Yih-Guei Wey, Kirk Giboney, John Bowers, Mark Rodwell, Pierre Silvestre, Prabhu Thiagarajan, and Gary Robinson
Abstract- Long-wavelength GaInAsIInP graded double heterostructure p-i-n photodiodes are demonstrated with 3-dB bandwidths over 100 GHz. The heterojunction hole trapping problem is significantly improved and the device contact resistivity is greatly reduced by using superlattice graded bandgap layers at the hetem-interfaces to reduce the barrier height. Selfaligned processes are used in the device fabrication to reduce device parasitics. Pulsewidths as short as 3.0 ps fnll-width-at-itshalf-maximum (FWHM) for 2 iLm x 2 16m device are measured by pump-probe electrooptic sampling. 3-dB bandwidths over 100 GHz are found for 2 ,Lm x 2 /Lm and 3 /Lm x 3 /Lm devices. The device with the integrated bias tee can be biased without nsing the external bias tee. The electrical resonance between the photodiode and external circuits was reduced by integrating an impedance matched resistor in parallel with the photodiode. The 7 /Lm x 7 p,m device with bias tee and matched resistor bas a measured pulsewidth of 3.8 ps and a 3-dB bandwidth over 100 GHz. The calculated pulse shape based on the saturation velocity model fits well with the measured response. A model for different components of the series resistance agrees with the measured area dependence of the series resistance.
I. INTRODUCTION
HIGH-SPEED GaInAslInP photodiodes are needed in long-wavelength applications such as ultrafast optical
communications and measurement. High-speed waveguide p
ion photodiode has been reported in [1]. The bandwidth of high-speed vertically-illuminated, photodetectors is limited by carrier transit times, RC time constant and hole trapping [2J-[4J. In this paper we will focus on reducing hole trapping and p-contact resistivity in order to fabricate high-speed vertically-illuminated, p-i-n photodetectors. Hole trapping is
caused by the hetero-barrier at the intrinsic GaInAs and p
doped InP interface. The contact resistivity is dominated by the barrier resistivity of the contact p+GaInAs/p-InP heterojunction [S]. The former further slows down the transit-time limited response of the photodiode while the latter increases the device
series resistance resulting in reduced RC bandwidth. Both of the problems have been greatly improved by introducing
Manuscript received December 3,1993; revised March 15,1995. This work wa; supported by the Office of Naval Technology Block Program on Electr()Optics Technology, DARPA, ULTRA, and Rome Laboratories.
y.·G. Wey was with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93 \06. He is now with AT&T Bell Laboratories, Murray Hill, NJ 07974 USA.
K. Giboney, 1. Bowers, and M. Rodwell are with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106 USA.
P. Silvestre, P. Thiagarajan, and G. Robinson are with the Department of Electrical Engineering, Colorado State University, Fort Collins, CO 80523
USA. IEEE Log Number 9412219.
superlattice bandgap grading layers so that the hole trapping effect is eliminated and p-contact resistivity is reduced.
The material is grown by gas source molecular beam epitaxy
(GSMBE). A self-aligned technique was used in fabricating small active area devices. The device response was measured with a Ti:Sapphire laser based electrooptic sampling system operated at 972 nm. The measured responses for 2 J.!m x 2 J.!m devices have puIsewidths as short as 3.0-ps FWHM. The 3-dB bandwidths of 2 J.!m x 2 J.!m and 3 J.!m x 3 J.!m devices are over 100 GHz. This indicates that the hole trapping problem is reduced and the RC bandwidth limitation is much increased due to the improved graded bandgap layers. Photodiodes are integrated with bias tees for large usable bandwidth.
The bias tee device with matched resistor will have low mismatch reflection when connected with other circuits. The 3-dB bandwidth of the 7 J.!m x 7 J.!m device is over 60 GHz without matched resistor and over 100 GHz with matched resistor. Further analysis of the frequency response based
on the theoretical model is investigated. Modified design curves for double heterostructure GaInAslInP p-i-n diode are calculated.
II. PHoTODIODE STRUCTURE
The photodiodes described in this paper are backside illumi
nated mesa diodes (Fig. 1). The mesa sidewalls are polyimide passivated. TilPtJAulNi is used as the p-metal and AuGelNiiAu as the n-metal. The final metallization forms the coplanar
waveguide structure for device testing. There is a single-layer anti-reflection film on the polished backside. The material
was grown by GSMBE and was lattice matched to a (100) semi-insulating (SJ) InP substrate as shown in Fig. 2. The growth temperature was SOO°c. Thermal decomposition of the gases PH3 and AsH3 was used to produce the P2 and AS2 molecular beams. The growth rates were O.S J.!m/h for InP and 0.9 J.!m/h for GaInAs. The doping levels of p+GaInAs, p+InP and n+InP are as high as possible so that the ohmic resistance
and other series resistance components were minimized. There were 6.6-nm-thick graded bandgap layers (GBL) at each hereto-interface. The GBL consists of unintentionally doped
GaInAs/GaInAsPlInP layers. The bandgap wavelength .Ay of GaInAsP is US J.!m.
