Nucleation and growth in the initial stage of metastable disilicide formation
Z. Ma, Y. Xu, and L. Ii. Allen

titanium

Department of Materials Science and Engineering and Coordinated Science Laboratory, University of Illinois, Urbana, IIlinois 61801

S. Lee

Microelectronics Division, NCR Corporation, Colorado Springs, Colorado 80916
(Received 27 January 1993; accepted for publication 4 May 1993) Initial stage of the C49-TiSi, formation was investigated at 530 C and at a rate of 10 C/m using transmission electron microscopy. Morphological studies reveal that the C49 phase first separately nucleates at the interface between amorphous silicide and crystalline silicon, then followed by simultaneous lateral and vertical growth. The growth proceeds very fast until the formation of a continuous layer of C49-TiSi2. Local chemical analysis shows that the composition range of the amorphous silicide is narrowed due to the C49 formation. For isothermal annealing, a linear density of the C49 nuclei is about 6.7X 10m3/A, and remains the same upon prolonged annealing. In the case of annealing at 10 C/m, the linear density depends on temperature, reaching a maximum of 7.2X 10m3/A at around 575 C.
The formation of titanium disilicides through the reaction of titanium with crystalline silicon has been extensively studied from different aspects because of their important technological applications in integrated circuits. *I It has been consistently reported that after an amorphous silicide formation, a high-resistivity metastable titanium disilicide (C49 structure) always forms before a lowresistivity stable titanium disilicide (C54 structure), and is inevitable during conventional furnace annealing3- as well as rapid thermal annealing. To form reliable shallow junctions and smooth interfaces, one desires an understanding of the reaction kinetics of both disilicides. Unfortunately, previous reports on the reaction rates of Ti with c-Si are far from consistent. - Hung et al showed difficulties in reproducing the kinetics of C49 phase formation, and attributed this lack of reproducibility to the presence of impurities at the interface. Recently, Raaijmakers et al8 have indicated that for the C49 phase formation, the reaction proceeds much faster in the initial stage before the diffusion-controlled stage of the reaction sets in. They found that the irreproducibility was observed in the initial stages of the C49 formation, and was not due to the interfacial impurities. Since their results were obtained by Rutherford backscattering spectrometry (RBS >, a technique that has limited depth resolution and is relatively insensitive to the initial stage of the reaction, it appears necessary to examine this initial stage more closely in order to acquire a more detailed picture about the two distinct kinetic regimes of the C49 phase formation. In this Communication, we report our studies on the initial stages of the C49 phase formation under the conditions of isothermal and constant-heating-rate annealing using cross-sectional transmission electron microscopy (XTEM) coupled with a scanning transmission electron microscope (STEM) probe. Our results clearly delineate the initial stage of the C49 formation. Morphological evolution is explained by considering both local chemistry and
J. Appl. Phys. 74 (4), 15 August 1993
kinetic feasibility. This initial fast evolving stage is also discussed on the basis of the competition between nucleation and growth of the C49 phase. p-type Si (100) wafers with a 750~nm-thick thermal oxide were employed in this study. After degreasing, a 350 nm phosphorus doped polycrystalline Si film was first grown onto the oxidized Si wafers using low-pressure chemical vapor deposition (LPCVD). A Ti film of 55 nm in thickness was then deposited over the polycrystalline Si using 1-f sputtering. Isothermal annealing and constantheating-rate annealing were carried out in high vacuum (lo- Torr) at 530 C for various times and at 10 C/m, respectively. Details of the experiment are discussed elsewhere.4 Growth morphology of the C49-TiSiz phase was characterized using XTEM. Local chemical analysis was performed using a VG HB5 STEM with a 10 A probe. The phase identification of the C49 phase was carried out using the TEM microdiffraction technique. Both isothermal annealing and constant-heating-rate annealing resulted in quite similar morphological development, as revealed by XTEM examinations. For the sake of clarity, we only show the results for samples annealed at a heating rate of 10 Wm. Figure l(a) shows a micrograph for a sample heated up to about 510 C. It is clearly seen that a metastable C49-TiSi, phase individually nucleated along the interphase boundary between amorphous silicide (a-TiSi,) and crystalline Si (c-Si). This is consistent with previous observations;3 see Ref. 11. The shape of the nu4 clei is typical of heterogeneous nucleation, and is featured by the curvature toward the c-Si being larger than that toward the a-TiSi,, implying that interfacial energy on the a-TiSi, side is larger than on the c-Si side. The same features were also seen from a sample annealed at 530 C for 13 min. Upon annealing to a higher temperature or at 530 C for a longer time, the C49-TiSiZ grains grew laterally (in a direction parallel to the a-TiSid+Si interface), as well as

@ 1993 American Institute of Physics 2954
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growth behavior of the C49 phase changed over to mainly

vertical growth.

