8
H. ATMANI: Thermodynamic Parameters of the Amorphous Se Crystallization 113 phys. stat. sol. (a) 88, 113 (1985) Subject classification: 1.5 and 3; 22.1.3 Laboratoire d'Etudes des Couches Minces Amorphes et Polycristallines, Pacultk des Sciences, Mont-Saint-Aignanl) Determination of Thermodynamic Parameters of the Amorphous Selenium Films Crystallization BY H. ATMANI Using experimental results obtained by DTA and optical microscopy, the thermodynamic param- eters governing the growth and nucleation rates of the crystallization of amorphous selenium films are determined. Furthermore are determined the number PIS of nuclei which exist in the native state, and also the critical number of atoms necessary to have a stable nurlei, i.e. 180 atoms at a temperature of 340 K. Unter Benutzung von experimentellen DTA-Ergebnissen und optischer Mikroskopie werderi die thermodynamischen Parameter bestimmt, die die Wachstums- und Keimbildungsraten dcr Kristallisation von amorphen Selenschichten steuern. Daritber hinaus wird die Anzahl PIS der Keime bestimmt, die im gewachsenen Zustand vorhanden sind, sowie die kritische Anzahl der Atome, die fur einen stabilen Keim notwendig sind: 180 Atome bei einer Temperatur von 340 K. 1. Introduction In previous papers 11, 21 we have studied the crystallization of amorphous selenium (a-Sej films evaporated on aluminium substrates. We have shown that in this case the nucleation is homogeneous; the number N of crystallites created per unit time and volume is given by [2] Ahm + Ali,) [ 1 -exp ( -~ N = N,v exp ( "m "") exp ( - kT with Ag' = g, - g, - Ag, the crystallization free energy, where N, represents the atomic density, v the jump frequency, ASm the entropy of migration, AS, the formation entropy of a nucleus, Ahm the enthalpy of migration, Ah, the formation entropy of a nucleus, g, the atomic free energy of the amorphous phase, g, the atomic free energy of the crystalline phase, Ag, the strain free energy due to the nucleus formation. Whether the crystals are created by nucleation or exist in the native state with a number PIS per unit surface, they grow at a rate [Z] where 6 is the atomic jump length at the interface amorphous-crystalline. The isothermal crystallization study by means of optical microscopy [l] has been undertaken in a narrow range of temperature and has permitted us to express the l) B.P. 67, F-76 130 Mont-Saint-Aignan, France. S physica (a) 8Xjl

Determination of thermodynamic parameters of the amorphous selenium films crystallization

Embed Size (px)

Citation preview

Page 1: Determination of thermodynamic parameters of the amorphous selenium films crystallization

H. ATMANI: Thermodynamic Parameters of the Amorphous Se Crystallization 113

phys. stat. sol. (a) 88, 113 (1985)

Subject classification: 1.5 and 3; 22.1.3

Laboratoire d'Etudes des Couches Minces Amorphes et Polycristallines, Pacultk des Sciences, Mont-Saint- Aignanl)

Determination of Thermodynamic Parameters of the Amorphous Selenium Films Crystallization

BY H. ATMANI

Using experimental results obtained by DTA and optical microscopy, the thermodynamic param- eters governing the growth and nucleation rates of the crystallization of amorphous selenium films are determined. Furthermore are determined the number PIS of nuclei which exist in the native state, and also the critical number of atoms necessary t o have a stable nurlei, i.e. 180 atoms a t a temperature of 340 K.

Unter Benutzung von experimentellen DTA-Ergebnissen und optischer Mikroskopie werderi die thermodynamischen Parameter bestimmt, die die Wachstums- und Keimbildungsraten dcr Kristallisation von amorphen Selenschichten steuern. Daritber hinaus wird die Anzahl PIS der Keime bestimmt, die im gewachsenen Zustand vorhanden sind, sowie die kritische Anzahl der Atome, die fur einen stabilen Keim notwendig sind: 180 Atome bei einer Temperatur von 340 K.

1. Introduction

I n previous papers 11, 21 we have studied the crystallization of amorphous selenium (a-Sej films evaporated on aluminium substrates. We have shown that in this case the nucleation is homogeneous; the number N of crystallites created per unit time and volume is given by [2]

Ahm + Ali,) [ 1 -exp ( -~ N = N,v exp ("m "") exp ( - kT

with Ag' = g, - g, - Ag,

the crystallization free energy, where N , represents the atomic density, v the jump frequency, ASm the entropy of migration, AS, the formation entropy of a nucleus, Ahm the enthalpy of migration, Ah, the formation entropy of a nucleus, g, the atomic free energy of the amorphous phase, g, the atomic free energy of the crystalline phase, Ag, the strain free energy due to the nucleus formation.

