Critical Optical Power Density in PIN-Photodiodes M. Meister ∗ , M. Reinhard ∗ , U. Liebold ∗ , D. Kirsten ∗ , D. M. Nuernbergk ∗ ∗ Institute for Microelectronics and Mechatronic Systems GmbH 98693 Ilmenau, Germany e-mail:
[email protected]
chosen. It is known that a higher reverse voltage influences RF-performance [8] and increases the 3dB frequency response of the photodiode. Nonetheless, an effect of the optical power density of the incident light on the RF-performance of PIN photodiodes can be shown. This article summarizes the measurement results and verifies the observed effect by numerical simulations. An analytical equation describing the critical optical Index Terms—PIN, Photodiode, critical optical power, power density is derived and compared to measureRF behavior, laser spot, high current space charge effect ments. This basic model allows physical insight in the phenomenon and the parameters like doping NA , width of the epi-layer Wepi and the reverse bias I. I NTRODUCTION voltage Vr . The findings of this paper are important Silicon optical integrated circuits (OEIC) require for system and circuit design engineers to guarantee fast photo detectors to implement optical intercon- the high system performance of OEIC. nects, optical data transmission via fibers or optical storage systems like CD-ROM, Digital Versatile II. S POT AND BANDWIDTH MEASUREMENTS Disc (DVD) and Blu-ray Discs (BD). To achieve To characterize PIN photodiodes for Blu-ray apsufficient data rates of 432 Mbits/s or 54 Mbyte/s plications, measurements were performed on wafer the required bandwidth of an integrated circuit is 400 MHz [1], [2]. Furthermore, a 12x Blu- for a 0.35 µm-CMOS technology with a 400 nm ray system has to support 3 different wavelengths laser source for the optical stimulation and a spec(λ = 405 nm, λ = 650 nm and λ = 780 nm). This trum analyzer as tracking generator. Various reverse requires a silicon photo detector that works faster voltages and different laser spot sizes were used [9]. The details on the measurement setup, test structhan the whole IC. tures and determination of the optical power density Therefore, the application of PIN photodiodes to detect the optical signal is state of the art [3], can be found in [9], [10]. In figure 1 two frequency [4], [5], [6]. PIN photodiodes contain a pn-junction responses of a photodiode at different spot characwhere the highly doped p- and n-diffusion areas are teristics are displayed. Measurements of the DCseparated by an almost intrinsic epitaxial semicon- sensitivity showed no such dependence on the spot ductor layer. The i-layer (epitaxial layer) is fully size of the laser. A frequency response change of PIN photodiodes depleted at higher reverse bias voltages and photo generated carriers achieve saturation velocity in the can be found by defocusing the laser spot (figure 1). space charge region [7]. Neglecting the capacitance The 3dB frequency increases for wider laser spots of the space charge region and the series resistance up to the maximum. Hence, it is concluded that of the contact system or parasitic capacitances, the there is a dependence on frequency response and transit time is mostly influenced by the carrier drift, incident optical power per unit area (refer to figure which is a fast transport process. Therefore, PIN 2). To gain a more detailed insight to the phephotodiodes feature a very good RF-performance if the width of the epitaxial layer Wepi is well nomenon, measurements with different spot sizes Abstract—PIN photodiodes are often used in optical integrated circuits. Although they can feature a very good RF-performance, this can be effected by the optical power density of the incident light. The influence of this effect on the RF-performance of PIN photodiodes is described. When a critical optical power density in the epi-layer is exceeded the 3dB frequencies are cut off. An analytical equation is derived to describe the effect. The results are compared to RF measurements and verified by numerical simulation.
