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Noise correlation and noise reduction in GaAs light-emitting diodes
Solid-StatsElectmics, 1976,Vol. 19,pp. 319-324. PergamonPress. Printed in Great Britain
NOISE CORRELATION AND NOISE REDUCTION IN GaAs LIGHT-EMITTING DIODES? W. BOLLETER,$J. CONTI,$ G. GUEKOS$ and G. TENCHIO~ Department of Advanced Electrical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland (Receioed 12June 1975;in revisedform 12September 1975) Abstract-The crosscorrelation between the random fluctuations of the light intensity and the current of GaAs LED’s has been measured in the l/f frequency range at room-temperature. A strong dependence of the crosscorrelation on the direction of radiation is found. The diodes with a plastic lens which increases the light intensity along the axis vertical to the emitting surface showa higher correlation than the diodes with the lens removed. From a simple LED equivalent circuit a relation linking the excess noise factor and the coherence function is calculated which fits qualitatively well with the measured results. Finally, it is shown how an optoelectronic feedback method eliminates the excess noise of the light intensity in the low frequency domain.
1. INTRODUCTION
The light intensity
of LED’s is subject to random
circuit greatly reduces the noise of the light beam, as we show in the second part of the paper.
fluctuations which have been treated in a number of papers [ 11. Experimental results published by different authors show a frequency independant light noise spectrum at room temperature for measuring frequencies above approximately lo4 Hz and up to the MHz region[ l31, where the frequency limits depend on the material used and device geometry. Below about l@Hz the radiation shows an excess noise component the magnitude of which increases with increasing current density for GaAs diodes [4,5] but shows a more complex behavior for GaP diodes according to [6]. The frequency dependence of the excess light noise for low frequencies (
2. EXPERIMENTAL The LED’s tested were commercial units. They were made by diffusion of the proper impurities into a n -GaAs substrate. The measurements of the light noise were performed by using the single detector technique [ 11.The current noise was determined from the measurement of the noise voltage across the diode. The experimental arrangement is shown in Fig. 1. The diodes mounted on a copper heat sink were fixed on a rotating table. A silicon photodiode EGG-SGD 100 was positioned in front of the LED. The relative positions LED-photodiode could be adjusted with the aid of micrometer screws. The distance LED-photodiode and the photodiode receiving area determine the solid angle in which the measurements are made. All LED’s had a clear lens mounted in front of the emitting surface. The lens could be mechanically removed without damaging the diode. Figure 2 shows the radiation pattern of a measured diode with and without lens in a plane vertical to the plane surface of emission with the d.c. diode current ID as a parameter. The directions of the light noise measurements are denoted by cpfor which the degree P of polarization is also given. The distances LED-photodiode used are such that the LED may be viewed as a point source and the solid angle was determined to be O-53. lo-* sr for the diode with lens and 0.08 sr for the diode without lens (hatched spaces in Fig. 2). The intersections of the radiation intensity curves of Fig. 2 with the concentric circles give the d.c. current in the photodiode for the LED current and direction used. The measurement of the light noise alone consisted of a comparison between the mean-square noise current of the photodiode illuminated by the LED and the shot noise of the photodiode for the same photocurrent, measuring frequency and noise bandwidth. For the measurement, tThis work was supported by the Swiss National Science the noise voltage generated by the photocurrent in a Foundation. lOO-K0 metal film load resistor RL is fed to a low-noise SNOWat Department of Electronics, Swiss Federal Institute of preamplifier (Brookdeal 450). The noise spectrum is Technology, Zurich. SNOWat The European Space Operation Center (ESOC), determined via the autocorrelation function given by a Darmstadt, Federal Republic of Germany. digital correlator (Hewlett Packard 3721A) or it can be 319
320
W. BOLLETERet al. channel
1
I d d
m
Fig. 1. Schematic diagram of the measuring apparatus
/-- ,
I
L351
Fig. 2. Radiationpattern of an investigateddiodewithlens (right)and withthe lens removed(left).The directionsof the light noise measurements are denoted by cp,the hatched spaces indicate the detection angle. P is the degreeof polarisation of the light.
measured directly by a frequency analyzer (Bruel and Kjaer 3347). The amplifiers A, and A2 of Fig. 1 (Brookdeal 431 and 450 resp.) are used for the measurement of the LED current noise. All measurements were performed at room temperature. For the determination of the crosscorrelation between light noise and current noise, the crosscorrelation function of the two noise measuring channels is measured by the digital correlator followed by a paper tape puncher for the subsequent computer analysis. All circuits except the correlator and the puncher are mounted on an optical table. The LED, photodiode and amplifiers are supplied by filtered Cd-Ni batteries. Extensive use of ymetal shielding minimized the perturbations due to external electromagnetic fields. The crosscorrelation can be expressed by the coher-
ence function y which is defined as[9]:
“)
P = d(G:$iP
cf)) = Ir(f)l exp o’@(f)).
