The field effect in amorphous chalcogenides: An investigation of localized states and electronic transport

Journal of Non-Crystalline Solids 24 (1977) 29-50 © North-Holland Publishing Company

THE FIELD EFFECT IN AMORPHOUS CHALCOGENIDES: AN INVESTIGATION OF LOCALIZED STATES AND ELECTRONIC TRANSPORT John E. MAHAN * and Richard H. BUBE Department o f Materials Science and Engineering, Stanford University, Stanford, California 94305, USA Received 1 November 1976 Revised mauscript received 16 December 1976

The temperature dependence of the field effect response permits an unambiguous determination of the identity of those states responsible for electrostatic screening in the amorphous chalcogenides. We observe (1) in As2Te3, field effect screening by localized states at the Fermi level at low temperatures (~1019 cm - 3 eV -1) and by mobile charge carriers (~1018 cm - 3 at 300 K) at high temperatures, and a transition from p-type to two-carrier (primarily n-type) conductivity as the temperature is raised above ~320 K; (2) in As2SeTe2, screening by mobile charge carriers (~1018 cm- 3 at 300 K) with strongly p-type conductivity; (3) in As2Se2Te, screening by localized states at the Fermi level (~1019 cm - 3 eV-1) with strongly p-type conductivity; and (4) in Sb2Te3, a very high density of localized states at the Fermi level (~2 X 1020 cm - 3 eV-1) with both electron and hole contributions to the conductivity. Correlation with thermoelectric power results suggests that the p-type conductivity in As2Te3 is due to near-equal contributions from two processes: hopping in localized states plus extended state conduction. Aging and annealing behavior is described with the aid of a "chaotic potential model" that appears to be able to account for large changes in mobile carrier density that leave the conductivity unaltered. 1. Introduction The investigation of the properties of amorphous chalcogenides has become an active branch of solid state physics over the last decade. Several band models have been proposed, as shown in fig. 1, to explain the behavior of these amorphous semiconductors. The field effect experiment can, in certain cases, measure the density of localized midgap states, and in other cases the density of electron or hole traps, or density of mobile charge carriers in the material. Indeed, Spear and LeComber [1] have used the field effect method with great success in mapping out the distribution of localized states in amorphous silicon fdms over a large portion of the band gap. It is important to perform the field effect experiment over a range of temperatures in order to determine the identity of the dominant screening states. The CFO model [2], shown in fig. 1, proposed broad, structureless tails of con* Present address; Dept. of Materials Science & Engineering, MIT, Cambridge, Mass. 02139, USA. 29

30

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

DISORDERED

CFO I~

BAND

MODELS Davis- Matt

Ec

EF

~

/

Ec

EF

. . . .

Ev

CFOwith Correlation J __

-~

Small

Polaron

Ec

.,,~., / Ec

EF

I... ---'--

Ev

FF Ev

Fig. 1. Proposed band models for amorphous semiconductors.

duction band valence band states that overlap near the center of what was formerly the forbidden gap of the crystalline material. The Fermi level is pinned near the center of the gap, its location determined by the requirement of charge neutrality and the state distributions of the valence and conduction band tails. The Davis-Matt model [3] also shown in fig. 1, was suggested because it was thought more compatible with the optical absorption characteristics of the amorphous chalcogenides [4]:their high transparency below a well-defined absorption edge. In these models E c and E v refer to conduction and valence mobility edges. If the screening of the field effect were controlled by localized states at the Fermi level, then these two models would be indistinguishable by the field effect measurement alone. If, however, the field effect were controlled by states away from the Fermi level, then the Davis-Matt model would be preferable to the CFO model, because the convolution of its density of states distribution with the Fermi function could probably provide a peak in the density of occupied states somewhat removed from EF, while that of the CFO model probably would not. Adler [5] suggested a modification of the CFO model that is also shown in fig. 1. Electronic correlation effects may be important for localized states at the mobility edges because occupation of localized states alters the energy of neighboring states. The result is a discontinuity in the density of states distribution. A nonmonotonic state distribution may also exist if there is a high concentration of defect states of a particular energy. In a material with such a distribution, the field effect screening is likely to be controlled by electron or hole traps. The field effect

31

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

experiment could measure the density of the traps and, from the temperature dependence of their occupation, their position with respect to the Fermi level. Marshall and Owen [6] have reported such traps through field effect measurements on As2Te3 and on a multicomponent chalcogenide thin film. The small polaron model proposed by Emin [7] is also shown in fig. 1. According to this model, charge carriers enter the self-trapped (small polaron) state via polarization of the atomic lattice. The field effect screening is accomplished by a redistribution of small polarons within the space charge layer. The small polaron density can be calculated, its thermal activation energy being the separation in energy of the polaron band from the Fermi level. The difference between this energy and the conductivity activation energy is equal to the hopping energy for polaron movement. The temperature dependence of the field effect is therefore capable of testing the small polaron model in a range where the field effect screening is controlled by polarons. One of the most important pieces of information that the field effect can provide is an immediate determination of carrier type: electrons, holes or, in the case of mixed conduction, the electron-hole conductivity ratio. It is necessary, of course, that the surface region of the sample be essentially identical to the bulk in its transport properties. On the basis of previous studies, we believe that such is the case for the amorphous chalcogenides we have investigated (for supporting evidence see [8]). Although there may be surface states present, they do not appear to influence the field effect measurement since bulk state densities are so large. Table 1 Evidence for localized gap states in amorphous chalcogenides from bulk measurements. Material