Three types of photodiodes were fabricated and measured: 1) p-i-n photodiode, 2) photodiode with a bias tee, 2) photodiode with a bias tee and a matched resistor. The bias diodes and matched resistors were placed very close to the photodiode to reduce electrical reflection. Fig. 3(a) shows the layout of the device with bias tee and matched resistance. The N-metal
Fig. 1. Cross section of a high-speed GaInAslInP p-i-n photodiode.
GBLll GaInAsP 0.6 om
InP 1.2om
GainAsP 0.6 om loP 0.6nm
GainAsP 0.6 om loGaAs 0.6 om
GainAsP 0.6 nm InGaAs 1.2nm
GaIoAsP 0.6 om
�
II
p+InG�O� (Be 5xiO em-)
GBL I 6.6 nm p+loP 300 om (Be 3xiO 18em-3)
GBLII 6.6 om iloGaA. �01l1:J
(u.d. 0 - 5xiO em ) GBLID 6.6nm
0+ loP 400 om (Si 3xl0 18cm-3)
u.d. InGaAs 5 nm
S.I. loP .ubstrate
Fig. 2. GSMBE grown material.
I
1\
\
GBLI GaInAsP 0.6 nm
InGaAs 1.2nm KJaInAsP 0.6 nm
InGaAs 0.6 nm GaInAsP 0.6 om
InP 0.6 nm GaInAsP 0.6 om
InP 1.2 om GaInAsP 0.6 nm
GBL III GalnAsP 0.6 nm
InGaAs 1.2nm GaloAsP 0.6 nm
InGaAs 0.6 om GaloAsP 0.6 om
loP 0.6 nm GalnAsP 0.6 nm
loP 1.2 nm GaIoAsP 0.6 nm
layer is not shown in Fig. 3(a) because it is covered by final metallization. The coplanar waveguide has 50 n impedance with a gap to center metal ratio of 9: 11. the bias capacitors are large reverse-biased photodiodes in paralleL Fig. 3(b) shows the equivalent circuit of the device.
III. GRADED BANDGAP LAYER
For high-speed device with small ohmic contact area, the p-contact resistivity usually is a dominant factor. With a pcontact grading layer, the p-contact resistivity was reduced to a value comparable with the resistance due to the nlayer and n-ohmic contact. The calculated band diagram of an abrupt interface double heterostructure GalnAslInP p-i-n photodiode is shown in Fig. 4. Since the ohmic resistivity on p+lnP is usually very high (�1O-4 n·cm2), a p+GalnAs contact layer on top of p+InP can bring the contact resistivity down about one order of magnitude. However, it is still not good enough_ For high-speed devices, the contact area is very small, typically less than 100 J.Lm2• The required ohmic contact resistivity should be around 10-6 n·cm2 or better in order to have a device series resistance less than the 50 n load. For an abrupt contact interface (Interface I), the calculated hetero-barrier height for hole is 0.2 eV. If we can lower the hetero-barrier height, the total contact resistivity can be lowered. The resistivity reduction will be discussed in a later section. Interface II has a barrier height for hole of 0.3 eV
Fig. 3. Bias tee device with matched resistor. (a) Device layout. (b) Equivalent circuit.
Interface I Inlerface II
n-InP
600 700 800 p+ GalnAs Distance from surface (nm)
. contact layer
Fig. 4. Band diagram of an abrupt GalnAs/InP p-i-n photodiode.
at the p-InP/i-GalnAs heterojunction. This barrier will cause a severe hole trapping problem that limits the bandwidth. The process for the trapped hole to re-emit through the barrier further slows down the hole response due to the transit time. The trapping time is estimated to be about 5 ps for the abrupt interface in [6]. For high-speed devices with bandwidth over one hundred gigahertz, the trapping time needs to be much smaller.
