Thermal Noise in Field-Effect Transistors
A. Der Ziel
1962
Proceedings of the IRE
The limiting noise mechanism in field-effect transistors is thermal noise of the conducting channel. The noise can be represented by a current generator Vi2 in parallel to the output. The value of j2 is calculated; for zero drain voltage the noise corresponds to thermal noise of the drain conductance, and for other bias conditions the noise at a given gate voltage depends only slightly upon the drain voltage. Because of modulation effects in the channel, j2 is somewhat larger than the thermal
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... ise of the dc drain conductance, except for zero drain bias and beyond saturation. The noise resistance of the device is approximately equal to gM/9g"'2 where g" is the transconductance of the transistor and gmax its maximum value. The approximation becomes even closer if feedback due to the series resistances of the channel must be taken into account. INTRODtUCTI(.)N S HOCKLEY' has given a theory of the field-effect transistor. This paper aims at applyinig his model for calculating the noise of the device, caused by thernmal noise generated in the conductinig clhanniiel. Let the field-effect transistor be a planiar tranisistor lllade oI1 p-type miaterial anid let it be provided with two gate conitacts G, a source conitact S and a drain conitact D (Fig. 1) . Let the transistor have unlit width, let 2a be the distanice between the gate conitacts anid L the length of the coniducting channel. Let, for a given bias W betveein the gate anid the channel, the width of the channel be 2b, anld let Woo be the bias nieedled for cuLtoff (b=0). Then, accordiing to Shocklev, If" = HW0o0(1-ba)2 or ba = [i-(W/IXFo)1121. (1) For a giveni gate voltage the field strength conmponeint E, in the X direction is dIV E-x = -. (2) If a0 is the conductivity of the p-type channiiel, then the dc currenit is dWr dIl where g(J'v) = 2oob [(117 )1 }] = go [1 -(IL)i and goi = 2oroa,. (3a) Consequently, the currenit is I= Wdg(w)dw I = g(W)dtlll L w -~~o[11., --~~~~2 ,~3 1772) L 3 If,(0 I /2 The transconductance gn, of the device is d l g°r/ W dXI W / l/9 (3Fu L 11W oo WIoM acnd the output coniductance gd of the device is gd = ----V= L Lt -V J 11(0 (4) (5) (6) At Vd = 0,117( = 1ff/ = ( V, + /7,lif), which is the smallest value 114 canl take for giveni 1k,. In thalt case I=0 and g=-0 anld L Fig. 1-Cross section of a planar field-effect tranisistor showing the source S, the gate G, the drain D, the conducting channel of width 2b and the space-charge regionis of width (b-a). W(x) is the bias between the conducting chaninel and the gate. Here W and b are slow funictioins of the distance x to the source. If V, is the potential of The gate with respect to the source, 174 the potential of the drain and Vdif the diffusion poteintial, thein W= W1 = (1V+ Vdif) at the source and W= Wd= (17+ (Iif -Vd) at the draini. *
doi:10.1109/jrproc.1962.288221
fatcat:oymwaabg2jahpj7t4vshzzx3jq