt Using the Czochralski Method, Based on the Control-Circuit Conditions Contact Sensor Liquid Level
Sergey P. Sakhanskiy*
Siberian Federal University 79 Svobodny, Krasnoyarsk, 660041, Russia
Received 20.01.2015, received in revised form 17.06.2015, accepted 13.09.2015
For crystals grown from the liquid melt using the Czochralski method, the mathematical model of the current control chip area by controlling the conditions of the contact sensor circuit level of the melt in the crucible, which allows to calculate the control signal, as the difference between the current and the target area grown crystals.
Keywords: crucible, growing crystals, the level sen.
DOI: 10.17516/1999-494X-2015-8-7-835-850.
Измерение площади кристаллов, выращиваемых из жидкого расплава по способу Чохральского, на основе управления условиями замыкания контактного датчика уровня расплава
С. П. Саханский
Сибирский федеральный университет Россия, 660041, Красноярск, пр. Свободный, 79
Для кристаллов, выращиваемых из жидкого расплава по способу Чохральского, разработана математическая модель контроля текущей площади кристалла на основе управления условиями замыкания контактного датчика уровня расплава в тигле, позволяющая вычислить сигнал управления как разность текущей и заданной площади выращиваемых кристаллов.
Ключевые слова: тигель, выращивание, кристаллы, датчик уровня.
© Siberian Federal University. All rights reserved
* Corresponding author E-mail address: [email protected]
Introduction
For growing single crystals of semiconductor material from the crucible to melt using the Czochralski method, developed by the contact method of measurement and control [14] of the current area of the crystal.
The basis of the method of measurement is that the crucible which performs rotational movement around its own axis with a speed of rotation WT, and has an inner diameter D, the molten metal to be molten (Fig. 1) from which the growing crystal diameter d, with the growing speed (drawing) V and a rotation speed W3 crystal. Grown crystal is placed in heat sealed to provide the necessary snap-temperature growth conditions. The entire process occurs in the growing chamber with an inert gas or in vacuo. The melt temperature is controlled by controlling heater power using temperature T3, the side surface of the heater. Floats on the surface of the melt conductive graphite screen, the function of which is closing and opening of the graphite isolated melt level sensor is fed to the control system signal H to change the level of the melt in the crucible. This signal is required to control the formation of the crucible lifting speed VT that provides stabilization of the melt level in the crucible and the conditions of constant opening and closing of the contact level sensor.
An important basis for the contact method of monitoring and control of crystal growth is to control the current area (or diameter with round shape) of the growing crystal, according to the control signal y, calculated as a function of the current deviation from a given chip area, using the movements of the crystal X3I and the crucible XTI for the period TI evaluating the control signal y.
The rate of decrease of the melt in the crucible Vp, as well as the accelerated rate of rise of the crucible after breaking up VTM contact sensor and the slow rate of rise of the crucible after the closure
Fig. 1. Schematic of a contact measurement method: 1 - camera; 2 - seed; 3 - crystal; 4 - pin level sensor; 5 - temperature sensor; 6 - crucible; 7 - conductive screen; e - molten metal; 9 - heater; 10 - thermal accessories
of the contact sensor VTM/M determined by the expression (1) - (5), which introduced the coefficients mcoease the speed (C = 4) and the; cruciWe lifting speed reduction (M = 4).
This control provides a crystal growth process peoiodic opening and closing of the contact sensor in the range of changes in the level of the melt about 1-2 microns.
V = V
P 3
PP
P-K
(1)
V =V •
TM p
= V
M = d, ■ . -
irx 1 vriTc
.JD
Px
D
(2) (3)
V
=v
M p
d = d •
_in max
= V
a/Mr
P
Ak
D
(4)
(5)
where Vp - the rate of decrease of the melt in the crucible; V - the rate of crystal growth; d - the current diameter of the crystal; D - inner diameter of tht crut ible; pT - beats. the density of the solid material; pK -a deati. density of rhr liqutdm-terial; d - telnet nominal diameter of the crystal grown on talie; cylinelrinal past; <imax - maximum diameter of the growing crystal, in compliance with which the basic condition under which the sensor and the screen closeness after opening; dmin - the minimum allowable value or the diameter of the cryttal, where the conditions of the backlog of the screen from the srnsor alter it has closed.
