Performance of InGaAs short wave infrared avalanche photodetector for low flux imaging

Abstract

Opto-electronic performance of the InGaAs/i-InGaAs/InP short wavelength infrared focal plane array suitable for high resolution imaging under low flux conditions and ranging is presented. More than 85% quantum efficiency is achieved in the optimized detector structure. Isotropic nature of the wet etching process poses a challenge in maintaining the required control in the small pitch high density detector array. Etching process is developed to achieve low dark current density of 1 nA/cm² in the detector array with 25 µm pitch at 298 K. Noise equivalent photon performance less than one is achievable showing single photon detection capability. The reported photodiode with low photon flux is suitable for active cum passive imaging, optical information processing and quantum computing applications.

Appendix

The effective carrier lifetime for electron (τ _e) and hole (τ _p) is given as

$${\tau _{\text{e}}}=\frac{1}{{\left[ {{G_{{\text{ee}}}}\frac{n}{{n_{0}^{2}{p_0}}}+{G_{{\text{hh}}}}\frac{{{p_0}}}{{{n_0}p_{0}^{2}}}+{G_{{\text{RAD}}}}{{\frac{1}{{{n_0}p}}}_0}} \right].\gamma +\frac{1}{{{\tau ^{{\text{SRH}}}}}}}}$$

(1)

$${\tau _{\text{p}}}=\frac{1}{{\left[ {{G_{{\text{ee}}}}\frac{n}{{n_{0}^{2}{p_0}}}+{G_{{\text{hh}}}}\frac{{{p_0}}}{{{n_0}p_{0}^{2}}}+{G_{{\text{RAD}}}}{{\frac{1}{{{n_0}p}}}_0}} \right].\delta +\frac{1}{{{\tau ^{{\text{SRH}}}}}}}}$$

(2)

where τ ^SRH = SRH life time. The n ₀ and p ₀ are carrier concentration for electron and hole at thermal equilibrium, respectively. G _ee, G _hh and G _RAD are respective generation rate. The γ and δ are given as

$$\gamma ={n_0}+{p_0}+{n_0}{N_T}.\left[ {\frac{{{\tau _{{p_0}}}(1 - f_{T}^{0}) - {\tau _{_{{{e_0}}}}}f_{T}^{0}}}{{{\tau _{{e_0}}}f_{T}^{0}{N_T}+{\tau _{{e_0}}}({p_0}+\alpha {p_1})+{\tau _{{p_0}}}({n_0}+{\alpha ^{ - 1}}{n_1})}}} \right]$$

(3)

$$\delta ={n_0}+{p_0}+{p_0}{N_T}.\left[ {\frac{{{\tau _{{e_0}}}f_{T}^{0} - {\tau _{{p_0}}}(1 - f_{T}^{0})}}{{{\tau _{{p_0}}}(1 - f_{T}^{0}){N_T}+{\tau _{{e_0}}}({p_0}+\alpha {p_1})+{\tau _{{p_0}}}({n_0}+{\alpha ^{ - 1}}{n_1})}}} \right]$$

(4)

where N _T is the trap density, α is the absorption coefficient and f _T is the Fermi level in the trap states.

Total SRH lifetime is given as

$$\frac{1}{{{\tau _{{\text{SRH}}}}}}=\frac{1}{{{\tau _{{\text{vac}}}}}}+\frac{1}{{{\tau _{{\text{ext}}}}}}$$

(5)

Empirically fitted formulation for lifetime in InGaAs is given as (N = doping density):

$$\tau ={[\tau _{{{\text{SRH}}}}^{{ - 1}}+BN+C{N^2}]^{ - 1}}$$

(6)

where τ _SRH = 47.4 μs, B = 1.43 × 10⁻¹⁰ cm⁻³ s⁻¹, C = 8.1 × 10⁻²⁹ cm⁻⁶ s⁻¹.

Surface recombination velocity (s) is given as

$$s=\frac{{{{({K_{\text{n}}}{K_{\text{p}}})}^{1/2}}{N_{\text{T}}}(n+p)}}{{2{n_{\text{i}}}\left[ {\cosh \left\{ {\left( {\frac{{{E_{\text{f}}} - {E_{\text{i}}}}}{{kT}}} \right) - {\psi _0}} \right\}+\cosh \left( {{\psi _{\text{s}}} - {\psi _0}} \right)} \right]}}$$

(7)

$$\frac{s}{{{s_{\hbox{max} }}}}=\frac{{\cosh \left[ {\left( {\frac{{{E_{\text{f}}} - {E_{\text{i}}}}}{{kT}}} \right) - {\psi _0}} \right]+1}}{{\cosh \left[ {\left( {\frac{{{E_{\text{f}}} - {E_{\text{i}}}}}{{kT}}} \right) - {\psi _0}} \right]+\cosh ({\psi _{\text{s}}} - {\psi _0})}}$$