Whether the crystals are created by nucleation or exist in the native state with a number PIS per unit surface, they grow at a rate [Z]

where 6 is the atomic jump length a t the interface amorphous-crystalline. The isothermal crystallization study by means of optical microscopy [l] has been

undertaken in a narrow range of temperature and has permitted us to express the

l) B.P. 67, F-76 130 Mont-Saint-Aignan, France. S physica (a) 8Xjl

Page 2: Determination of thermodynamic parameters of the amorphous selenium films crystallization

114

growth rate by

v = vnl exp (- g;) H. ATMANI

(4)

and we have found for the apparent activation energy El = 0.95 eV and tiol = 6.5 x lo5 ni/s .

The study of the non-isothermal crystallization by differential thermal analysis (DTA) [2] has shown that the crystallization peaks obtained for different heating rates occixr in a narrow temperature range so that we may write

= vn2 exp ( - &) and

N = N , exp (-&) (5 )

and we have found E2 = 0.89 eV and T i = 1.3 eV. Unfortunately it has not been possible to determine vcz and No. Our purpose is to show now that it is possible to determine cryst'allization para-

meters using both the results obtained by isothermal as well as non-isothermal techniques.

2. Determination of Ah' and 5s' We represent the variation of the rate v versus temperature by a In w = f ( l / T ) curve (Fig. 1) [2]. In a narrow temperature range, we may approximate the curve by a straight line

(7) h?

l n v = --+lnv,,, bT

d (111 v) E d - k ' ~ - _ _

Then, starting from (3) it is possible to write

(7')

Fig. 1. In v = f(l/!/') (theoretical curve) 7lT-

Page 3: Determination of thermodynamic parameters of the amorphous selenium films crystallization

Thermodynamic Parameters of the Amorphous Sclcnium Films Crystallization 115

and, taking into account that Ay’ = Ah’ - II’ AS’,

For optical microscopy where El = 0.95 eV in a domain centred at T, = 340 K, we may write (see (7’) and (9))

For DTA, E2 = 0.89 eV in a domain centred on T2 = 398 K, we may write

Ah’

exp ( -T) exp (g) - 1 ’ AS‘

E, = Ah, - - -

We have to equations (10) and (11), in order to determine the three parameters Ah,, Ah’, and As’.

Following Zellama et al. [3], the value of Ah,, is very close to the apparent activa- tion energy, i.e. 0.95 eV; so that we have chosen to take Ah, as parameter, with values around El. Then, from (10) and (11) we have

Ah’ I - ___

1 - -

El - Ah,,, = exp [At’ ($-$)I Ah’

E2 - Ah,

This equation gives Ah’ as a function of Ah,, and the value AS’ can be obtained from (10) or (11). Values of Ah’ and A F / k for different Ah, are reported in Table 1.

T a b l e 1

Crystallization enthalpy and entropy for different values of migration enthalpy

Ah,(eV) Ah’(eV) AS’lk

~~ ~ ~-

0.96 0.97 0.98 0.99 1 .OO 1.01 1.02 1.03

0.36 0.24 0.17 0.12 0.08 0.05 0.03 0.01

8.67 5.62 3.90 2.70 1.77 1.10 0.67 0.22

8’

Page 4: Determination of thermodynamic parameters of the amorphous selenium films crystallization

H. ATMANI 116

3. Determination of AS, and PIS

As in the optical microscopy domain, we know the values of El and vnl, it is possible to equate (7) (with T = TI) and (8). Then

furthermore

Equation (13) shows that AS, is a function of Ahrn, ALL’, and AS’. It is generally admitted [4] that the enthalpy of crystallization is close to the enth-

alpy of fusion Ah, which is about 0.054 eV [ 5 ] . From the values shown in Table 1, it is clear that the most probable value of Ah, (corresponding to Ah‘ = 0.05 eV) is 1.01 eV and then AS’lk = 1.10. AS, is then calculated with El = 0.95 eV, vnl = = 6.5 x lo5 mjs [I], the jump frequency v = 1013 s-l [3] and the distance between two nearest neighbours 6 = 0.232 nm [6].

We have shown using thermograms obtained with different heat,ing rates that there are domains where the heterogeneous crystallization becomes preponderant. In all these domains, we obtain a linear law [2],

where

and

(17)

The values of z (crystallized fraction) and dx/dt (crystallization rate) are determined from the thermograms by Borchard’s method [7] (see Fig. 2).

Fig. 2. dx/dt = f ( t ) (Borchard’s method [7])

Page 5: Determination of thermodynamic parameters of the amorphous selenium films crystallization

Thermodynamic Parameters of the Amorphous Selenium Films Crystallization 117

Fig. 3. Yi = f ( l / T ) . o r = 0.05, x = 0.1 0.2, a 0.3 K/s

Fig. 3 shows the straight line Yi = f ( l / T ) plotted for thermograms obtained for different heating rates and corresponding to it value of Ah, = 1.01 eV, the ordinate a t the origin enables us to calculate PIX knowing AS, (see (13)) which is given in Table 2.