Type of measurement

Density

Reference

As2Te3 Te53As32Si10Ge5 As2Se3 As2S3 As2Te3 As2SeTe2 Sb2Te3 As2Se3 As2Sel.STel. 5 As2S3 wide variety of chalcogenides As2S3 As2Se3 As2Se3

ac conductivity

5.0 X 1019 cm-3 eV-1 4.5 × 1019 1018 5.0 X 1017 3.0 X 1019 4.4 X 1018 6.4 X 1019 1016 to 1018 cm-3 a 1018 1017 1014

[9]

2.0 X 1018 2.0 × 1018 3.0 × 1015 to

{14]

Sb2Se3

photoconductivity decay photoluminescence electronspin resonance optical absorption current-voltage characteristics

1017

a Note the change in units starting with photoluminescence.

[10] [ 11 ] [12] [13]

[15]

32

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

Table 1 is a summary o f the previously published results of various bulk measurements o f localized gap states. These results are consistent with the estimates o f localized state densities we have obtained. There appears to be an approximately inverse correlation between the size of the band gap and the magnitude of the localized state density.

2. Sample

preparationand experimental technique

All the materials discussed here were prepared as thin films by rf sputtering in argon. The f'rims, 1 /am thick, were deposited on to fused quartz substrates, on to which gold interdigital electrodes had previously been evaporated. These electrodes have an effective length and separation of 5 and 0.02 cm respectively. The sputtering system was initially pumped down to below 10 -5 Torr, the deposition then being carried out at an argon pressure of 2 × 10 -2 Torr. The deposition rate was 67 A/min. The film composition was determined by electron microprobe analysis, accurate to 2 or 3 at%. The structure of the thin films was checked by X-ray diffraction. We detected no crystalline peaks in the range 20 = 20 ° to 120 °. The sample configuration and the field effect measuring circuit are shown in fig. 2. The gold interdigital electrodes are the source and drain of the field effect struc-

DIELECTRIC/

FIELD ELEC~

.

/%

m

KEITI- E'~ 610~ ELECl METI

FIELD EFFECT MEASURING CIRCUIT Fig, 2. Field effect sample configuration and measuring circuit.

MOSELEY X--Y RECORDER

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides

33

ture. Three different materials were used as the dielectric insulator for the gate electrode: mica sheet cleaved to between 10 and 30/am, 12.5 ~tm mylar, and a sputtered SiOz layer ( 1 - 2 / a m thick). The three dielectric materials gave essentially the same results. All of the results reported in this paper were made using mica for the gate insulator. The field electrode, a slab of transparent glass with a conducting surface, was placed on top of the gate insulator. The field voltage was provided by an external voltage supply. The field effect experiment consists of measuring the change in source-to-drain resistance as a function of applied field voltage. The change in resistance is usually quite small; it must be measured with a Wheatsone bridge. When the field voltage is switched on the initial change in resistance is large; there is typically a relaxation time of several minutes, during which the field effect response approaches a steadystate value. All of the field effect measurements were made under vacuum in the 1 0 - 3 0 ~tm Tort range.

3. Field effect models A band diagram for an accumulation layer in a p-type material is shown in fig. 3. When the field voltage is applied, excess charge is induced in the region of the sample nearest the gate insulator. The resultant shape and magnitude of the bandbending is given by the solution of Poisson's equation: dZV(x)/dx 2 = - p ( x ) e

(1)

with the requirement that ea Vv qd

D =f

p(x) dx,

(2)

0

where V(x) is the electrostatic potential as a function of depth within the semiconducting f'flm as shown in fig. 3, p(x) the charge density, e the dielectric constant of the semiconducting film, ea the dielectric constant of the gate insulator material, Vv the applied field voltage, q the electronic charge, d the gate insulator thickness and D the semiconducting film thickness: In general, there are many terms that comprise p(x), but usually only one or two are significant. Two terms are pertinent for the results presented in this paper: p(x) = --q (N(EF)AEf(x) + [p(x) - Pb] }.