FIG. 1. XTEM micrographs for samples annealed at 10 C/m up to (a) -510-c (b) -560C, and (c) -585 C.
vertically (in a direction perpendicular to the interface) at the expense of a-TiSi, and Si. The lateral growth (lengthening) appears faster than the vertical growth (thickening). The vertical growth is characterized by the further protrusion of the C49-TiSi,/c-Si boundary into the c-Si, thus giving rise to the rough interface, but the growth at the a-TiSi,/C49-TiSi, interface seems very slow [Fig. l(b)]. Further simultaneous lateral and vertical growth resulted in the coalescence of the individual grains originally separately formed at the interface. This initial growth stage proceeds very fast, as illustrated in Fig. 1 (b) for a sample annealed up to -560 C. The stacking faults are revealed by the (020) lattice fringes in larger C49-TiSi, grains, as typically observed along this stacking sequence in the C49 phase.13 Figure 1 (c) shows an XTEM micrograph obtained from a sample heated to-585 C. As seen from the figure, finally, the individual growing C49-TiSiZ grains connected each other to form a continuous layer of polycrystalline C49-TiSiZ before the Ti film and a-TiSi, phase are exhausted. It is also worth noting that in either case, a continuous layer of C49 phase is formed from a relatively few large C49 nuclei, thus resulting in very large C49 grains [see Fig. l(c)]. At this stage, the simultaneous
2955 J. Appl. Phys., Vol. 74, No. 4, 15 August 1993
In both annealing cases, a linear density of the C49 nuclei was measured along the interface based upon a number of XTEM micrographs made for each sample. Our preliminary results indicate that for isothermal annealing at 530 C for about 15 min, the linear density is about 6.7~ 10A3/A and remains almost the same during prolonged annealing. But in the case of annealing at 10 C/m, the linear density initially depends upon temperature, increasing from 3.2~ 10-/A ( -520 C) to 7.2~ 10-//A ( - 570 C). The relative large increase is observed at about 535-540 C (6.0x 1O-3 /A,. To understand the morphological evolution described above, we also performed a local chemical analysis along boundaries, i.e., Ti/a-TiSi, , several interphase a-TiSi,/c-Si, and a-TiSi,/C49-TiSi,. Figure 2 (a) shows approximate locations of the STEM probe during analysis. The effective probe size was estimated to be -40 A, based upon the possible drifting of the specimen and beam broadening effect. The compositions measured for the C49 phase were also included for comparison. These results are summarized in Fig. 2(b). It reveals two important facts: ( 1) the a-TiSi, layer has a composition range from - 33 at. % Si (at the Ti/a-TiSi, interface) to -67 at % Si (at the a-TiSiJc-Si interface), similar to the results reported by Ogawa et aZ.;14and (2) due to the formation of the C49 phase the composition range for the a-TiSi, layer is narto rowed, changing from -67 at. % Si (a-TiSi,/c-Si) - 52 at. % Si (a-TiSi&49-TiSQ. This can also be explained qualitatively using a schematic Gibbs free energy versus composition diagram shown in Fig. 3. Thus, the results should be qualitatively quite general though the actual local compositions are temperature dependent. As pointed out by Raaijmakers et al., the kinetics of the C49 formation can be described as two regimes: initial fast reaction and diffusion-controlled growth, being repre sented by different kinetic rates. From this study, we have shown that the initial stage of the reaction is essentially associated with the discontinuous nucleation of the C49 phase, then followed by the simultaneous lengthening and thickening. The simultaneous growth exhibits a large disparity in growth rates of the C49 grains in vertical and lateral directions. This initial growth stage proceeds very fast until a continuous layer of C49 phase forms. The disparity in the growth rates can be easily understood based on the local chemical information. Before the C49 phase forms, the a-TiSi, layer has a larger composition range across the entire layer. The composition at the a-TiSiJ&i interface is about 33 at. % Ti and 67 at. % Si, very close to the composition required for the C49 formation.14 After the formation of the C49 phase, the composition shifts at. % Si at the from -67 at. % Si to -52 a-TiSi,/C!49-TiSi* interface. Such a composition barrier slows down the vertical growth at this interface, since a further growth would require more Si supply either through the already existing C49 phase (lattice diffusion) or along the interphase boundaries (interphase boundary diffusion) to the growth front. This explains the slow

Ma et a/. 2955

L&P.l
100 (b) 80 _ mmm 8 Ii c60.* 40.aAAh E.
D I S T A N C E( n m ) FIG. 2. (a) A n X T E M m i c r o g r a p h for a s a m p l e a n n e a l e d at 0 C for min, s h o w i n g approximate locations of the S T E M n a n o p r o b e during analysis; (b) local compositions at different interphase b o u n d a r i e s m e a s u r e d by S T E M ( O = = u - T i S i d S i interface; A =a-TiSidC49-TiSi, interface; n =Tiia-TiSi, interface, 0 - C - T i S Q.
growth o b s e r v e d at this interface. Instead, the lateral growth c a n b e facilitated by the local transport of Si a l o n g the C49-TiSiz/c-Si interface to the growth front. This point is supported by the k n o w n fact that Si is the d o m i nant m o v i n g species in the C p h a s e grow&. Also from the o b s e r v e d simultaneous growth behavior, w e suggest that the initial fast growth is d o m i n a t e d by the preferential diffusion of Si a l o n g the interphase b o u n d a r i e s to the growth front rather than through the existing C phase. T h e lattice diffusion is expected to b e operative in the later stage of the growth, so as to give a slow reaction rate.8 T h e r e a s o n for the lack of control of the initial C p h a s e formation is still not quite clear at present. It is mostly likely related to the nucleation dii% culties of the disilicide o n c-Si. A s indicated by d Heurle, l2 nucleation of C49-TiSi, at the a-TiSi,/c-Si interface is driven by a very small negative free e n e r g y change. S o it c a n b e very sensitive to temperature, stress, a n d the p r e s e n c e of heterogen e o u s nucleation sites. O u r n u m b e r density data suggest that there exists a threshold temperature ( a r o u n d 0 C) for the nucleation of the C phase. A t a temperature close to the threshold temperature, o n c e the C p h a s e is successfully nucleated, the next step is m o r e likely associated with the growth of the present nuclei rather than further nucleation, e v e n t h o u g h such nucleation sites m a y still exist. A s the temperature is far a b o v e the critical temperature, all the nucleation sites a r e expected to b e tiled within a very short tim e , a well-defined diffusion-controlled growth r e g i m e will quickly take over the initial growth stage of the C phase. Therefore, to b e m o r e precise, w e think that the initial stage of the C p h a s e formation m a y represent the competition b e t w e e n the nucleation a n d growth of the disilicide. This work is partially supported by the Joint Services Electronics P r o g r a m ( J S E P ) u n d e r Contract No. N O g o - J - (A. G o o d m a n ).

