Physica 98B (1980) 303-305 © North-Holland Publishing Company

NOISE IN HYDROGENATED AMORPHOUS SILICON RESISTORS*

S. K. KIM and A. van der ZIEL EE Department, University of Minnesota, Minneapolis 55455, USA

Received 6 August 1979

Measurements are reported on the noise in hydrogenated amorphous silicon resistor~ At zero bias the device can be represented by a resistance R and a leaky capacitor C in parallel. With bias there is excess noise varying as the square of the voltage, as expected for resistance fluctuation noise, but saturating at high voltage. The excess noise is of the form const/ (1 + w2r~) and can approximately be represented as white noise flowing into the RC parallel circuit. Any I / f noise, ff present, is completely masked by the latter noise source. The device characteristic shows space charge limited behavior, but the noise at high voltage cannot be fully described by the theory of Zijlstra and Driedonks for such devices.

Recently there has been considerable activity [ 1 - 3 ] in the s tudy of hydrogenated amorphous silicon resistorsl We report here on noise measurements on those resistors.

The devices had a very high resistance and were therefore measured at somewhat elevated temperature (160-175°(2) . Because the dc resistance was a strong function o f temperature, different runs o f data were only reproducible to within a factor 2, whereas the data in a single run were much more accurate than that.

Fig. 1 shows the noise resistance R n at 160°C at zero bias for device A; R n here corresponds to the real part of the device impedance at that temperature. The

2 2 spectrum is o f the form const/(1 + co r ) but with a l / f tail. We shall see in a moment that the device impedance can be represented by a resistance R in parallel to a leaky capacitor C.

Fig. 2 shows the noise resistance R n at 170°C and 100 I-Iz for device B as a function o f the dc bias VDD. When one subtracts the noise resistance R n for zero bias, one obtains a residual noise resistance that varies as V2D, as expected for resistance fluctuation noise. At higher voltages the VDD-relationshi p changes and R n becomes practically independent o f VD~ ,.

Fig. 3 shows the noise resistance at 160 C at 6 V bias for device A, as a function o f frequency. The noise varies as const/(1 + co2r2), as expected for

* Supported by ARO and RCA grant~

genera t ion- recombina t ion noise. There was no indica- t ion o f I / f noise, i f there was any it was completely masked by the const/(1 + oa2r 2) noise.

Fig. 4 shows the L V characteristic o t aevice B at

R. (~) lOs - - ~

,o"

I I I I I~10 I 0 0 IK IOK lOOk

f (Hz|

Fig. 1. Noise resistance spectrum at zero bias at 160°C for device A. Full drawn curve passesithrough measured points, broken curve corresponds to eq. (1) with the parameters as used in text.

303

304 S. K. Kim and A. van der Ziel/Noise in hydrogenated amorphous silicon resistors

10 *4

Rn ( n )

,d 3

i012

Id'

i01

,o"

/ I

I I

I /

c

r I I I I 0.1 I I0 I 0 0

v~(v)

Fig. 2. Noise reshtance R n at 100 Hz and 170°C for device B as a function of the bias voltage VDD. Fully drawn curve passes through measured points, broken curve corresponds to eq. (2).

170°C. It shows a strong nonlinearity that can be des- cribed by space charge limited flow; the full drawn curve gives a good theoretical match to the measured data.

In order to explain the data o f fig. 1, we turn to fig. 5, which shows a resistance R with a leaky capa- citor C in paraUel, having a loss factor tan 8 = ~oCr. It is easily shown that for R ~, r

02 = 4 k T R ~ f ( 1 + tan 2 8)

1 + c02~ "2

4kT tan 6 ~ f c02T 2 + coC 1 + c02~ "2 = 4 k T R n ~ f ' (1)

where ~ = CR. Fig. 1 shows that R -- 2 X 109 ~ and since the upper corner frequency is 135 Hz, r = 1.18 X 10 -3 s. I t furthermore follows that C = 0.59 pF and tan 6 = 4.45 X 10 -2. Measurements at T = 175°C gave

m

Rn( 'a) ~, o

t,o'-

,o '

,o '

,o °

.,I I i I I I~10 I 0 0 I K IOK lOOK

f ( H ~ J

Fig. 3. Noise resistance R n at VDD = 6 V and 160°C for device A as a function of frequency. Fully drawn curve passes through measured points, broken curve corresponds to eq. (3).

R = 5.5 X 108 f~, so t h a t R shows a considerable tem- perature dependence, as expected.

The curve of fig. 2 can be represented by the for- mula

R n = 8 X 10 9 + 2.5 X 10 9 F'D2D ohm, (2)

where the second term is due to resistance fluctuation noise. We are presently unable to interpret the constant in front of VDD numerically.

The measurements o f fig. 3 can be represented by a formula o f the type

6.5 X 101° 6.5 X 1010 Rn = 2 ohm = ohm,

] + 0790) 1 + (3)

where f i s in Hz. This provides a good fit up to 50 kHz.

S. K. Kim and A. van der Ziel/Noise in hydrogenated amorphous silicon resistors 305

to ~

? (a)

I

16* I l I0 I I0 I00

voo(v)

Fig. 4. I, V characteristic of device B. The full-drawn curve is the matched theoretical curve for space charge limited flow; the circles are measured points.

We see that ~1 = 1.77 X 10 -3 s. Measurements at 175°C gave about the same value for r 1. In view of the closeness of the two time constants r and r l , we con- sider the noise presented in fig. 3 as being caused by a white noise current generator (2eIeqZkf) ~ flowing into

R

A C

ir" tm 8/we

Fig. 5. Equivalent circuit of aewce tbr zero bias, consisting of a resistance R and a leakage capacitance C in parallel together with thermal noise sources.

the impedance Z = R/(1 + j~CR) of the device. This would yield

4 k T R n = 2eIeqR2l(1 + ~2C2R2). (4)

The theory of trapping noise in space charge limited flow devices having shallow traps gives a V 2- dependence o f R n in the linear regime and a V-depen- dence o f R n in the quadratic regime [4]. In our devices there should be traps distributed all over the energy gap, and in that case a different relationship might occur. This will require further study.

We are thus able to obtain a reasonably consistent picture of the observations, though some features need further clarification.

Acknowledgement

The authors are indebted to Drs. J. I, Pankove and S. T. Hsu of RCA Laboratories for providing the samples used in this investigation. They also gave the following additional information. The samples were made by chemical vapor deposition in a glow discharge chamber with silane (Sill4) at 0.125 Tort. The samples contain a few percent to up to 50% atomic hydrogen; in our samples the concentration was 10-20%. The samples are most likely a mixture of Si, Sill, Sill2, Sill 3 and Sill4, with Si and Sill predominating at the lower concentrations. The conductivity seems to some extent be controlled by the surface charge between film and substrate, which causes band bending.

References

[1] J. I. Pankove and D. E. Carlson, AppL Phy~ Lett. 31 (1977) 450.

[2] J.I. Pankove and D. E. Carlson, Proc Seventh Intern. Conf. on Amorphous and Liquid Semiconductors, W. E. Stear, ed., Univ, of Edinburgh, Edinburgh (1977), p. 402.

[3] J.I.P.ankove, M. A. Lampert and M. L. Tarng, AppL Phys. Lett. 32 (1978) 439.

[4] R.J.J. Zijlstra and F, Driedonks, Physica 50 (1970) 331.