(13)

Here, N ( E v ) is the density of localized states at the Fermi level in cm -3 eV - 1 and p(x) is the mobile hole density in cm -3, as a function of depth within the film. The subscript b refers to the bulk value. One could also include various trap densitites or surface state distributions, if appropriate. Neither traps nor charged surface states appear to play a part in electrostatic screening in our samples. The data can be

34

J.E. Mahan, R.H. Bube

/Field effect in amorphous chalcogenides X

,.•v(x)

Ec

.++ ~

E i

. . . . . . . . . . . . . . . . . . . .

t..~f(x) FIELD ELECTRODE

EF

Ev SAMPLE

BAND DIAGRAM FOR ACCUMULATION LAYER Fig. 3. Band diagram for accumulation layer in pitype material. modeled best by assuming initially flat bands. Assuming that p(x) is of the form p(x) = Nv exp(-Ef(x)/kT), eq. (3) may be simplified as follows for the small signal case:

p(x) = - q z~kEf(x)(N(EF) + Pb/k T}.

(4)

The screening of the field effect is controlled by the larger of the terms within the brackets: N(EF) or Pb/kT. Detailed field effect models based on each of these two possible cases are given below.

3.1. The localized state model {LSM) In this model we assume that all of the space charge resides in localized states at the Fermi level. Poisson's equation is written as follows:

d ~ V(x)/dx: = (q:/e)N(EF) V(x).

(5)

The potential distribution within the film thus has the form

V(x) = - Vs exp(-x/X),

(6)

where the subscript s refers to the value at the surface (x = 0) and X is the effective Debye length, given by

X = (e/q2N(Ev) l/z

(7)

From eq. (5) one may calculate the fractional change in source-to-drain resistance as a function of reduced surface potential os (=q Vs/kT): R

D

~

F(-vs) •

(8)

J.E. Mahan, R.H. Bube / Field effect in amorphous ehalcogenides

35

Here, R is the zero-field resistance. We assume in this analysis that the carrier mobility is not a function of position within the semiconducting film [8]. There are two material parameters which may be adjusted to fit the model to experimental data: c, the electron-hole conductivity ratio, and N(EF); F(os) is a convergent infinite series in Vs: c~

F(os) = G (--1)m(os)m rn=l m- ~z!

(9)

For small os we can approximate F(os) by F(os) ~ -Vs.

(10)

This leads to a convenient expression for estimating the localized state density from the small-signal field effect response:

~d

R

(11)

N ( E v ) - qdDk T dR/d VFI VF:0 3.2. The mobile carrier model (MCM)

In this model we assume that the field effect screening occurs through a redistribution of mobile charge carriers within the space-charge region. Poisson's equation, including both mobile electron and mobile hole densities, takes the form dZV(x)/dx 2 = (q/e) {n(x) - n b - [p(x) - Phi }.

(12)

The small-signal case may be readily solved, the solution being of the same form as eq. (6), except that the effective Debye length is given by ~. = (ekT/q2(nb + pb))l/2

(13)

Although Poisson's equation may be solved for an intrinsic material (n b = Pb) in the large-signal case, an exact solution is not possible in general. However, numerical solutions are possible [ 16]. Theoretical field effect curves can be calculated and fitted to the data with the aid of several adjustable material parameters: Pb the bulk mobile hole density, ub the bulk potential [nb = Pb exp(--2Ub)], and b the electron-hole mobility ratio. The procedure we have followed is to calculate excess carrier concentrations An and Ap corresponding to a particular Us, to relate these excess concentrations to the applied field voltage as follows: ed Vv/qd = (Ap - An)O,

(14)

and then to calculate the fractional change in source-to-drain resistance as follows: AR _ Ap + b An R Pb + bnb

36

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenMes F Ivsl

pbN[:

eu-

1

Iosl

f(lubl,vs) dV+ b exp(--21ubl)

_

f

e-v-

1

O]

F ( l u b l ,Vs) d

0

05)

Pb [ 1 + b exp(-2 l ubl)] where

]1/2.

1"2Fc°sh(ub + v) F(lUbl ,Us) : 2 / I ~--::ET:..~

(16)

v tanh(ub) - 1g

k t;UMll,Ulo )

4. Experimental results and discussion

4.1. As2Te 3 Representative field effect data for As2Te3 are given in figs. 4 and 5, obtained at 223 K and 273 K, respectively. The accumulation regime of the high-temperature I

I

I

1

AszTe ~ 223°K

_------ x -

o°

x

/

° z

MCMII

-0.5

/

iiiI I

U.J

a. --

w

/

/

z •"r

-I.0-

/

/

x

X

1 -500

-200 FIELD

0 VOLTA6E,

I

I

200

500

V

Fig. 4. Field effect curve for As2Te 3 at 223 K. R = 7.12 X 108 12, d = 19/am, D --- 1 ~tm. [:or the MCM, Pb = 7.0 X 1016 cm - 3 , b = 0.0 and u b = 0.0; for L S M , N ( E F ) = 8.0 × 1018 cm - 3 eV - 1 and c = 0.0.

