Hopping conductivity due to bipolarons in amorphous silicon nitride films

] O U R N A L OF

Journal of Non-Crystalline Solids 137&138 (1991) 515-518 North-Holland

NON-CRYSTALLINE SOLIDS

HOPPING CONDUCTIVITY DUE TO BIPOLARON$ IN A M O R P H O U S SILICON NITRIDE FILMS Yacov Roizin, Leonid Tsibeskov Odessa State University, 2 P.Velikogo st., 270100 Odessa, U S S R

W e have utilized ac conductivity versus frequency measurements to study defect centers in silicon nitride films. A physical model of bipolaron hopping in a m o r p h o u s silicon nitride was developed which accounted, for the spatial correlation in the defect center positions. W e observed a decrease in the density of deep centers in the films subjected to degrading treatment and registered the structural rearrangement in the volume of the investigated samples.

i. INTRODUCTION

2. m X P E R I M E N T A L

A m o r p h o u s silicon nitride (a-Si3N 4) has properties typical of disordered solid-state systems and, in particular, a high density of structure defects i. The presence

of

these

defects (dangling bonds, Si-Si bonds, silicon clusters incorporating hydrogen, etc.) gives rise to deep localized states in the

mobility

PROCEDURES

We i n v e s t i g a t e d a-Si3N 4 f i l m s deposited, o n t o crystalline silicon substrates. The films were fabricated in the standard low-pressure CVD process at

a

ammonolysis

of

temperature silicon

of

6500

C

tetrachloride.

thickness of films ranged from 40 to 400 nm. Metal electrodes (AI, In] were evaporated

g a p of a-Si3N 4. Due to the considerable importance of silicon nitride films in semiconductor device technology the electronic properties of

these

traps

have

been

extensively

characterized a-5 Small-signal ac conductivity measurements are efficient for the determination of the densities,

energies

and

distributions of localized states

spatial

when

the

hopping conductivity dominates in a m o r p h o u s solids. The present paper gives the results of m e a s u r e m e n t s of the dynamic conductivity gac of silicon nitride in a wide frequency range at r o o m and elevated temperatures.

Both

the

initially fabricated and subjected to degrading treatment

Si3N 4 films were investigated

in

t h i s s t u d y . We h a v e a l s o d e v e l o p e d a p h y s i c a l model o f b i p o l a r o n h o p p i n g c o n d u c t i v i t y which accounted

for

the

effects

of

spatial

correlation in the positions of traps and was consistent with our experimental observations.

by The

the surface of Si3N4 or a

special

onto

mercury

contact was brought in contact with the surface of the investigated sample. Measurements were m a d e in the frequency range iO l-iO 7 Hz using E8-2 and Wayne-Kerr B 60i ac bridges supplied with l o c k - i n d e t e c t o r s y s t e m s . A BM-560 Q m e t e r was also used. The error in determination of the active component of the ac conductivity was 2% of the m e a s u r e d quantity. The amplitude of an alternating signal across a sample did not exceed O.i V and no constant bias was used. The maximum

value oi" the electric field in these

measurements was E -< 8- iO~ V/cm, which avoided injection conduction in silicon nit,r'ide~ . The investigated structures were in the regime of charge accumulation at the silicon - silicon nitride interface. The capacitance of structures changed by less than 5%

these in

the

investigated frequency range, The

experimentally • determined

0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

active

516

Y. Roizir~ L. Tsibeskov ~Hopping conductivity due to bipolarons

component of the admittance of structures with

In the range ~ -< iO a Hz it was found that the

a thin insulating layers was equal to the s u m

power exponent was s ~ 0.8-0.9, whereas in the

of the insulator conductance aac and of a term

range iOa Hz < ~ < iO 7 Hz it was s ~!.4-+ O.i.

due to a series-connected 6 contacts

At frequencies ~ > iOa Hz the inequality (la~c

resistance of the

"C R > (7ac was obeyed by s o m e of the samples [for example, in the case of

%c = %c + J c2

is the angular frequency; R is of

the

silicon

the

series

were injected into the the

the

silicon

semiconductor

nitride

substrate.

film The

quantities of charge Q* transmitted through silicon nitride films were in the range iO -2 to i C/cm 2.

corresponded

to

the

appearance of a quadratic dependence of q~*c on w. The temperature dependences of the conduc-

substrate.

