Trapping and recombination measurement by a light modulation technique

J. Phys. Chem. Solids

Pergsmon Press 1961. Vol. 22, pp. 514.5.

Printed in Great Britain.

TRAPPING AND RECOMBINATION MEASUREMENT BY A LIGHT MODULATION TECHNIQUE I

G. CHEROFF, International

J. HEER

and S. TRIFBWASSER

Business Machines Corporation, Thomas J. Watson Research Center, Yorktown Heights, New York

Abstract-A technique is described by which recombination lifetime may be resolved from trapping effects. Analysis is shown by which trap capture and release times may be measured as well as density and energy level of trapping levels. It is shown that superlinearity in CdSe sintered layers arises not from “activation”, as described in currently held models of variation of recombination time with light level, but rather is associated with increase of mobility with light level.

explaining the super- sub- and linear dependence of u on I have concentrated on models that result in assignment of responsibility for these variations to Tr. Unfortunately measurements of 7,. thus far reported have been indirect. For example, if p, a and p are known, 7,. can be found from equation (1). The difficulties are obvious. If there were no traps, or if DkT/n were very small, then equation (2) could be used. This relation predicts exponential variation of n with time, a behavior generally observed either for very small time intervals or very high light intensities. As a matter of fact, NIEKISCH(~) used equations (2) and (3) and an a.c. light method to measure D as a function of the depth below the conduction band.t We have extended NIEKISCH’S technique to show how examination of the a.c. response as a function of frequency can yield trapping times, recombination lifetime and trap concentrations.

I. INTRODUCTION

BOTH from a practical and academic standpoint, it has long been recognized that trapping, _ . sensitivity and time of response are intimately related in photoconductive processes. In particular, for the simple case of a single current carrier (electrons in CdSe), the conductivity may be written :

u = ep&I)j3

(1)

where e is the charge on the electron, p the electron mobility, 7r the recombination lifetime of electrons, cc the optical absorbtion coefficient, I the light intensity and j3 the quantum efficiency. Response time is defined by the differential equation: dn

n (2)

dt=-70

where n is the density of electrons in the conduction band and 7s the response time. Equation (2) should determine n for at least a short time interval after the exciting radiation is turned off. ROSE(~) pointed out that 7s is related to 7,. by : To=Tr(l+F), where D is the density Fermi level (Q.F.L.).*

2. THEORY

In NIEKISCH’S earlier work(s) two assumptions were necessary: (a) 7,. is independent of light level and (b) mobility is independent of light level. In general if these assumptions were valid, conductance vs. light intensity curves would be lineara condition rarely seen in a photoconductor. In fact, a good deal of effort has been directed at finding models to explain the wide variety of

(3) of carriers Theories

at the quasi directed at

* BROZER and WARMINSKY give a detailed statistical argument supporting equation (3). It can also be shown quite simply that for traps all well above the Q.F.L., 7 = rr(l -l-h/n), where h = number of trapped electrons per unit volume.

j’ The relations between noise measurements and response to sinusoidal variations of light are discussed in Ref. 2. 51

52

G.

CHEROFF,

J.

HEER

slopes of log o vs. log I plots observed. In addition, BUBB and MACDoNALDt3) showed recently that p also varies with light level. This has been confirmed by FOWLER@) in this laboratory on samples similar to those on which our experiments were performed. It is important to unravel the various factors that contribute to the observed photoconductive response. The model under examination is that shown in Fig. 1. It is assumed that the single trapping

and

S.

TRIEBWASSER

S, the capture cross-section of the traps for electrons, TJ, the average thermal velocity of electrons in the C.B., H, the density of traps at a depth E, E, the depth of the trap below the conduction band. If now we assume an incremental change in F of 6F and write F = Fo+ 6F, n = no+ 6n, h = ho+6h, then equations (4) and (5) become to first order:

4no) 4w -++---_ at TRAP

-

dho

--dho

4W

dt

at

-+-

BAND

If all the zero subscripted steady state values, then

considered in this treatment.