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides f

37

I

As2Te 3 273 °K 0.5

% 0.0

./

u_l (._.) Z

u~ -0.5 (/3 UJ r"r"

_

Z

S/

M CM~/~//

uJ -I .0 Z "I(_)

-15

I -600

I -300

I

I

300

600

FIELD VOLTAGE (VOLTS)

Fig. 5. Field effect curve for As2Te 3 at 273 K. R = 6.2 × 106 ~2, d = 13 um, D = 1/~m. For the MCM, Pb = 3.0 X 1017 cm -3, b = 0.0 and u b = 0.5; for the LSM, N(EF) = 2.0 X 1019 cm - 3 eV -1 and c = 0.0. curve is linear in field voltage, while that o f the low-temperature curve reveals superlinear behavior. Such behavior is consistent with a transition from screening dominated b y mobile charge carriers to screening dominated by localized states at the Fermi level as the temperature is lowered. Both figures indicate that the material is very strongly p-type at these temperatures. Although the field effect data o f fig. 4 do not have sufficient curvature to match the LSM curve in the accumulation regime, this may be accounted for by suggesting that the rapidly increasing carrier density within the accumulation layer decreases the magnitude o f the field effect response by progressively shortening the screening length as VF is made increasingly negative. One might eliminate this mobile carrier influence by further reducing the temperature. Unfortunately, high sample resistivity made this impractical. If the LSM is applied to all the available field effect data on amorphous As2Te3, we obtain the plot shown in fig. 6. The electrical conductivity is also shown in this figure for reference. This "apparent localized state density" varies at high temperature as though it were thermally activated, and at low temperatures approaches an

38

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides i "r

L

As2Te3

E u

u2 z

10-5

I 0 zl

T

I-

E t.j

i

Z hi 121 U.I I-'ff)

G

>_-

i020

÷

_ 1 o -6

_ >

I--t..)

O W N -.I 12) -.1

•

a Z O t_)

4- ÷

1019

i0"r

Z n" n

I

3.0

4.0 IO00/T,

OK "1

Fig. 6. Electrical conductivity and field effect screening densities for As2Te3, interpreted as if they were the density of localized states at the Fermi level.

apparently constant value of about 1019 cm -3 eV -1. This behavor leads to the hypothesis that at high temperatures the field effect screening is dominated by mobile charge carriers, and only at low temperatures is the field effect actually controlled by localized states. In this interpretation, the thermally activated density of mobile charge carriers exceeds the background N(Ev) only for temperatures above approximately 273 K. This "apparent localized state density" actually represents the sum within the brackets of eq. (4). Figure 6 suggests that the mobile carrier model is the appropriate model in the temperature range where the apparent N(EF) has the same temperature dependence as the conductivity. The data of fig. 6 may be reinterpreted in terms of the MCM with the results given in fig. 7. Both analyses yield the same general features: a constant background plus a thermally activated component with an activation energy of ~0.47 eV. From the values of mobile carder density given in fig. 7, the carder mobility can be calculated; using corresponding values of a = 3.4 X 10 - s (ohm-cm) - j and Pb = 3.7 X 1018 cm -3, a value of mobility of 5.7 X 10 -5 cm 2 /V-s is obtained. The temperature dependence of the field effect response can be displayed in an

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides '

~,

I

~

'

I

,~

10,9 _

39

'

O

_ 10_ 5

E

"7

Z a

1018

\

or w

•

10-6

+~+ ~+'~" • • +~


F-L) .

tO

(:3 Z

+ - - %__+ + +

0 (')

I..t.I

_-J 10,7

A s2"l'e3

tic) 0 =E

i

l

I-

10-7

,

I

,

\

4.0

3.0 IO00/T,

oK - I

Fig. 7. Electrical conductivity and field effect screening densities for As2Te3, interpreted as if they were the density of mobile charge carriers. alternative manner (fig. 8). This figure shows the change in source-to-drain conductance as a function of temperature for two specific field voltages and dielectric thinknesses. At high temperatures AG is effectively constant; at low temperatures AG becomes thermally activated with an activation energy approaching that of the bulk conductivity. The high-temperature behavior indicates that the extra charge contributes directly to the mobile carrier density, whereas the low-temperature behavior indicates that the extra charge goes into traps. The fraction of mobile charge in the latter case is proportional to a Boltzmann factor with an energy corresponding to the energy separation between the traps and the conduction states. Fig. 8 indicates that the traps are at the Fermi energy. Marshall and Owen [6] define a field effect mobility, which is an "effective mobility" for the injected charge carriers. It is equal to AG multiplied by a few constants and geometrical factors: Wd AG(VF) # F - L ea VF '

(17)

where L is the interdigital electrode length and W is their separation. Their measured field effect mobilities indicate that the field effect screening is dominated by hole traps lying between the Fermi level and the valence band in their amorphous As2Te 3. If such traps are present in our material, they were not detected.