at constant light power were carried out. So the light power density was swept for different reverse voltages. The results are shown in figure 2 and as a contour plot in figure 6 (left hand side of figure 2). The three-dimensional plot shows the 3dB frequency of the photodiode in dependence of the reverse bias voltage Vr and the object lens height z. A low reverse bias voltage Vr and focussed light (z ≈ 0 µm) result in decreased bandwidth values. Changes in the 3dB frequency from f3dB,max = 800 MHz down to 20 MHz were found [11]. So the dynamic range is limited by the incident light power density. III. T HEORY
AND
S IMULATION R ESULTS
Following [12], figure 3a) shows a schematic drawing of the internal field distribution across the epi-layer of the diode. The two cases included are depletion and an ohmic voltage drop across the non-depleted epi-layer. The junction is assumed to be single sided abrupt and to have a constant epidoping NA . The thickness of the epitaxial layer and depletion layer is Wepi and xD , respectively. Using the voltage drop across the internal junction VJ , the thickness of the depletion region is given by: xD = xD0
v u u ·t
1 + VJ /Vbi 1 − JP hoto /JHC
xD ≤ Wepi
(1)
q
with xD0 = 2 · ε0 · εSi · Vbi /(q · NA ) and the builtin voltage Vbi . It is assumed that the field in the depletion layer is high enough to cause the holes to travel with saturation velocity vsp , therefore, the limiting current is JHC = q·vsp ·NA . The modulation of the space charge region by the photo-generated carriers is described by the term 1 − JP hoto /JHC in equation (1). The space charge region is pushed towards Wepi if JP hoto ≈ JHC and total depletion of the junction occurs (refer to figure 3b) ). At this point the critical current density JP hoto,c is reached. The photo-current is related to the optical power density by the DC-sensitivity of the photodiode S = f (λ) = JP hoto /Popt . Therefore, it is possible to derive a relation for the critical optical power density of a photodiode. Combining the equations above using xD = Wepi yields: Popt,c
1 1 + VD /Vbi − (Wepi /xD0 )2 = · Wepi (W /x )2 S − epi D0 q·Vbi ·NA ·µp
q·vsp ·NA
(2)
The measured sensitivity S of the PIN photodiode is shown in figure 4 for λ = 0.35...1.05 µm [11] and used in equation (2). Figure 5 displays the corresponding critical optical power densities for the same range of wavelength and for different reverse bias voltages. The parameters used for equation (2) are Vbi = 0.68 V, NA = 2.88 · 1013 cm−1 , xD0 = 5.94 µm and Wepi = 6.32 µm. The critical optical power density increases linearly with reverse bias voltage and nonlinearly with the doping NA . With higher doping levels the space charge capacitance rises. As this is not favorable for input capacitance of transimpendance amplifiers, there is a trade-off between capacitance of the photodiode and the critical optical power. Figure 6 shows the comparison between the normalized 3dB frequencies at λ = 400 nm and the model equation (2). The save operating area with good high frequency behaviour of the photodiode is limited to the area encircled by the yellow symbols. The model equation gives a good estimate for this area. It can be seen that the critical power density is very sensitive to the epi-layer thickness Wepi . Similar results are achieved by numerical simulations (refer to figure 7). After total depletion the internal pn-junction is forward biased. In addition to the photo generated carriers, this causes an injection of mobile carriers into the epi-layer. The total storage charge in the epitaxial layer is the sum of these photo generated and injected carriers: Qepi = q · Aspot ·
Zxi
(n + p)dx
(3)
0
The main difference between the epi-layer of a photodiode and an epi-layer in a bipolar transistor [12] is that the transport of both types of carriers, electrons and holes respectively, has to be taken into account. The storage of mobile carriers in the epi-layer causes a significant increase of the diode capacitance. dQepi (4) dV CSCR is the space charge capacitance without any illumination. The carrier transport changes from fast drift with almost saturation velocity to low diffusion. The increase of the capacitance in the epi-layer up to a factor of 40 reduces the f3dB as can be seen from numerical simulations of the CD = CSCR +
capacitance versus reverse bias voltage and optical power density (refer to figure 8). Following [12] and [13] it is possible to derive a model for the cut off of the 3dB frequencies at high optical power densities of the incident light by integration of the current equation under illumination. IV. C ONCLUSIONS There is a set of parameters where PINphotodiodes have very low speed. This behavior is approached if the power density of the incident light is too high. A simple equation for the critical power density was derived and compared to measurement results. This equation includes velocity saturation of the mobile carriers and ohmic voltage drop in the epi-layer. The reason for the cut down of the 3dB frequencies is the space charge modulation by the photo generated holes. This causes the push out of the space charge region towards the neutral region of i-layer under illumination. At the end of this process the pn-junction is internally forward biased and additional injection of carriers takes place. This increases the stored mobile charge in the epitaxial layer, causing a significant increase of the diode capacitance and, therefore, the degradation of 3dB frequency. The observed effect is important for test engineers, who are doing characterization measurements of photodiodes, as well as for system and circuit design engineers, as the system performance is affected significantly. ACKNOWLEDGEMENTS The authors wish to thank Andreas Voerkel and Konrad Bach (X-FAB Semiconductor Foundries AG) for valuable discussions on photodiodes and providing the input data for the device simulations. The work was funded by the Thüringer Aufbaubank project number 2006FE0395 "Modellierung und Optimierung von Fotodioden und DVD Front End Verstärkerschaltungen". R EFERENCES [1] R. Swoboda and H. Zimmermann. A 2.5-Gb/s Receiver OEIC in 0.6 µm BiCMOS-Technology. IEEE Photonics Technology Letters, 16(7):1730–1732, July 2004. [2] Filip Tavernier and Michel S. J. Steyaert. High-Speed Optical Receivers With Integrated Photodiode in 130 nm CMOS. IEEE JOURNAL OF SOLID-STATE CIRCUITS, 44(10):2856–2867, October 2009.