(1)
G”, cf) cross spectral density function which is the Fourier transform of Rup(7) Rup(7) crosscorrelation function between the fluctuations of the LED voltage and those of the voltage across RL f measuring frequency CUD(j) spectral density function of the LED voltage fluctuations G,(f) spectral density function of the voltage fluctuations across the load resistance RL
Noise correlation and noise reduction in GaAs light-emittingdiodes r time delay between the two noise signals 13 phase angle of y
The spectral density function G,(f) is related to the spectral density function G,(f) of the photocurrent fluctuations by:
The function y has values between 0 for uncorrelated noise signals (&,(T) = 0) and 1 for fully correlated signals.
3.
MEASUREMENTS AND RESULTS
The coherence function y was measured for several diodes as a function of diode current and emission direction in the frequency range l-2 x lo3 Hz. For the diode with lens of Fig. 2 the results are given in Fig. 3. The measurements show a clear frequency dependence of y. This is not surprising since both the light and the current noise have an l/f”-dependence in the same frequency range although the exponent CYneed not be the same for both types of noise. For a fixed frequency and emission direction the function y increases with increasing diode current. This increase was found with all diodes although the shape of the measured curves differed somewhat from sample to sample. The curves of Fig. 3 show that the crosscorrelation depends strongly on the emission direction in which the measurements are performed. The function y is always higher for direction cp,, than for (pz2for the same diode current and frequency and decreases regularly as the
Fig. 3. Measured coherence function y in absolute magnitude and phase as a function of frequency f for the diode of Fig. 2 with lens for two emission directions.
321
detector is moved from cp,, to (pz2.This behaviour was expected from the previous measurement of the excess noise factor of the light under the same experimental conditions. The light excess noise factor showed a similar behaviour with y as regards the emission direction although the degree of change between the directions (p,, and (pz2was not the same. The dependence of the phase angle B on frequency is also given in Fig. 3. For a given emission direction the angle changes little with frequency. This angle was, however, heavily dependent on the LED current or on the emission direction. For a fixed frequency and emission direction cp the angle 0 changed abruptly as the diode current was altered showing two preferred values around 0 and 180”.This was particularly the case when the diode current was increased into the high injection region. Fig. 3 gives values of 0 for relatively low current densities where 13was dependent only on the emission direction. In addition, when the frequency and the direction of the optical detection was altered by means of the rotating table, the angle 0 also changed between its two preferred values 0 and 180”.A characteristic pattern is given in Fig. 4. Remarkably, no essential phase shift was found in the plane perpendicular to the plane of Fig. 4. Figure 5 shows the results for the same diode with the lens removed (see Fig. 2). The coherence function is given for the directions (p,and cpsand has a similar behaviour as in Fig. 3. The values of 1y 1for all other emission directions between (p, and (p5lay on curves between those of Fig. 5 and had similar shape. The phase angle 0 had a similar behaviour as for the diode with lens. The values corresponding to the directions cp,and cpsare given in Fig. 5. Similar results were obtained from other commercial LED’s. When the lens was removed, the pattern became more or less lambertian and the optical excess noise was remarkably lower than with the lens on. This behaviour was again found in the experimental results for the coherence function.
Fig. 4. Dependence of the phase angle 0 of the function y on the emission direction for the same diode as in Fig. 2 but in a different emission plane.
W. BOLLETER eta/.
322
between 1 and 200 A/cm’ where the noise measurements were performed. We assume that the emitted radiation is due to Z,. Moreover, we assume the internal quantum efficiency due to Z, to be equal to one and we neglect any anisotropy in the internal propagation of the emitted photons as well as of the absorption coefficient. We further assume that the current density is constant over the junction plane and that the photons detected by the photodiode are not due to any internal reflections. We can now calculate the function r(f) from (1) as a function of the spectral density function G.,cf) of the voltage fluctuations. For this we have to express G”,(j) and G,(f) as functions of GUDcf). Let Z, be the photoelectric current of the photodiode and U, the luminescent diode voltage. We assume a linear relationship between Z, and IL and write:
for the same diodeas in Fig. 3 but with the lens
Fig. 5. Function y
removed.