40

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides .

I

'

10-8 _

(J z ttJ ,~(.9

\ 1

i

I

e~

_

10-6

+÷*

"T A E

~ Io-9 z,,,

io-7 ; .K

E

I---

E 10.1o R~

16 8

'

ttl

i,lfl.

o~) (.9 Z"' T O

Z

O

As2Te3

~o~\ 10.9

i0-. t

3.0

J

I

I

4.0 1000/T, OK-|

I

5.0

Fig. 8. Field effect conductance modulation for As2Te 3 as a function of temperature (+) VF = -182 V, d = 13 vm; (0) g F = -4.70 V, d = 8 #m.

A series o f relatively high-temperature field effect data, shown in fig. 9, reveal a transition from p-type to two-carrier (primarily n-type) conductivity as the temperature is raised. This transition is reversed by lowering the temperature. Apparently the localized states pin the Fermi level at low temperatures at a position slightly below midgap, which results in p-type conductivity. The transition from localized state to mobile carrier-controlled field effect response coincides with a transition from extrinsic to intrinsic Fermi level position. If at high temperatures the mobile electron and hole densities are equal, fig. 9 indicates that the electron mobility is greater than that of holes in As2Te 3. 4.2. h s 2 S e T e 2

This material exhibits the mobile carrier-controlled field effect over practically the entire measurable temperature range. Fig. 10 show the mobile carrier density as a function of temperature calculated from field effect data and indicates the beginning of a transition toward localized state-controlled field effect response at the lowest measurable temperature [with N(EF) ~ 6 × 1018 cm -3 eV-1]. A conductivity mobility of 2.4 X 10 -6 cm2/V-s is obtained from the data of fig. 10.

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

F

41

L~

L~

AsaTe3 /

//

,,

321 °

"\x~x\ ~

\

354°K

% /

hi t..) Z

-0.75

,q/

/

// /Ix /

o/

/ iI

I--

/

561

•/iii

rr

-I,5 Z

/

hi

/

t..9 Z

!

-r ~)

I \

A iI

2.25

! !

!

I ~X

I

q

I

! ! A

-500

I

I

-200 0 200 500 FIELD VOLTAGE CVOLTS)

Fig. 9. Field effect curves for As2Te3: R = 3.5 × 105 ~2 (321 K), 1.84 × 105 ~2 (334 K), 9.8 X 104 ~2 (347 K) and 4.7 × 104 ~2 (361 K),d = 13 um,D = 1 urn.

Conduction is strongly p-type in As2SeTe2; it is not possible to produce an inversion layer even for voltages approaching the dielectric breakdown strength. The large-signal accumulation regime field effect response is linear with respect to field voltage and is very similar to the curve for AsETe 3 shown in fig. 5.

4.3. As2Se2Te Figure 1 1 shows both the electrical conductivity and the results of the field effect measurements as a function o f temperature. The calculated localized state density is virtually independent o f temperature, while the conductance change AG follows the conductivity closely' in its temperature dependence. We take this as strong evidence that the field effect screening occurs in localized states at the Fermi level in AszSezTe. At the two highest temperatures where measurements were made, the electrical conductivity increased during the course of the measurement. However, there are no detectable annealing effects in N(Ev).

•[

l

r

I

i

As2SeTez

_ iO -5

u

,,? E

u

10 j9 03 Z hi a n" UJ

_ io-6 5ff Y I->

E: n.-


1018

- i 0 -? ~ 121 Z 0

UJ _1 m O

~E

1017

_ i 0 -8

i

30 1000/T,

4.0 °K-I

Fig. 10. Mobile carrier density and electrical c o n d u c t i v i t y as a function of temperature for As2SeTe 2. )..

- I0"~ A

I--

"7

E

t~

Z

W ,,,_-~ I--,

>h-

u') ,,-, 1020 r ~ 'E W N ~ m ....I

AszSe2Te

id

\

8 _~ I-C_) a Z 0

t...) O .J Z

(I

16 9

1019

n-n.. r'., O UJ

d ~ io-II Z,~U-

-r O ~ f0f.)

~

10-12

p

f 2.0

I 1000IT

~1 30

\l

(°K-)

Fig. 11. L o c a l i z e d state d e n s i t y , electrical c o n d u c t i v i t y and field e f f e c t c o n d u c t a n c e m o d u l a t i o n as a f u n c t i o n o f t e m p e r a t u r e for A s 2 S e 2 T e .

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides I

I

/ /x

0

uS L) Z

43

I

Sb2Te3~ x

x

218°K O9 I/J nZ

-2.5

x-

x/ / -7.5 /,

-5.oL Z -r U

-600

I -300

0

I

L

3OO

60O

FIELD VOLTAGE, V Fig. 12. Field effect curve for Sb2Te3: R = 4.25 × 106 ~ , d = 23 um, D = 1 ~m, N (EF ) = 2.4 X 1020 cm 3 eV - l , c = 0.6.