dno

level is in contact with the conduction band (C.B.), but not the valence band. In addition, it is assumed that the dependence of recombination rate on the density of trapped electrons is a higher order effect-i.e. the recombination rate for small signal theory depends only on n. Using the sHOCKLEY-hAD(5) relation for this case, the differential equation governing both conduction electrons and trapped electrons can be written :

an - =

-f(n)-

dho

-ZZ

-

at

(5)

where :

f(n) describes the dependence of recombination on n,

h, the density of trapped electrons, F, the electron generation rate via optical excitation, NC, the effective density of states in the C.B.,

represent

= Fo

also, bN,Sv

exp( - E/kT)

= no(H- ho)Sv

(8)

Now letting,

6F = Fl exp(iwt) Sn = nl exp(iwt)

(9)

6h = hl exp(iwt)

?I1 =

exp(-E/kT)+n(H-h)Sv

(7)

quantities

= 0 andf(ns)

at

and taking relations directly

G+F

at dh = -hN,Sv at

exp( - E/kT)

+no(H-ho)Sv+Sn(H-ho)Sv-no8hSv.

1 FIG. 1. Transitions

(6)

exp( - E/kT) -GhN,Sv

= - hoN& VALENCE

@f'(no)

d(ah) -+Fo+SF at

at

RECOMBINATION PROCESS

-

-f(n0)

dt

(9) into account, Fr

wo+iw[l

+w2/(w1+iw)]

it follows

(10)

where

wo =f’(no),

w1=

2 ()

HA,

w2 = (H- ho)Sv (11)

In the simple case that f(no) = no/~~, and TV is independent of no, ws = l/~r. In the case that the trap is well above the Q.F.L., wr represents the trap release frequency, and ws represents the

TRAPPING

AND RECOMBINATION

MEASUREMENT

trapping rate. Wben there are many trapping levels the term ws/(wl+iw) in the denominator of (10) is replaced by a summation of appropriate W’S, or for the continuous distribution case by an integral. The cases previously described in the literature deal with WI and ws s wa. Then if measurements are carried out at frequencies below wr and 01s where w < ~1, equation (10) reduces to: F1 n1 = wo+iw[l +(wz/wl)]

(12)

For the case of a trap well above the Q.F.L., ,(H-ho) M H and w,‘jwr = he/no. The behavior described by equation (3) is predicted; i.e. a with a response time of photoconductor 7s = ~,.[l +(h&e)]. This is the case treated originally by NIEKISCH.In a more recent publication,(s) he extended the work to larger w, (w > WI), but assumed that rr and the electron mobility were not a function of n. The results we have found are at variance with those predicted by NIEKISCHfrom his assumptions with respect to the variation of nl with frequency. 3. EXP~MJWTAL REsuL7X The measurements reported were made on sintered CdSe doped with 100 p.p.m. Cu. The Cu was added in the form of CuCle. In addition, CdCls was used as a flux so that the Cl content of the samples was not controlled. Measurements of impedance vs. frequency were made to look for barrier relaxation effects. In the frequency range and light levels of interest in this experiment no relaxation effects were observed. In addition, preliminary examination of a Cu-doped CdSe single crystal gave the same qualitative results as those reported here. The sample thickness was large compared with an absorption length. The effect of the nonuniform distribution of carriers on the quantitative results can be calculated, and has been included in the stated results. Measurements have been made over a wide range of wavelengths-all of which showed the same qualitative behavior. Actual data shown here are either taken from an unfiltered neon lamp or with monochromatic light at 6000 A. The neon lamp is a handy source for CdSe since its spectrummatches the CdSe response reasonably

BY LIGHT

53

MODULATION

well and it has the added advantage that it can be easily modulated. There are several cases of interest. The simplest is that in which os s wr and ws, and ws/wl < 1. This will be the case for very deep traps or traps located below the Q.F.L. Effectively in such a case the traps do not contribute to the dynamic response and equation (12) reduces to Fr n1 = ____ wa+iw

(13)

and the normalized amplitude R becomes R=

a(w % wo) a(oJ

e

F$b = -=

%)

$.