a-TiSi. &~wilhout D

C Tikiz with C TiSbl
R. B e y e r s a n d R. Sinclair, J. Appl. Phys. 57, (1985). R. Beyers, D. C o u l m a n , a n d P. Merchant, J. Appl. Phys. 61, (1987). A. Kirtikar a n d R. Sinclair, Mater. Res. Sot. S y m p. Proc. 260, 7 (1992). 4Z. Ma, L. H. Allen, a n d S. Lee, Mater. Res. Sot. S y m p. Proc. 237, 1 (1992). 5R. D. T h o m p s o n , H. Takai, P. A. Psaras, a n d K. N. Tu, J. Appl. Phys.

61,540 (1987).

Tl, at.%

1-. 1 1

FIG. 3. S c h e m a t i c G i b b s free. e n e r g y vs composition d i a g r a m for the Ti-Si binary system, s h o w i n g the local equilibria establishedby the c o m m o n tangents a m o n g different phases.
L. A. Clevenger, I. M. E Harper, C. Cabral, Jr., C. Nobilli, G. O ttaviani, a n d R. M a n n , J. Appl. Phys. 72, (1992). L. S. Hung, J. Gyulai, J. W. Mayer, S. S. Lau, a n d M. A. Nicolet, J. Appl. Phys. 44, (1983). s1. J. M. M. Raaijmaker, L. J. V. IJzendoom, A. M. L. Theunissen, a n d K. B. K i m , Mater. Res. Sot. S y m p. P r o c 6 , 7 ( ). 9C. A. P i c a a n d M. G. Lagally, J. Appl. Phys. 64, (1988). *O S.S. Iyer, C. Y. Ting, a n d P. M. Fryer, J. Electrochem. Sot. 132, (1985). V e r y occasionally, TiSi is detected, but its further growth is not seen. F. M. d Heurle, J. Mater. Res. 3, 7 (1988). 13T. C. Chou, C. Y. W o n g , a n d K. N. Tu, J. Appl. Phys. , (1987). S O g a w a , T. Kouzaki, T. Yoshida, a n d R. Sinclair, I. Appl. Phys. 70, 8i7 (1991). W K. Chu, S. S. Lau, J. W. Mayer, H. Muller, a n d K. N. Tu, Thin S o i i d Films 25, 3 (1975). M a et al.
J. Appl. Phys., Vol. 74, No. 4, A u g u s t 9 3

BIOLOGY OF REPRODUCTION 66, 14851490 (2002)
Is Intracellular Ice Formation the Cause of Death of Mouse Sperm Frozen at High Cooling Rates?1
Peter Mazur2 and Chihiro Koshimoto3
Fundamental and Applied Cryobiology Group, Department of Biochemistry and Cellular and Molecular Biology, The University of Tennessee, Knoxville, Tennessee 37932-2575

ABSTRACT

Mouse spermatozoa in 18% rafnose and 3.8% Oxyrase in 0.25 PBS exhibit high motilities when frozen to 70C at 20 130C/min and then rapidly warmed. However, survival is 10% when they are frozen at 260 or 530C/min, presumably because, at those high rates, intracellular water cannot leave rapidly enough to prevent extensive supercooling and this supercooling leads to nucleation and freezing in situ (intracellular ice formation [IIF]). The probability of IIF as a function of cooling rate can be computed by coupled differential equations that describe the extent of the loss of cell water during freezing and from knowledge of the temperature at which the supercooled protoplasm of the cell can nucleate. Calculation of the kinetics of dehydration requires values for the hydraulic conductivity (Lp) of the cell and for its activation energy (Ea). Using literature values for these parameters in mouse sperm, we calculated curves of water volume versus temperature for four cooling rates between 250 and 2000C/min. The intracellular nucleation temperature was inferred to be 20C or above based on the greatly reduced motilities of sperm that underwent rapid cooling to a minimum temperature of between 20 and 70C. Combining that information regarding nucleation temperature with the computed dehydration curves leads to the conclusion that intracellular freezing should occur only in cells that are cooled at 2000C/min and not in cells that are cooled at 2501000C/ min. The calculated rate of 2000C/min for IIF is approximately eightfold higher than the experimentally inferred value of 260C/min. Possible reasons for the discrepancy are discussed.
or 530C/min (Fig. 1). In the companion paper, we suggest that the large drop in viability at these two higher rates is a consequence of the formation of lethal quantities of intracellular ice crystals. At sufciently low cooling rates, intracellular water leaves the cells rapidly enough to keep the chemical potential of the remaining intracellular water in near-equilibrium with that of the water in the progressively freezing solution outside the cell. However, if cells are cooled too rapidly, they will undergo intracellular ice formation (IIF), because their water cannot leave fast enough to prevent extensive supercooling and eventual nucleation of that supercooled water in situ. As shown some years ago [2, 3], the kinetics of cell dehydration can be described by four coupled equations. The rst equation relates the rate of loss of cytoplasmic water to the difference in chemical potentials of intracellular and extracellular water expressed as a vapor pressure ratio: dV/dt (LpART ln pe /pi )/vo where V is the volume of cell water, t is time, Lp is the permeability coefcient for water (i.e., hydraulic conductivity), A is the cell surface area, R the gas constant (m3 atm/deg mole), and vo is the molar volume of water. The ratio pe/pi is that of the external and internal vapor pressures of water. It is less than one, because the intracellular water is supercooled and the vapor pressure of supercooled water is greater than that of ice or of water in a solution in equilibrium with ice. The change in this vapor pressure ratio with temperature can be calculated from a second differential equation derived from the Clausius-Clapeyron relation and the Raoult law: d ln (pe /pi)/dT Lf /RT2 [n2vo/(V n2vo)V]dV/dT Here, n2 is the osmoles of solute in the cell, and Lf is the molar latent heat of fusion of ice. Time and temperature are related by the cooling rate (B), which, if linear, is given by dT/dt B Finally, the hydraulic conductivity (Lp) decreases with falling temperature. If it is assumed to follow an Arrhenius relation, then its value at a given absolute temperature (T) is given by Lp Lpg exp {Ea/R[(1/T) (1/Tg)]} where the subscript g is the value at a given reference temperature (commonly 22 or 0C), R is the gas constant (expressed here as cal/deg mole), and Ea is the activation energy of Lp (cal/mole). The values of R, R, Lf, and vo are constant and are given in Mazur et al. [3]. The values of A, n2, and Lpg are constant for a given cell but differ in different cells. Lp and Ea are adjustable parameters. Knowledge of Lpg, Ea, n2, and A/V