The calculated band diagrams near interface I and II are shown in Fig. 5 for wafer I and II. The dotted lines are the calculated band diagram assuming that the bandgap changes
1492
O. 2 ��r---'Irnte",rfra",ceT-I:...,..--.---, � O.l >: 0.0 tf =-0.1
Fig. 5. Heteco-barrier height of valence band at the graded interfaces. (a) Wafer I. (b) Wafer II.
abruptly at each heterojunction. For hole transport, the carrier will not see an abrupt band edge but an averaged band edge since each layer is much thinner than the bulk hole wavefunction_ The solid line shows the averaged band structure. In wafer I, the hetero-barrier heights are 0.115 e V at both helerointerfaces. Compared with barrier heights of 0.2 e V and 0.3 e V for abrupt interfaces, the hetero-barrier heights are about 58% and 39% of their original values. Graded interface I can be directly tested with a modified transmission line measurement (TLM) pattern using reactive ion etching (RIE) to remove the p+GaInAs contact layer. The reason to use RIE dry etch rather than wet etch is that wet etch tends to degrade ohmic contact. Fig. 6 shows the current flow in the hetero-barrier TLM test structures. The current flows predominantly through the p+GaInAs contact layer if it is not etched away. After the p+GaInAs contact layer is removed by RIE, the current has to flow through the p-InP layer. The total p-contact resistivity of a photodiode can be determined when p+GaInAs layer not covered by p-metal is etched away. The contact layer with GBL has a contact rcsistivity fc of7.5 x 10-7 n·cm2 without removing the p+GalnAs layer. The contact resistivity increases to 1.5 x 10-6 n·cm2 for wafer I after RIE. The measured contact resistivity is twice that of the wafer without the RIE etch. For comparison, the abrupt contact interface (without GBL) is also tested with TLM pattern. The contact resistivities of an abrupt interface wafer without RIE and with RIE etch are 9.7 x 10-7 n·cm2 and 3.0 x 10-5 n·cm2, respectively. The total ohmic contact resistivity of the abrupt interface wafer is 20 times that of the graded interface wafer.
For wafer II, a longer graded bandgap layer (18.6 nm) is designed and GBL-I consists of 2 periods of InP(0.9 nm)/GaInAs(1.5 nm), 3 periods of InP(1.5 nm)/GaInAs(1.5 nm) and 2 periods of InP(1.5 nm)/GalnAs(0.9 nm). GBL-II is arranged in reverse order of GBL-I. The barrier height is 0.16 eV at both interfaces. The resistivities of samples
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO.7, JULY 1995
(b) Fig. 6. The current flows of the heteco-barrier lLM. Cal Without RIB etch. (b) With RIE etch.
TABLE I TOTAL CON'lACI' R.!;SlTlVITY rc
measured p-conlaCt resitivity(O-cm2) relative value wafer w/o GalnAs elch wI GaInAs etch fclrcA exp(
-.q�b)A
Abrupt Interface 9.7 x 10 .7 3.0xlO-5 1 1 I (Graded Interface) 7.5 x 10-7 1.5 X 10-6 0.05 0.045 II (Graded Interface) 7.0 x 10-7 6.7x 10-6 0.22 0.21
(A = Abrupt Interface)
without and with RIE etch are 7.0 x 10-7 !2-cm2 and 6.7x 10-6 n·cm2, respectively. The resistivities are much higher than those of wafer I due to the higher barrier heights. The exponential factors were calculated assuming that thermionic emission dominates the barrier resistivity. The numbers are 0.045 and 0.21 relative to that of the abrupt interface wafer. Due to the local doping level and band bending at the heterointerface, thicker GBL in wafer II does not result in lower barrier height than that of wafer L Table I summarizes the measured resistivities and the exponential factors. It can be clearly seen that the hetero-barrier resistivity is the dominant factor in the total p-contact resistivity.
IV_ FABRICATION
The p-metal consists of Ti(50 nm)lPt(75 nm)/Au(150 nm) with Ni(l OO nm) as a mask for el2 RIE. The p-metal is liftoff with a trilevel mask which consists of PMMA(l Jim), Si(50 nm), and AZ411O(1 11m). The undercut of PMMA is performed with O2 plasma enhanced etching followed by buffered HF (BHF) cleaning of residual scum to ensure good metal lift-off. After the p-metal lift-off, the p-mesa is etched with Cl2 RIE until etching through the intrinsic GalnAs layer. 200 nm thick Si02 is deposited with plasma enhanced chemical vapor deposition. A combined CF4 plasma etch and BHF ctch is used to pattern the Si02 mask for
IHCl: IH2 0 wet etching of the n-lnP layer. The stop etch layer is removed by IH3P04: IH202 : 38H20 and the Si02 mask is removed. The n-metal consisting of AuGe(50 nm)/Ni(7.5 nm)/Au(lOO nm) is lift-off using a trilevel mask. The ohmic contact annealing is perfonned by rapid thennal annealing (RTA) at 420°C for 30 s in N2 ambient. The mesa sidewall is etch cleaned with IH2S04: 1H202 : 100H20 for 5 s prior to passivation. Dupont PI2723 polyimide is immediately spun on at 5000 rpm and photolithographic ally patterned. The polyimide is then cured up to 370°C (thickness �1 /-Lm)AZ4330 is spun on and softbaked as a planarizing layer. 02 RIE is used to etch away the polyimide on the mesa top and expose the p-metal for final metallization. Afterward, the residual AZ4330 layer is removed. The Ti(25 nm)/Au(400 nm) layer is lift-off with AZ4110 mask. The wafer is then chemicalmechanically polished with bromine methanol. The silicon nitride anti-reflective coating with a center wavelength at 1.3 /-Lm was deposited on the polished backside with a reactive sputtering machine.