To contnet method for me-susing the rontrob signal or the amount of movement of the crucible XTIf and the seed X3If for the evaluation of Tn can be represented in the form of expressions (61(10) e
aoy
y = X
ky=B
x„.
y = -
X„.
HII< A-B
VPt
D_ d
_ _ 2 \
d -1
d.
V /
(6)
(7)
(8)
V — V = Y X зц X X3
X = X ■ x
Am X nm T
(9) (10)
where A, B - scaling factors; Ky - the setting of a give n diamete r (area) of the growing crystal; Xmi -moving from seed sampled o3; XHTI - moving the crucible with discrete samples xT; x3 - sampled move seed; xT - sampled move the crucible.
2
2
2
2
Equation (8) shows the direct connection of the control signal y from the current deviation from a give n chip area. During the evaluation cycle control T, signal p is calculated in the control syotem for the expression (6). With the entry into sloe control system installation drawing aetpoint diameter Ky on the cylinfrical part op sfe grow ing efystal ia defined by a given area of cuStivation.
As the hoist crucible to control the speed climbing up used open stepper drive stepper motor, which provides multiple process changes ascent rate of the crucible, at a signal from the contact level seosor.
Specifying fast VTM and elow nlM/0h crucible lifti ng spe ed at the ti me of ope n and closed states of the contact sensor is produced by the expressions (11)(12):
1
X = P—^-, (11)
H3PP - B
XgpM= P- M-^-B-, (12)
B
where; XH3pp - numbes of pulsos seed is? productd through the issuance of P pul ses move the crucible woitP often contact sensors; XH3pM - number of pulres seep, -which is issoed by P pulses move the crucible with closed contact sensoys; P - the number of pulses issued by lifting rhe crucible to the stepper drive.
The above oxpressions fon mabe control of the ceucible moving upwards as valid crucible provided movement at slow speed in the contact points of the sensor circuit of the melt (M = 4) and provided to stop racing of the eracible of the closed state of the sensor points of the melt(M = co).
Expressifg for fge momentum moving XH3„ steof, the crucibVe X^ time T, and evaluation of the control signal n can be repsesented as expressfons (rf)(14):
X- =Xom-Ky (13)
-"■mn, B
T _ r^H3S ' X3 _ _ 'K y' X3 (14)
s e V ~V3~ B' V3 '
where T, - the evaluation period of the control signal (the ti me of pro c e s sing a predetermined number
of pufsesXHTI().
Total movement time t in the process of closing the contact sensor in slow motion and time of the total traffic at an accelerated speed of the crucible after the opening of the sensor tR, as well as the number of cycles K on opening and closing sensor for the evaluation period signal control T, can be repstsentef as expre srions (15)(16):
e _| dmin d
t(d) = : •
dmax I _ e
(15)
where t - while driving at slow speed crucible VTM/M after closing sensor for the assessment period signal mfnagemenl; tR - the moveme nt of Ihhe c rucible at an acc ele rated pace VTM after opening sensor for the evaluation period signal management; K„ - number of cycles of opening and closing the sensor during T,
Schedule crucible lifting drive in accordance with the expressiog (15) shown in Fig. 2. Automatic control system provides a range of changes in the diameter according to the expressions (17)(19):
d c d ...d , (17)
mp pp >
= d 1 (18)
dpp =d 1
I-1
C ■ a
mp
^'fH
where d - the current diameterof thL^ crystal; dpp - mcximum diameter; dmp - minimum diameter; a -eoefficient rf maximum diameter; (3 - coefficient of tht mtnPmum diamfter.