assisted reproductive technology, in vitro fertilization, male reproductive tract, sperm, sperm motility and transport

INTRODUCTION

As reported in the companion paper [1], mouse sperm suspended in 18% rafnose pentahydrate and 3.8% Oxyrase (an oxygen-removing membrane fraction of Escherichia coli) in 0.25 PBS exhibit high motility (60% relative to that of unfrozen controls) when frozen to 70C at cooling rates ranging from 27 to 130C/min and then rapidly warmed at 1875C/min. However, survival drops sharply, to less than 10%, when they are cooled to 70C at 261
Supported by NIH grant R24-RR13194 (J. Critser, PI) under subcontract with Indiana University. A preliminary report was presented at the 37th Annual Meeting of the Society of Cryobiology; Cambridge, MA; 30 July to 1 August 2000. 2 Correspondence: Peter Mazur, Fundamental and Applied Cryobiology Group, Dept. of Biochemistry and Cellular and Molecular Biology, The University of Tennessee, 10515 Research Dr., Suite 300/10, Knoxville, TN 37932-2575. FAX: 8027; e-mail: pmazur@utk.edu 3 Permanent address: Experimental Animal Center, 5200 Miyazaki Medical College, Kiyotake, Miyazaki 889-1692, Japan.
Received: 10 September 2001. First decision: 1 November 2001. Accepted: 10 December 2001. 2002 by the Society for the Study of Reproduction, Inc. ISSN: 0006-3363. http://www.biolreprod.org

MAZUR AND KOSHIMOTO

(the surface:volume ratio of the cell) permit one to compute the volume of cell water (and the extent of supercooling) versus subzero temperature and cooling rate. In the present paper, we use the above equations to compute the kinetics of water loss in mouse sperm cooled at rates ranging from 250 to 2000C/min. From those curves and experimental estimates of the ice nucleation temperature of supercooled cells, we then discuss the probability of IIF as a function of cooling rate, and we compare those estimates with cooling rates that have been experimentally inferred to induce IIF.

MATERIALS AND METHODS

Mouse sperm of the ICR strain were isolated and suspended in a solution of 18% (w/v) rafnose pentahydrate and 3.8% (w/v) Oxyrase in 0.25 modied Dulbecco saline buffer (SD-PBS [4]) as described in detail elsewhere [1, 5]. Oxyrase (Oxyrase Corp., Manseld, OH) is a preparation of membranes of Escherichia coli that, in our procedure, reduces the oxygen concentration in the media to 3% or less of that in media equilibrated with air [5, 6]. One hundred microliters of the suspension were drawn into 0.25-ml straws (catalog no. AAA201; IMV, lAigle, France), and a 36gauge, copper-constantan thermocouple was inserted into the column of suspension so that the tip of the junction was approximately midway in the column. A central aim of the experiment was to estimate the nucleation temperature in supercooled sperm by determining their viability after rapid cooling to 20, 30, 40, or 70C. One could not achieve rapid cooling of 200C/min to a temperature such as 30C by placing the straws in an ethanol bath at 30C, because the rate would slow markedly when the straw temperature fell to within 5C of the bath temperature. To obviate that problem and to obtain high cooling rates to 20, 30, and 40C, the straws were rst immersed to near their tops in ethanol baths precooled to 35, 35, and 45C, respectively. They were removed from those ethanol baths when the thermocouple reading indicated that their temperatures had reached 20, 30, and 40C, respectively, and were then immediately transferred to ethanol baths at the latter three temperatures. Approximately 5 min later, they were immersed in a water bath at room temperature to warm and thaw rapidly. To achieve rapid cooling to 70C, the naked straw was immersed in a 42C bath until its temperature fell to 30C and was then transferred to an ethanol bath at 70C. To achieve a somewhat lower cooling rate to 20C (163C/min), the straw was immersed in a 25C ethanol bath until its temperature fell to 20C, at which time it was transferred to a bath held at 20C. Representative cooling curves for the above ve procedures are given in Figure 2. To achieve the optimal cooling rate of 25C/min to 70C, the straw was inserted coaxially in an outer Pyrex tube and the assembly placed in an ethanol bath at 42C. When the sample temperature had fallen to 30C, the assembly was transferred to a 70C ethanol bath. This is the procedure that yielded the optimum cooling rate in our companion study [1]. The thawed suspensions were diluted 15-fold with SD-PBS (containing Oxyrase) within 5 min after thawing and washed by centrifugation to reduce the rafnose concentration. The percentages of motile sperm were then determined. Details are in Koshimoto and Mazur [1].