where qP,,is the quantum efficiency of the photodiode, Q the extraction efficiency of the luminescent diode, and Q the detection efficiency, i.e. the ratio of the detected to the total radiated power. The fluctuations of R, and a are independent of the fluctuations of UD.For G,,(f) we can write:
4.DISCUSSIONOF THE RESULTS
Our attempt to explain the results given in Figs. 3,4 and 5 is based on a simple equivalent circuit for the LED which is similar to the one discussed in [5] and given in Fig. 6. The diode current I,, the diffusion current IL, and the deep-level recombination current ZRare given by: ZD = ILt ZR = ILoexp
e(E-Z,R)+z mkT
e,,e(E-ZJU R”
2kT
G,(f)
1 = aRL lim-{dUB(f)dZL(f)) T- T
(6)
where dUW) is the inverse Fourier transform of the fluctuations of U, and dZ,Cf)the Fourier transform of the fluctuations of Z,. dZ, is derived from Fig. 6 as follows. For dZ, we write, taking into consideration the fluctuations of R,, ZLo nad ZRoas noise sources:
(3) ILo and Z,, are the saturation currents, E the battery voltage, R, the series resistance of Fig. 1, R,, the contact and bulk semiconductor resistances, R = R, t R,, r, the junction resistance due to recombination, and r, the junction resistance due to diffusion: r
=
r
2kT and e&Z
r,
=
c, 4.
dZ, = +
dR, t +
10
dl,, + -$= dZ,,. RO
(7)
We can now differentiate the term for Z, given in (3) with respect to R,, ILo and ZRo and we obtain after some algebraic reductions: dI
(4)
From the measured current-voltage characteristics no tunnel current could be detected for current densities
n
L
(8)
=
where r,rI r, = r, + r,’
Expressing dZ, as a function of dlJD and replacing it in (8) leads to:
I
1
1
Fig. 6. Simple equivalent for the LED used for the calculation of ‘y.
for R, s R. + r, as is our case. Equations (6) and (9) lead
Noise correlation and noise reduction in GaAs light-emittingdiodes
323
have any reliable information concerning their fabrication procedure. If, instead, we use the measured values of G.n(f), the functions ]rCf)l and 0(j) have a frequency dependence which qualitatively fits well with the measured curves. The attempt we have made to explain the correlation The spectral density function G,(f) can be calculated behaviour does not make any distinction for the different from (2) if we assume that the spectral density function emission directions. In order to find a spatial dependence GiP(f) of the photocurrent fluctuations is connected with of 0y) and (p(j) it is necessary to consider the current the spectral density function G.(j) of the photon density distribution in the LED due to the contact fluctuations in a way given by the partition noise geometry, as this is explained in Conti[l], and the theorem [ lo]: anisotropy in the photon generation and propagation due to the temperature distribution and to the internal G,(f) = Z?~{eZa2G.(j) t 2eZP(l-a)} = R,2Gi,,Cf). reflections. We can take account in our equivalent diode (11) circuit of the fact that the photons are mainly generated in so-called “peculiar regions” having distinct excess noise The mean number of photons generated per second is characteristics, see for instance [5]. The mechanism of the given according to our assumptions by: light extraction would then lead to emission directions having their own excess noise characteristics. We can also think of the possibility of optical correlation between (12) these directions which could enhance the noise level of the radiation when collected by a lens. Furthermore, as we For an ideal diode (Shockley model) the fluctuations of Z, measure a smaller crosscorrelation than the theoretical are pure shot noise. Equation (11) would then give for value (see Fig. 5 dashed curve), we must admit the G,(j) = R,*2eZ,, the well known formula of the shot noise existence of excess noise sources in the photodiode which density. For G.(j) we can write in our case: cannot be correlated with those in the LED. This can be illustrated as follows. The excess light noise is given by the ratio S:
(n)=$.
6 = Gi,IGipo Replacing (13) into (11) and taking into account (lo), the eqn (1) can be rewritten as: Mf)l= 1 ]‘,? = J(Y) 2eZP(1- a) lt dG.d) . W/r,1 - D/r,l)* (14) with a = Z,/Z, = Z,r,/Z,r, and S being the excess noise factor of the optical fluctuations. This factor is defined as the ratio of the measured spectral density function value GiP(f) (see eqn (11)) of the photocurrent fluctuations with LED light incident on the detector to the measured shot noise value of the photocurrent (see also eqn (16)). In our case a 4 1 and (14) can be approximated by:
(16)
where GiPO is the noise current generated in the photodiode under “white” light illumination from an incandescent tungstem lamp at about 2800°K producing the same d.c. photocurrent Z,. After subtracting the thermal noise of the load resistance and the amplifier, the spectral density G,o is constant between the frequencies 60 Hz and 10kHz. In this range GiPOwas measured to be 1.08 times greater than the expected value GiPO= 2eZ,.For frequencies lower than 6OHz GiPOincreases lightly according to l/f” (a ~0.21). 5. LJGHTNOISE COMPENSATION
The use of an optoelectronic feedback circuit similar to the method described in [ll] allows a substantial compensation of the excess light noise of the LED. The light noise voltage of the LED as detected by the photodiode is phase shifted by 180”and is fed back to the (15) supply of the diode by means of a variable gain low noise IrCf)l= amplifier and a coupling network. The current noise of the The phase spectrum 6(f) is given by the phase of G,(f), compensated LED shows virtually no frequency depensee eqns (1) and (10). Since all the impedances of Fig. 6 dence in the range l-104Hz whereas the expected are real in our frequency range, e(f) is +180” if the l/f” function is measured for the uncompensated diode. fluctuations of R. or ILo dominate or 0” if those of ZRO Figure 7 represents the frequency dependence of the dominate. The calculation of ]r(f)] from (14) supposes the light excess noise S for both the uncompensated and existence of an analytic expression for G&(f). Such an compensated circuits. The upper two curves in Fig. 7 expression can only be derived from a known noise indicate the measurements in two emission directions equivalent circuit of the luminescent diode comprising all (IS”, 3459 without compensation. The lower curve is the noise sources, such as those due to ZL0,ZROand also the result obtained with optoelectronic feedback. In the sources located in the contacts. The latter were not known frequency range between 1 Hz and 10kHz GiPcf) tends to to us since the diodes were commercial and we did not G&j) (S+ 1) and has the same magnitude for both
J(l-g.