The conductivity of this material is strongly p-type. The field effect curves can be fitted satisfactorily by the LSM over the entire voltage range.

4.4. Sb2Te3 A typical field effect curve is shown in fig. 12. The three regimes of accumulation, depletion and inversion are apparent. The LSM is preferred to the MCM for describing the behavior of Sb2Te3; although the field effect curves can be fitted well with either model the calculated screening density is temperature independent. Fig. 13 shows the calculated localized state density for two samples, together with electrical conductivity as a function of temperature. Apparently the midgap localized states pin the Fermi level very close to the intrinsic position.

4.5, Aging and annealing behavior The field effect properties of these amorphous chalcogenide films change with time. Aging, or room-temperature annealing, occurs during approximately the first two weeks of the life of the sample; during this period the apparent localized state density decreases by an order of magnitude or more. All the results given earlier in this paper were obtained from samples whose room-temperature aging was completed.

44

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

~~o~Sb2Te3 '

u.I Z

i

I

io

'7

10-2 J

C

I-Z w 121

o\

10 21

W

Id 3

I--I-(3

if) Z

x

N ._1

id °

fd ~

o

n

(.3 0 _.1

1019 3.0

]

l

I

4.0

5.0

I000/T,

°K -~

Fig. 13. Localized state density and electrical conductivity as a function of temperature for Sb2Te3. Figure 14 illustrates aging and the effect of high-temperature annealing upon As2Te 3. The changes in conductivity due to aging and annealing are very small. The conductivity data were obtained, starting when the sample was 1 h old, through the completion of the annealing study. Field effect measurements were made on the first day of the life of the sample, beginning about 1 h after the film had been sputtered. The first measurement was made at room temperature; then the sample was cooled and further measurements were made. The calculated apparent localized state density is represented by the plus signs in fig. 14. A final measurement (represented by the asterisk) was taken at room temperature, about 9 h after the first measurement was made and reveals a drop in calculated density by about a factor of three. This change is too large to be attributed to experimental error. The circles in fig. 14 are obtained from data taken when the sample was 11 days old. Ignoring for the moment the three highest temperature points, the circle points illustrate a further decrease in screening density due to room-temperature aging. The measurements were made by first starting at room temperature (1000/T--- 3.4) and then at lower temperatures, then returning to room temperature and then at higher temperatures to a maximum of 361 K (1000/T = 2.7). The three highest temperature points indicate that the screening density drops as the temperature is increased above 321 K. These points are calculated from the data of fig. 9. When the field effect measurement was made on the following day, ("x" data points) the effect appeared to be at least a partially reversible one. When the sample was 24 days old the measurements represented by the triangles in fig. 14 were made, starting at room temperature and then at lower temperatures

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides '

I

45

r

.--.

\

As2Te

3

E u

10-4

t,l 7,

>c I.-

\

Z i,I

c~ iOZl t.d I---

I

16 ~

,+, \

.q

I-U3

7-

5

LIJ U

,~ {_)

~

l0~°

0 J

,,

+,\ ,,o X ", ~L_. "

I-Z bJ

/4,,

10-6 z t,.)

'7.'+

w 0~..~0

0.2 3

rr

n~ 13_

I019

MC

1

I 3.0

IO00/T

I

1 4.0

I"

(*K -I)

Fig. 14. Electrical conductivity (small symbols) and field effect screening densities (large symbols) for As2Te 3, interpreted as if they were the density of localized states at the Fermi level, showing the effects of aging and annealing.

as the transition to localized state screening occurred, approaching a value of ~ 6 × 1018 cm -3 eV -1. We attribute this decrease of the localized state density to annealing which occurred when the previous measurement at 361 K was made. The lowtemperature behavior was strongly p-type, as usual. Then the sample was brought back to room temperature and measurements were made at higher temperatures. These densities coincide with the x's, indicating that no additional room-temperature aging had occurred. Again the densities decreased at high temperatures. The same p-type to 2-carrier transition occurred. The temperature dependence of the screening density and of Oe/Oh was found to be reversible as the temperature was lowered from 364 K, except for some small additional annealing that occurred at that temperature. If our previous interpretation of the field effect behavior of As2Te3 is correct, then through aging and annealing both the localized state density and the mobile carrier density decrease by more than an order of magnitude~ but the conductivity

46

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenMes

/" /

/

/

Fig. 15. Chaotic potential model, after Fritsche [11].