[3] M. Yamamoto, M. Kubo, and K. Nakao. Si-OEIC with Build-in PIN-Photodiode. TED, ED-42(1):58–63, January 1995. [4] M. Kyomasu. Development of an Integrated High Speed Silicon PIN Photodiode Sensor. IEEE Transactions on Electron Devices, ED-42(6):1093–1099, June 1995. [5] S. Malyshev and A. Chizh. High-speed Photodiodes for Radio-on-fiber Communication Systems. Proceedings of the Symposium on Photonics Technologies for the 7th Framework Program, pages 286–290, October 2006. [6] Kartikeya Murari, Ralph Etienne-Cummings, Nitish Thakor, and Gert Cauwenberghs. Which Photodiode to Use: A Comparison of CMOS-Compatible Structures. IEEE SENSORS JOURNAL, 9(7):752–760, July 2009. [7] Keith J. Williams, Ronald D. Esman, and Mario Dagenais. Effects of High Space-Charge Fields on the Response of Microwave Photodetectors. IEEE Photonics Technology Letters, 6(5):639–641, May 1994. [8] H. Zimmermann. Integrated Silicon Optoelectronics. Springer Verlag, Heidelberg, London, New York, Dortrecht, 2. edition, 2009. [9] M. Reinhard, U. Liebold, G. Methner, M. Meister, and D. Nuernbergk. Test structure for the characterization of the laser spot size for the modelling of the rf behavior of pin-photo diodes. Analog 2010, 11:103–108, March 2010. [10] M. Reinhard, M. Meister, U. Liebold, T. Cohrs, and D. Nuernbergk. Erhöhung der Testqualität für optoelektrische Schaltungen durch Charakterisierung des Strahlprofils. 22. GI-GMMITG-Workshop, pages 286–290, October 2010. [11] Process Specification XO 035 - 0.35 µm Modular CMOS for Fast Optical Applications. XFAB-Semiconductor Foundries AG, Release 1.0, 1. edition, 2009. [12] H.C. de Graaff and W.J. Kloosterman. Modeling of the Collector Epilayer of a Bipolar transistor in the MEXTRAM Model. TED, ED-42(2):274–282, February 1995. [13] S.M. Sze. Physics of Semiconductor Devices. John Wiley and Sons New York, Chichester, Brisbane, Toronto, Singapore, 1. edition, 1981.
3
f 3dB = 52 MHz 0
f 3dB = 74 MHz
Laser−beam lens System
S / [dB]
−3
z
−6
large visible Laser spot
visible Laser spot
small visible Laser spot (focus)
11111111 00000000 00000000 11111111 n+ p+ p+
0
−9
i
p
PIN−Photodiode 1e+06
1e+07
f / [Hz]
1e+08
1e+09
Fig. 1. Measurement setup and measurement results for the frequency response of the PIN photodiode for different laser spot sizes. The variation of 3dB frequencies with the spot size (or focus height) is shown. (wavelength λ = 400 nm)
Fig. 2. 3 dB frequencies versus focus and reverse bias voltage (wavelength λ = 400 nm)
E
E Wepi
xD
xj = 0
x
Wepi
xj = 0
x
J Photo > J HC Popt
Vj
Emax
J Photo < J HC
R‘ J Photo VD
a) depletion and ohmic voltage drop E Wepi
Low carrier velocity Large charge storage
c) injection and charge storage
x
Wepi
xj = 0
x
0
E / [V/cm]
xj = 0
b) total depletion
Popt= 0...200W/cm
2
x / [um] d) Numerical results
Fig. 3. Electrical field distribution for a) depletion and ohmic voltage drop across the epi-layer, b) for total depletion of the epi-layer. c) injection of carriers because of the forward biased internal pn-junction for different optical wavepower. d) Simulation results.
200
0.6 Sensitivity theor. Limit
0.5
2
P opt,c / [W/m ]
S / [(A/cm 2)/(W/cm 2)]
150
0.4
0.3
0V
100
=1
V
D
V
D
=7
.0 V
0.2 V
50
.5 V =5
D
.5
V
0.1
=1
V
0
0.5
0.4
0.6
0.7 λ / [µm]
0.8
0.9
1
0.4
1.1
0.5
0.6
0.7
f3dB /f3dBmax / [1]
0.5
0.4 0.3 0.2
0.9
6.0
2.0
10 Model 10
100
P opt / [W/cm 2]
1
9
8
7 6 V D/ [V] 5 4
3
2
120
40
60
8
7
6
VD / [V]
39.8 25.1 15.8 10 6.31 3.98 2.51 1.58
10
9
1000
Fig. 6. Normalized 3 dB frequencies f3dB /f3dB,max versus optical power and reverse bias voltage (wavelength λ = 400 nm)
10
1
0.01
0.7 0.6
100
1.1
1 0.631 0.398 0.251 0.158 0.1 0.0631 0.0398 0.0251
0.1
0.0
1
0.1
0.8
4.0
0.9
Fig. 5. Critical optical power density Popt,c for different wavelengthes and reverse bias voltages using equation (2) and the measured sensitivity of the diode.
10
8.0
0.8
λ / [µ m]
Fig. 4. Measured sensitivity S of the photodiode versus wavelength λ [11]. The diodes are optimzed for blue light (The blue line is the fundamental limit for the sensitivity.)
V r / [V]
V
VD
0
C /C min / [1]
=2
D
160 120 140 80 100 2 P opt / [W/m ]
180 200
Fig. 8. Simulation results of the normalized capacitance versus optical power and reverse bias voltage (wavelength λ = 400 nm)
5
4
3
2
120
40
60
180 200 140 160 120 80 100 Popt / [W/m 2 ]
Fig. 7. Simulation results for the normalized 3 dB frequencies versus optical power and reverse bias voltage (wavelength λ = 400 nm)