W. BOLLETER etal. r
\
the phase shift induced by the feedback circuit I minimized.
L 35 with lens ~=15”~1,=21~A,1,=80mA~
30
6.CONCLUSIONS
~=345°&,=20~A.ID=80mA)
IO
A,
\
‘Q_
__
/
c=15°(I,=21pA,I,=80mA,w~thfeedback) ~=345°(I,=20~A,lo=80mA
IO
z rlk,
.with feedback)
103
Fig. 7. Frequency dependenceof the ratio 6 with and without feedbackfor two emissiondirectionsfor the diode of Fig. 2 with lens. directions. With the feedback circuit we can compensate the optical excess noise of the LED but not the excess noise inherent to the photodiode itself. The nearly complete compensation of the optical excess noise of the LED in a range where y is well below 1 is explained by the fact that y takes into account the total noise of the photocurrent (see eqn (11))and not only the noise which is in excess of the shot noise. It is remarkable that for the two significant emission directions (15”, 345”) it was not necessary to alter the phase shift ‘although the phase angle 19 of the cross correlation factor y changed from 0 to 180”as displayed in Fig. 4. Substituting the constant voltage source E in Fig. 6 by a variable source U that expresses the influence of the feedback and supply circuit, the sensitivity behavior of the circuit can be expressed as follows
(17) Equation (17) shows that the sign of d& can be changed depending on the magnitude of the last term of the right hand side which can be altered by means of the feedback circuit [see also eqn (9)]. Therefore the influence of fI on
The experimental results presented in this paper shol that the correlation between light noise and current nois of LED’s depends not only on diode current but also o the direction in which the photons are emitted. The resuli extend those presented in [8] where a dependence of ligf noise on the direction of emitted radiation was reported. The absolute value of the coherence function varie strongly depending on whether the radiation is emitte through the plastic lens on the LED or not. Diodes wit lens have shown a much stronger crosscorrelation. W have made use of this fact in order to develop a optoelectronic feedback method to reduce the light nois of the LED. The results are excellent in the I/f frequent domain where the excess light noise virtually disappear: We believe that LED sources without excess light nois can find promising applications in optoelectronic circuits. Acknowledgements-The authors wish to thank Prof. Dr. N Strutt for his support of the work. They also wish to thank th Swiss National Science Foundation for financial support of thi project. REFERENCES
1. See for example: A. van der Ziel, Proc. IEEE, Vol. 58, No. pp. 1178-1206 (1970); J. Conti, Thesis No. 5250 Swiss Feder Institute of Technology Zurich, (1974); T. J. Hazendon, Thesis University of Amsterdam (1973). 2. G. Guekos, Thesis No. 4350, Swiss Federal Institute ( Technology Zurich, p. 42 (1974). 3. T. P. Lee and C. A. Burrus, IEEE J. of Quantum Electronic QE-8, 370 (1972). 4. J. J. Brophy, J. Appl Phys. 38, 2465 (1967). 5. N. B. Lukyanchikova, N. P. Garbar, N. K. Sheinkman and h N. Zargarjantz, Solid St. Electron. 15. 801 (1972). 6. N. B. Lukyanchikova, M. K. Sheinkman, N. P. Garbar and ! V. Svechnikov, Physica 58, 219 (1972). 7. G. Guekos and M. Strutt, IEEE J. of Quantum Electronic QE-4, 502 (1968). 8. J. Conti and M. Strutt, IEEEJ. ofQuantum Hectronics QE-1 815 (1972). 9. J. Bendat and A. Pierson, Measlrremenr and Analysis c Random Data. Wiley, New York (1966). 10. H. M. Fijnaut and R. J. J. Zijlstra, J. Phys. D3, 45 (1970). 11. G. Guekos and M. Strutt, Proc. IEEE 58, 949 (1970).