FIG. 1. Survival of mouse sperm as a function of the cooling rate to 70C and after warming at either 1875 or 125C/min. The sperm were suspended in a solution of 18% rafnose and 3.8% Oxyrase in 0.25 SD-PBS. (Modied from Koshimoto et al. [1]).
FIG. 2. Representative cooling curves for suspensions of mouse sperm in 0.25-ml straws cooled either rapidly (R) at approximately 250C/min to 20, 30, 40, or 70C or at a slower a rate (S) of approximately 160C/min to 20C. In curve 20S, naked straws were placed in an ethanol bath at 25C and then transferred to a 20C bath when their temperature had fallen to 20C. In curve 20R/30R, the naked straws were placed in an ethanol bath at 35C. For the 20R treatment, the straw was transferred to a separate 20C bath when its temperature reached 20C. For the 30R treatment, it was transferred into a 30C bath when its temperature reached 30C. In curve 40R, the naked straw was placed in a 45C bath and transferred to a 40C bath when its temperature reached 40C. In curve 70R, the naked straw was rst placed in a 42C bath and then, when its temperature had fallen to 35C, was transferred to a 70C bath. The time-temperature values for the 70R curve were obtained with a potentiometric thermocouple recorder that printed temperatures at 1-sec intervals. The values for the other curves were obtained by measuring with a stopwatch the time that elapsed between the start of cooling and the time the temperatures reached approximately 0, 10, 20, 30, and 40C. The cooling rates were based on the time for the temperature to fall from 10C to 20, 30, 40, and 65C, respectively.

RESULTS

Computed Kinetics of Water Loss as a Function of Cooling Rate
The values of the parameters specic to mouse sperm that are required to solve the equations were taken from the literature. The values used in the computations were Lpg at 22C 1.03 m/min atm, Ea 12.6 kcal/mole, A 355 m2, and the volume of water in the isotonic cell (Viso) 43 m3. The value for Lpg is the mean of values ranging from 0.7 to 1.5 as reported by Noiles et al. [7] and Phelps et al. [8] for osmotic water ux in the absence of a permeating cryoprotectant at room temperature. The value of Ea is the mean of values reported by Noiles et al. [7] based on measurements of Lp between 0 and 37C. The value for the surface area (A) is the mean of values pub-
INTRACELLULAR ICE FORMATION IN MOUSE SPERM
lished by Du et al. [9] and Noiles et al. [10]. The value of Viso is the average of two values reported by Du et al. [9]. Also required is a value for the number of osmoles of solute in the cell, which is calculated as the volume of cell water in the isotonic cell in liters multiplied by the isotonic osmolality (0.29 Osm). The other values required for solving the equations are independent of the cell type and have been listed elsewhere [2, 3]. Using these parameters, curves of relative cell water volume versus temperature were calculated for cooling rates of 250, 500, 1000, and 2000C/min and are plotted in Figure 3. The values plotted are relative to the volume of water in a cell at isotonic volume (V/Viso). (Note that the initial relative cell water content at the freezing point is 0.72, because the osmolality of the rafnose 0.25 SD-PBS in the medium is 400 mOsm, not the isotonic value of 290 mOsm.) The vertical dashed line at 20C labeled Nucleation Temperature will be discussed shortly. The curve labeled EQ is the extent of shrinkage that would occur as a function of temperature in cells cooled innitely slowly; this is equivalent to the water content of cells that remain in chemical potential equilibrium with the outside medium. It is calculated from analytical solutions to the following equation [2]: ln[V/(V n2vo)] (Lf/R) (1/273 1/T) or to the following equivalent: V V/Vi voMi 1015/exp[Lf /R(1/T 1/273)] 1 where V is the fractional water volume, Vi is the initial water volume, and Mi is the initial osmolality [3]. The higher the cooling rate, the more the curves shift to the right of the equilibrium curve. The number of degrees the curve is shifted is the number of degrees the cell water is supercooled at given temperatures. At these four rates, the cells are computed to lose 90% of their initial water by 7.4, 9.6, 14, and 25C, respectively. The water content falls to 110% of the equilibrium value by 8, 11, 17, and 40C, respectively.

Estimation of the Nucleation Temperature At some sufciently low temperature, supercooled water in a cell must freeze, whether by seeding from external ice or by the action of internal heterogeneous nucleators [11]. The temperature at which this occurs is referred to as the nucleation temperature. To relate the dehydration curves in Figure 3 and the degree of supercooling to the likelihood of intracellular freezing, one must have an estimate of that nucleation temperature. In cells such as mouse embryos, this can be ascertained directly with a cryomicroscope. However, that direct approach is not feasible in the sperm because of their small size and their low water content. Approximately 45% of the mouse spermatozoon is nonaqueous [9]. Thus, we chose an inferential approach in which the sperm were rapidly cooled to a series of temperatures between 20 and 70C at rates exceeding 200C/min. Representative cooling curves are shown in Figure 2. These rates, as shown in Figure 1, result in survival rates of less than 10% when the cells are cooled to 70C, presumably from IIF. The argument is that if cooling at high rates produces low survivals when it is terminated at 30C, for example, but produces high survivals when it is terminated at 20C, then the nucleation temperature lies between 20 and 30C. The results of these experiments are summarized in Figure 4. The four white bars show the motilities of samples
FIG. 3. Computed kinetics of dehydration of mouse sperm as a function of the cooling rate and subzero temperature. The vertical dotted line at 20C labeled Nucleation Temperature is the inferred low temperature boundary for the nucleation of sperm containing supercooled water. It will be discussed in connection with Figure 4.
cooled at 200300C/min to 20, 30, 40, and 70C, respectively. These rates are calculated from 10C to the nal temperature. Survival after rapid thawing was reduced to 16% or less in each case. In contrast, the motilities of sperm cooled to 30 and 70C at an approximately 10fold lower rate (28C/min; solid bars) were 81% and 64%, respectively. The motility of sperm cooled to 20C at 163C/min (leftmost bar) is 35%, which is more than double that of sperm cooled to the same temperature at a higher rate. Recall from Figure 1 that the break in the survival curve in cells cooled to 70C occurs somewhere between a cooling rate of 130 and 261C/min.