Fig. 7(a) shows the picture of a photodiode with its coplanar waveguide transmission line, which is tapered from photodiode gradually to the bondpad. The bondpad has a center metal of 55 /-Lm and gap width of 45 /-Lm. Fig. 7(b) shows the scanning electron microscope picture of a photodiode. The dark film around the mesa is the polyimide layer. The center metal reaches to the mesa top and the ground-plane metal covers the n-metal.
V. MEASUREMENTS AND RESULTS
A. Photodiodes
The response of the high-speed photodiode was measured by an electrooptic sampling system [7] based on a Ti:Sapphire laser. The passively modelocked Ti:Sapphire laser generates a pulse train at 105 MHz repetition rate with 200 fs FWHM autocorrelation. The operating wavelength is 971.7 nm and the average output power is �IOO mW. Fig. 8 shows the electrooptic sampling measurement setup. The Ti:Sapphire laser output is split into two beams. The pump beam is chopped with an acoustooptic (AO) modulator at 1 MHz, and the probe beam is sent through a motorized variable delay stage. A tuned receiver is used along with the AO modulator for lock-in detection. A microwave probe is used for 50 n tennination and the dc bias is connected through a bias tee. The photoresponse is monitored with a sampling oscilloscope.
The external quantum efficiency measured on a 30/-Lm x 30 /-Lm photodiode with AR coating optimized for 1.3 /-Lm is 50% at 0.97 /-Lm. If the measurement wavelength is 1.3 /-Lm, the hole contribution to total current will be less than that at 0.97 /-Lm, therefore, the bandwidth will be higher at 1.3 /lm. Fig. 9(a) shows the bias dependent response of a 2 /-Lm x 2 /-Lm device on wafer I under low excitation intensity (�9 fJ of absorbed optical energy per laser pulse). The 2 /-Lm photodiode has a leakage current of about 200 nA at -4 V bias. The device series resistance is 158 n. At zero bias, the pulsewidth is broad and the responsivity is low. As the reverse bias increases, the pulsewidth becomes shorter and the tail becomes smaller.
Ca)
(b)
Fig. 7. A finished p-i-n photodiode. Cal Photograph of a device. Cb) SEM picture of device mesa.
Also, the photocurrent is higher than that at 0 V bias. This means that the intrinsic region is not fully depleted at zero bias. At -2 V bias, the pulsewidth is 3.0 ps FWHM with a small tail at the trailing edge of the response. This tail is due to hole trapping. At -3 V, the tail almost disappears. The pulsewidth decreases at first and increases when reverse bias increases over 2 V. This is due to the increase in the
1494
0.8 n-rrn-n-n-rnrnrn-n-n-n.".,
�
0.6
0.4 Ii""--wr
E 0 @' r-_""",.. ..:
·0.2
Time (ps) (a)
-1.5V
-2V
l.5 n-r-rr-rTTTTTTTTTTTTTTTTTT'Tl
0.5 """,, __ ,,",
-0.5
- 1
10 20 30 Time (ps) (b)
40
OV
-O.5V
-l.OV
-1.5V
-2.0V
-3.0V
-4.0V
50
Fig. 9. Responses of a 2 /lm pholOdiode on wafer I. (a) Low excitation intensity. (b) High excitation intensity.
depletion layer thickness since the doping concentration at the edge of the intrinsic layer changes to a higher concentration not abruptly. The increase of the depletion layer thickness causes the decrease of junction capacitance and the increase of carrier transit time, resulti ng in the effect of shortening and broadening of the pulsewidth.
The bias dependent carrier velocity was at first suspected to have some effect on the pulsewidth. Based on some calculations, that effect is found to be very small. Fig. 9(b) shows the bias dependent response of a 2 /lm device under high excitation intensity (�44 fJ absorbed energy for each laser pulse). The high excitation intensity is limited by the maximum power available. The pulsewidth becomes broader than that under low excitation intensity and slight saturation due to the space charge effect is observed. The space charge effect is due to the electric field reduction resulting from the high photocarrier density inside the depletion region and charge separation. Again, pulsewidth initially decreases as the reverse bias increases. The response at -3 V bias has the shortest
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO.7, JULY 1995
J
\0 20 50 Time (ps)
Fig. 10. Responses of a 4-/lm device on wafer IT under low excitation.
response rather than that under low excitation at -2 V. The shortest pulsewidth at -3 V under high excitation intensity is reached when the space charge effect [8] and the reduction of the hole trapping is best compromised. Further increase of the reverse bias results in a broadened depletion layer thickness and the pulsewidth increases as under low excitation.
