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Simplified switching model in chalcogenide thin film
Journal of Non-Crystalline Solids 59 & 60 (1983) 1215-1218 North-Holland PublishingCompany
1215
SIMPLIFIED SWITCHING MODEL IN CHALCOGENIDE THIN FILM Masamori IIDA and Tadashi SHIRAISHI Department of Electronics,Tokai University *Department of Communications, Tokai U n i v e r s i t y , 1117 Kitakaname, Hiratsuka Kanagawa 259-12 Japan A simplified model of bias-induced switching in chalcogenide amorphous semiconductor films is proposed. The behavior of valence a l t e r n a t i o n pairs and the c a r r i e r generation aided by e l e c t r i c f i e l d are considered in t h i s model. Current-voltage c h a r a c t e r i s t i c s are calculated using the simple formula f o r impact i o n i z a t i o n process. The results show switching c h a r a c t e r i s t i c s which agree with those observed experimentally in chalcogenide amorphous f i l m s .
I . INTRODUCTION Although many phenomena in chalcogenide amorphous semiconductors, such as memory effects and structure changes induced by l i g h t i r r a d i a t i o n are understood, some questions s t i l l
remain about the mechanism of high speed threshold switch-
ing. Many models for the l a t t e r mechanism have been proposed. Since these models are based on an analogy of the properties of c r y s t a l l i n e semiconductors, no close matching exists between the proposed models and properties of chalcogenide amorphous materials. Thus, i t is necessary to describe the switching process in terms of the e l e c t r o n i c processes peculiar to chalcogenide amorphous materials. One such model was proposed by Kastner et a l . , 1 which indicates the presence of intimate valence a l t e r n a t i o n pairs ( IVAPs ) of chalcogenide atoms. These IVAPs generate an equal number of p o s i t i v e l y and negatively charged trap states. In a d d i t i o n , Kimata and Kani2have proposed that generation of c a r r i e r pairs by impact i o n i z a t i o n contributes to the switching c h a r a c t e r i s t i c s of semiconductors doped with deep level i m p u r i t i e s . In this paper, we consider the e f f e c t of the n e u t r a ] i z a t i o n o f ( and consequently, reduced ionized center scattering due to ) the IVAP trap states by the c a r r i e r s generated by impact i o n i z a t i o n . The reduced s c a t t e r i n g due to the n e u t r a l i z a t i o n of trap states is l i k e l y to increase th~ m o b i l i t y of c a r r i e r s and t h i s increased m o b i l i t y is shown in t h i s paper to a f f e c t the switching c h a r a c t e r i s t i c s of chalcogenide amorphous semiconductor f i l m s . 2. VALENCE ALTERNATION MODEL FOR CHALCOGENIDE AMORPHOUSSEMICONDUCTORS The most stable defect state of chalcogen atoms in an amorphous material is realized a f t e r the following reaction 2Cj
~ C+3 +
c~,
0022-3093/83/0000-0000/$03.00 © 1983 North-Holland/Physical Society of Japan
(1)
1216
M. /ida, T. Shiraishi/ Simplified switching model where C is a chalcogen atoms; the s u f f i x shows .
•
the number of the coodination. The combination of + C3 and C~ _ forms an intimate val ence a l t e r n a t i o n
E C ~
C3 _u_ E3
i
/
cT "- E, £ _ Z Ev C~+C~" ~
p a i r , where the superscript shows charge states.
...........
(a)
Figure 1 (a) and (b) show hole and electron
2Co
Figure 1
+
emission from C3- and CL-centers. In this f i g u r e ,
(b)
i t is assumed that electrons are emitted from the
Energy band mode] including
energy level El and holes from the level E3.
IVAP
The empty level corresonds to neutral centers.