(8)

where Ψ _s and Ψ ₀ are the surface potential and bulk potential, respectively. K _n and K _p are the probability of capturing electron and hole, respectively; K _n = 2–6 × 10¹⁵ cm², K _p = 1–3 × 10¹⁵ cm² and ${\psi _{\text{s}}}=\frac{{qNW}}{{2{\varepsilon _{\text{s}}}}}$

$$G - R{\text{ bulk contribution is given as}},{I_{{\text{gr}}}}=\frac{{q{n_{\text{i}}}f(b)}}{{{\tau _{{\text{eff}}}}}}W{A_{\text{j}}}$$

(9)

where A _j and W are area and width of the junction. The n _i and τ _eff are intrinsic carrier concentration and effective life time, respectively. $f(b)=\frac{{\left| {{E_{\text{t}}} - {E_{\text{i}}}} \right|/kT}}{{\exp \left( {\left| {{E_{\text{t}}} - {E_{\text{i}}}} \right|/kT} \right)}}$; In general f(b) ~ 1 is taken.

G–R surface contribution in the mesa geometry is given as

$${I_{{\text{gr}}}}=\frac{{q{n_{\text{i}}}f(b)}}{{{\tau _{{\text{eff}}}}}}[{A_{\text{s}}}.{d_{\text{s}}}]=\frac{{q{n_{\text{i}}}f(b)}}{{{\tau _{{\text{eff}}}}}}[4A_{{\text{j}}}^{{1/2}}.W.{d_{\text{s}}}]$$

$${I_{{\text{gr}}}}={\text{ }}q{\text{ }}{n_{\text{i}}}f\left( b \right){\text{ }}\left[ {{P_{\text{j}}}W} \right]{\text{ }}.s{\text{ }};{\text{ where }}{P_{\text{j}}}\left( {{\text{perimeter of the diode}}} \right){\text{ }}={\text{ }}4.{\text{ }}{A_{\text{j}}}^{{1/2}}$$

(10)

where collection area, A _o,p = (A _j ^1/2 + 2L _e)²; L _e is diffusion length of electron.

The photo current is given as

$${I_{{\text{ph}}}}=q.A.\left[ {\int\limits_{{{\lambda _1}}}^{{{\lambda _2}}} {{\eta _{(\lambda )}}.} {\phi _{(\lambda ,T)}}.d\lambda } \right]$$

(11)

Quantum efficiency (η) is given as

$$\eta =\frac{{(1 - R)\alpha {L_{\text{e}}}}}{{{\alpha ^2}L_{{\text{e}}}^{2} - 1}}\exp \left\{ {\left( { - \alpha ({W_{\text{f}}}+{W_{\text{j}}})} \right)} \right\}.\left[ {\alpha {L_{\text{e}}} - \frac{{\frac{{{S_{\text{e}}}{L_{\text{e}}}}}{{{D_{\text{e}}}}}(\cosh \frac{{{W_{\text{b}}}}}{{{L_{\text{e}}}}} - \exp ( - \alpha {W_{\text{b}}}))+\sinh \frac{{{W_{\text{b}}}}}{{{L_{\text{e}}}}}+\alpha {L_{\text{e}}}\exp ( - \alpha {W_{\text{b}}})}}{{\left(\frac{{{S_{\text{e}}}{L_{\text{e}}}}}{{{D_{\text{e}}}}}.\sinh \frac{{{W_{\text{b}}}}}{{{L_{\text{e}}}}}+\cosh \frac{{{W_{\text{b}}}}}{{{L_{\text{e}}}}}\right)}}} \right]$$

(12)

where R is the back side reflection of infrared radiation. The W _f, W _j and W _b are the thickness of the front region, junction region and back side region, respectively. The thickness of back side region changes with the variation of the absorber layer.

The number of electrons collected from the detector as a function of irradiance and IR background is given as

$${\text{No}}.{\text{ of electrons }}=\left( {\frac{{{I_{\text{d}}}+{I_{{\text{ph}}}}}}{q}} \right).q.\eta .M$$

(13)

where t _i is the integration time, M is the avalanche gain, and η _i is the injection efficiency for a DI/BDI circuit. The I _d and I _ph are the dark current and photo current, respectively.

Then, NEPh is given as

$${\text{NEPh}}=\frac{1}{{M\eta }}\sqrt {\frac{{{I_{\text{d}}}{\tau _{{\text{gate}}}}{M^2}F(M)}}{q}}$$

(14)

where F(M) = excess noise factor and τ _gate = integration period.