**Author details**

sion (21) from (Pospelov et al, 1974). It determines dependence *χ*(*t*)≡*r* /*r*0, where *r*(*t*) and *r*<sup>0</sup> – current and initial radii of charge "drop" of parabolic type. Implying under capacity in

The above analysis shows that to create high performance SAM-APD (in particular, based on widely used *InP* / *I nxGa*1−*<sup>x</sup>AsyP*1−*<sup>y</sup>* / *InP* heterostructures) it is necessary to maintain close tolerances on dopants concentration in wide-gap multiplication layer I – *N*1 and in narrowgap absorption layer II – *N*2, and also on thickness *W*<sup>1</sup> of wide-gap multiplication layer (Fig. 1). This is due to strong dependence of interband tunnel current in such heterostructures on *N*1,*N*2 and *W*1. Allowable variation intervals of values *N*1,*N*2 and *W*1, and, optimal thick‐ ness of absorber also, can be determined using results obtained in Sections 4 and 5. Value of minimal possible time-of-response *τ*min depends not only on photocurrent's gain *Мph* but on allowable noise density at preset value of photocurrent's gain also. The lower noise density, the larger is value *τ*min. For example, for heterostructure *InP* / *I n*0.53*Ga*0.47*As* / *InP* minimal time-of-response equals to *τ*min <sup>≈</sup>0.6 ns, when noise current equals to 3.3×10−<sup>11</sup> А/Hz1/2 and current responsivity 10.3 A/W. Analysis shows that operational speed can be slightly in‐ creased by means of inhomogeneous doping of wide-gap multiplication layer. To ensure op‐ erational speed in picosecond range it is necessary to use as multiplication layer semiconductor layer with low tunnel current and impact ionization coefficients of electrons and holes much different from each other, for example, indirect-gap semiconductor silicon. As has long been known maximal operational speed is achieved by APD if light is absorbed in space-charge region. In this case, as it was shown in Section 6, when bias voltage *Vb* ex‐ ceeds breakdown voltage *VBD* of no more than a few volts, then, for *K* ≡*β* / *α* values lying in interval from a few hundredths to a few tens, elementary relations (145) can be used for ap‐ proximate description of Geiger mode in *p* −*i* −*n* APD. Moreover if cross-section area

, then we can expect that in single-photon case under *S* in (145) should imply

value of order *S*1. This is due to finite size of single-photon spot *S*<sup>1</sup> and not intensive spread‐ ing of charge during time of avalanche Geiger process *tav* when photogeneration of charge carriers occurs in *i* – region of *p* −*i* −*n* structure depleted by charge carriers. Proposed ap‐ proach allows describing Geiger mode by elementary functions at voltages higher *Vb* as well. Note that equation (140) and physical grownds allow to expect three possible process modes at pulse illumination under *Vb* >*VBD*. When *RC* < <*tav* then generated photocurrent will tend to reach some constant and flow indefinitely (unless, of course, ignore energy loss‐ es). When *RC* =*tav* then generated photocurrent will be of infinitely long oscillatory charac‐

*GE* =1 μm, *r*<sup>0</sup> <sup>=</sup>*<sup>λ</sup>* =1 μm, in the case of single-

21/4≅1.2. This justifies our assumption that charge spreading

and putting *Wi*

over sample cross-section during avalanche Geiger process is not intensive.

˜

(Pospelov et al, 1974) value *Ci*

94 Photodiodes - From Fundamentals to Applications

photon process we get *χ*(*tav*)<

**7. Conclusions**

*<sup>S</sup>* <sup>&</sup>gt;*S*<sup>1</sup> <sup>≈</sup>*<sup>π</sup>* <sup>×</sup>*<sup>λ</sup>* <sup>2</sup>

ter. When *RC* > >*tav* then Geiger mode is realized.

Viacheslav Kholodnov1 and Mikhail Nikitin2

1 V.A. Kotelnikov Institute of Radio Engineering and Electronics Russian Academy of Scien‐ ces, Moscow, Russia

2 Science & Production Association ALPHA, Moscow, Russia