Tab le 2 Thermodynamic and crystallization parameters for a-Se films

4. Determination of Ah,, Ni and AS,

We have shown that for the same thermograms there exist domains where the homo- geneous crystallization is preponderant so that

where

i"". : NA = N,v exp

and vh is the value calculated above with

Y.; = 1n ($) + ~n ('>-? 2 ~n ~n (-L) - ~n [I - exp (-%)I. 1 - x 1 - x

(20)

Fig. 4 shows the straight line plotted through the experimental points determined a t different heating rates and corresponding to Ah, = 1.01 eV. The slope of the straight line leads to the value of Ah,. The ordinate a t the origin enables the deter-

Page 6: Determination of thermodynamic parameters of the amorphous selenium films crystallization

118 H. ATMANI

I I I I 1

2 35 2 45 2.55 265 1u3 -I --[K --- T

Fig. 4

Fig.4. Yk =f(l/T). o r = 0.05, x 0.1, 0.2, A 0.3 K/s

Fig. 5. m, = f ( T )

Fig. 5

mination of &. Then taking N , = 3.25 x 10z8 m-3 (atomic density), v = 1013 s-1 (jump frequency), it possible to calculate AS,.

All the parameters determined above are reported in Table 2.

5. Determination of the Number of Atoms Required for the Formation of a Critical Nucleus

The number rn, is given by the formula [a] Ah, - T AS,

]Ah‘ - T A R ‘ = 2 rn,=2-- AG, IAg’l

We have plotted (Fig. 5) the curve rn, = f ( T ) L.x 11, = 1.01 eV. This curve shows that the number m, increases with temperature. The number rn, of atoms required to form a nucleus is about 180 atoms at T = 340 K (optical microscopy domain) and 280 atoms at 1’ = 398 K (DTA domain).

6. Values of v and N

We have plotted the curves In w = f(l /T) and In N = f ( l / T ) (Fig. 6 and 7 ) for Ah, = = 1.01 eV determined from (1) and (3). We notice that for the two temperature ranges corresponding, respectively, to isothermal and non-isothermal techniques, the curves may be approximated by straight lines which confirms our assumptions 6‘ a posteriori”.

In order to compare our results with those of Grenet et al. [9], we have calculated (Tables 3 and 4) w and N for the temperatures used by them. The growth rate v is of the same order of magnitude. On the other hand, the number of crystallites N differs by about two orders of magnitude; however, as shown by Grenet 1101, N decreases with ageing of the samples and our results concerned 24 months aged samples whereas Grenet’s samples are only aged for 18 months. Furthermore, Grenet has in his cal-

Page 7: Determination of thermodynamic parameters of the amorphous selenium films crystallization

Thermodynamic Parameters of the Amorphous Selenium Films Crystallization 119

5

2 -16

-15

-2G

2 3 4

I I

opticol t o m e i n micmscapy .

I I -25 I 2 3

I I

culation neglected the [l - exp (-Ag’/kT)] term. Taking into account these factors, our results may be considered, within the experimental errors, to be in good agreement with those of Grenet et al. This confirms the influence of the age of an amorphous sample on its physical properties.

T a b l e 3 Growth rate a (ms-I)

T (K) 375 380 385

Grenet [lo], aged 18 months 0.37 x 10-7 0.49 x 10-7 0.68 x 10-7 our results, aged 24 months 1.25 x 10-7 1.57 x 10-7 2.26 x 10-7 - T a b l e 4 Number N (m-3 s-1) of crystallites

T (K) 386 394 403

Grenet [lo], aged 18 months 9.57 x loll 1.43 x 10l2 2.42 x 1012 our results, aged 24 months 1.2 x 1O1O 2.59 x 1O1O 5.9 x 1Olo our results, neglecting the term 3.63 X 1O1O 8.37 X 1O1O 2.06 X 10l1 [l - CXP ( - Ag’/lcT)]

Page 8: Determination of thermodynamic parameters of the amorphous selenium films crystallization

120 H. ATMANI: Thermodynamic Parameters of the Amorphous Se Crystallization

References

[1] H. ATMANI, P. MICHON, and C. VAUTIER, phys. stat. sol. (a) 75, K5 (1983). [2] P. MICHON, H. ATMANI, and C. VAUTIER, phys. stat. sol. (a) 85, 399 (1984). [3] K. ZELLAMA, P. GERMAIN, S. SQUELARD, 5. C. BOURGOTN, and P. A. THOMAS, J. appl. Phys.

[4] J. ZARZYCKI, Les Verres et 1’Etat vitreux, Masson, Paris 1982. [5] P. ANDONOV, J. non-crystall. Solids 47, 297 (1982). [6] C. MAZIERES, Les Solides non cristallins, impremerie des presses universitaires de France

[7] H. J. BORCHARD, J. inorg. nuclear Chem. 12, 252 (1960). [S] J. W. CHRISTIAN, Phys. Metallurgy, Chap. 10, Ed. R. W. CAHN, North-Holland, Publ. Co.,

[9] J. GRENET, J. P. LARMAGNAC, and P. MICHON, 3. thermal Analysis 25, 539 (1982).

50, 6995 (1979).

VendBme) 1978 (p. 142).

Amsterdam 1970.

[lo] J. GRENET, These doctorat d‘Etat, Rouen 1983.

(Received November 30, 1984)