# Presentation: 568342

## The Physics of Low Noise Avalanche Photodiodes

**John P. R. David & Graham J. Rees**
***Electronic & Electrical Engineering***
***University of Sheffield, U.K.***

_**Talk Outline**_
**Low noise mechanisms in thin APDs**
**Temperature dependence**
**Speed improvements**
**New materials**
**Conclusions**

## Excess avalanche noise 

***Excess avalanche noise ***

***Multiplication buildup time ***
***required to achieve M***

***An APD can give us gain.***
***Unfortunately the avalanche noise can degrade the S/N ratio.***
***An optimum value for <M> exists.***

## McIntyre’s avalanche noise theory (1966)

***McIntyre’s avalanche noise theory (1966)***

*** ********** ***= electron probability of ionization per unit length [m****-1****]**
*** ********** ***= hole probability of ionization per unit length [m****-1****]**

- where

***Assumes:***
**Multiplication process does not depend on carrier history.**
***k = ************ ******/*********** is a constant**

## McIntyre’s model for electron injection F v Me

***McIntyre’s model for electron injection ******F v M******e***

*k *= 0

*k *= 1

- 0.4

- 0.2

- 0.6

***The excess noise depends only on the ionization coefficient ratio (k) and the multiplication value.***

***k *****= *********************a***

## GaAs Ionization Coefficients 

***GaAs Ionization Coefficients**** *

****

****

****

**0.5********m**

**1********m**

**0.1********m**

***k *****=**** ********/******** ****= 1****	****          ****0.9 0.8**

***Field dependence of GaAs***
*** ******ionization coefficients***

***Most III-V semiconductors have ******0.4 ************ k ************ 2.5****** ***
***High excess noise expected, especially at higher electric fields when ******k************1***

## Excess noise in Si and GaAs, Me

***Excess noise in Si and GaAs, M******e***

**In thick structures, the excess noise *****F***** is determined by *****k*****, the ********/********* *****ratio.**
**Silicon has a ****small *****k***** compared to GaAs, hence ****low noise****.**

## Schematic of a SAM-APD

***Schematic of a SAM-APD***

***Light is absorbed in thick ******InGaAs****** layer***
***Photogenerated holes impact ionize in ******InP***
***Conventional designs involve thick multiplication layers, so that *********/********* ratio is small, to achieve low excess noise***

## p-i-n diode schematic

***p-i-n diode schematic***

***Pure ******M******e****** & ******M******h****** obtained by illuminating thick p******+****** & n******+****** layers with short wavelength illumination.***
***n******+******-i-p******+****** s also grown to obtain M******h****** more easily.***

***Intrinsic thickness, ******w****** varies from 1************m to 0.05************m.***

## Multiplication from GaAs p+-i-n+s

***Multiplication from GaAs p******+******-i-n******+******s***

**Multiplication factors**

***M******e****** and M******h****** were  measured in different thickness p******+******-i-n******+******s.***
***Lock-in techniques allow M******e****** and M******h****** to be determined in the presence of large dark currents.***
***M******e****** ************ M******h ******as ‘w’ decreases, suggesting that ********* ******** ******

## Excess noise in GaAs p+-i-n+s

***Excess noise in GaAs p******+******-i-n******+******s***

***The excess noise decreases as w decreases, instead of increasing as k************1***

***Electron initiated noise measurements showed unexpected and significant ******noise reduction as w became smaller***

## Excess noise in GaAs n+-i-p+s

***Excess noise in GaAs n******+******-i-p******+******s***

**The excess noise *****decreases***** as *****w***** decreases, instead of increasing according to *****k*****.**

***Hole initiated noise measurements also showed unexpected and significant noise reduction as w became smaller***
***B******ehav******io******r cannot be explained by McIntyre theory***

## Multiplication characteristics in InP

***Multiplication characteristics in InP***

**Measured *****M******e****** *****(symbols)**
**Calculated *****M******e***** (solid lines)**
**using bulk ionization coefficients**