3.1MPACT IONIZATION MODEL The p o s s i b i l i t y of field-induced switching was suggested by Ovshinsky 3 and Adler et alo 4. In this paper, the model of e l e c t r i c a l switching is proposed taking into account impact i o n i z a t i o n due to c a r r i e r s accelerated by f i e l d . Although chalcogenide amorphous semiconductors generally show high r e s i s t i v i ty at thermal e q u i l i b r i u m , s t i l l
a small amount of c a r r i e r s w i l l be present in
both bands. Furthermore, f o r s i m p l i c i t y , we shall consider only electrons in the conduction band. The material at thermal e q u i l i b r i u m contains IVAPs and free electrons whose densities are denoted by N (m-3) and no (m-3), respectively. Figure 2 shows the switching process. Figure 2(a) shows the low current level condition which is named as the o f f - s t a t e . In this state, the current is carried only by free electrons
I ~ --F C~ o+ o + ~ + CT ~ - ~ - ~ -
EC E3 El Era
,rH/I//i//HH,~,r
0
t r i c f i e l d . Figure 2(b) shows the impact i o n i z a t i o n
"
process. Since the Cl-centers emit electrons into the conductlon band and C3-centers accept electrons from
Ea
the valence band a f t e r the c o l l i s i o n , both types of
-I--ir~o,i,~o,,, El ,,,i,H Ev xl (b)
charge, Un is the electron m o b i l i t y and F is the elec-
Ec
(a) -~A l
_~-~
0
and expressed as q~nnoF where q is the e l e c t r o n i c
L
Figure 2 Electrical switching process due to impact ionization
•
+
centers are e l e c t r i c a l l y neutralized and densities of c a r r i e r s increase. When Xl=O, a l l centers in the f i l m are neutralized and the high conduction state ( the on-state ) is r e a l i z e d . The densities of free electron and hole in the on-state are denoted by no + N and N, respectively•
4. THE DERIVATION OF SWITCHING CHARACTERISTICS The impact i o n i z a t i o n model proposed by Kimata and Kani
2
w i l l be applied to
the case of chalcogenide amorphous semiconductor. The region I , O
M. Iida, 71 Shiraishi / Simplified switching mode/
12 17
the neutral centers whose density is also 2N. The mobility in the region I UlL is given by II~IL = II~I(2N) + II~ L , (2) where ~I (2N) and ~L are m o b i l i t i e s due to the ionized centers and l a t t i c e scattering, respectively. The m o b i l i t y in the region ~ ~NL is the sum of the m o b i l i t i e s due to neutral center UN(2N) and ~L' as f o l l o w s llPNL = I/PN(2N) + I / p L. (3) M o b i l i t i e s Pl(2N) and PN(2N) are the functions of the density of centers,2N. The e l e c t r i c a l
resistances RI and R~ of regions I and ~ are described as
RI = x l / q p l L n o s,
(4)
R~ = (L-Xl)/qpNL(no+2N)S, where S is the cross section of the specimen.
(5)
The voltage drop across the specimen can be expressed as follows V = ( I / S ) [ x l / q p l L n o + (L-Xl)lqpNL(no + 2N)], where I is the current through the specimen.
(6)
In the impact i o n i z a t i o n process, the c a r r i e r density n(x) at the p o s i t i o n x is given by n(x) = noexp(~x), (7) where ~ is the i o n i z a t i o n c o e f f i c i e n t which is derived by Gunn5, as f o l l o w s
n(x)~
= Clexp(C2F), (8) where Cl and C2 are constants. Since the resistance of the region ~ is considerably
n~N
low, i t is assumed that the d r i f t current through the region I is directly related to
:
n,
0
~
I
the electric f i e l d F, as follows
L
Figure 3 D e f i n i t i o n of boundary x I
F = I/q~iLnoS. (9) According to the definition of xI in Fig.3, eqn.(7) is rewritten as
no + N : noexp(~xl). (I0) Then, combining eqns.(8) - ( I 0 ) , the p o s i t i o n of the boundary x I is given as xI = (I/Cl)exp(-C21/qUlLnoS)In[l+(N/no)]. Substituting e q n . ( l l ) in e q n . ( 6 ) , the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c as follows V = (I/S){exp(-C21/q~iLnoS)In[l+(N/no)]/(CLq~iLno)
(II) is expressed
+ L/q(2N+no)~NL
-exp(-C21/q~iLnoS)In[l+(N/no)]/Clq(no+2N)~NL ,
(12)
M. lida, 71 Shiraishi / Simplified switching model
12 18
5. RESULTS Figure 4 shows the results calculated from eqn.(12). The insert in Fig.4 shows the definitions of Vth, Vh, Ith and I h. The curve marked A: ~NL/mIL = l corresponds to the regime where mobilities are assumed unchanged during the impact ionization process. On the other
10-6
hand, the curve marked B: ~NL/~IL = 5×I03 is obtained by considering the ~ncrease
ith
in mobility during the impact ionization.