For comparison, the bias dependent responses of a 4 /lm x 4 /lm device on wafer II were measured under low excitation (shown in Fig. 10). The responses have a big tail as the reverse bias varies from -1 V to -4 V. The hetero-barrier height is reduced by the applied bias, but not enough to eliminate hole trapping before the reverse breakdown. This is because the longer graded bandgap layer in wafer II has a higher heterobarrier and it is relatively insensitive to the reverse bias as in wafer I.
The ringing after the photodiode pulses in Figs. 9 and 10 is due to reflections from the microwave probe. The frequency responses will also show the artifact ringing due to the reflections. Since the reflection occurs with a period longer than the pulse width, its effect on the calculated frequency response can be removed by eliminating the ringing portion of the time waveform. The maximum bandwidths were obtained at -3 V bias for various device sizes. Fig. l1(a) shows the frequency responses of various size devices from wafer I under low excitation. Fig. I I (b) shows the 3-dB bandwidth versus device size. For the 2 J.tm x 2 J.tm and 3 /lm x 3 J.tm devices, the bandwidths are 110 GHz and 109 GHz, respectively. The 4 /lm x 4 J.tm device has a bandwidth of 95 GHz, 5 /lm x 5 J.tm device 66 GHz and 7 11m x 7 J.tm device 63 GHz.
B. Photodiodes with Bias Tees and Without Matched Resistor
The 7 J.tm x 7 J.tm device with bias tees has a forward resistance of 20 n and the reverse leakage current of 200 nA at -4 V. The reverse biased bias diodes have a leakage current of 5.4 itA at -4 V. During the electrooptic sampling measurement, a lOO-J.tm pitch microwave probe on device ac port is connected to an external bias tee with a dc termination of 50 n and the ac output is monitored by a sampling osciIIoscope. The measurement is performed under low excitation (�20 fJ of absorbed optical energy per laser pulse).
These results are shown in Fig. 12(a). The pu)sewidth of the photodiode response at 0 V bias was very broad and the efficiency was low. At -1 V bias, a small tail can
Fig. 11. Frequency responses of various size devices on wafers I. (a) Frequency responses of various size photodiodes. (b) Photodiode 3-dB electrical bandwidth versus device area.
still be seen at the falling edge of the response and the
pulsewidth becomes much narrower (5.0 ps). At -3 V bias,
the pulsewidth becomes the narrowest (4.4 ps) and tail is
also much reduced. At -4 V bias, the pulsewidth becomes
broadened again (4.6 ps). This slight increase in pulsewidth
could be due to the increased depletion layer thickness or the
measurement fluctuation. Fig. 12(b) shows the corresponding
frequency responses of each time domain response. The 3-dB
bandwidth of zero bias response is only 15 GHz. As the bias
increases, the 3-dB bandwidth increases to 55 GHz at - I V bias and over 60 GHz at -3 and -4 V bias.
Fig. 13 shows the measured impedances from 45 MHz to 40
GHz of the 7 /Jm x 7 /Jm device with bias tees on wafer I, with
and without the matched resistor. The impedance of the device
with bias tee and without matched resistor has an open circuit
impedance at low frequency and capacitively revolves toward
short circuit at high frequency. The impedance of the bias tee device with matched resistor has an impedance close to 50 n
from low frequency to high frequency. The matched resistor
effectively reduces the device load impedance and consumes
some output power from the photodiode. The bandwidth is
increased and the device efficiency is reduced.
C. Photodiodes with Bias Tees and Matched Resistor
The 7 /lorn x 7 /Jm device has a series resistance of 17 n and
a leakage current of 400 nA at -4 V. The total leakage current
of bias diodes is about 12 /loA at -4 V. During the electrooptic
sampling measurement, the dc port is used to provide the dc
bias and a microwave probe is connected to the device ac
0.5
-0.5
10
40
20 30 Time (ps)
(a)
80 120 Frequency (GHz)
(b)
OV
-I
-2
-3V
-4V
40 50
160 200
Fig. 12. Responses of a 7 I'm device with bias tees and without matched resistor. (a) Bias dependent time responses. (b) Bias dependent frequency responses.
