Photodiodes: UNM
Avalanche Noise, Breakdown, and Response Time
ECE-565 Optical Communication Majeed M. Hayat University of New Mexico Albuquerque, New Mexico, USA
Outline
I. II. III. IV. Motivating APDs Gain, excess noise and bandwidth The dead space effect The heterostructure & initial energy effects V. Optimization VI. APDs buildup-time-limited bandwidth
Modes of Operation of an APD
APDs are photodetectors enjoying optoelectronic gain Linear mode (sub-breakdown): photocurrent optical power e.g., optical communication Geiger mode (post-breakdown): Ideally, each detected photon results in breakdown e.g., photon counting, coincidence counting
Current Photodetectors Needs for Long-haul Optical Communication
High quantum efficiency at 1.55 m (beyond 80%). High speed: 10 Gbps (OC 192) and beyond. Internal gain: ~10-50 (preferred over external EDFA amplification). Wavelength selectivity (WDM). Low noise (excess noise, dark current). Compactness, reduced cost, OEIC (solid-state).
Current Photodetectors Needs for Photon Counting
High detection efficiency (QE x Pd). Low dark current counts. Low sensitivity to reverse-bias fluctuation. Low operational reverse bias Reasonable speed (~MHz)
Avalanche Photodiodes
An SAGCM heterostructure APD
Au-Sn Contact + n InP n : InGaAa
E
absorption
n: InGaAaP (grading)
n or i InP (multiplication) p: InP (buffer) Au-In-Zn Contact
p: InP substrate
input light Traditional APDs: BW ~ 1-3 GHz Gain ~ 10 40 High quantum efficiency
[Campbell et al] Current direction for OC: Thin SAGCM APDs: reduce the absorption and multiplication region width
GND
p: InP substrate
absorption
input light
+V
SAGCM APD
Photon absorbed e p multiplication layer (high field) n h absorption layer (low field)
carrier multiplication
Thin Multiplication- & Absorption-Region APDs
Benefits: High speed (up to 40 GHz +) Low multiplication noise (factor of ~2) similar mechanism as noise suppression in superlattice MQW APDs). Higher optimal gain values: better SNR and BER Breakdown characteristics (Geiger mode) not so good Challenges: Quantum efficiency must be enhanced by employing new structures: Waveguide structures (lateral absorption) Resonant-cavity structures (vertical absorption) Detection efficiency is low 1.55m and beyond Dark current is always a problem
Edge-coupled waveguide APDs:
Idea: Reduce absorption-region (~0.8 m or less) width without killing quantum efficiency. High gain-bandwidth (> 12 GHz at gain of 10) Reduce charge-space effects Challenge remains: coupling efficiency (QE ~25%) [Kinsey et al, 00]
1
m 0
InGaAs cap p: InAlAs InGaAs 800 nm absorption
t gh li
n: InAlAs InP buffer
p: charge InAlAs 400 nm multiplication
InP Substrate
800nm
Resonant cavity photodiodes
Increase: Quantum efficiency Increase: Bandwidth Wavelength selectivity Drawbacks: Increased fab. complexity p Selectivity may not be desirable in some i applications n
...
Input light p: InP InGaAs absorption layer n: InP InP/InGaAsP Bragg reflector n- contact
}
[Unlu et al, 1995]
Why study APD gain and bandwidth characteristics?
Receiver Performance in digital (ON-OFF) optical transmission: If ISI is negligible, the BER is primarily dependent on RL the front-end SNR: trans-impedance
SNRD =
I
2 s
2 p 2 T
pre-amp
Cj
+
Ip
2 I p = (< G > RPin ) 2 ; Electrical power 2 T = 4(k BT / RL ) 2 f ; Thermal noise s2 = 2q < G 2 > ( RPin + I d )f Pin
IP(t)
I p = R < G > Pin
F<G>2
Shot noise
Conventional Model for Carrier Avalanche multiplication process in APDs: conventional model Multiplication
Avalanching mechanism
Initiating electron First impact ionization Hole
p
n
W
Ionization probabilities depend on field strength and material and are considered independent of carrier history. This is what is essentially assumed in the McIntyre multiplication model
Ionization Coefficients
Ionization probabilities per unit length: Unit: cm-1
Important parameter k = hole ionization & increase with electric coefficient field. k = / Conventional theory: Ionization coefficients are independent of position and carrier history. They are material specific. (E) = A exp[-(Ec/E)m] Model parameters determined Exponential model: [Wolff, Moll & experimentally.
Meyer, Shockley, Bulman et al.]