io-~
~j/~
Obviously, switching action is enhanced in the l a t t e r case. For the same applied
io1°~~NL
voltage range, the ratio of the on-state dynamic resistance Ron to the off-state dynamic resistance R_ffu obtained from the curve A is about lO- l , on the other hand, the ratio from the curve B is IO-6. Adler4 pointed out nearly same value of this ra-
I
i0 4
I
I
i~ 2 v (v)
i
I,
I~ 0
Figure 4 8 l Current-voltage curves. CI= IO (m-) Cp=IO-7 (m/v), S:IO-8 (m2), " ~m=iO-5 (m2/vs), N=lo2O(m-3) ,L=lO-6im), no= lol7(m-3).Curve A: ~iL=lO-5(m2/vs), Curve B: ~iL=2XlO-9(m2/vs).
tio. The very large change in dynamic resistance in the curve B is well agree with experimental observations3. 6. CONCLUSIONS Current-voltage curves of chalcogenide amorphous films were calculated taking into account the presence of IVAPs and the effect of impact ionization. The results of this rather simplified model
are much closer to the practical results than conventional model yields. ACKNOWLEDGEMENT We would like to thank Dr. T.Kurosu and Mr.Y.Akiba of Tokai Univertity, also Dr.M.S.Niranjan of Spektraglobal Associates, Inc. for their stimulating discussions and cooperation. REFERENCES l) M. Kastner, D. Adler and H. Fritzsche, Phys. Rev. Lett. 37 (1976) 1504. 2) M. Kimata and K. Kani, Jpn. J. Appl. Phys. 4 (1965) 737. 3) S. R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. 4) D. Adler, M. S. Shur, M. Silver and S. R. Ovshinsky, J. Appl. Phys. 51 (1980) 3289. 5) J. B. Gunn, Progress in Semiconductors, Vol.2, (London Heywood & Company L. T. D. ) pp.224.
1215
SIMPLIFIED SWITCHING MODEL IN CHALCOGENIDE THIN FILM Masamori IIDA and Tadashi SHIRAISHI Department of Electronics,Tokai University *Department of Communications, Tokai U n i v e r s i t y , 1117 Kitakaname, Hiratsuka Kanagawa 259-12 Japan A simplified model of bias-induced switching in chalcogenide amorphous semiconductor films is proposed. The behavior of valence a l t e r n a t i o n pairs and the c a r r i e r generation aided by e l e c t r i c f i e l d are considered in t h i s model. Current-voltage c h a r a c t e r i s t i c s are calculated using the simple formula f o r impact i o n i z a t i o n process. The results show switching c h a r a c t e r i s t i c s which agree with those observed experimentally in chalcogenide amorphous f i l m s .
I . INTRODUCTION Although many phenomena in chalcogenide amorphous semiconductors, such as memory effects and structure changes induced by l i g h t i r r a d i a t i o n are understood, some questions s t i l l
remain about the mechanism of high speed threshold switch-
ing. Many models for the l a t t e r mechanism have been proposed. Since these models are based on an analogy of the properties of c r y s t a l l i n e semiconductors, no close matching exists between the proposed models and properties of chalcogenide amorphous materials. Thus, i t is necessary to describe the switching process in terms of the e l e c t r o n i c processes peculiar to chalcogenide amorphous materials. One such model was proposed by Kastner et a l . , 1 which indicates the presence of intimate valence a l t e r n a t i o n pairs ( IVAPs ) of chalcogenide atoms. These IVAPs generate an equal number of p o s i t i v e l y and negatively charged trap states. In a d d i t i o n , Kimata and Kani2have proposed that generation of c a r r i e r pairs by impact i o n i z a t i o n contributes to the switching c h a r a c t e r i s t i c s of semiconductors doped with deep level i m p u r i t i e s . In this paper, we consider the e f f e c t of the n e u t r a ] i z a t i o n o f ( and consequently, reduced ionized center scattering due to ) the IVAP trap states by the c a r r i e r s generated by impact i o n i z a t i o n . The reduced s c a t t e r i n g due to the n e u t r a l i z a t i o n of trap states is l i k e l y to increase th~ m o b i l i t y of c a r r i e r s and t h i s increased m o b i l i t y is shown in t h i s paper to a f f e c t the switching c h a r a c t e r i s t i c s of chalcogenide amorphous semiconductor f i l m s . 2. VALENCE ALTERNATION MODEL FOR CHALCOGENIDE AMORPHOUSSEMICONDUCTORS The most stable defect state of chalcogen atoms in an amorphous material is realized a f t e r the following reaction 2Cj
~ C+3 +
c~,
0022-3093/83/0000-0000/$03.00 © 1983 North-Holland/Physical Society of Japan
(1)