45 MHz - 40 GHz wI Matched Resistor: r, S-15dB
SWRSI.41
wlo Matched Resistor: fs S -I. 9dB
SWRS9.25
Fig. 13. Measured impedances of a 7-l'm device with bias tees on wafer I.
port without using an external bias tee to provide the dc 50 n
load. The ac output is monitored by a sampling oscilloscope.
Fig. 14(a) shows the traces at different biases. At zero bias,
the pulsewidth is very broad but it is much shorter than that
shown in Fig. 12(a) for device without matched resistor. The
reduced effective series load resistance (�25 n) results in a
much faster RC discharge time for the space charge saturated
device under zero bias. Further increase in reverse bias results
in faster response than those of the devices without matched
resistor at low excitation intensity. The pulsewidth remains
the same (3.8 ps) as bias increases from - 1 V to -4 V. The
Fig. 14. Responses of a 7'/lm device with bias tee and matched resistor. (a) Bias dependent time responses. (b) Bias dependent frequency responses.
frequency responses obtained by Fourier transform are shown in Fig. 14(b). The 3-dB bandwidth is over 70 GHz at - J V
and over 100 GHz at -2 V, -3 V, -4 V. The cost of the increased 3-dB bandwidth is that the output ac signal power through the ac port is reduced by half. The other half of the power is consumed in the 50 n matched resistance.
The bandwidth for bias tee devices at - 1 V is apparently limited by hole trapping. At -2, -3, and -4 V, the time and frequency responses change very little for both 7 Mm bias tee device with and without matched resistor. The difference in responses between these two devices is that the device without matched resistor is limited more by the RC time than the device with matched resistor when balanced with the effect of the broadened depletion region under bias. We did not see more prominent pulsewidth changes from -2 V to -4 V in Fig. 14(a) than Fig. 12(a). It could be due to the slight measurement fluctuation. However, the 7 Mm devies are more RC limited than the 2 Mm devices so that the effect of carrier transit time modulation due to the change in depletion width is not so obvious.
VI. ANALYSIS AND DISCUSSION
The photodiode response can be modeled by an equivalent circuit shown in Fig. 15. The current source I.(t) is in parallel with the photodiode junction capacitance C J and junction resistance Rd, and in series with device series resistance Rs plus the bondpad capacitance in parallel with the load impedance ZL. Usually, Rd is very large and its effect is negligible. The circuit transfer function can be simplified as
JOURNAL OF LIGHTWAVE TECHNOLOGY. VOL. 13. NO.7. JULY 1995
follows.
1 [1 - w2(CpZoCJR.)] + jw[CpZo + Cj(R. + Zo)]
(I) where ZL = Zu is typically a 50 n load resistance. The current source due to n-side illuminated photodiode is the sum of electron and hole intrinsic currents. The normalized drift responses are given below
where,), = Vh/Vh and vee Vh) represents the electron (hole) saturation velocity, a is the optical absorption coefficient and W is the active layer thickness. teeth) is the electron (hole) transit time across the depletion region, i.e., W/Ve(W/Vh). u(t) represents a step function. 11 O+\gamma) and ')'/ 0+')') are the normalizing factors due to the fact that the electrons and holes provide different current density due to their different saturation velocities. The term exp (-aW) comes from the exponential-function-like carrier generation at I. = o and exp (-avet) (or exp (avht) describes the process by which the carrier is swept out of intrinsic region with its saturation velocity. The expression for normalized current sources for electron and hole of p-side illuminated photodiode are similarly given by
For n-side illuminated photodiode with a top metal reflection of R"" the normalized response is given by
I. ( ) _-,-,[(_2a�) _+�(_2b�)]�+_ R�m= -x_ ex� p�(_-� a_W�)=x�[(�3�a)�+�(�3�b)] mt t - - [1 + Rm x exp (-aW)]
(4) The effect of hole trapping in time domain can be modeled by the convolution of drift hole response and an exponential function with a time constant of Th. The corresponding frequency response for the interfacial hole trapping is
1 H(wlt,,,p = 1 + . (5) JWTh The net frequency response will be the product of the circuit transfer function and the transit time response including the
Fig. 16. Calculated response of a 2 I'm photodiode.
hole trapping effect. In the GaInAslInP material system, the bandgap offset ratio between the conduction band and the valence band is about I: 2. The conduction band offset is relatively small compared with that of the valence band. Besides, the effective mass of the electron is much smaller than that of the hole. Therefore, the effect of electron trapping is assumed to be negligible, and for the GaInAslInP material system, the time constant for electron, Te, can be set to zero during the bandwidth calculation.