**Multiplication factors**

## Excess noise factor in InP

***Excess noise factor in InP***

***F*****(*****M*****)**

**Same symbols as before**
**Noise measured using wrong (electron) carrier type**
**Fujitsu SAM-APD gives **********/*********** *****=**** ****1.4 ******** *****k******eff****** *****=**** ****0.7**
**Structure with *****w***** = 0.24 gives *****k******eff***** = 0.4 - much better than SAM-APD with hole multiplication**
**Low noise**** possible even  with electron injection with ****thin *****w***

## Multiplication characteristics in Silicon

***Multiplication characteristics in Silicon***

**Measurement of *****M******h***** and *****M******mix***** on 0.84********m n****+****-i-p****+**
**Measurement ****of *****M******e***** and *****M******mix***** on 0.32, 0.18, 0.12********m p****+****-i-n****+****s**

**Multiplication factors**

## Local noise model prediction vs. experiment in submicron Si p+-i-n+s

***Local noise model prediction vs. experiment in submicron Si p******+******-i-n******+******s***

***F******e*****(*****M******e*****)**

**Local field noise model gives increasing excess noise from *****k *****= 0.4-0.7 as *****w***** decreases from 0.32-0.12********m.**
**Experiment shows that *****F*****(*****M******e*****) however is virtually constant at *****k ********* 0.2.**

## McIntyre Noise Model

***McIntyre Noise Model***

**McIntyre’s noise model assumes that a carrier’s ionization probability is *****independent***** of distance ******** probability density function (PDF) is exponential**
**This assumption leads to the McIntyre expression for excess noise factor**
**Avalanche noise ****depends on the**** *********** /***********  ratio **

***Probability density function ***
***of ionization***

## Dead Space Models

***Dead Space Models***

**More realistic picture of ionization probability shows ****significant *****dead space***** at high electric field**
**Presence of dead space reduces *****CoV***** ******** makes multiplication more deterministic ******** less noisy**
**A significant dead space reduces the importance of the ***********/*********** ratio & the carrier type initiating multiplication**

***Probability density function ***
***of ionization***

## Monte Carlo Estimation of F

***Monte Carlo Estimation of F***

*w*

**Excess Noise Factor,**

- 

**Multiplication via**
**impact ionization**

- 1

***N******e***

***N******h***

*M**trial* = 1 + *N**e* + *N**h*

## Probability distribution of electron ionization path lengths (<M> = 5)

***Probability distribution of electron ******ionization path lengths (<M> =**** 5)*

**(********m)**

**(********m)**

**<*****l******e*****> = 0.39********m**
***CoV *****= 0.86**

**<*****l******e*****> = 0.032********m**
***CoV***** = 0.31**

***Probability density function ***
***of ionization***

***CoV***** = stand. dev. in *****l******e***** / <*****l******e*****>**

**At *****low fields***** ******** relatively small dead space & low ionization probability**
**At *****high fields***** ******** relatively large dead space & higher ionization probability ******** narrow  ionization probability distribution.**

## Distribution of Multiplication for <M> = 5

***Distribution of Multiplication for <M> = 5***

***There are more high order multiplication events at lower electric fields, giving rise to more noise***

***Probability function of multipliplication***

## Typical path lengths as a function of electric field 

***Typical path lengths as a function of electric field***** **

***Monte Carlo model results***

**Scatters per ionization event**
**Ballistic dead space **
**	*****d***** = 2.1eV/*****qE***
**Mean ionization path length <*****l******e*****>**

***Scattering becomes less important as the electric field increases***
***Ionization tends towards ballistic ideal, i.e. like PMT***

## APD multiplication is very temperature sensitive
	Not a problem when input signal is large - BER increases when at the limit of sensitivity 
Breakdown variation is ~ 0.06-0.2V/°C

***APD multiplication is very temperature sensitive***
***	******Not a problem when input signal is large - BER increases when at the limit of sensitivity ***
***Breakdown variation is ~ 0.06-0.2V/°C***

- M=4

- M=12

***Active circuit required to vary bias to ensure constant multiplication***

***Bias required for M = 4 & M = 12 at different temperatures***

***Temperature dependence of avalanche multiplication***

## Photocurrent, dark current and breakdown  measured on different thickness GaAs p-i-n diodes, from 20K-500K
Sharp Vbd observed at all temperatures.
Dark currents increase with temperature
Avalanche multiplication reduces with increasing temperature