1216
M. /ida, T. Shiraishi/ Simplified switching model where C is a chalcogen atoms; the s u f f i x shows .
•
the number of the coodination. The combination of + C3 and C~ _ forms an intimate val ence a l t e r n a t i o n
E C ~
C3 _u_ E3
i
/
cT "- E, £ _ Z Ev C~+C~" ~
p a i r , where the superscript shows charge states.
...........
(a)
Figure 1 (a) and (b) show hole and electron
2Co
Figure 1
+
emission from C3- and CL-centers. In this f i g u r e ,
(b)
i t is assumed that electrons are emitted from the
Energy band mode] including
energy level El and holes from the level E3.
IVAP
The empty level corresonds to neutral centers.
3.1MPACT IONIZATION MODEL The p o s s i b i l i t y of field-induced switching was suggested by Ovshinsky 3 and Adler et alo 4. In this paper, the model of e l e c t r i c a l switching is proposed taking into account impact i o n i z a t i o n due to c a r r i e r s accelerated by f i e l d . Although chalcogenide amorphous semiconductors generally show high r e s i s t i v i ty at thermal e q u i l i b r i u m , s t i l l
a small amount of c a r r i e r s w i l l be present in
both bands. Furthermore, f o r s i m p l i c i t y , we shall consider only electrons in the conduction band. The material at thermal e q u i l i b r i u m contains IVAPs and free electrons whose densities are denoted by N (m-3) and no (m-3), respectively. Figure 2 shows the switching process. Figure 2(a) shows the low current level condition which is named as the o f f - s t a t e . In this state, the current is carried only by free electrons
I ~ --F C~ o+ o + ~ + CT ~ - ~ - ~ -
EC E3 El Era
,rH/I//i//HH,~,r
0
t r i c f i e l d . Figure 2(b) shows the impact i o n i z a t i o n
"
process. Since the Cl-centers emit electrons into the conductlon band and C3-centers accept electrons from
Ea
the valence band a f t e r the c o l l i s i o n , both types of
-I--ir~o,i,~o,,, El ,,,i,H Ev xl (b)
charge, Un is the electron m o b i l i t y and F is the elec-
Ec
(a) -~A l
_~-~
0
and expressed as q~nnoF where q is the e l e c t r o n i c
L
Figure 2 Electrical switching process due to impact ionization
•
+
centers are e l e c t r i c a l l y neutralized and densities of c a r r i e r s increase. When Xl=O, a l l centers in the f i l m are neutralized and the high conduction state ( the on-state ) is r e a l i z e d . The densities of free electron and hole in the on-state are denoted by no + N and N, respectively•
4. THE DERIVATION OF SWITCHING CHARACTERISTICS The impact i o n i z a t i o n model proposed by Kimata and Kani
2
w i l l be applied to
the case of chalcogenide amorphous semiconductor. The region I , O
M. Iida, 71 Shiraishi / Simplified switching mode/
12 17
the neutral centers whose density is also 2N. The mobility in the region I UlL is given by II~IL = II~I(2N) + II~ L , (2) where ~I (2N) and ~L are m o b i l i t i e s due to the ionized centers and l a t t i c e scattering, respectively. The m o b i l i t y in the region ~ ~NL is the sum of the m o b i l i t i e s due to neutral center UN(2N) and ~L' as f o l l o w s llPNL = I/PN(2N) + I / p L. (3) M o b i l i t i e s Pl(2N) and PN(2N) are the functions of the density of centers,2N. The e l e c t r i c a l
resistances RI and R~ of regions I and ~ are described as
RI = x l / q p l L n o s,
(4)
R~ = (L-Xl)/qpNL(no+2N)S, where S is the cross section of the specimen.