FIG. 4. Survival of sperm cooled at rates (CR) of 200300C/min to 20, 30, 40, or 70C (white bars) compared with that of sperm cooled to 20C at 160C/min (diagonal hatched bar) and to 30 and 70C at 28C/min (black bars). Representative cooling curves for the white bars and the diagonal hatched bar are given in Figure 2. Data for cooling at 28C/min to 30 and 70C (black bars) are from Table 3 (treatment 12 of Koshimoto et al. [5]). The number of animals and straws per treatment are given in Table 1. Error bars are SEM, where N is the number of replicate straws in Table 1.
TABLE 1. Number of animals and straws used for each treatment shown in Figure 4. Treatmenta 20S 20R 30R 40R 70Rb 30VSc 70VSc

Cooled to (C) 70

Cooling rate (C/min) No. animals 2 5

No. straws 5

R, Rapid cooling; S, slow cooling; VS, very slow cooling. Data from Koshimoto and Mazur [1] (Table 4, treatment 6). Data from Koshimoto et al. [5] (Table 3, treatment 12).
Because slow warming tends to exacerbate the detrimental effects of IIF [11], one might ask why we used rapid warming in estimating the nucleation temperature. The answer is twofold. First, from Figure 1, we see that the rate of warming was nearly without effect in cells cooled at the high rate that we had hypothesized as inducing intracellular ice; that is, nearly all cells cooled at 261C/min or greater are killed after either slow or rapid subsequent warming. Second, slow warming is highly detrimental to cells cooled at 27130C/min, rates that we think do not induce IIF during cooling. Rather, we believe that within this cooling rate range, the damage from slow warming is a consequence of recrystallization or devitrication of the external medium. Our inference from these data in Figure 4 is that most of the sperm are undergoing intracellular ice nucleation by 20C. The region above 20C is difcult to study by our procedure. If, for example, one attempts to cool a straw to 15C at rates 250C/min by placing it in a bath at 35C until its temperature has fallen to 15C, then the cooling rate in the region of 5 to 15C will be capriciously affected by how much the sample supercools before extracellular nucleation occurs and by the shape and duration of the temperature plateau associated with the release of the latent heat of fusion. Using a somewhat different approach, but one similar in concept to that used here, Watson et al. [12] concluded that the ice nucleation temperature of bull sperm lies between 20 and 40C, a value that is lower than that which we infer for mouse sperm. Also, Woelders et al. [13] found that a cooling rate of 250C/min was lethal to bull sperm, as is the case here in mouse sperm.

Probability of Intracellular Freezing as a Function of Cooling Rate
the curve of the volume of intracellular water merges with the equilibrium curve well before the temperature has fallen to the nucleation zone. If the chemical potential of the cell water is equal to that of the water in the external medium, it is, by denition, not supercooled, and if it is not supercooled, then it cannot freeze. (The boundary of the nucleation zone has been drawn vertical in Fig. 3, implying that the nucleation temperature is independent of the cooling rate and the extent of dehydration of the cell. In some cells, this is so, but in others, the nucleation temperature is cooling-rate dependent, commonly rising with increasing rate [11]. If the nucleation temperature were to depart greatly from the vertical line drawn, then it could affect conclusions regarding the cooling rate dependence of IIF. However, the procedures used here do not permit us to draw conclusions with respect to this point.)

DISCUSSION

The conclusion that IIF will only occur if the cooling rate exceeds 1000 C/min represents an approximately eightfold discrepancy in comparison to the inference drawn from the experimental results, shown in Figure 1, that intracellular freezing occurs at cooling rates of between 130 and 261C/min. This kind of discrepancy is not restricted to mouse sperm. For example, Duncan and Watson [17] reported that the motility of ram sperm drops markedly when the cooling rate is increased from 5060 to 100C/ min. However, their calculation from kinetic shrinkage curves like those of the present study indicate that IIF should not occur unless the cooling rate exceeds 500C/ min, which is at least a vefold discrepancy. This discrepancy may also be much higher than that, because their modeling was based on an Lp at 20C of 0.22 m/min atm, which is a value derived from time-to-lysis measurement. Curry et al. [18] recently reported a 15-fold higher value (2.8 m/min atm) based on uorescence quenching. Other examples of comparable discrepancies between the cooling rates computed to produce intracellular freezing in sperm and those inferred to do so based on experimental curves of survival versus cooling rates have been reviewed by Gao et al. [19] and Devireddy et al. [20].
Possible Causes for the Discrepancy
The vertical dashed line at 20C in Figure 3 represents our estimate of the intracellular ice nucleation temperature of rapidly cooled mouse sperm. Mazur [14] has suggested that intracellular freezing will not occur if cells enter the nucleation zone with less than 10% of their isotonic water or if the water is supercooled to less than 2C. Toner et al. [15, 16] have dened much more mechanistic criteria based on heterogeneous nucleation theory, but the inferences with respect of IIF using that mechanistic theory agree quite closely with those drawn from the more qualitative criteria of Mazur [14]. Based on the qualitative criteria, we conclude from Figure 3 that most sperm cooled at 250, 500, or 1000C/min should not undergo intracellular freezing, but that sperm cooled at 2000C/min should do so. The reason for this conclusion is that, at the three lower rates,