remains practically unaltered. We suggest a possible explanation of this phenomenon based on a chaotic potential model proposed by H. Fritzsche [ 17]. Its main feature is a randomly varying local potential, as shown in fig. 15. This model provides a mechanism for both reversibly and irreversibly varying the band structure that may account for the aging and annealing effects we have observed. There are essentially three kinds of states in this model: (1) localized states, in which the charge carrier is confined to a certain region, (2) channel states, which extend throughout the material but yet have prohibited spatial regions and (3) fully extended states, for which the probability of finding the electron anywhere in the material is finite. Here, E c and E v represent the threshold energies for channel conduction in fig. 15. If the conductivity in a p-type material is due to holes in channel states it may be written as Och = q/achNch exp [ - ( E F - Ev)/kT]

(18)

with an essentially temperature-independent mobility, #cn- The conductivity may also be written in an equivalent way by assuming that holes in localized states above E v (at Ev + W) become the active charge carriers as they are thermally promoted to valence channel states. In this formulation, the carrier density is given by Ploc= Nch exp [ - ( E v - E v - W)/kT]

(I 9)

and the carrier mobility is /lloc = Pch exp(-- W/kT).

(20)

The conductivity activation energy is still (Ev - Ev). The total mobile carrier field effect screening density is then Ploc+ Pch ~ Ploc.

J.E. Mahan, R.H. Bube / FieM effect in amorphous chalcogenides

47

It is proposed that aging of amorphous As2Te3 decreases the number and magnitude of fluctuations in the chaotic potential through structural rearrangements that satisfy dangling bonds and "clean up" assorted centers at the Fermi level with localized charge. This decrease is shown in the monotonic decrease in N(Ev) of approximately an order of magnitude in fig. 14. This removal of isolated pockets of charge that smooths out the chaotic potential causes Wandploc to decrease. But the decrease in Ploc is exactly compensated by an increase in laloe so that the total conductivity is not altered by the removal of charge carriers through aging. This mechanism is a feasible explanation for the irreversible annealing and aging effects in As2Te3 that decrease the carrier density without radically altering the conductivity. We should add that the conductivity due to carriers in extended states probably will not be affected by aging or annealing. To account for the reversible changes in mobile carrier density that have been observed in As2Te3 at high temperatures within the chaotic potential model, it is necessary to find a mechanism for reversibly altering the chaotic potential. Compensating changes in both mobility and carrier density are again required. The occupation of the charged defect states may be expected to change with temperature in accordance with Fermi-Dirac statistics which describe the occupancy of states in the immediate vicinity of the Fermi level. Negatively charged states just below EF and positively charged states just above EF are increasingly neutralized as the temperature is raised. This would decrease 14I in the above analysis and provide the required compensating changes in mobility and carrier density. These changes are entirely reversible, depending only upon the expression for state occupation given by the Fermi-Dirac distribution function. A recent band model proposed by Mott et al. [18] for amorphous chalcogenides does postulate such charged centers. They suggest that pairs of neutral dangling bonds lower their energy by a transfer of charge, creating two overlapping bands of donor and acceptor levels that pin the Fermi level near midgap. 4.6. Two-channel model

Figures 7 and 10 suggest that, if the total temperature dependence of conductivity is due to that of the carrier density, then the conductivity mobility is not a strong function of temperature in the amorphous chalcogenides. Others who have made thermoelectric power measurements on these materials [19-22] have attributed the difference between the thermoelectric power and conductivity activation energies to a thermally activated conductivity mobility. A possible resolution of this difficulty may be found through a two-channel model of conduction, proposed by Nagels et al. [23], wl~ich suggests that two p-type bands provide nearly equal contribution to the conductivity. According to this model, the observed thermoelectric power activation energy has no direct physical significance, but is generated by a transfer of conduction from one p-type band to the other as the temperature is raised.

48

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

We may use the chaotic potential model to provide the two p-type conductivity mechanisms: extended state conduction and channel state conduction. The extended state conductivity is written as Oext = qlZextNex t exp [ - ( E F - Eext)/kT]

(21)

and the channel state conductivity is given in eq. (18). The total conductivity is Och + Oext. The mobile carrier screening density is then Ploc +Pch +Pext- Since Oloc Och ~ Oext and probably/atoc
5. Summary The field effect behavior of As2Te3 shows regimes of screening by localized states and by mobile carriers and regimes of p-type and two-carrier conductivity. The density of localized states at the Fermi level is ~1019 cm -3 eV -1 and the mobile carrier concentration at 300 K is ~1018 cm -3. As2SeTe2 has approximately the same mobile carrier density at 300 K as As2Te3, but only p-type conduction is observed. The largest band-gap material, As2Se2Te, also has a localized state-controlled field effect response with N ( E v ) = 1019 cm - a eV -1 and strongly p-type conductivity. The smallest band-gap material, Sb2Te3, has the largest N(EF), 1 - 2 × 1020 cm -3 eV -1, and a OdOh of ~0.6. Both aging and annealing effects were observed in As2Te3 in which both the density of localized states at the Fermi level and the density of mobile charge carriers were made to decrease by more than an order of magnitude. Since the electrical conductivity was unchanged by aging or annealing treatments, we suggest that the decreases in carrier density were exactly compensated by increases in carrier mobility. A possible explanation for this behavior is given by the chaotic potential model. , In order to integrate the field effect results with those of thermoelectric power measurements, we invoke a two-channel model, which suggests that the total conductivity is composed of contributions from holes in extended states and holes in localized states at the valence band mobility edge. These field effect results on the amorphous chalcogenides do not support the small polaron model. Similarly, peaks in N(E) between EF and E c or Ev such as found in Adler's modification of the CFO model are not detected. The results on Sb2Te3 and As2Se2Te could accommodate either the CFO or the Davis-Mott model, since all that is required is ,a p~rticular N(EF). However, As2Te3 and As2SeTe 2 favor a Davis-Mott type of density of states distribution because the localized state-mobile carrier-screening transition requires a fairly discrete state distribution compared to that of the CFO model.