(5)
The voltage drop across the specimen can be expressed as follows V = ( I / S ) [ x l / q p l L n o + (L-Xl)lqpNL(no + 2N)], where I is the current through the specimen.
(6)
In the impact i o n i z a t i o n process, the c a r r i e r density n(x) at the p o s i t i o n x is given by n(x) = noexp(~x), (7) where ~ is the i o n i z a t i o n c o e f f i c i e n t which is derived by Gunn5, as f o l l o w s
n(x)~
= Clexp(C2F), (8) where Cl and C2 are constants. Since the resistance of the region ~ is considerably
n~N
low, i t is assumed that the d r i f t current through the region I is directly related to
:
n,
0
~
I
the electric f i e l d F, as follows
L
Figure 3 D e f i n i t i o n of boundary x I
F = I/q~iLnoS. (9) According to the definition of xI in Fig.3, eqn.(7) is rewritten as
no + N : noexp(~xl). (I0) Then, combining eqns.(8) - ( I 0 ) , the p o s i t i o n of the boundary x I is given as xI = (I/Cl)exp(-C21/qUlLnoS)In[l+(N/no)]. Substituting e q n . ( l l ) in e q n . ( 6 ) , the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c as follows V = (I/S){exp(-C21/q~iLnoS)In[l+(N/no)]/(CLq~iLno)
(II) is expressed
+ L/q(2N+no)~NL
-exp(-C21/q~iLnoS)In[l+(N/no)]/Clq(no+2N)~NL ,
(12)
M. lida, 71 Shiraishi / Simplified switching model
12 18
5. RESULTS Figure 4 shows the results calculated from eqn.(12). The insert in Fig.4 shows the definitions of Vth, Vh, Ith and I h. The curve marked A: ~NL/mIL = l corresponds to the regime where mobilities are assumed unchanged during the impact ionization process. On the other
10-6
hand, the curve marked B: ~NL/~IL = 5×I03 is obtained by considering the ~ncrease
ith
in mobility during the impact ionization.
io-~
~j/~
Obviously, switching action is enhanced in the l a t t e r case. For the same applied
io1°~~NL
voltage range, the ratio of the on-state dynamic resistance Ron to the off-state dynamic resistance R_ffu obtained from the curve A is about lO- l , on the other hand, the ratio from the curve B is IO-6. Adler4 pointed out nearly same value of this ra-
I
i0 4
I
I
i~ 2 v (v)
i
I,
I~ 0
Figure 4 8 l Current-voltage curves. CI= IO (m-) Cp=IO-7 (m/v), S:IO-8 (m2), " ~m=iO-5 (m2/vs), N=lo2O(m-3) ,L=lO-6im), no= lol7(m-3).Curve A: ~iL=lO-5(m2/vs), Curve B: ~iL=2XlO-9(m2/vs).
tio. The very large change in dynamic resistance in the curve B is well agree with experimental observations3. 6. CONCLUSIONS Current-voltage curves of chalcogenide amorphous films were calculated taking into account the presence of IVAPs and the effect of impact ionization. The results of this rather simplified model
are much closer to the practical results than conventional model yields. ACKNOWLEDGEMENT We would like to thank Dr. T.Kurosu and Mr.Y.Akiba of Tokai Univertity, also Dr.M.S.Niranjan of Spektraglobal Associates, Inc. for their stimulating discussions and cooperation. REFERENCES l) M. Kastner, D. Adler and H. Fritzsche, Phys. Rev. Lett. 37 (1976) 1504. 2) M. Kimata and K. Kani, Jpn. J. Appl. Phys. 4 (1965) 737. 3) S. R. Ovshinsky, Phys. Rev. Lett. 21 (1968) 1450. 4) D. Adler, M. S. Shur, M. Silver and S. R. Ovshinsky, J. Appl. Phys. 51 (1980) 3289. 5) J. B. Gunn, Progress in Semiconductors, Vol.2, (London Heywood & Company L. T. D. ) pp.224.