One contributor to the discrepancy could be that the actual upper boundary of the nucleation temperature is higher than the value of 20C depicted in Figure 3. Indeed, the data shown in Figure 4 suggest that 20C is the lower limit. If, for example, the nucleation temperature were 10C, then intracellular freezing would be predicted to occur at or above a cooling rate of 1000C/min. Unfortunately, for the reasons given, the region above 20C cannot be explored by the approach used in the present study. However, the literature provides a number of examples in which direct microscopic observation of larger cells (mouse oocytes and embryos, V79 hamster cells, hepatocytes) has demonstrated nucleation temperatures of 12C and higher [15, 2124]. Most of these instances, however, have involved cells frozen in the absence of cryoprotective agents. In the presence of 1.01.5 molar concentrations of permeating cryoprotective agents, the nucleation temperature is suppressed to less than 30C in mouse embryo and oocytes [21, 25]. Whether comparable reductions in nucleation temperature occur in the presence of nonpermeating cryoprotectants, such as the rafnose used in the present study, is unknown; however, the nucleation temperature of
FIG. 5. Computed kinetics of dehydration of mouse sperm as a function of the activation energy (Ea) of the hydraulic conductivity (Lp) and of subzero temperature. The assumed cooling rate was 500C/min. The values of the other required parameters are those given in the text in connection with Figure 3.
mouse oocytes is reduced in hyperosmotic (nonpermeating) NaCl [15]. Two other possible contributors to the discrepancy are the value used for Lp at 22C in the calculations and the value for its activation energy (Ea). If, for example, the actual value of Lp at 22C were half of that used, then the cooling rates assigned to each of the curves in Figure 3 would be half of those shown; for example, the curve labeled 1000C/min would become 500C/min. The value used in the calculations (1.03 m/min atm) was based on determinations of the rate of osmotic volume changes in an isosmotic medium lacking a cryoprotectant. Phelps et al. [8] reported that, in the presence of ethylene glycol or glycerol, the value of Lp at 22C for mouse sperm drops to 0.38 m/min atm. This decrease is consistent with the general nding that Lp in the presence of a cryoprotectant is roughly half that in the absence of cryoprotectant in a variety of cells [20, 26, 27]. Changes in Lp shift the dehydration curves left or right, but they do not change their shapes. Changes in Ea, in contrast, shift the curves and produce major changes in shape. This is illustrated in Figure 5, in which we plot the kinetic dehydration curves for a cooling rate of 500C/min for activation energies of 12, 16, and 20 kcal/mole. With an Ea of 20 kcal/mole, a cooling rate of 500C/min would now be predicted to cause intracellular freezing in the mouse sperm. The published value of Ea used in the calculation was based on Arrhenius plots of measurements of Lp at several temperatures between 0 and 37C. Our equations assume that the value of Ea continues to be applicable when freezing occurs at less than 0C. Two published experimental reports, one involving yeast [28] and one involving mouse oocytes [15], support this assumption. In these studies, Lp in the partly frozen state was calculated from ts to microscope-derived measurements of cell shrinkage during cooling at given rates to 20 or 30C. When these Lp values were extrapolated back to 22 or 0C, the extrapolated values were quite similar to those directly measured at 22 or 0C. However, that agreement may not necessarily be maintained as freezing progresses to yet lower temperature. This is because, as freezing progresses, the viscosity of the medium rises sharply as the rafnose concentrates, and the high viscosities may lower the rate of water efux above and beyond the effect of lowered tem-

perature per se. In addition, and more speculatively, the inherent permeability of the plasma membrane may change. Devireddy et al. [20] have used a very different approach to estimate the Lp and Ea of mouse sperm (and other cells) at subzero temperatures. Their procedure yields very different values for Lp at 0C and for Ea than those based on above-zero water permeability measurements. They used differential scanning calorimetry to estimate the rate at which the water leaves the sperm cells and freezes externally in cells cooled at 5 or 25C/min. They did this by measuring the increase in the exotherm contributed by the freezing of the cell water that has left the intact cells and then comparing that to the exotherm contributed by the freezing of the water in the same sample in which the cells are disrupted. They then used an Arrhenius equation to back-calculate the value of Lp at 0C. In the absence of cryoprotectant, their approach yields an Lp at 0C of 0.01 m/min atm, which is 30-fold lower than the measured value of 0.33 m/min atm at 0C reported by Noiles et al. [7]. In the presence of cryoprotectant, their value of Lp at 0C (0.004 m/min atm) is also approximately 30-fold lower than the value measured at 0C by Phelps et al. (0.10 m/min atm [8]). In the absence of cryoprotectant, their approach yields a value of Ea of 22.5 kcal/mole, which is approximately double that obtained from measurements made at above-zero temperatures. If the values of Devireddy et al. [20] for Lp and Ea are used to calculate shrinkage curves like those shown in Figures 3 and 5, then the resulting curves lead to the conclusion that mouse sperm will undergo intracellular freezing at a cooling rate of approximately 2540C/min, which is approximately 50-fold lower than the rate estimated in the present study and approximately vefold lower than that inferred from our experimental data. Devireddy et al. [20] concluded that their study shows mouse sperm to have dramatically different water transport properties at superzero temperatures in the absence of extracellular ice and at subzero temperatures in the presence of extracellular ice. Perhaps a more cautious statement would be that a large discrepancy exists between the two sets of data for the mouse, and currently, no independent evidence is available for deciding which is the more applicable to subzero events. Clearly, the range of possible values for the critical parameters is large enough to account for the approximately eightfold discrepancy between the cooling rates we calculate to induce intracellular ice and those cooling rates inferred to do so from the measurements of survival as a function of cooling rate. However, we cannot currently exclude two alternative explanations. One, pointed out by Gao et al. [19], is that injury could be a consequence of internal freezing in critical organelles such as mitochondria rather than a consequence of ice formation in the whole cytoplasm. If so, then the applicable permeability parameters would be those of the organelles membrane rather than those of the plasma membrane, and the two sets of values could be different. A second alternative is that the abrupt drop in survival at cooling rates greater than 130C/min is caused by something other than IIF. One possible something other is cold shockthe inactivation of cells from a rapid fall in temperature per se. Whereas this is possible, we think it is unlikely. Although rapid chilling is well documented in porcine, ram, and bovine sperm [12], it occurs at cooling rates of approximately 1015C/min, and we have found that mouse sperm cooled from room temperature to 0C at those rates show, at most, a marginal loss in motility [4, 5,