***1************m GaAs p-i-n***

***Photocurrent, dark current and breakdown  measured on different thickness GaAs p-i-n diodes, from ******20K-500K***
***Sharp V******bd****** observed at all temperatures.***
***Dark currents****** increase ******with temperature***
***Avalanche multiplication ******reduces ******with increasing temperature***

***Temperature dependent I-V for 1************m GaAs***

## Change in Vbd with Temperature

***The breakdown change is ******more significant in thicker structures***

*w*=1m

*w*=0.5m

*w*=0.1m

***w = 1.0 ************m, 0.5************m & 0.1 ************m***

***Percentage change in V******bd***

***Temperature coefficient****** decreases from 0.032V/******o******C to 0.004V/******o******C****** ***

***Change in V******bd****** with Temperature***

## Ionization coefficients derived from multiplication data 
Ionization coefficients decrease with increasing temperature
The change is much larger at lower electric fields
Thinner avalanche widths operate at higher electric-fields
Phonon scattering relatively less important at higher electric fields

**500K**

**300K**

**100K**

- GaAs

***GaAs ionization coefficients***

***Ionization coefficients derived from****** ******multiplication data ***
***Ionization coefficients ******decrease with increasing temperature***
***The change is much larger at lower electric fields***
***Thinner avalanche widths****** ******operate at higher electric-fields***
***Phonon scattering relatively less important at higher electric fields***

***Temperature dependent ionization coefficients***

## APD speed limitations-multiplication build-up time

***APD is slow c.f. p-i-n diodes due to multiple transits required for high gains***
***Difficult to achieve 10****** ******Gb/s operation with thick avalanching structures***

***APD speed limitations-multiplication build-up time***

## Thin avalanche region multiplication build-up time

***	******Decreasing w results in shorter transit times - higher speed***

***Thin avalanche region multiplication build-up time***

## APD frequency response approximates a 1st order system
Figure of merit - Gain bandwidth  product (GBP)
Motivation of thin avalanche regions < 1m to increase GBP

***M *****= 1**
***B *****= 40GHz**

***M***** = 5**
***B***** = 8GHz**

***M *****= 10**
***B *****= 4GHz**

***APD frequency response approximates a 1st order system***
***Figure of merit - Gain bandwidth  product (GBP)***
***Motivation of thin avalanche regions < 1**********m to increase GBP***

***Frequency response of APDs for fixed reverse bias***

***APD limitations - frequency response***

## Monte Carlo model cf. constant v = vsat model
Same dead space, d

***Monte Carlo model****** cf. ******constant v = v******sat****** model***
***Same****** dead space, d***

***w = 0.1************m, M = 12.5***
***Enhanced speed****** in MC model leads to faster decay of current impulse response ********* *****higher****** ******f******3dB***

***Dead space and enhanced speed effects compete!******	*****[Hambleton et al, 2002]**

***Carrier speed assumptions***

## Simulation result comparisons

***Constant GBP***
***f******3dB****** (******Monte Carlo******) >****** ******f******3dB****** (******Emmons******) for****** ******all w and all M***
***Enhanced carrier speed dominates dead space***

**w = 1.00********m**

***w *****= 0.20********m**

***w *****= 0.05********m**

***Monte Carlo***
***Emmons***

***Simulation result comparisons***

## Published experimental f3dB

***But ******larger d/w****** in w = 200nm device ******slows ******frequency response***
***Suggests ******v******200nm****** > v******400nm***

***Lenox et al. (PTL 1999) measured f******3dB****** of InAlAs RCE APDs***
***w =****** 400 nm****** ******GBW =****** ******130 GHz***
***w = ******200 nm****** ******GBW****** ******=****** ******290 GHz***
***GBP******200nm ******> 2 ************ GBP******400nm ***

***Published experimental f******3dB***

## 4H-SiC Device Structures

***4H-SiC Device Structures***

**2******** +ve bevel edge & multistep junction extension termination**
**Square mesas with areas : 50 ******** 50 ~ 210 ******** 210 ********m****2**
**Passivated with SiO****2**** & SiN*****x***
**Al/**** ****Ti top contact with optical access**