Expression (15) for fhe time of accelerated growtf cnucible tB, for different values of the operating range of the diameter of the crystal can be represented in the form of expressions (20)(22):
„ C • a
C • a- a--
^ ^ v M y tMj = ,--—-. (20)
t, d) = tc -1 - (21)
Vp, Vt, H t tg
P
Vt
Vtm/M
Fig. 2. Graph of formation of the crucible lifting speed: V - the rate of decrease of the melt in the crucible; V - the rate of rise of the crucible; H - fhe contact level sensor (P - sensor open)
If you specify a condition for the maximum reduction of the melt in contact mode control Lp (1-2 microns), the expression of time delayed recovery crucible t(d) will take the form of (23):
t (d) =
L„
= lp • T •
xt
d, 2
d
i d
1 - d
f
M 11
C
(23)
where Lp - the maximum reduction in the melt; T, - the period of tine signal evaluation.
Slow ascent graph crucible /(d), in accordance with the expression (23) shown in Fig. 3. Here, the estimate of the rlow motion of the crucible corresponds to an extreme minimum value oO the range of diameter O(dmp) is defined as the expression (24):
where E =
(P-1)
M-I 1 -
C
t . T
t (dmp ) = t =
(24)
The number of cycles of cij5eir:ijngg ant:! closing hOa sensor can be represented as the expression (25), the schedule of opening and closing cycles K, is shown in Fig. 4.
K„ =
X m ' E
1 1 dl 1 1
C J C M J
-(C -1-C- M
(25)
In accordance with the expressions (15) - (25) a control signal y can be represented as equations (26) - (27). In this case, at the time of closing and opening of the contact sensor in the program to pause t, is calculatedby the; expression (24), during which the state of a contact sensor is not analyzed and there is a software time delay to the simultaneous movement with slow and fast speed recovery crucible. Graph signal y, in accordance with the expression (27) for different diameters of germanium crystals is shown in Fig. 5.
y = tg (d ) - tg (di) = tg (d ) -Z-\C - 1 - M
(26)
2
1
1
t, ms
d, mm
Fig. 3. Diagram of time slow motion speed when lifting the; crucible t: d1 = 70 mm; dpp = "74 mm; dmp = 64 mm; Lp = 2 microns ; Tg = 120 000 ms; XTI = 100 microns
Kg
d, mm
Fig. 4. Diagram of the number ofcycles of opening and closing sensor Kg at: d1 = 70 mm; dpp = 74 mm; dmp = 64 mm; Lp = 2 microns; XTII = 1 00 microns; MM = 4; C = 4
1 -c )- d1 ~d ' M
d1 2 (i- 0}
c-i-Ç-
M
(27)
To program the control signal in the plant stretching germanium applied timing chart control shown in Fig. 13. The proposed algorithm is that the control system at the time of clo sing the contact
y, ms
d, mm
Fig. 5. Diagram ofthe control signal y for: dn = 70 mm; dpp = 74 mm; dmp = (54 mm;т = 3052 ms, M = 4,C = 4
d, mm
Fig. 6. Diagram of the control signal y for: d1 = 100 mm ; dpp = 92 mm; dmp = 106 mm; т = 1 782 ms, M = 4, C = 4
d, mm
Fig. 7. Diagram of the control signal y for: di = 120 mm; dpp = 110 mm; dmp = 1 28 mm; t = 1 4199 ms, M = 4, C = 4
y, ms
d, mm
Fig. 8. Diagram of the control signal y for: d1 = 140 mm; Mpp = 127 mm; dmp = 149 mm; t = 1 221 ms, M = 4, C = 4
d, mm
Fig. 9. Diagram of the control signal y for: d° = 16 0 mm; dpp = 146 mm; dmp = 171 mm ; = = 1 128 ms, Mi = 4, C = 4
d, mm
Fig. 10. Diagram of the control signal y for: d1 = 180 mm; dpp = 165 mm; dmp = 192 mm; t = 1 124 ms, M = 4, C = 4
d, mm
Fig. 11. Diagram of the control signal m for: 1 = 200 mm; dpp = 1833 mm; dmp = 213 mm; t = 1 232 ms, Mi = 4, C = 4
d, mm
Fig. 12. Diagram of the contol signml^y ford = 2220 mm; dpp = 201 mm; dmp = 235 mm; t = 1 573 ms, M = 4, C = 4
* t
Fig. 13. Timing diagram ofthe sensorlevel: H - the contact level sensor (P - sensor open)
of the sensor should tie; kept soft pause t closed and the subsequent pause t open state level sensor. In moments ofsilence t value of the state of the contact sensor control system does not analyze and manage the rise of the crucible occurs with slow and fast speed of recovery in the crucible moments "conditionally" closed and "conditional" open state level sensor.