10. Noiles EE, Bailey JL, Storey BT. The temperature dependence in the hydraulic conductivity, Lp, of the mouse sperm plasma membrane shows a discontinuity between 4 and 0C. Cryobiology 1995; 32:220 238. 11. Mazur P. Freezing of living cells: mechanisms and implications. Am J Physiol 1984; 247:C125C142. 12. Watson PF, Gao DY, Mazur P, Critser JK. Ice nucleation temperature of bovine spermatozoa and causes of sperm cell lysis below 0C. Cryobiology 1991; 28:526. 13. Woelders H, Matthijs A, Engel B. Effects of trehalose and sucrose, osmolality of the freezing medium, and cooling rate on viability and intactness of bull sperm after freezing and thawing. Cryobiology 1997; 35:93105. 14. Mazur P. The role of intracellular freezing in the death of cells cooled at supraoptimal rates. Cryobiology 1977; 14:251272. 15. Toner M, Cravalho EG, Armant DR. Water transport and estimated transmembrane potential during freezing. J Membr Biol 1990; 115: 261272. 16. Toner M, Cravalho EG, Stachecki J, Fitzgerald T, Tompkins RG, Yarmush ML, Armant DR. Nonequilibrium freezing of one-cell mouse embryosmembrane integrity and developmental potential. Biophys J 1993; 64:19081921. 17. Duncan AE, Watson PF. Predictive water loss curves for ram spermatozoa during cryopreservation: comparison with experimental observations. Cryobiology 1992; 29:95105. 18. Curry MR, Kleinhans FW, Watson PF. Measurement of the water permeability of the membranes of boar, ram, and rabbit spermatozoa using concentration-dependent self-quenching of an entrapped uorophore. Cryobiology 2000; 41:167173. 19. Gao D, Mazur P, Critser JK. Fundamental cryobiology of mammalian spermatozoa. In: Karow AM Jr, Critser JK (eds.), Reproductive Tissue Banking. San Diego: Academic Press; 1997: 263328. 20. Devireddy RV, Swanlund DJ, Roberts KP, Bischof JC. Subzero water permeability parameters of mouse spermatozoa in the presence of extracellular ice and cryoprotective agents. Biol Reprod 1999; 61:764 775. 21. Rall WF, Mazur P, McGrath JJ. Depression of the ice-nucleation temperature of rapidly cooled mouse embryos by glycerol and dimethyl sulfoxide. Biophys J 1983; 41:112. 22. Harris CL, Toner M, Hubel A, Cravalho EG, Yarmush ML, Tompkins RG. Cryopreservation of isolated hepatocytes: intracellular ice formation under various chemical and physical conditions. Cryobiology 1991; 28:436444. 23. Muldrew K, McGann LE. The osmotic rupture hypothesis of intracellular freezing injury. Biophys J 1994; 66:532541. 24. Acker JP, McGann LE. Cell-cell contact affects membrane integrity after intracellular freezing. Cryobiology 2000; 40:5463. 25. Leibo SP, McGrath JJ, Cravalho EG. Microscopic observations of intracellular ice formation in mouse ova as a function of cooling rate. Cryobiology 1978; 15:257271. 26. Mazur P. Equilibrium, quasi-equilibrium, and non-equilibrium freezing of mammalian embryos. Cell Biophys 1990; 17:5392. 27. Gilmore JA, Liu J, Woods EJ, Peter AT, Critser JK. Cryoprotective agent and temperature effects on human sperm membrane permeabilities: convergence of theoretical and empirical approaches for optimal cryopreservation methods. Hum Reprod 2000; 15:335343. 28. Levin RL. Water permeability of yeast cells at subzero temperatures. J Membr Biol 1979; 46:91124. 29. Mazur P, Katkov II, Katkova N, Critser JK. The enhancement of the ability of mouse sperm to survive freezing and thawing by the use of high concentrations of glycerol and the presence of an E. coli membrane preparation (Oxyrase) to lower the oxygen concentration. Cryobiology 2000; 40:187209.

29]. Moreover, Watson et al. [12] have found that although bull spermatozoa are sensitive to chilling injury from room temperature to 10C, they undergo little injury when cooled from 10 to 0 or 5C at 220 and 300C/min, which are rates similar to those used in the present study. The discrepancies observed in mouse and other sperm between the rates calculated from permeability parameters to produce IIF and those that produce major drops in survival are unusual. In mouse oocytes and embryos, yeast, human red cells, human lymphocytes, hamster tissue culture cells, and plant protoplasts, a close correlation is observed between the cooling rates that produce a drop in survival, the cooling rates that are visually observed to produce IIF, and the cooling rates that are predicted to do so from modeling (see [11] for older references and [16] for a more recent study). As discussed, the discrepancy in mouse sperm is resolvable if other possible values of Lp and Ea are substituted for those used in the present study. However, at the moment, that resolution is a hypothesis, not a fact.

ACKNOWLEDGMENT

We thank Edna Gamliel for expert technical assistance.

REFERENCES

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