To stimulate degradation p h e n o m e n a holes from

i

capacitance was C -~iO -I0 F and the resistance was R ~-5 ~]), which

where C is the capacitance of the structure; resistance

sample

from

tivity ~ c [ J obtained at low frequencies were sublinear, whereas at high frequencies (~ > iO 4 Hz)

the

value

of

~ac

was

practically

independent of T. The observed changes in Cac spectra after the charge injection are shown in Fig.2. For Q~ < i C/cm z the changes of characteristics for

8. E X P E R I M E N T A L

RESULT5

The results of our measurements

of

the

frequency dependence of the conductivity of S

G, ~-1. om-1 lO -6

M N O $ structure (Fig.i) indicated that Oac cc a) . 10-..~Q G,Q-1. ore-1

lo-lO

10-8~

,t

10 2

1

10 4

~ ,H~

lo-lO i

i

i

104 106~O,?Iz

FIGURE 2 Frequency dependencies of the degraded silicon nitride, sample~ The t~ansmitted through the f11m charge Q [C/cm ~] i - O, 2 - O.i, 3 - i, 4-3 characteristics for samples fabricated on one

FIGURE i Frequency dependence of the dynamic conductivity of various M N O S structures" i. silicon nitride layer thickness d- = 80 nm, phosphorus d o p e d (p = 4.5 2,cm) silicon substrate of thickness d=3OO~Lm; 2. d ~ lii rim, p = i ~,cm, d =iO0~rn; 8. d ~ 3 2 0 n m , p = 4 . 5 ~ . c m d ZO ~m.

substrate were identical. The value of Oac decreased in the range ~ < iO 4 Hz while in the high frequency range an increase was observed. Similar peculiarities were registered after the U V illumination. They disappeared after the annealing of the degraded samples at 300 ° C for" an hour. For the injected charge Q W >- 8 C/cm 2

Y. Roizin, L. Tsibeskov /Hopping conductivity due to bipolarons the

changes

in

irreversible and

Si~Nc differed

parameters from

sample

517

were

frequency in a crystal; ~-~ is the localization

to

radius equal to several angstromsg; r is the

sample. A characteristic "shoulder" appeared

distance between the D+ and D

on (7ac[O~)plot in this case Fig.m). An increase of the dc leakage current~accompanled--

the concentration of the centers per unit energy interval. The function g(T) represents

the observed OacI~) changes. For Q ~ > iO C/cm ?"

the energy interval in which ,jumps occur the

local leakage current channels were usually revealed under the electrode of the degraded

pair correlation function f(r) represents the states.

The

structure.

quantlty (i/2) ~" N (E)f(r)dr is equal to

the

spatial distribution of D÷, .

2

D

states; N(E) is

2

number of pairs per unit volume with dimensions 4. PHYSICAL MODEL AND DISCUSSION

from r to r + dr. In the case of closely spaced

It was shown in Refs.4,5 by ESR measurements that dominant traps in a-5i.sN 4 have negative correlation energy (U
studies~ ~8.

pairs and bipolaron jumps an allowance for the Coulomb correlations gives 2 g(T) = e /~,880r W > kT

(8)

The U
where 8 is the static

the state with two electrons and D+ is an empty

the condition ~

state. In this study it was a s s u m e d that the dependence

qac(te,T) was

due

to

tunnel

permittivity

and

the

characteristic ,jump length r ~ c a n be found from = i.

The proposed model makes it possible to use the experimental results in calculation of the

transitions of bipolarons between D_ and D+

density of states involved in the

states. Our model allowed for the contribution

process and to analyze the

of just pairs (and not of triplets,

spatial correlations of these states. W e shall

quadru-

tunneling

nature

of

the

plets, etc.) o f centers, which was j u s t i f i e d at

represent the pair correlation function in the

not too low frequencies, when the jump length

form fir)= A

was less than the average distance between the

sufficiently low frequencies such that ~r << i,

traps. It was a s s u m e d that the height of the

the spatial correlation can be ignored. Bearing

potential barrier and the length of a j u m p were

in mind that dr = (i/2 O0(d'~/~) we obtain

uncorrelated.

A

nonadiabatic

regime

was

considered in which the tunneling of carriers was the slowest process. In this case we can use the results of Refs. 6 and 9 , and show that r 4eZra ~(r)g(T)[f(r)+i]

%c=

K [

N2(E)dr

(2)

exp(-~r).