The impulse response of the electrooptic sampling system is subpicosecond and its effect is not included in these calculations. The 3-dB bandwidth of the photodiode is actually greater than the 3-dB bandwidth based on the measured responses. Using the measured R .. Cp = 13 fF, Zo = 50 n and high Rd values, the temporal response and frequency response can be calculated. Fig. 16 shows the calculated response (dotted line) based on this model for a 2 J.lm device. The pulsewidth of the calculated response is 3.0 ps. Compared with the measured 3.3 ps pulse (solid line), the agreement is quite good. The calculated pulse shape for different device areas is shown in Fig. 17(a) and the corresponding frequency responses are shown in Fig. 17(b). As the device area increases, the tail becomes bigger due to a faster RC roll-off. Even for 2 J.lm device, there is still a small tail. The transit-time response limitation has a 3-dB bandwidth of over 140 GHz for 200-nm intrinsic layer thickness. The 2 f1.m device is primarily limited by transit time. For 3 f1.m device, the transit time bandwidth limitation is about equal to the circuit bandwidth. For 4 f1.m or bigger devices, the bandwidth is limited by the RC bandwidth.
Since the device area is very small, the device series resistance becomes very significant. With the improved pcontact resistivity, the total device series resistance becomes comparable with the standard 50 n load resistance for small area devices. Fig. 18 shows the resistance model of a p-i-n photodiode. G, T, W and L represent the gap width, p-InP layer thickness, mesa width, and mesa length, respectively.
ZOOnm intrinsic layer
! 0.2 U 0.1
4 8 10 12 \4 16 Time (ps) (a)
� 0
" _._t.t:ansit-time limit :rl -2 _ 3dB
�
�
------�����
--
��" -... -.. ���
� -4 >. 5 -6 [ !l.o -8
- 100L.L1-L.LLLL.L1l-LLllL.LU...Ll..L.L111..20l..Ul..Cl...illl1lLW200 Frequency (GHz)
(b)
Fig. 17. Calculated photodiode responses and their frequency responses. (a) Time responses of various device size. (b) Frequency responses of various device size.
For a square mesa as in our design, G = 1 f1.m, T = 0.3 f1.m and W equals L. The total resistance consists of the following resistance components
rep Rep = -L-- total p-contact resistance Rep xW (6a)
T2 Rvp = Rp-sheet L X W p-layer vertical resistance Rvp
G Rgn = Rn-sheet W n-layer gap resistance Ryn (6d)
1 . Ren = Ten W L n-layer contact resIstance Ren (6e) x tn
where Tep is the total p-contact resistivity, Rp-sheet is the pInP sheet resistance, Rn-sheet is the n-InP sheet resistance, Tm is the n-contact resistivity, and Ltn is the transfer length of n-ohmic TLM resistance versus gap width plot. The total p-contact resistance includes the p-ohmic resistance on p+GaInAs, p-GaInAs resistance, and p+GaInAs/p-InP interface resistance. The total device series resistance Rs(total) is approximately given by
Table II shows the resistivity parameters for wafer I and wafer II. These resistivity values are measured from the TLM testing. Wafer I has a much lower (total) p-contact resistivity (normalized by area) and a higher n-contact resistivity (normalized by mesa width) than wafer II. Fig. 19 shows the calculated
Fig. 18. Components of series resistance of a p-i-n diode.
10 100 Area (�rn2)
Fig. 19. Series resistance components.
1000 10000
resistance components based on the ideal resistivity values (Le., the best resistivity values among all the GSMBE wafers we have measured) and the square mesa type device geometry shown in Fig. 18. The p-contact and p-Iayer (p-InP) resistances are inversely proportional to the device area and become dominant terms when the device area is less than 10 Jtm2• The n-contact resistance is inversely proportional to the mesa width and becomes dominant for device from 10 11m2 to 200 p,m 2• The spreading resistance due to the current crowding effect becomes dominant for device areas larger than 200 p,m2. Also shown in Fig. 19 are the calculated and measured series resistances of wafer I and II. The measured resistances are higher than those of the calculated resistance due to the degradation of resistance during the fabrication process.
Based on the best of our measured resistance values, the design curves for the high-speed GaInAslInP p-i-n photodiode are recalculated and shown in Fig. 20. The bondpad capacitance is assumed to be 15 fF which is typical for microwave probe on 50 n, 100 11m pitch bondpad. The absorption wavelength is 1.3 p,m. The maximum bandwidths for the 2 p,m
JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO.7, JULY 1995
120
�IOO Q. :g 80
]60 � 40
20
0.1 0.2 0.3 Active layer thickness (I'm)
Fig. 20. Bandwidth versus active layer thickness.
