# Presentation: 402140

## Single Photon Detector Workshop

- NIST Gaithersburg

**Physical Model for Dark Count and the Development of InGaAs/Si Single Photon Detectors**

_***Y.-H. Lo***_***, Yimin Kang, Huaxin Lu ***
**UC San Diego**
***A. Pauchard, M. Bitter, Z. Pan, R. Dimitrov, S. Hummel ***
**Nova Crystals, Inc.**

## Outline

- Physical model for dark count and afterpulsing effect
-  -  critical dependence on device parameters and   operational conditions.
-  -  single photon quantum efficiency and the importance of k-factor (electron/hole ionization ratio)
- Development of InGaAs/Si APDs

## Counting in the Dark

_**Dark count probability**_:  Pd = 1 - e (-Nd*)
- the probability that there is at least one dark carrier triggering a breakdown when the average effective dark carriers number is Nd*
- where                                 Nd*= Nd Pa
- Nd is the number of dark carriers in SPAPD’s gain region within gated
-       pulse duration
- Pa is the probability of a carrier initiating an avalanche with Geiger
-       mode gain [1]

- [1]  R.J. McIntyre,  *IEEE Transactions on Electron Devices*, vol. ED-20, pp.637-641, 1973.

- Dark carrier generation

- Avalanche initiation

- +

- Dark count

## Four Mechanisms for Dark Carrier Generation

**Four Mechanisms for Dark Carrier Generation**

-  **Primary dark carrier:**
-      IDM -- primary dark current which undergoes the multiplication process
-  **Residual  primary dark carrier:**
-       GB -- gain-bandwidth product of APD
-         M0 -- gain when APD is biased at the DC offset
**Afterpulse dark carrier:**
**Residual afterpulse dark carrier:**
**       **d -- detrap time    T-- pulse period   tr -- transit time
-          Ntrapped0 -- trapped carriers per pulse

## Effect of Primary Dark Current on Dark Count 

**  **voltage pulse width**: **2ns
-   detrap time d : 200ns
-   pulse repetition rate f:
-      100kHz
-   GB = 30GHz
-   DC offset gain M0 :5

- Dark count rate is approximately proportional to the ***primary dark current*** IDM of APD, provided afterpulse effect is negligible.

## Effects of the DC Bias and the Gain-Bandwidth Product

**  **voltage pulse width**: **2ns
-   detrap time d : 200ns
-   pulse repetition rate f:
-      100kHz
-   IDM=0.1pA

***Low DC bias*** (therefore low DC gain) and ***large GB product*** can reduce the dark count rate, but the effect is relatively modest.

## Effect of Afterpulse

-   voltage pulse width: 2ns
-   single-photon quantum
-     efficiency: 20%
-   number of photon per
-     pulse: 0.1pp
-   Gain at DC offset M0: 10

**The contribution of afterpulse depends critically on the ratio between the detrap time and the interpulse interval.  When ********d****/T > 10%, the afterpulse effect rises sharply.**

## Afterpulse Effect (Cont.)

-  Voltage pulse width: 2ns
-  Single-photon quantum
-     efficiency: 20%
-  Number of photon per
-     pulse: 0.1pp
-  Gain at DC offset: 10

**The relative importance of afterpulse effect increases with the increasing Geiger mode threshold gain.**

## Breakdown Probability – Calculation of Single Photon Quantum Efficiency

- Mt is the discriminator threshold setting.

- Low*** ionization ratio (k-factor)*** increases the breakdown probability triggered by a single incident photon (i.e. high SPQE)

- * H. Dautet, et.al., Applied Optics, vol.32, No.21, pp.3894-900 (1993).

## Simulated Sub-Geiger Mode APD Impulse Response

**Simulated Sub-Geiger Mode APD Impulse Response**

**DC Gain used in this simulation: 6,000 (before breakdown)**
**The Geiger-mode gain (within 2ns pulse window) of InGaAs/Si APD is about 40 times higher than InGaAs/InP APD, manifesting the importance of k-factor.**
**The result indicates that InGaAs/Si APDs can have a much higher single-photon quantum efficiency than InGaAs/InP APDs under the same operation condition.**

## Summary

- To achieve **low darkcount** and **high single-photon quantum efficiency**, one likes to have APDs that have
- Low primary dark current (< 1pA)
- Low trap density in the multiplication region
- Short detrap time (< 10% of the interpulse time interval)
- Low DC bias (low prepulse gain) and high GB product
- Small k-factor (critical to single-photon quantum efficiency)

- All these lead to the conclusion that Si APDs should have superior performance to InGaAs/InP APDs for single-photon detection.

## Large Area, Covalently Bonded InGaAs/Si Structure

**TEM**

**Large Area, Covalently Bonded InGaAs/Si Structure**

**SEM**

- III-V

- Si

**4x4 cm****2**** InGaAs/Si wafer**

## InGaAs-on-Si APDs

**InGaAs-on-Si APDs**

## Room Temperature DC Characteristics of InGaAs/Si APD

## Temperature Dependence of Breakdown Voltage

**Temperature Dependence of Breakdown Voltage**

- si = 0.026 V/C
- Si 4 times smaller than InP

## Excess Noise and k-Factor

**Excess Noise and k-Factor**

- F (M=10) = 2.2
- F (M=50) = 2.8

## Summary

- InGaAs/Si APDs can be fabricated on large area wafers with high process yield.
- InGaAs/Si has shown high DC gain and normal breakdown behavior.
- Both the k-factor and the temperature dependence of the breakdown voltage of InGaAs/Si APDs are the same as Si APDs.
- The temperature dependence of the primary dark current needs to be investigated.