= electron ionization coefficient
APD Mean Gain
Gain G is the total random number of electron-hole pairs generated including the initiating electron. Mean gain (McIntyre, 1966):
G
k=1 k = 0.5 k = 0.2 k = 0.1
k=0
< G >= exp[ (11kk)W ] k
w
Growth of gain with aw for different k values
Excess Noise Factor
Gain noise from random amplification. Each detected photon generates a random G number of carriers. Common measure of this uncertainty is the excess noise factor. G 2 F= Defined as: G 2
k = 100
F
k = 50 k = 10 k=5 k=1 k = 0.5 k = 0.1 k = 0.05 k = 0.01 k=0
G
1 F = kG + (1 k )( 2 ) G
Excess noise factor F is a function of the mean gain G and k only
Measured Gain-Noise Characteristics of Thin APDs
Thin APDs have low noise characteristics. For a fixed gain, the excess noise factor is significantly lower than that predicted by the McIntyre theory. This cannot be explained with the conventional theory; no common parameters of ionization coefficients are attainable
14
Measured Excess Noise Factor
12
Excess Noise Factor
W = 100nm W = 200nm W = 500nm W = 800nm
10 8 6 4 2 2 6 10 14 18 22 26 30
(E) = A exp[-(Ec/E)m]
Measured gain Gain
Experimental gain and excess noise factor for thin GaAs APDs with four different multiplication region widths [Anselm et al., 1997, Yuan et al 2000].
Conventional Ionization Model for Thin APDs?
3.E+05
4.E+05
100nm 200nm 500nm 800nm
2.E+05
100nm 200nm 500nm
3.E+05
800nm
(1/cm)
(1/cm)
1.E+05 0.E+00 2.E+05 4.E+05 6.E+05 8.E+05
2.E+05
1.E+05
0.E+00 2.0E+05 4.0E+05 6.0E+05 8.0E+05
E field (V/cm)
E field (V/cm)
Using the conventional relation between <G> and F, ionization coefficients cannot be fit into a single width-independent model. New model parameters (A, EC, m) are needed for each width.
(E) = A exp[-(Ec/E)m]
Dead-Space Model
Multiplication layer
Injected electron First impact ionization
p de dh de
W
n dh de
x
Eie de = qE
Eie and Eih are the average ionization threshold energies
Eih dh = qE
Probability density function of carrier ionization distance X (from the birth location)
Distance to ionization
X
Hard-threshold dead-space pdf:
he ( x) = e u( x de ) ( x d h ) hh ( x ) = e u( x d h )
he(x)
( x de )
de x
More general: Heterojunction
Material I
I
Material II
II
x yb y
he ( y| x) = ( y )exp{ d e ( x) satisfies Eth ( x + d e ( x)) = q
x+de ( x)
x+ de ( x )
(u )du}
y
E (u )du
x
Dead Space in Thin APDs
GaAs
E Field Width (nm) ( 105 V/cm) 100 200 500 800 6.3 6.8 4.7-5.0 3.5-3.7 3.2-3.3 Mean Gain 8-29 6-30 4-28 5-20 de/W (%) 25-27 17-18 9.2-9.8 6.4-6.6 dh/W (%) 21-22 14-15 7.6-8 5.3-5.8
Gain Statistics
Renewal (recurrence) theory approach: [Hayat et al., 92; Spinelli et al, 96 ; Hayat et al. 99; McIntyre, 99] Application to measurement: [David et al, Spinelli et al. , Yuan et al., 1999, 2000; Saleh et al. 2000
Renewal equations for avalanche multiplication
Z(x) = total number of electron and hole offsprings produced by placing a parent electron created at x (including it self). Y(x) = total number of electron and hole offsprings produced by placing a parent hole created at x (including it self). Z(x + ) Note: G = 0.5(Z(0)+1) First impact ionization parent electron Z(x) p secondary Z(x + ) Y(x + ) hole Xe 0 x Key renewal observation: Conditional that the first impact ionization occurs after distance e = , E[Z(x) | X = ] = 2z(x + ) + y(x + ), where z(x) = E[Z(x)] and y(x) = E[Y(x)].