A=1.31'1TI
R1oad=500
Cpa<! = 15 IF Rs (modeled)
Active layer thickness (I'ITI)
0.4 0.5
3.0
Fig. 21. 3-dB bandwidth contours of a GainAslInP p-i-n diode at ,\ = 1.3 I'm.
and 3 11m devices are over 100 GHz at their optimum active layer thicknesses. When the active layer is too thin, the device is limited by the RC bandwidth. On the other hand, the device is limited by the transit time when the active layer is too thick. Fig. 21 shows the 3-dB bandwidth contours of GaInAslInP photodiode in the area versus active layer thickness plane. With the parasitics of the photodiode taken into account, the area for high-speed GaInAslInP is confined to a relatively small comer of the plot. However, for useful photodiode with reasonable efficiency, it is still possible to achieve higher 3-dB bandwidth by reducing device parasitics or by integration with other matched circuits.
VII. SUMMARY
Graded bandgap layers can improve the device series resistance and reduce the hole trapping by lowering the barrier height at the hetero-interfaces. A self-aligned polyimide passivation technique has been developed for device fabrication, A Ti:Sapphire laser based subpicosecond e!ectrooptic sampling system was used for measuring the device responses. A 2 11m photodiode has a 3-dB bandwidth of 110 GHz measured at 0.97 11m. The quantum efficiency is 50% at 0.97 11m and 32% at 1.3 p,m. The bias tee device has bandwidth over 60 GHz without matched resistor and over 100 GHz with matched resistor. The dominant resistance components were identified for different device sizes. The modified GaInAslInP p-i-n
photodiode design curves are given by taking into account the measured electrical parasitics. The integration of bias tee
with high-speed photodiode is used to eliminate the bandwidth iimitation due to external bias tee. The inclusion of a matched resistor has improved the device's frequency response at the cost of the lower efficiency. With the graded bandgap layer, bias tee, and matched resistor, the performance of high-speed, long-wavelength photodiodes is much improved.
ACKNOWLEDGMENT
[8] K J. Williams. R. D. Esmanand. and R. F. Carruthers, "Photodetector bandwidth reduction and signal distortion," in Proc. Opt. Fiber Commun. Con! '91, San Diego, Th05, Feb. 1991, p. 198.
yth-Guei Wey, photograph and biography not available at the time of puhlication.
Kirk Giboney, photograph and biography not available at the time of The authors thank T. Reynolds for depositing the AR publication.
coatings.
REFERENCES
[1] K Kato, A. Kozen, Y. Muramoto, Y. Itaya, T. Nagatsuma, and M. Yaita, "11O-GHz, 50%-efficiency mushroom-mesa waveguide p-i-n photodiode for a 1.55-/Lm wavelength," IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 908--912, July 1992.
[2] D. T. Cheung, S. Y. Chiang, and G. L. Pearson, "A simplified model for graded-gap heterojunctions." Solid-State Electron, vol. 18, pp. 263-266, 1975.
[3] S. R. Forrest, O. K. Kim, and R. G. Smith, "Optical response time of Ino.53Gao.47As/InP avalanche photodiodes," Appl. Phys. Lett., vol. 41, no. I, pp. 95-98, 1 July 1982.
[4] K K Law, R. H. Van, A. C. Gossard, and J. L. Merz, "E1ectricfield-induced absorption changes in triangular quantum wells grown by pulsed-beam molecular-beam-epitaxy technique," J. Appl. Phys .• vol. 67, no. 10, pp. 6461-6465, 15 May 1990.
[5] J. G. Wasserbauer, J. E. Bowers, M. J. Hafich, P. Silvestre, L. M. Woods, and G. Y. Robinson, "Specific contact resistivities of InGaAslInP pisotype heterojunctions," in Proc. 4th 1nt. Con! Indium Phosphide and Related Materials, pp. 593-595.
[6] Y. G. Wey, D. L. Crawford, K Giboney, J. E. Bowers, M. J. Rodwell, P. M. Sylvestre, M. J. Hafich, and G. Y. Robinson, "Ultrafast graded double-heterostructure GaInAs/InP photodiode," Appl. Phys. Letl., vol. 58, no. 19, pp. 2156-2158, 13 May, 1991.
[7] K J. Weing'f!!:!'n, M. J. W. Rodwell, and D. M. Bloom, "Picosecond optical samplirili df GaAs integrated circuits," IEEE 1. Quantum Electron., vol. 24, no. 2, pp. 198--220, Feb. 1988.
John Bowers, photograph and biography not available at the time of publication.
Mark Rodwell, photograph and biography not available at the time of publication.
Pierre Silvestre, photograph and biography not available at the time of publication.
Prabhu Thiagarajan, photograph and biography not available at the time of publication.
Gary Robinson, photograph and biography not available at the time of publication.
