Measurement of the effective carrier lifetime by a distortion technique

394

NOTES

present model might provide an alternative interpretation, if the high resistivity region is at least as thick as suggested in Fig. 2 of Ref. 2. However, the w -lja dependence predicted for the present model (3) does not seem to fit the capacitance versus frequency data shown in Fig. 3 of Ref. 2. Depending on their position in the energy gap, deep levels can have vastly different effects on the capacitance of p-n-junctions. These deep levels influence C(V) plots which are a standard tool in the evaluation of semiconductor materials. Department of Electrical Engineering University of Washington Seattle, Washington 98105.

E. SCHIBLI

References 1. E. SCHIBLI and A. G. MILNFS, Solid-St.

323(1968).

Electron.

11,

which the above mentioned distortion just disappears. I d” = [l +(wc7)2]-1’4 I B0

Pergamon Press 1970. Vol. 13, Printed in Great Britain

tanh d/L

(1) where : I = 7= W, = L = D = d =

I& + lac cos w,t, I,, > I& effective lifetime critical angular frequency diffusion length = ~DT diffusion constant thickness of diode base (lightly doped) region.

Bilotti observed that for d/L 2 5 this expression reduces to :

2. R. G. HIJNSPERGER,0. J. MARW and C. A. MEAD, Appl. Phys. Lett. i3, 29.5(1968).

Solid-State Electronics $p. 394-395.

Itanh W/4 141 +ieu,dl I

I d” = [l +(w,+]-1’4. I BC

This relation may be manipulated to yield an explicit relation between r and wc. (3)

7 = tJ[@‘-I]. Measurement of the effective carrier lifetime by a distortion technique* (Received

29 November

1968)

wave form consisting of a forward d.c. bias plus a sinusoidal component with an amplitude greater than the d.c. level cannot be passed through an ideal diode. The net current cannot be negative. In a real diode, however, such a waveform can pass undistorted if the frequency of the a.c. component is great enough. This is because stored minority carrier densities must be depleted before the diode will cease to conduct in the reverse direction. A. BILOTTG) described a method of using this effect to measure the effective lifetime of minority carriers as they are injected through an asymmetrical junction. Bilotti derived an implicit relation between the effective lifetime and the frequency at A CURRENT

+ This work was supported by the National Science Foundation

under grant GK-783.

(2)

Recently we applied this technique to the measurement of lifetime in a “thin base” diode, i.e. d/L c 5. It was therefore necessary to evaluate the magnitude of the hyperbolic tangent of a complex variable. This was done by straightforward expansion of the hyperbolic tangent. Then, using a computer, values of (u+, 7) were found by trial and error for the specific values of IJIm and d/dD. Results of this calculation for two values of IaC/IaC are shown in the graph. In both cases d/l/D was chosen to be 0.001. For either of these values of IaC/Iao curves appropriate to other values of d/l/o are easily found by translating the given curve parallel to the w = constant asymptote as can be seen by rewriting equation (1) as follows : R, = [l +(wc7)s]--1’4 x

ltanh[(s/dW(l +iw)ll tanh

s/2/7

(14

395

NOTES IO-’

I

I -

fC=7.64~105

Hz. +I

I -

fC=2.535x10v-lz.

10-S

’ I I I I I I I

11‘ _T

(sec.)

-lo-’

I

I

I,,,,,

IO”

I lo5

f,= z

I

,,I,,,

(Hz.) +

II

‘O’

FIG. 1. Lifetime vs. critical frequency.

where : RI = 41,lL s = d/dD. For a fixed value of RI, a new value of s, say s’ = as, implies the transformation T’ = a27 and W’ = ,/a2. On log-log graph paper this corresponds to shii parallel to the T and UJ axes respectively. Therefore, given the curve of lifetime vs. critical angular frequency (or equivalently, real frequency) for one value of S, the corresponding curve for any other value of s is the given curve translated parallel to the short lifetime asymptote. As can be seen from the curves the range of the lifetime measurement using the distortion tech-

nique may be extended by roughly an order of magnitude beyond the range applicable to thick base diodes. Beyond this increased range the critical frequency rapidly becomes insensitive to lifetime. Department of ekctrical Engineering, University of Rochester, Rochester, New York. U.S.A.

R. B. RENBECK L. P. HUNTER

Reference 1. A. BILOTTI,Solid-St.

Electron. 10,445 (1967).