20 Avalanche and Quantum Well Photodetectors

1. Avalanche Photodetector (APD) Principles

Ionization coefficient αe ≈ αh Ionization coefficient αe >> αh

The avalanche process is asymmetric (i.e., the probability for initiating an avalanche is usually greater for one type of carrier than for the other). For Si, ionizing collisions are 30-50 times more frequent with electrons than holes. This asymmetry is characterized by the ratio αe /αhwhere αe and αh are impact ionization coefficients for electrons and holes, respectively.

Avalanche Multiplication: Ionization Threshold Energies

• If the width of the high field region (e.g. the depletion region) is W, then the probability of ionization is αW

• No analytical expression for the dependence of the ionization coefficients on electric field exists, but from the measurement of these parameters in a variety of semiconductors it is found that their relation to electric field is roughly given by

Here α∞ is the value of α for E —» ∞ and b and m are the coefficients.

For example, in GaAs, α∞ = 1.3 x 106 cm-1, b = 2 x106 V/cm; and m = 2.

Avalanche Multiplication: Ionization Threshold Energies

In Si, αe > αh. However in most III-V compounds αe > αh.

Avalanche Multiplication: Ionization Threshold Energies

The threshold ionization energy εi , is defined as the minimum energy needed for impact ionization.

For the simplest case of parabolic conduction and valence bands,

If me = mh,

Multiplication and Ionization Coefficients

If the ionization takes place, the “output” current density is greater than the “input” one:

Multiplication and Ionization Coefficients

First, consider uniform electric field in the avalanche region(pin diode)

α ≈ const (x); also, assume αe = αh

The condition for avalanching: (every carrier has one ionizing collision)

Multiplication and Ionization Coefficients

The characteristic time for impact ionization (single electron collision)

se vt

α1

≈∆

For α ~ 2x104 cm-1,

vs ~ 107 cm/s,

∆t ~ 5 ps

The depletion region width needed to achieve the avalanche breakdown,

W ~ α−1 ∼ 0.5 µm

Multiplication and Ionization Coefficients

Non- uniform electric field in the avalanche region(p-n diode)

The total electron and hole current densities through the p-n junction,

For the electrons,

After passing a short distance, ∆x, the electron current increases as

Multiplication and Ionization Coefficients

The breakdown condition

Multiplication and Ionization Coefficients

≠

For the electron initiated process, the integration results in:

For the hole initiated process, the breakdown condition is identical:

Breakdown voltage

The breakdown voltage corresponds to the voltage drop across the junction when the peak electric field reaches the critical value for ionization:EM = ECR

(Assuming the built-in voltage to be much smaller than the VBR)

Silicon

Impurity concentration, cm-3

Practical APD designs

Typical Si or GaAs APD with guard rings for high voltage operation

Practical APD designs

Separate absorption and multiplication (SAM) APD, or SAM-APD.

The structure combine low leakage, due to the junction being placed in the high-bandgap material (e.g., InP), with sensitivity at long wavelengths provided by the low-bandgap absorption region (e.g., InGaAs).

Dark currents ~ pA-nA; gains ~ 10.

APD response time

In the APD the overall response is made up of three parts:

a) the electron transit time across the drift region,

(ttr)e = w/νs,

b) the time required for the avalanche to develop, tA,

c) the transit time of the holes produced in the avalanche back across the drift space, (ttr)h = w/νs.

Parts b) and c) represent delays additional to those experienced in a non-avalanching diode.

APD response time

The avalanche delay time, tA, is a function of the ratio of the ionisation coefficients, k = αh/αe.

When k = 0, the avalanche develops within the normal electron transit time across the avalanche region (wA/υse). We assume wA << w for SAM-APD.

When k > 0, the avalanche develops in multiple passes across the avalanche region and at high levels of multiplication,

tA ≈ MkwA/υse

The overall response time, τ ≈ (w + MkwA)/υse + (w + wA)/vsh

The (-3dB) bandwidth to be given approximately byf(-3dB) ≈ 0.44/ τ

k = 0k > 0

2. Quantum Well Photodetectors

• The width of the wells and the composition of the barrier material are so chosen for a QW inter-subband detector that the wells have two energy levels separated by the energy of a photon to be detected. The upper energy level is arranged to be either a resonant level in the continuum or a level just below the barrier level in the presence of the applied voltage.

• The wells are heavily doped n-type to a concentration of about 1018/cm-3 . The incident radiation excites electrons from the lower ground state to the upper level and the electrons so excited are transported out of the well freely or by tunneling due to the applied field

2. Quantum Well Photodetectors

QW PD absorption spectra

Energy above the QW ground level, ∆E, meV

QW PD photocurrent

where np is the number of photo-excited carriers exiting per unit time per unitarea at the output end. Ar is the surface area of the detector.

The number of photo-excited carriers:

pe is the probability of escape from the well and Nw is the number of QWs, τtr is the transmit time of the escaped electron across one period, Lp = (Lw + Lb), τr is the recapture or recombination lifetime.

the number of electrons reaching the output end per unit area

QW PD responsivity

Performance of a detector is characterized by responsivity

For this mode of carrier transport the responsivity is

The responsivity, therefore, increases exponentially with the increase in voltage.

QW PD responsivity – experimental results