NOISE CORRELATION AND NOISE REDUCTION IN GaAs LIGHT-EMITTING DIODES? W. BOLLETER,$J. CONTI,$ G. GUEKOS$ and G. TENCHIO~ Department of Advanced Electrical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland (Receioed 12June 1975;in revisedform 12September 1975) Abstract-The crosscorrelation between the random fluctuations of the light intensity and the current of GaAs LED’s has been measured in the l/f frequency range at room-temperature. A strong dependence of the crosscorrelation on the direction of radiation is found. The diodes with a plastic lens which increases the light intensity along the axis vertical to the emitting surface showa higher correlation than the diodes with the lens removed. From a simple LED equivalent circuit a relation linking the excess noise factor and the coherence function is calculated which fits qualitatively well with the measured results. Finally, it is shown how an optoelectronic feedback method eliminates the excess noise of the light intensity in the low frequency domain.
1. INTRODUCTION
The light intensity
of LED’s is subject to random
circuit greatly reduces the noise of the light beam, as we show in the second part of the paper.
fluctuations which have been treated in a number of papers [ 11. Experimental results published by different authors show a frequency independant light noise spectrum at room temperature for measuring frequencies above approximately lo4 Hz and up to the MHz region[ l31, where the frequency limits depend on the material used and device geometry. Below about l@Hz the radiation shows an excess noise component the magnitude of which increases with increasing current density for GaAs diodes [4,5] but shows a more complex behavior for GaP diodes according to [6]. The frequency dependence of the excess light noise for low frequencies (
2. EXPERIMENTAL The LED’s tested were commercial units. They were made by diffusion of the proper impurities into a n -GaAs substrate. The measurements of the light noise were performed by using the single detector technique [ 11.The current noise was determined from the measurement of the noise voltage across the diode. The experimental arrangement is shown in Fig. 1. The diodes mounted on a copper heat sink were fixed on a rotating table. A silicon photodiode EGG-SGD 100 was positioned in front of the LED. The relative positions LED-photodiode could be adjusted with the aid of micrometer screws. The distance LED-photodiode and the photodiode receiving area determine the solid angle in which the measurements are made. All LED’s had a clear lens mounted in front of the emitting surface. The lens could be mechanically removed without damaging the diode. Figure 2 shows the radiation pattern of a measured diode with and without lens in a plane vertical to the plane surface of emission with the d.c. diode current ID as a parameter. The directions of the light noise measurements are denoted by cpfor which the degree P of polarization is also given. The distances LED-photodiode used are such that the LED may be viewed as a point source and the solid angle was determined to be O-53. lo-* sr for the diode with lens and 0.08 sr for the diode without lens (hatched spaces in Fig. 2). The intersections of the radiation intensity curves of Fig. 2 with the concentric circles give the d.c. current in the photodiode for the LED current and direction used. The measurement of the light noise alone consisted of a comparison between the mean-square noise current of the photodiode illuminated by the LED and the shot noise of the photodiode for the same photocurrent, measuring frequency and noise bandwidth. For the measurement, tThis work was supported by the Swiss National Science the noise voltage generated by the photocurrent in a Foundation. lOO-K0 metal film load resistor RL is fed to a low-noise SNOWat Department of Electronics, Swiss Federal Institute of preamplifier (Brookdeal 450). The noise spectrum is Technology, Zurich. SNOWat The European Space Operation Center (ESOC), determined via the autocorrelation function given by a Darmstadt, Federal Republic of Germany. digital correlator (Hewlett Packard 3721A) or it can be 319
320
W. BOLLETERet al. channel
1
I d d
m
Fig. 1. Schematic diagram of the measuring apparatus
/-- ,
I
L351
Fig. 2. Radiationpattern of an investigateddiodewithlens (right)and withthe lens removed(left).The directionsof the light noise measurements are denoted by cp,the hatched spaces indicate the detection angle. P is the degreeof polarisation of the light.
measured directly by a frequency analyzer (Bruel and Kjaer 3347). The amplifiers A, and A2 of Fig. 1 (Brookdeal 431 and 450 resp.) are used for the measurement of the LED current noise. All measurements were performed at room temperature. For the determination of the crosscorrelation between light noise and current noise, the crosscorrelation function of the two noise measuring channels is measured by the digital correlator followed by a paper tape puncher for the subsequent computer analysis. All circuits except the correlator and the puncher are mounted on an optical table. The LED, photodiode and amplifiers are supplied by filtered Cd-Ni batteries. Extensive use of ymetal shielding minimized the perturbations due to external electromagnetic fields. The crosscorrelation can be expressed by the coher-
ence function y which is defined as[9]:
“)
P = d(G:$iP
cf)) = Ir(f)l exp o’@(f)).