F&JO

(14)

8~

When R is plotted as a function of ljw, it is obvious that the slope gives ws. Fig. 2 shows three such

A

0.1 5

0

I -10/rW/cm2

Slope 53 cps

-fw=450) 53cps

Theory: -G, (w>>u,1 = -u. G,Iw<
0.5

I.5

2.0

2.5

:

.O

FIG. 2. Gl( w> uo)/Gr(w < ~0) vs. CU.Gr cc nr. It can be shownthat the fact that 9~1actually varies with depth of penetration of the light leads to a slope of [w(Io)]-I where T+(I) is defined by n(l)/n(I) = f(n).

plots for three different light intensities. In addition, when u = ~0, a phase shift of 45” between nl and F is observed according to equation (13). The agreement is excellent.

54

G. CHEROFF,

J. HEER

A more interesting case is one in which ws/wl > 1, and WI and ws > ws. In this case, if the magnitude of the inequality is large, two (nl cc l/w) regions are observed, one following equation (14) and the other giving a slope of ws(l+ ws/w$l. If the frequencies are not very well separated, the two regions are not resolved and only the former is observed at w 9 ws. A more typical plot is shown in Fig. 3. For a case such as this, the relative phase between nl and Fl is most sensitive to the exact values of ws, WI and

and

S. TRIEBWASSER

w2 and H, but the results are tentative and will not be reported at this time. On the other hand, rr(Is), the value of 7r for small attenuation, can be found from exploration of Gl at high frequencies (as in Fig. 2). It can be shown that -

where

dG dro

= eP(~o)%(~o),

G is the conductance

per square,

(15)

IO the

I

I 100 FREQUENCY

FIG. 3. Gl/Go vs.ffor

I

I

1000

10.000

(CpS)

the Q.F.L. 0.3 eV below the C.B. I=

wg. Because the conductance

(an integration performed over the sample thickness) is the experimentally observed quantity, no simple phase relationship can be expressed except for the simple case where ws is widely separated from WI and ws. For this case, internal consistency with the model is observed. (See Fig. 2.) Work is in progress on many samples including single crystals which will lead to values for WI,

0.6 pW/cm2.

incident photon flux and AIs) is the mobility for the case of small attenuation (or that near the surface of the photoconductor). Fig. 4 shows dG/dIo and ~~(10) for two different samples. The G vs. 1s data show a superlinear region at the lower light intensity. We must conclude that the observed non-linear behavior is associated with a variation of mobility with light intensity, not with “activation” described in terms of recombination passing from “fast” to “slow” recombination centers. In the region of slow variation of ~1, where we have Hall mobility data,“) the results agree; i.e. inserting measured p and assuming

TRAPPING

AND

RECOMBINATION

MEASUREMENT 3

BY

LIGHT

MODULATION

55

SAMPLE C69-I SAMPLE C56-7

=I

O’lI

1

I

IO

100

LIGHT

INTENSITY

I 1000

(pW/Cm21

FIG. 4. dG/dIo and rr(10) for two different samples.

a quantum efficiency of one, agreement with equation (15) is found.

F. HOCHBERGfor assistance in some of the measurements reported here. REFERENCES

4. CONCLUSIONS

Since variation of photoconductance with light intensity has been explained in terms of variation of recombination lifetime, it is important to measure this quantity independently. Amethod has been described by which rs can be found directly. From the results found it is concluded that current models of photoconductor “activation” are incomplete. Acknowledgements-We

wish to thank R. CHANG and

1. ROSE A., RCA Rew. 12, 363 (1951); BROSER I. and WARMINSKY R., Ann. Phys. Leipzig (6), 16, 361

(1955). 2. NIEKISCH E. A., Ann. Phys. Leipzig (6), 15, 279, 288 (1955); VAN VLIET K. M., BLOK J., RIS C. and STEKETE J., Physica 22, 723 (1956) and VAN VLIET K. M. and BLOK J., Physica 22, 525 (1956). 3. BUBE R. H. and MACDONALD H. E., Phys. Rev. 12, 473 (1961). 4. FOWLEIX A. B., International Conference on Photoconductivity, New York (1961). 5. SHOCKLEY W. and READ W. T., Phys. Rev. 87, 835 (1952).

DISCUSSION Van der MAELXEN:You reported changes in mobility and in lifetime as functions of intensity. Due to what mechanism in your experiments were the changes in p occurring?

S. TRIEBWASSER:This question is dealt with at length in papers.* *Pp.

173 and 181 of this issue.