## Responsivity at Unity Gain, Beveled APDs

***Responsivity at Unity Gain, Beveled APDs***

**Similar to typical 6H-SiC photodiodes**
**Responsivity cutoff at ~380 nm ******** *****visible-blind***
**Peak responsivity of 144 mA/W at 265 nm ******** *****quantum efficiency of ~ 67%***

## Reverse IV Characteristics

**Avalanche breakdown is sharp & well-defined at *****V******bd***** = 58.5V & 124.0V**
**Carriers injected with 230 ~ 365 nm light to initiate multiplication**
***I******ph***** is 1 ~ 3 orders of magnitude > *****I******dark***
**AC measurements corroborate DC results**

***Dark***

***297 nm***

***365 nm***

***230 nm***

***Dark***

***297 nm***

***365 nm***

***230 nm***

**Beveled APDs****, 160********160********m****2**** **

**Reach-Through APDs, 150********150mm****2**

## Multiplication Characteristics

***Multiplication Characteristics***

***M***** of > 200 measured**
***M***** at various ******** more disparate for thicker APD structure**
**Smaller *****M***** from shorter ******
**	********  *****M******h***** > *****M******e***** ******** ******** > ******

**Beveled APDs**

**Reach-Through APDs**

## Excess Avalanche Noise Characteristics

***Excess Avalanche Noise Characteristics***

**Excess noise measured for *****M***** > 40**
**	******** *****good quality of APDs, very stable avalanche multiplication***
**Very low excess noise of *****k *****= 0.1 & 0.15 measured with 365 nm light**
**Excess noise from electron injection (230 nm) gave *****k *****= 0.8 & 2.8**

***Beveled APDs***

***Reach-Through APDs***

## Al0.8Ga0.2As : A Very Low Excess Noise Multiplication Medium for GaAs-based APDs

_***Device structures***_

**Homojunction p-i-n/n-i-p grown by conventional MBE with *****w***** = 1 ********m**
**1 heterojunction p-i-n with *****w*****=0.8 ********m to obtain *****M******e***** & *****M******h***** from same diode**
**Optical access window fabricated by wet etching**
**Pure carrier injection obtained with 442nm & 633nm light **
**542nm light used to produce mixed carrier injection**

***Al******0.8******Ga******0.2******As : ******A Very Low Excess Noise Multiplication ******Medium for GaAs-based APDs***

## Al0.8Ga0.2As : A Very Low Excess Noise Multiplication Medium for GaAs-based APDs

_***Avalanche excess noise of thin diodes***_

**Comparable excess noise for bulk ****	****and thin diodes**

**V****bd**** ******** with decreasing *****w***

***Al******0.8******Ga******0.2******As : ******A Very Low Excess Noise Multiplication ******Medium for GaAs-based APDs***

## Al0.8Ga0.2As : A Very Low Excess Noise Multiplication Medium for GaAs-based APDs

_***Comparison with InP-based APDs***_

***Al******0.8******Ga******0.2******As : ******A Very Low Excess Noise Multiplication Medium for GaAs-based APDs***

**Commercial InP-based APD give excess noise of *****k******i*****=~0.7 with hole initiated multiplication**
**Much lower excess noise can be obtained with Al****0.8****Ga****0.2****As as avalanche medium**

## Al0.8Ga0.2As : A Very Low Excess Noise Multiplication Medium for GaAs-based APDs

_***Comparison with lower aluminium Al***__***x***__***Ga***__***1-x***__***As***_

**Al*****x*****Ga*****1-x*****As (*****x***** ******** 0.6) has large avalanche excess noise**
**Excess noise of Al****0.8****Ga****0.2****As is much lower**
**Al****0.8****Ga****0.2****As also has lower excess noise than a commercial InP-based APD**
**At *****M*****=10, excess noise of Al****0.8****Ga****0.2****As is at least 2 times lower**

***Al******0.8******Ga******0.2******As : ******A Very Low Excess Noise Multiplication Medium for GaAs-based APDs***

## Conclusions

***Conclusions***

**Low noise results from a more deterministic impact ionization process at high fields as *****dead space***** becomes more important**
**Thin avalanching regions should be less**** temperature ****sensitive**
**Thin avalanching regions should be capable of ****high speed**** operation**
**SiC & AlGaAs have bulk Si-like noise behaviour**
**Advantages of thin avalanching regions to geiger mode APDs not fully understood**