(1)
G”, cf) cross spectral density function which is the Fourier transform of Rup(7) Rup(7) crosscorrelation function between the fluctuations of the LED voltage and those of the voltage across RL f measuring frequency CUD(j) spectral density function of the LED voltage fluctuations G,(f) spectral density function of the voltage fluctuations across the load resistance RL
Noise correlation and noise reduction in GaAs light-emittingdiodes r time delay between the two noise signals 13 phase angle of y
The spectral density function G,(f) is related to the spectral density function G,(f) of the photocurrent fluctuations by:
The function y has values between 0 for uncorrelated noise signals (&,(T) = 0) and 1 for fully correlated signals.
3.
MEASUREMENTS AND RESULTS
The coherence function y was measured for several diodes as a function of diode current and emission direction in the frequency range l-2 x lo3 Hz. For the diode with lens of Fig. 2 the results are given in Fig. 3. The measurements show a clear frequency dependence of y. This is not surprising since both the light and the current noise have an l/f”-dependence in the same frequency range although the exponent CYneed not be the same for both types of noise. For a fixed frequency and emission direction the function y increases with increasing diode current. This increase was found with all diodes although the shape of the measured curves differed somewhat from sample to sample. The curves of Fig. 3 show that the crosscorrelation depends strongly on the emission direction in which the measurements are performed. The function y is always higher for direction cp,, than for (pz2for the same diode current and frequency and decreases regularly as the
Fig. 3. Measured coherence function y in absolute magnitude and phase as a function of frequency f for the diode of Fig. 2 with lens for two emission directions.
321
detector is moved from cp,, to (pz2.This behaviour was expected from the previous measurement of the excess noise factor of the light under the same experimental conditions. The light excess noise factor showed a similar behaviour with y as regards the emission direction although the degree of change between the directions (p,, and (pz2was not the same. The dependence of the phase angle B on frequency is also given in Fig. 3. For a given emission direction the angle changes little with frequency. This angle was, however, heavily dependent on the LED current or on the emission direction. For a fixed frequency and emission direction cp the angle 0 changed abruptly as the diode current was altered showing two preferred values around 0 and 180”.This was particularly the case when the diode current was increased into the high injection region. Fig. 3 gives values of 0 for relatively low current densities where 13was dependent only on the emission direction. In addition, when the frequency and the direction of the optical detection was altered by means of the rotating table, the angle 0 also changed between its two preferred values 0 and 180”.A characteristic pattern is given in Fig. 4. Remarkably, no essential phase shift was found in the plane perpendicular to the plane of Fig. 4. Figure 5 shows the results for the same diode with the lens removed (see Fig. 2). The coherence function is given for the directions (p,and cpsand has a similar behaviour as in Fig. 3. The values of 1y 1for all other emission directions between (p, and (p5lay on curves between those of Fig. 5 and had similar shape. The phase angle 0 had a similar behaviour as for the diode with lens. The values corresponding to the directions cp,and cpsare given in Fig. 5. Similar results were obtained from other commercial LED’s. When the lens was removed, the pattern became more or less lambertian and the optical excess noise was remarkably lower than with the lens on. This behaviour was again found in the experimental results for the coherence function.
Fig. 4. Dependence of the phase angle 0 of the function y on the emission direction for the same diode as in Fig. 2 but in a different emission plane.
W. BOLLETER eta/.
322
between 1 and 200 A/cm’ where the noise measurements were performed. We assume that the emitted radiation is due to Z,. Moreover, we assume the internal quantum efficiency due to Z, to be equal to one and we neglect any anisotropy in the internal propagation of the emitted photons as well as of the absorption coefficient. We further assume that the current density is constant over the junction plane and that the photons detected by the photodiode are not due to any internal reflections. We can now calculate the function r(f) from (1) as a function of the spectral density function G.,cf) of the voltage fluctuations. For this we have to express G”,(j) and G,(f) as functions of GUDcf). Let Z, be the photoelectric current of the photodiode and U, the luminescent diode voltage. We assume a linear relationship between Z, and IL and write:
for the same diodeas in Fig. 3 but with the lens
Fig. 5. Function y
removed.