After holding two pauses is evaluated control signal y by the expression (28) I)ased o n counting the length of the pause tBM(d) until the first closed state of the sensor. This control lifting up the crucible elimmntes the "extra" trigger levef sensor and the reaction to tliem in the control system, which improve o noi se i mmunity hf the metho d of me asure me nt .
P^skO-if {C rye. (28)
Furthen confrol hignal if eacli ft * measuremfnt cyile i s subSected to avnraging, during its cycle by evaluating U numbet of measueements if en accoodance with thee etpression (29):
i Kt
t* = d- S\am (d)-t-{C - y}]. (29)
d t i
The algorithm for calculation of the co ntrol signal from the expressions (28)(29), provided contro l without stopp ing tho c rucib l e at a level s enso r closing the co ntact (when M = 4; C = 4) is app.ied on the cytindricsl part of the growing cryetal (for control and stabilization of the current chip aoea), due; to the introduction of an integrated management system and the proportional component of the control signal on channels o" temperature and the crystal growth rate, respectively.
Growing on the plot of the direct and inverse cone crystals used algo rithm for calculating a control signal by the expression (6 ) with the complete stop) of lifting of the crucible in the closed condition of the sensor points of the melt (at M = C = 4). A control signal at the same time use only as the control information on the current area of the geowing crystal, and erf the shape of farmed cones made indirectly" through input from the memony of the control oof the co ntroller software by scheduling the change in temperature and the rate of crystal growth.
Basic principles of setting temperature and rate of growth of semiconductor crystals, based on the geometry of the crystal, its thermal properties and thermal conditions of crystal growth (axial gradient in the solid part of the crystal during growth) are given in [5].
Schedule change control signal, which is calculated based on the above given measurement model, drawing on the installation of a single crystal of germanium is shown in Fig. 14, and Fig. 15 and Figure 16 shows the form of graphite floating screen, a level sensor and melt grown crystals of germanium.
Graphite sensor working growth vessel for growing a crystal of germanium is an insulating quartz tube and closes relative floating on the melt surface in a crucible of graphite of the screen to the housing
Fig. 14. Diagram of the control signal y (d_Diametra)
Fig. 15. Floating screen graphite graphite melt level sensor
Fig. 16. Cast germanium diameter 104 mm
unit. Analyze the contact sensor circuit conditions of the melt on the installation housing is possible due to the fact that the germanium melt in the crucible has a significant conductivity.
An additional condition in this method of measurement is the condition of continuous rotation floating graphite screen that is provided by fabricating ultra-light graphite needles at the end of the sensor (Fig. 15), which is tapered in a free state under its own weight goes down in one and the the same point of tangency, and upon touching the sensor screen, the screen can rotate freely in the crucible with a speed of rotation of the crucible.
Test check of the control system on the installation drawing germanium was performed through a special program mode of the control system and was intended to test the functioning of the measuring system, with an open chamber furnace (no mode crystal pulling from the melt). The algorithm for calculation of the control signal thus asked by the expression (6) with the complete stop of lifting of the crucible in the closed condition of the sensor points of the melt.
The scheme of the test checks the installation is shown in Fig. 17. The test system microprocessor control checks on the plant consists in the fact that the system without metal open chamber at a complete stop of rotation of the crucible and a seed sensor graphite layer through the insulator fixedly secured to the rod and the seed is introduced into contact with the bottom of the crucible for receiving the housing of the sensor circuit unit.
After that, the control system of the program set out a number of test setpoint diameter Ky (16, 18, 20, 22), with a period of change jobs every 30 minutes, and then include the step drive crucible lift up and set the test speed of crystal growth V = 0,2 мм/мин.
With proper operation of all control systems takes delivery of graphs (Fig. 18) shows the change of the control signal y, calculated by the expression (6).