In

the

case

e4~ ~ac(W,T)= - - - lnZ[1;ph(T)/~] N2(E) 48 a ~ 88 0

which corresponds to the part of the frequency dependence

of

the

dynamic

conductivity

characterized by the power exponent s <- i. A s s u m i n g that ~ h ~ iolOHz and ~-i ~ 0.5 n m 9,

cm-3-eV -i which is in agreement with w h e r e K ~ 2; ~(r) = ~,h e x p ( 2 ~ ) i s t h e t i m e c o n s t a n t o f t h e i n t e r c e n t e r t r a n s i t i o n ; ~,h iS characteristic

similar

to

(4)

and using the experimental values Gacl~), we obtain the density of states N(E) ~ (2-8)-~019

,J

i + ~'-~2(r)

a

of

the

phonon

1,4.

In

the

case

of

strong

Refs. spatial

correlations, when f(r) = A exp(-~r) > i,

518

Y Roizir~ L. Tsibeskov / Hopping conductivity due to bipolarons

concentration.

It

means

that

long-range

structural rearangements take place in

gac(~)= - -

×

matrix of the a m o r p h o u s silicon nitride in the

cos(~/2~) a ~ e e

48

the

process of degradation. This is also consistent

×

n

N2 (E)

(5)

with an appearence of local leakage channels for large transmitted charges. 5. CONCLUSIONS

which explains the superlinear dependence range ~0 ~ iO ~ Hz. W e then find that s = i + ~/2(x and = i.6-10 -7 cm -3. Substituting in Eq.(5) the

W e have for the first time observed

the

superlinear regions on a-Si3N 4 ac conductivity versus frequency plots. This observation

value of N(E) calculated from Eq.(4), we obtain

provides convincing evidence that

A = iO0. This m e a n s that the situation which

correlated pairs of defect centers exist in the

needs allowance for the spatial correlations

investigated films. W e have developed a bipo-

changes to the case of ordinary ac hopping

larch hopping conductivity model

conductivity in the range rw->

corresponds to the condition A exp(-~r) ~ i and

consistent with the experimental data. observed changes in g(W) spectra of

a kink in the experimental dependence Oac(~)at ~ iO 4 H z .

degraded samples are explained by structural

r ~

~ 8 nm, which

spatially

which

is The the

rearrangement in the volume of silicon nitride.

It therefore follows that in the frequency .

range iO 2 Hz < a~ < iOa Hz the dependence gac[~)

REFERENCES

is governed

i. A.V. Rzhanov (ed), Silicon Nitride in Electronics (Nauka, Novosibirsk, 198,-°.,in Russian).

centers

with

by

stochastically

an

average

distributed

distance

r 0--

[T,~c/N(E)e~]I/2 ~-8 n m , where r < rw< r,:,.At frequencies ~ > iO~ Hz the main contribution to the dynamic conductivity is m a d e by spatially correlated pairs of defects with the m a x i m u m distance r~ = r

between the centers.

The presence of spatially correlated pairs of defects (incorporating

dangling

separated by the m a x i m u m distance r cleary implies the

presence

of

bonds) ~-3 n m

structural

2. J. R o b e r t s o n , M.J. Powell, J. Appl. Phys. 44 (i984) 4i5. 8. S. Fufita, A. 5asaki, J. Electrochem.5oc. 132 (1985) 898. 4. M. Numeda, H. Yokomichi, T. Shimuzu, Jpn. J. Appl. Phys. Pt.2 28 (1984) LB.

5. D.T. Krick, P.M. Lenahan, J. Kamichi, J. Appl. Phys. 64 (i988) 3558.

imperfections such as pores or microcracks in

6. A.R. Long, Adv. Phys. 8i (i982) 558.

the a-SiyN~ matrix. The decrease of Oac for ~ <

7. Ya.O. Roizin, Ha Huy Dung, Photoelectronics i (1987) 8i (in Russian).

iO 4 Hz in the degraded silicon nitride

films

corresponds to the decrease

total

of

the

density of traps. At the same time the increase of Oac in the superlinear (Tac((~)region implies the increase of the closely located pairs

8. A.F. Akhmed, Ya.O. Roizin et al., Ukrainian Physical Journal. 8i (i986) 789 (in Russian). 9. A.L. Efros, Philos. Mag. 518 (i@Si) 829.