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M. B. DAS and P. M. SANDOW

308

respectively,

where

k is Boltzmann’s constant, T is absolute temperature, 4 is electronic charge, A, is the junction area, and X, and X,, represent the junction depletion width in the forward and reverse bias conditions, respectively. Using these equations, the diode differential conductance in the reverse and low forward bias conditions can be written as

dZ, dZ,o- L) m/g

Note that an empirical constant m is used in place of 2 which would result from idealized eqns (4). For practical junctions M is usually smaller than 2[4]. From eqns (6) and (7) it is apparent that when Z, = I, = 0, g, obtains its minimum value and g, obtains its maximum value. When Zr,,= 1.2pA and m = 1.65, this corresponds to a dynamic resistance of 3.5 X IO’Q If the diode is to be useful as a dynamic resistor in the low bias range, it is important that its noise performance should at least be comparable to that of pure resistors. Considering first the shot noise source, and the fact that noise associated with the reverse saturation current is uncorrelated[5] to the forward current, the mean squared equivalent noise current, for the bandwidth Af, can be written as -2

~,.sllot forward

= 4kTAf;

and

(11)

For the flicker noise the equivalent resistor is as given in eqn (10). The diffusion current in the planar structure arises mainly due to hole injection in the lightly doped n-region (ND = 2 x lOI cm-‘) and may be expressed in the manner

and

gr=dv,=

N, is the effective value of r-g centers representing a distribution of energy levels, (Y is a numerical factor smaller than unity, E is the absolute permittivity of silicon and f is the frequency. For the reverse bias case the conductance g, should replace g, in eqn (9). When the diode functions as a current monitoring resistor, as shown in Fig. I, its open-circuit noise voltage must be small compared to the measuring voltage. This can be represented in terms of equivalent noise resistor for the shot noise in the following manner:

(12) where

D,, is the diffusion

constant

and Lh is the effective

(g, + g,m,,,)

and

(8) iLotlreverse= 4kTAf;(g,-,,, _

+ g,)

where g,_,,. is the value of g, when I, = 0 and g,.,,, is the value of g, when Z, = 0. The flicker noise or l/f noise associated with the diode can be a serious limitation for its use as a resistor for d.c. and low-frequency a.c. measurements. At the low forward bias range the mean squared equivalent noise current can be written as[6] ‘2

L.nicker =

4kTAfM;

L -_..__1

where

(b)

R

_

F

’

@Ntx;,a

kT 8

Aif

’

(10)

Fig. I. Measurement of I/V characteristics in the low bias range: (a) forward bias and (b) reverse bias arrangements of the test diode D2.

309

High-value dynamic resistors usiqg pn-junctions diffusion length for holes in the n-on-n+ base region. In the low bias range the diffusion current is usually negligible compared to the depletion region r-g component of current. RESULTS AND

The point of intersection gives V,c = 0.415V and is related to m, I,,,, and Zd0,according to the equation

(13)

DISCUSSION

For the purpose of the measurement, p’n diodes D, and D, were selected and arranged in the manner shown in Fig. 1.The low bias test diode D2 was selected to be of larger area than that of D, which acted mainly as a current source in both arrangements (a) and (b). Measurements below lO_“A become rather difficult because of large time constants of the meters (Keithley 602 and 610) and high impedance of the test diode. The results of both forward and reverse current measurements are graphically shown in Fig. 2. The saturated behavior of Z, in the low reverse bias range provides the value of Z,0which can be regarded equal to Z& since both the forward and reverse bias voltages used were small compared to the built-in barrier potential (-0.8 volt). Using this value of Z,,, ( 1.2 PA), curve (2) was drawn to determine the value of m as indicated in Fig. 2, curve (3) was constructed to match rhe diffusion current eqn (10) at V, greater than 0.5 volts.