When checking a test without pulling the metal due to the "conditional" equality (рж=рт) setpoint Ky for germanium crystals can be represented as:
флЛл ¡&ММДО ЦОМОШ»
п н 4 . I Ifl v :| лпм_PitM^h TP _
T«« , П1П_ -->-
■i ::: . ,_
. . oo
0,50. -J SC. 80. -sii, on.
&«.no \ L \ |
ii/Ol/tflO-li ;Oi=CG vnr 4(i4»«nDi9i t*/Ql/tOCT-1J , it
Fig. 17. Scheme of the test setup: 1 - camera; 2 - insulator melt level sensor; 3 - pin level sensor; 4 - crucible; 5 - rod crucible; 6 - seed stock
Ky = 20 [D/dtf,
where d - diameter of the cylindrical part of the grown crystal.
When growing crystals of germanium melt on the existing installation (due to inequality px 4 pT) setpoint Ku will be given in the form:
Ky = 19 [D/dj]2.
Zero control signal (y = 0) is fixed on the chart by setting the value equal to the setpoint Ky 20 (at D = d1). Thus, the growth rate of the crystal and the crucible lifting is equal, and the process of validation testing takes to open and close a level sensor for the amount of movement Lp = 1-2 microns.
Testing allows you to test the functionality of the control system in the open position the camera without installing metal and crystal pulling mode.
Advantage of this method of control area for the growing crystal germanium material is the fact that during the growth of single crystals of many brands in the insulated (low gradient conditions) in the section of the crystal is not that round shape, so crystallographic direction of Germany "111" brings him closer to the triangle in cross-section, and the direction of the "100" to square. All this leads to great difficulties in controlling crystal diameter grown by conventional optical process monitoring and control of the crystal diameter, processing the digital camera of the crystal shape of the meniscus, which is due to reflection of illumination at the meniscus of the growing crystal brighter regions oven chamber and having a complex geometric shape, virtually all types of materials grown using the Czochralski method.
For ultrapure materials in the production are widely followed as an additional method of cultivation of the liquid melt in the growth vessel Czochralski method. For the cultivation of ultrapure materials of copper and aluminum has been successfully applied this method for monitoring and control of the current area of the crystal, with a contact sensor liquid level in the form of a floating screen and isolated
Fig. 18. Testing the Installation Schedule: V3 - drawing speed; Ky - setting the diameter; y (d Diametr) - control signal
graphite rod with a needle. Given the very low luminosity halo meniscus materials for copper and aluminum, the use of them controls the optical diameter of the crystal has become almost impossible.
Findings
For grown from molten liquid crystals using the Czochralski method, the mathematical model of the current control chip area, based on the control-circuit conditions contact sensor melt level in the crucible.
The model allows, through programmable intervals closed and open states of the level sensor to calculate the control signal, as the difference in time to first closed state of the melt level sensor and the previous time delay, allowing you to determine the accuracy of the current deviation from the given chip area better than 1%.
References
[1] Пат. 2128250 Российская Федерация, МПК С30 В15/20, 15/22, 15/26. Способ управления процессом выращивания монокристаллов германия из расплава и устройство для его осуществления / С.П. Саханский, О.И. Подкопаев, В.Ф. Петрик - заявлено 16.01.97, опубл. 27.03.99, Бюл. № 9.
[2] Пат. 2184803 Российская Федерация, МПК С30 В15/20, 15/22, 15/12 29/08. Способ управления процессом выращивания монокристаллов германия из расплава и устройство для его осуществления / С.П. Саханский, О.И. Подкопаев, В.Ф. Петрик, В.Д. Лаптенок - заявлено 12.11.99, опубл. 10.07.02, Бюл. № 19.
[3] Сахански, С. П. // Вестник СибГАУ 2005. Вып. 7. С. 85-88.
[4] Саханский С. П. Управление процессом выращивания монокристаллов германия: монография. Красноярск: СибГАУ, 2008. 104 с. ISBN 978-5-86433-366-2.
[5] Саханский С.П. // Журнал СФУ Техника и технологии. 2014 (7). № 1. 20-31.