where qP,,is the quantum efficiency of the photodiode, Q the extraction efficiency of the luminescent diode, and Q the detection efficiency, i.e. the ratio of the detected to the total radiated power. The fluctuations of R, and a are independent of the fluctuations of UD.For G,,(f) we can write:
4.DISCUSSIONOF THE RESULTS
Our attempt to explain the results given in Figs. 3,4 and 5 is based on a simple equivalent circuit for the LED which is similar to the one discussed in [5] and given in Fig. 6. The diode current I,, the diffusion current IL, and the deep-level recombination current ZRare given by: ZD = ILt ZR = ILoexp
e(E-Z,R)+z mkT
e,,e(E-ZJU R”
2kT
G,(f)
1 = aRL lim-{dUB(f)dZL(f)) T- T
(6)
where dUW) is the inverse Fourier transform of the fluctuations of U, and dZ,Cf)the Fourier transform of the fluctuations of Z,. dZ, is derived from Fig. 6 as follows. For dZ, we write, taking into consideration the fluctuations of R,, ZLo nad ZRoas noise sources:
(3) ILo and Z,, are the saturation currents, E the battery voltage, R, the series resistance of Fig. 1, R,, the contact and bulk semiconductor resistances, R = R, t R,, r, the junction resistance due to recombination, and r, the junction resistance due to diffusion: r
=
r
2kT and e&Z
r,
=
c, 4.
dZ, = +
dR, t +
10
dl,, + -$= dZ,,. RO
(7)
We can now differentiate the term for Z, given in (3) with respect to R,, ILo and ZRo and we obtain after some algebraic reductions: dI
(4)
From the measured current-voltage characteristics no tunnel current could be detected for current densities
n
L
(8)
=
where r,rI r, = r, + r,’
Expressing dZ, as a function of dlJD and replacing it in (8) leads to:
I
1
1
Fig. 6. Simple equivalent for the LED used for the calculation of ‘y.
for R, s R. + r, as is our case. Equations (6) and (9) lead
Noise correlation and noise reduction in GaAs light-emittingdiodes
323
have any reliable information concerning their fabrication procedure. If, instead, we use the measured values of G.n(f), the functions ]rCf)l and 0(j) have a frequency dependence which qualitatively fits well with the measured curves. The attempt we have made to explain the correlation The spectral density function G,(f) can be calculated behaviour does not make any distinction for the different from (2) if we assume that the spectral density function emission directions. In order to find a spatial dependence GiP(f) of the photocurrent fluctuations is connected with of 0y) and (p(j) it is necessary to consider the current the spectral density function G.(j) of the photon density distribution in the LED due to the contact fluctuations in a way given by the partition noise geometry, as this is explained in Conti[l], and the theorem [ lo]: anisotropy in the photon generation and propagation due to the temperature distribution and to the internal G,(f) = Z?~{eZa2G.(j) t 2eZP(l-a)} = R,2Gi,,Cf). reflections. We can take account in our equivalent diode (11) circuit of the fact that the photons are mainly generated in so-called “peculiar regions” having distinct excess noise The mean number of photons generated per second is characteristics, see for instance [5]. The mechanism of the given according to our assumptions by: light extraction would then lead to emission directions having their own excess noise characteristics. We can also think of the possibility of optical correlation between (12) these directions which could enhance the noise level of the radiation when collected by a lens. Furthermore, as we For an ideal diode (Shockley model) the fluctuations of Z, measure a smaller crosscorrelation than the theoretical are pure shot noise. Equation (11) would then give for value (see Fig. 5 dashed curve), we must admit the G,(j) = R,*2eZ,, the well known formula of the shot noise existence of excess noise sources in the photodiode which density. For G.(j) we can write in our case: cannot be correlated with those in the LED. This can be illustrated as follows. The excess light noise is given by the ratio S:
(n)=$.
6 = Gi,IGipo Replacing (13) into (11) and taking into account (lo), the eqn (1) can be rewritten as: Mf)l= 1 ]‘,? = J(Y) 2eZP(1- a) lt dG.d) . W/r,1 - D/r,l)* (14) with a = Z,/Z, = Z,r,/Z,r, and S being the excess noise factor of the optical fluctuations. This factor is defined as the ratio of the measured spectral density function value GiP(f) (see eqn (11)) of the photocurrent fluctuations with LED light incident on the detector to the measured shot noise value of the photocurrent (see also eqn (16)). In our case a 4 1 and (14) can be approximated by:
(16)
where GiPO is the noise current generated in the photodiode under “white” light illumination from an incandescent tungstem lamp at about 2800°K producing the same d.c. photocurrent Z,. After subtracting the thermal noise of the load resistance and the amplifier, the spectral density G,o is constant between the frequencies 60 Hz and 10kHz. In this range GiPOwas measured to be 1.08 times greater than the expected value GiPO= 2eZ,.For frequencies lower than 6OHz GiPOincreases lightly according to l/f” (a ~0.21). 5. LJGHTNOISE COMPENSATION
The use of an optoelectronic feedback circuit similar to the method described in [ll] allows a substantial compensation of the excess light noise of the LED. The light noise voltage of the LED as detected by the photodiode is phase shifted by 180”and is fed back to the (15) supply of the diode by means of a variable gain low noise IrCf)l= amplifier and a coupling network. The current noise of the The phase spectrum 6(f) is given by the phase of G,(f), compensated LED shows virtually no frequency depensee eqns (1) and (10). Since all the impedances of Fig. 6 dence in the range l-104Hz whereas the expected are real in our frequency range, e(f) is +180” if the l/f” function is measured for the uncompensated diode. fluctuations of R. or ILo dominate or 0” if those of ZRO Figure 7 represents the frequency dependence of the dominate. The calculation of ]r(f)] from (14) supposes the light excess noise S for both the uncompensated and existence of an analytic expression for G&(f). Such an compensated circuits. The upper two curves in Fig. 7 expression can only be derived from a known noise indicate the measurements in two emission directions equivalent circuit of the luminescent diode comprising all (IS”, 3459 without compensation. The lower curve is the noise sources, such as those due to ZL0,ZROand also the result obtained with optoelectronic feedback. In the sources located in the contacts. The latter were not known frequency range between 1 Hz and 10kHz GiPcf) tends to to us since the diodes were commercial and we did not G&j) (S+ 1) and has the same magnitude for both
J(l-g.