W
n
Recall, E[Z(x) | X] = 2z(x + X) + y(x + X). Now average over all possible realizations of X : E[Z(x)] = 2E[z(x + X) ] + E[y(x + X) ]
w x
=
{2 z ( x + ) + y( x + )}h
0
X
( )d
+
w x
he ( x)dx
Probability that no impact ionization occurs
Renewal equations for the first and second moments
z ( x) = [1
W x
x
he ( )] + [2 z ( ) + y ( )]he ( x)d
x
x 0
W
y ( x ) = [1 hh ( )] + [2 y ( ) + z ( )]hh ( x )d
z 2 ( x) = [1
W x
he ( )] +
W
x
[2 z 2 ( ) + y 2 ( ) + 4 z ( ) y ( ) + 2 z 2 ( )]he ( x)d
x
y2 ( x) = [1 hh ( )] +
x 0
[2 y2 ( ) + z 2 ( ) + 4 z ( ) y ( ) + 2 y 2 ( )]hh ( x )d
Calculation of the mean gain and excess noise factor
< M (x) > = 0.5 ( z (x) + y (x) )
Mean multiplication at x
1 G = ( z (0) + 1) 2
Mean gain
z 2 ( 0) + 2 z ( 0) + 1 F= ( z (0) + 1) 2
Excess noise factor
G 2 F= G 2
Determining the physical ionization coefficients from gain-noise measurement
Given 1 E-field, Eth Compute de and dh Unique and
& recurrence eqs. exhaustive search
2 W, E-field, Eth, G, and F 3 and for each W
Exponential-model parameters
curve fit
4 Adjust Eth and Repeat 1-3
Optimize model
recurrence eqs. exhaustive search &
Width-Independent Ionization Coefficients
) 1
-
T N E I C I F F E O C N O I T A Z I N O
m c (
5 4 3 2 1
x 10
4
Model 281 nm 317 nm 582 nm 1110 nm
(E) = A exp[-(Ec/E)m]
5 6 ELECTRIC FIELD (V/cm) 7
5
0 4
for InP APD (G,F data from J. C. Campbell)
Width-Independent Ionization Coefficients
) 1
-
m c ( T N E I C I F F E O C N O I T A Z I N O
10 8 6 4 2
x 10
4
Model 281 nm 317 nm 582 nm 1110 nm
0 4
5 6 ELECTRIC FIELD (V/cm)
7
5
for InP APDs(G,F data from J. C. Campbell)
Conventional Ionization Model for Thin APDs?
3.E+05
4.E+05
100nm 200nm 500nm 800nm
2.E+05
100nm 200nm 500nm
3.E+05
800nm
(1/cm)
(1/cm)
1.E+05 0.E+00 2.E+05 4.E+05 6.E+05 8.E+05
2.E+05
1.E+05
0.E+00 4.0E+05 2.0E+05 6.0E+05 8.0E+05
E field (V/cm)
E field (V/cm)
Using the conventional relation between <G> and F, ionization coefficients cannot be fit into a single width-independent model. New model parameters (A, EC, m) are needed for each width.
(E) = A exp[-(Ec/E)m]
Ionization Energy Thresholds
Theoretical electron Eth
InP 1.84 eV [Pearsall, Appl. Phys. Lett, 1979] 1.90 eV [Watanabe et al., JQE, 1995]
Optimized electron Eth
2.05 eV
hole Eth
1.65 eV
hole Eth
2.20 eV
In0.52Al0.48 As
2.00 eV
2.15 eV
2.30 eV
Device Width Independent Ionization Coefficient Model
(E), (E) = A exp[-(Ec/E)m]
Correct Prediction of Noise
Gain-noise characteristics for all four InP APDs with different widths agree with experimental results.
Correct Prediction of Noise
Gain-noise characteristics for all four InAlAs APDs with different widths agree with experimental results.
Initial-Energy Effect
cold electron hot (energized) electron
E ini = 0
GaAs p GaAs i GaAs n
E ini = ( x )dx
a
b
Electric field, E(x)
AlGaAs GaAs AlGaAs p i n
a b
Initial Energy of Injected Carriers
p p i n n
7 6 ELECTRIC FIELD (V/cm) 5 4 3 2 1
AlGaAs GaAs 5 x 10 x
E
GaAs
GaAs AlGaAs 2v 4v 6v 8v
p : AlGaAs (410 nm) p : GaAs (10 nm) i : GaAs (130 nm) n : GaAs (20 nm) n : AlGaAs
0 300
400
500 600 POSITION, x (nm)
700
Device and data from the Microelectronics Research Center, U. Texas, Austin
Initial Energy Effect
Multiplication layer
Injected electron First impact ionization
p de,0
E E0 = th qE field
n dh de dh
W
de
x
d e, o
Eih dh = qE
Eie de = qE
Noise Reduction
Nonzero electric field in p-layer
Photogenerated electrons start accumulating energy before entering the multiplication layer Energetic electrons start the multiplication Reduce the first dead space Localization of initial impact ionization Reduce the excess noise factor F
Modified Dead-Space Multiplication Theory
We have modified the existing analytical model for characterizing the gain and excess noise factor to:
