Low temperature effects in Si FETs

82

NOTES

Solid-State

Electronics Pergamon Press 1965. Vol. pp. 82-83. Printed in Great Britain

Low

temperature (Received

effects

8,

in Si FETs

29 July 1964)

SILICON Field Effect Transistors might be expected to exhibit at low temperatures effects due to quantisation.(l-3) For this reason we have investigated the characteristics of these devices at liquid helium temperature; and while the effects observed are as yet unexplainable in terms of quantisation, breakdown, or simple carrier density fluctuations, we think they are sufficiently unusual and intriguing to merit some attention. When an n-p-n Si FET is cooled to liquid helium temperature, the first obvious change is that the surface channel is no longer inverted, or in the enhancement mode, but rather it is nonconducting for small drain voltage VD and gate voltage Vo. Conductance from source to drain can be initiated by applying positive gate voltages and/or drain voltages. The magnitudes of the thresholds depend on doping and geometry and also vary somewhat from device to device. The most striking effect, however, is that the source drain current does not vary smoothly with increasing gate voltage near threshold. Figure 1 shows the surface drain current for one device as a function of gate voltage for constant drain voltage.

“G

FIG.

1. Source-drain

current vs. gate voltage drain voltage.

for fixed

In units such as this, where the effect is prominent even in the current variation, there is appreciable hysteresis when the gate is swept rapidly, but the shape of the curve for increasing gate voltage is

preserved to 30 kc. In most units the structure is clearly revealed only in derivative form, that is, as peaks in the transconductance gm or in gi,z. Since these measurements are made slowly, there is little hysteresis in them. The effects have been seen in all samples of devices with substrate resistivities of n-p-n -10 &cm and 100 Q-cm, obtained from three different sources. Effectively two geometries were used: closed-path uniform width channels(4) and channels with small “point” contacts.(5) The greater the positive voltage applied to the gate the lower is the drain voltage at threshold, and vice versa. Although some weak structure was observed in one unit with no drain bias, generally sufficient drain voltage was required so that Vc: at the conductance threshold was less than 10 VT. For 1 Q-cm units this requirement is prohibitive since for Vo = 10 V, they do not turn on until breakdown, at -35 V for 10 p channels. The shapes of curves relative to threshold have been found to be reproducible from day to day even with exposure to the atmosphere between runs, but thresholds tend to drift as much as 10 per cent. The results are not reproducible from device to device, the spacing of steps is not uniform and does not seem to vary consistently from the 10 Q-cm to the 100 (l-cm units. As the threshold is shifted by varying either ID or L-o, the structure shifts rigidly, to a first approximation; i.e. the voltage separations between peaks remain about the same. For this reason it is simpler to display the variation of the g?,$ as a function of source drain current 1~0 as in Fig. 2, where the curves are shown for various fixed Vo’s. One can distinguish in Fig. 2 independent variations of peaks, whereas in some units with fewer peaks, all peaks are seen to shift in similar manner. Very likely the former case is a superposition of effects in several regions of the device. Figure 2 should not be interpreted as indicating current as the only significant factor, since for sufficiently large changes of P7u, the structure would be completely wiped out. P-n-p devices show only smooth variations of gm vs. gate voltage or drain voltage in our experiments. While qualitatively one is tempted to propose that these steps are the result of quantisation, quantitatively this argument cannot be supported.

NOTES

83

References 1. J.

2. 3.

4.

0

I

I

I

3

6

9

IsD (IO

-5

AMP

-

I

12

I

15

1

16

5.

R. SCHRIEFFER, Mobility in Inversion Layers; Theory and Experiment, Conf. Phys. Semiconductor Surfaces, Philadelphia (1956). R. MISSMAN and P. HANDLER, J. Phys. Chem. Solids 8, 109 (1959). P. HANDLER and S. EISENHOUR, Experimental Evidence for the Quantization of Light Hole States in the Space Charge Region of a Clean (111) Germanium Surface, International Conf. the Physics and Chemistry of Solid Surfaces, Brown University (1964). G. CHEROFF and F. F. FANG and F. HOCHBERG, IBM J. Res. Develop. 8,416 (1964). A. B. FOWLER, F. F. FANG and F. HOCHBERG, Mobility Variation of Surface Carriers from Hall Measurements, IBM J. Res. Develop. 8, 427 (1964).

1

!. Transconductance vs. source-drain various drain voltages.

current for

Solid-State

In the effective mass approximation, the conduction electrons are like free electrons in a onedimensional well which is nearly triangular in shape. An approximation to the empty channel energy levels can, therefore, be obtained rather easily. For the space charge fields which exist in n-p-n Si FETs, the splitting between successive two-dimensional bands is of the order of kT at room temperature. However, the density of states for the two-dimensional energy bands is so large in this model that the gate voltage change required to fill to the second band should be of the order of 100 V, not O-1 V. Further, the expected step-like density of states variation should lead to breaks in the slope of the current gm variation, not steps. The fact that large source-drain voltages (say > 2 V) are not necessary for the observation of structure would seem to imply that breakdown is not always involved. Also, fluctuations due to the randomness of “uniform” doping can be shown to be unimportant, although gross inhomogeneities cannot be ruled out as a source of the effects. W. E.

HOWARD

F. F. FANG

IBM Watson Research Center Yorktown Heights, N. Y.

Electronics Pergamon Press 1965. pp. 83-85. Printed in Great Britain

Vol. 8,

The effective lifetime of stimulated and spontaneous emission in semiconductor laser diodes (Received RECENT

12 May 1964; in revised form 11 August measurements(l)

with

a GaAs

1964)

injection

laser at 77°K give for the spontaneous emission lifetime rspont z 2nsec. A model with only one spontaneous lifetime was assumed. The measurements show further that the lifetime of excited states during stimulated emission can be less than O-2 nsec. This smaller lifetime for stimulated emission of frequency u is physically plausible, since the number of transitions stimulated in unit time is proportional to the radiation density U(U). With increasing radiation density the lifetime of excited states decreases still further. The described process has particular importance for the high frequency modulation capabilities of laser diodes. It is therefore necessary to derive a lifetime 7stirn for stimulated emission as well as an effective lifetime ~~fr for the superposition of stimulated and spontaneous emission. At the starting point we choose the Einstein derivation of Plancks radiation law.(aJ) Einstein considers a black body radiator, which he represents as a large number N of harmonic