Figure 2 indicates m = 1.63, Z,, = 1.2 x lO~“A, and Ido = ’ 1 x lo-” A. _. Using the values of ZrO= 1.2 pA, Ai = 6.7 x lO~‘cm’, .I~, = 7.7 x 10m5cm, C, = 7 x IO-* cm’/sec in eqns (3) and (5), we obtain 7” = 9.75 x 10m6set and N, = 2.9 x 10” cm-‘. The value of C,, taken from published literature[7], is applicable to a high temperature process induced defect close to the mid gap. Thermally stimulated measurements were carried out to determine the nature of this particular defect[8]. Using the extrapolated value of the diffusion current from Fig. 2, when V, = 0, the effective value of minority carrier diffusion length Lb can be calculated according to eqn (10). This yields Lb = 50.5 pm which is quite realistic in view of the fact that the n-type base region consists of an approximately IO pm epitaxial layer on an n+ substrate. The noise performance and values of dynamic diode resistors are indicated in Table 1. The effects of shot noise in the diode are seen to be not significantly greater than that of the thermal noise present in ideal resistors of similar values. The flicker noise equivalent resistance was calculated assuming the value of fi, to be that of N, and the value of a = 1. In reality, the &-value that can be achieved is much smaller than that of N, identified in this investigation. Even with this exaggerated value of N,, the rms value of the l/f noise voltage for a frequency range of 1Hz to 10 KHz can be calculated to be approximately

2i

Fig. 2. Forward and reverse NV characteristics. Curve I: Forward current as measured; Curve 2: Extrapolated forware current; Current 3: Diffusion component of the forward current; Curve 4: Reverse current.

SSE Vol. 20 No. LC

/

Fig. 3. Forward and reverse I/V characteristics in the low bias range. Curve 1 is the forward current with representing theoretical results for m = 1.63 and A representing experimental results; Curve 2 is the extrapolated behavior of I,; Curve 3 is the diffusion component of the forward current; Curve 4 is the reverse current with -representing theoretical results for m = 1.63 and A representing experimental results.

’

M. B.

DAS

and P. M.

SANDOW

Table 1. Noise performance of dynamic resistors

an

5.‘h109

ii.9lslO9

40

1. 15x101°

1.53x10

20

2.16~10

10

?.R5xlO

IO

10

_. 40 PV which is negligible compared to the voltages that the diode is often required to monitor in measurement circuits. The assumption of an ideal l/f noise spectra applies only for an effective density of r-g centers occupying a distribution of energy levels within the band gap. In the case of a single level r-g centers, as identified in this investigation, the detailed nature of the lowfrequency noise spectra is somewhat different[9-111 and the value of the rms noise voltage for the same frequency range can be shown to be lower than the calculated value of 4opv. REFERENCES I.

C. T. Sah. R. N. Noyce and W. Shockley. Proc. IRE 45, 1228 (1957).

2. W. Shockely, W. T. Read and R. N. Hall, Proc. IRE 46. 973 (1958). 3. C. T. Sah. Proc. IEEE 55, 654 (1967). 4. P. Ashburn. D. V. Morgan and M. J. Howe\. Solid-St. Electron. 18, 569 (1975). 5. R. D. Thornton, D. Dewitt. E. R. Chenette and P. E. Gray, Characteristics and Limitations of Transistors. SEEC Vol. 4. p. 134. Wiley, New York (1966). 6. M. B. Da\. IEEE Trmc. Elwlrrm DPL. ED-Z 1092 (1975). 7. C. T. Sah and C. T. Wang. ./. .4[@. Phy\. 46. IX7 I IYi). X. P. Sandow, M. B. Da\ and J. Stach. I.tr\ \‘cxo\ j2fc,ctirr,v of r/w EI~c~rroc~hemid Sohfy. 17-22 Oct.( lY76). 9. P. 0. Lauritzen. Solid-St. Electron. 8. 41 (1965). IO. M. B. Das. fEEE Truns. Electron Droicrs ED-IY, 33X (1972). Ii. C. T. Sah. Proc. IEEE 52. 795 (1964).