Capture the initial energy effect as well Capture arbitrary dead-space profiles for heterostructure multiplication regions
Predicted Noise Reduction
8 EXCESS NOISE FACTOR, F 7
p
100 nm GaAs
DSMT FULL INITIAL ENERGY
n
6 5 4 3 2 1
Electron injection
43 % Noise reduction
5
10 MEAN GAIN, G
15
20
Predicted Noise Reduction
8 EXCESS NOISE FACTOR, F 7
p
50 nm GaAs
DSMT FULL INITIAL ENERGY
n
6 5 4 3 2 1
Electron injection
45 % Noise reduction
5
10 MEAN GAIN, G
15
20
RELATIVE INITIAL DEAD SPACE de0/de(x)
Relative Magnitude of the Initial Dead Space
1
DEVICE I p : GaAs (820 nm) i : GaAs (120 nm) DEVICE II p : AlGaAs (800 nm) p : GaAs (10 nm) i : AlGaAs (100 nm) i : GaAs (130 nm) n : GaAs (20 nm) n : GaAs n : AlGaAs i : GaAs (30 nm) n : GaAs (10 nm) n : AlGaAs DEVICE III p : AlGaAs (810 nm)
0.8 0.6 0.4 0.2 0
DEVICE I DEVICE II DEVICE III
2 4 6 8 5 ELECTRIC FIELD (V/cm) 10 x
homojunction
heterojunctions
Devices and data from the Microelectronics Research Center, U. Texas, Austin
8 EXCESS NOISE FACTOR F 7 6 5 4 3 2 1 0 0
Comparison with Experiment: I Device I
Experimental DSMT MDSMT Minimum F DEVICE I
p : GaAs (820 nm) i : GaAs (120 nm) n : GaAs
5
10 GAIN G
15
20
GaAs Ionization coeff. By Saleh et. al., IEEE TED 2001
Device and data from the Microelectronics Research Center, U. Texas, Austin
Comparison with Experiment: Device II II
8 EXCESS NOISE FACTOR F 7 6 5 4 3 2 1 0 0 5 10 GAIN G 15 20 Experimental DSMT MDSMT Minimum F DEVICE II
p : AlGaAs (410 nm) p : GaAs (10 nm) i : GaAs (130 nm) n : GaAs (20 nm) n : AlGaAs
Device and data from the Microelectronics Research Center, U. Texas, Austin
8 EXCESS NOISE FACTOR F 7 6 5 4 3 2 1 0 0
Comparison with Experiment: III Device III
Experimental FDSMT FMDSMT Fmin AlGaAs DEVICE III
p : AlGaAs (810 nm) i : AlGaAs (100 nm) i : GaAs (30 nm) n : GaAs (10 nm) n : AlGaAs
AlGaAs Ionization 20 coeff. By Plimmer et. al.,IEEE TED 2000
5
10 MEAN GAIN G
15
Device and data from the Microelectronics Research Center, U. Texas, Austin
Optimization to Minimize Noise
Problem: No control of the initial energy Solution:
Add an extra layer before the multiplication layer that serves as the energy charge layer Energy-buildup layer must have high ionization threshold energy to prevent ionization therein
Note: Low-noise heterostructure APDs Yuan, et. al., IEEE PTL Oct. 2000. Wang, et. al., IEEE PTL Dec. 2001. F<G>=20 ~ 2.5 F <G>=20 ~ 4
Two-layer Multiplication Region Structure
wb p
Energy buildup i layer
Multiplication i layer
n
Eth,charge > Eth,mult.
Thickness of the Energy Charge Layer
E Energy Criterion: p ec m Eth.cha Eth.mul Eini Echa x
Eth. mul < Eini + Echa < Eth.cha Echa = q E dx
0 w
For constant electric field
Echa = field w q
Eth. mul Eini Eth.cha Eini < wopt < Efield Efield
7.5 GaAs EXCESS NOISE FACTOR, F 7 6.5 6 5.5 5 4.5 4 3.5 0 wGaAs = wGaAs = wGaAs = wGaAs = 50 nm 100 nm 150 nm 200 nm 100 Al0.6Ga0.4As
20 40 60 80 Al0.6Ga0.4As layer width (nm)
Optimized Structure
8 EXCESS NOISE FACTOR, F 7 6
p
100 nm GaAs 30 nm Al0.6Ga0.4As
DSMT FULL INITIAL ENERGY 2-layer DSMT 2-layer Full Initial Energy
n
5 4 3 2 1
30%Noise Reduction
43% Noise Reduction
5
10 MEAN GAIN, G
15
20
Time Response and Bandwidth of APDs
Time Response of APDs
Number, locations, and times of impact ionizations are random. Time response is gain-dependent avalanche buildup time Electron ionization x Hole ionization t p E Impulse response I(t) =Ie(t) + Ih(t) n Ie(t) Ih(t) t area under I(t) = q Gain
Renewal equations: Impulse response
Ze(x,t) = number of electrons at t units after a parent electron is created at location x. Ye(x,t) = number of electrons at t units of time after a parent hole is created at x. I(t) = q w-1 {ve Z...