J.E. Mahan, R.H. Bube ] FieM effect in amorphous chal¢ogenides

49

Marshall and Owen's field effect measurements [6] on As2Te3 and on a complex, multicomponent, chalcogenide-based glass indicate that the field effect in their materials is controlled by centers lying approximately 0.13 eV below the bulk Fermi level, with densities of 1017-1018 cm -3. Their results, together with ours, suggest that there are at least three kinds o f states that can control the field effect response in the amorphous chalcogenides: mobile charge carrier states, localized states at the Fermi level and hole traps. Which o f these states dominates the field effect screening in a given sample depends upon their relative densities (probably set by the thermal history o f the sample) and the temperature at which the measurement is made.

Acknowledgements The authors are grateful to William Holmes for assistance in preparing sputtered thin t'rims, to Hubert A. Vander Plas for stimulating discussions concerning the interpretation o f the field effect results, and to Sir NeviU Mort for his personal enthusiasm and interest in the project. This research was supported by the Army Research Office, Durham.

References [1] W.E. Spear and P.G. LeComber, J. Non-Crystalline Solids 8-10 (1972) 729; Solid State Commun. 17 (1975) 1193. [2] M. Cohen, H. Fritzche and S. Ovshinsky, Phys. Rev. Letters 22 (20) (1969) 1065. [3] E.A. Davis and N.F. Mott, Phil. Mag. 22 (1970) 903. [4] N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials ch. 9 (Oxford University Press, 1971). [5 ] D. Adler, Amorphous Seimiconductors (Chemical Rubber Press, Cleveland, Ohio, 1971) p. 58. [6] J.M. Marshall and A.E. Owen, Phil. Mag. 33 (1976) 457. [7] D. Emin, in Electrical and Structural Properties of Amorphous Semiconductors, ed. P. LeComber and D. Mort, (Academic Press, London, 1973) 201. [8] T. Arnoldussen, C. Menezes, Y. Nakagawa and R. Bube, Phys. Rev. B9 (8) (1974) 3382. [9] H.K. Rockstad, Solid State Commun 9 (1971) 2233. [10] A.E. Owen and J.M. Robertson, J. Non-Crystalline Solids 2 (1970) 40. [11] R.T. Shiah and R.H. Bobe, J. Appl. Phys. 47 (1976) 2005. [121 S. Bishop, U. Strom, and P. Taylor, Phys. Rev. Letters 34 (21) (1975) 1349. [13] S. Agarwal, Phys. Rev. B7 (2) (1973) 685. [14] J. Tauc, A. Menth and D. Wood, Phys. Rev. Letters 25 (1970) 749. [15] B.T. Kolomiets, in Amorphous and Liquid Semiconductors, ed. J. Stuke and W. Brenig (Taylor and Francis, London, 1974) p. 189. [16] See A. Many, Y. Goldstein and N. Grover, Semiconductor Surfaces, Ch. 4 (North-Holland New York, 1971). [17] it. Fritzsche, J. Non-Crystalline Solids 6 (1971) 49. [18] N.F. Mott, E.A. Davis and R.A. Street, Phil. Mag. 32 (5) (1975) 962.

50 [19] [20] [21J [22]

J.E. Mahan, R.H. Bube / Field effect in amorphous chalcogenides

H. Rockstad, R. Flask and S. lwasa, J. Non-Crystalline Solids 8-10 (1972) 326. C. Seager, D. Emin and R. Quinn, Phys. Rev. B8 (1974) 4746. R. Bube, J. Mahan, R. Shiah and H. Vander Plas, Appl. Phys. Letters 25 (1974) 419. A. Grant, T. Moustakas, T. Penney and K. Weiser, in Amorphous and Liquid Semiconductors, ed. J. Stuke and W. Brenig (Taylor and Francis, London, (1974) p. 325. [23] P. Nagels, R. Callearts and M. Denayer, in Amorphous and Liquid Semiconductors, ed. J. Stuke and W. Brenig (Taylor and Francis, London, 1974) p. 867.