W. BOLLETER etal. r
\
the phase shift induced by the feedback circuit I minimized.
L 35 with lens ~=15”~1,=21~A,1,=80mA~
30
6.CONCLUSIONS
~=345°&,=20~A.ID=80mA)
IO
A,
\
‘Q_
__
/
c=15°(I,=21pA,I,=80mA,w~thfeedback) ~=345°(I,=20~A,lo=80mA
IO
z rlk,
.with feedback)
103
Fig. 7. Frequency dependenceof the ratio 6 with and without feedbackfor two emissiondirectionsfor the diode of Fig. 2 with lens. directions. With the feedback circuit we can compensate the optical excess noise of the LED but not the excess noise inherent to the photodiode itself. The nearly complete compensation of the optical excess noise of the LED in a range where y is well below 1 is explained by the fact that y takes into account the total noise of the photocurrent (see eqn (11))and not only the noise which is in excess of the shot noise. It is remarkable that for the two significant emission directions (15”, 345”) it was not necessary to alter the phase shift ‘although the phase angle 19 of the cross correlation factor y changed from 0 to 180”as displayed in Fig. 4. Substituting the constant voltage source E in Fig. 6 by a variable source U that expresses the influence of the feedback and supply circuit, the sensitivity behavior of the circuit can be expressed as follows
(17) Equation (17) shows that the sign of d& can be changed depending on the magnitude of the last term of the right hand side which can be altered by means of the feedback circuit [see also eqn (9)]. Therefore the influence of fI on
The experimental results presented in this paper shol that the correlation between light noise and current nois of LED’s depends not only on diode current but also o the direction in which the photons are emitted. The resuli extend those presented in [8] where a dependence of ligf noise on the direction of emitted radiation was reported. The absolute value of the coherence function varie strongly depending on whether the radiation is emitte through the plastic lens on the LED or not. Diodes wit lens have shown a much stronger crosscorrelation. W have made use of this fact in order to develop a optoelectronic feedback method to reduce the light nois of the LED. The results are excellent in the I/f frequent domain where the excess light noise virtually disappear: We believe that LED sources without excess light nois can find promising applications in optoelectronic circuits. Acknowledgements-The authors wish to thank Prof. Dr. N Strutt for his support of the work. They also wish to thank th Swiss National Science Foundation for financial support of thi project. REFERENCES
1. See for example: A. van der Ziel, Proc. IEEE, Vol. 58, No. pp. 1178-1206 (1970); J. Conti, Thesis No. 5250 Swiss Feder Institute of Technology Zurich, (1974); T. J. Hazendon, Thesis University of Amsterdam (1973). 2. G. Guekos, Thesis No. 4350, Swiss Federal Institute ( Technology Zurich, p. 42 (1974). 3. T. P. Lee and C. A. Burrus, IEEE J. of Quantum Electronic QE-8, 370 (1972). 4. J. J. Brophy, J. Appl Phys. 38, 2465 (1967). 5. N. B. Lukyanchikova, N. P. Garbar, N. K. Sheinkman and h N. Zargarjantz, Solid St. Electron. 15. 801 (1972). 6. N. B. Lukyanchikova, M. K. Sheinkman, N. P. Garbar and ! V. Svechnikov, Physica 58, 219 (1972). 7. G. Guekos and M. Strutt, IEEE J. of Quantum Electronic QE-4, 502 (1968). 8. J. Conti and M. Strutt, IEEEJ. ofQuantum Hectronics QE-1 815 (1972). 9. J. Bendat and A. Pierson, Measlrremenr and Analysis c Random Data. Wiley, New York (1966). 10. H. M. Fijnaut and R. J. J. Zijlstra, J. Phys. D3, 45 (1970). 11. G. Guekos and M. Strutt, Proc. IEEE 58, 949 (1970).