TECHNICAL FIELD
The present invention relates to an ultra high speed avalanche
photodiode.

BACKGROUND ART
An avalanche photodiode (APD) is a photodetector device,
which multiplies carriers (electrons and holes) generated by light absorption through
an avalanche mechanism and is used as an optical receiver with a low noise by taking
out its output current. Recent APDs for a long wavelength band generally have a
separated absorption and multiplication (SAM) structure, where a light absorbing
layer and an avalanche multiplication layer are separated. In this SAM structure,
in order to control electric field intensities of the light absorbing layer and
the avalanche multiplication layer, an electric field control layer and a graded
bandgap layer are provided between the two layers.

APDs are widely introduced to systems of 2.5Gbit/s and
10Gbit/s and are in a midst of development as elements for 40Gbit/s system of the
next generation.

In a technical field of such ultra high speed APD, APDs
of "electron injection type", which are advantageous from the view points of high
speed operation, are attracting attention rather than those of "hole injection type"
adopting InP, which is a structure hitherto been typically used as a structure for
relatively slow speed operation, as the avalanche multiplication layer. Typical
APDs of electron injection type reported so far are those having depleted InGaAs
as the light absorbing layer and the InAlAs as the avalanche multiplication layer,
respectively.

Fig. 1 is a band diagram of the APD of such electron injection
type under operating conditions. In this diagram, reference numerals 41, 42, 43,
44, 45, 46, and 47 denote an n-type electrode layer, an avalanche multiplication
layer (InAlAs), an electric field control layer, a graded bandgap layer, a low-doped
light absorbing layer (InGaAs), a p-type electrode layer, and a p electrode, respectively.
Note that the light absorbing layer 45 is depleted throughout its entire region.

A structure of the APDs of such "electron injection type"
is advantageous in the high speed operation. However, on the other hand, since a
bandgap of InAlAs used as the avalanche multiplication layer is larger than that
of InP, which has been used as the avalanche multiplication layer in a "hole injection
type", the reduction in ionisation coefficient when a constant electric field intensity
is applied, is inevitable and there is a problem that an operating voltage of the
device is increased.

Apart from such a structure, a structure of the APD of
"electron injection type" where the light absorbing layer is constituted of a p-type
neutral layer (undepleted region) and a neighbouring thin low concentration layer
(depleted region), and making the p-type neutral layer which is the undepleted region
as the major light absorbing layer, is also reported (see Document 1).

Fig. 2 is a band diagram of such an APD of electron injection
type under operating conditions. In this diagram, reference numerals 51, 52, 53,
54, 55, 56, 57, and 58 denote an n-type electrode layer, an avalanche multiplication
layer, an electric field control layer, a bandgap inclined layer, a low concentration
light absorbing layer (low concentration layer), a p-type light absorbing layer
(p-type neutral layer), a p-type electrode layer, and a p electrode, respectively.
Note that the p-type neutral layer, which is a non-depleted region, is an InGaAs
layer.

A light absorbing layer of electron injection type APD
of this structure is mostly occupied by a p-type light absorbing layer 56, which
is the undepleted region. In other words, this structure is a "structure of making
the light absorbing layer as p-type as much as possible." Although the major advantage
of the APD with a structure shown in this figure is the dark current reduction,
it is also an effective structure for reduction in an operating voltage.

Determination of the light absorbing layer thickness is
important in order to obtain a desired performance of the APD. If a carrier generation
rate (quantum efficiency) is not high during a state where the avalanche multiplication
is absent (a pin photodiode operation), a high S/N ratio cannot be ensured even
if the avalanche multiplication is carried out. Thus, this is the reason why designing
a thickness (W_{A}) of light absorbing layer as thick as possible in a condition
of a frequency response bandwidth needed to be ensured.

However, when an attempt is made to realize an operating
speed of 10Gbit/s or higher with the structure shown in Fig. 2 where the p-type
neutral layer is the main light absorbing layer, a problem of reduction in a light
absorption efficiency (quantum efficiency) arises due to a trade-off relationship
between a carrier transit time and a quantum efficiency. This is caused by a fact
that the carrier velocity in the p-type neutral InGaAs layer is usually smaller
than that in the depleted InGaAs layer. In other words, this is because when the
carrier transit time is designed so as to become equal to or lower than a certain
value, an upper limit of a thickness of the p-type neutral InGaAs layer (p-type
neutral layer) becomes thinner than that when using a depleted InGaAs layer.

Semiquantitative estimation for the frequency response
bandwidth as a function of the light absorbing layer thickness will be described
below.

The APD can be considered as a structure where a relatively
thin avalanche multiplication layer is connected to a pin-type photodiode. Its bandwidth
gradually decreases from an intrinsic bandwidth (intrinsic 3dB bandwidth) in a state
operating as the pin-photodiode and in then gradually approaches along a line of
constant gain-bandwidth product as the avalanche multiplication factor increases.
It is important to maintain the intrinsic 3dB bandwidth high enough during the pin-photodiode
operation together with the gain-bandwidth product high in order to obtain appropriately
high gain. The intrinsic 3dB bandwidth during the pin-photodiode operation is determined
by the carrier transit time in the light absorbing layer and the multiplication
layer. However, since the multiplication layer is far thinner than the light absorbing
layer in a normal APD structure, the carrier transit time in the light absorbing
layer is a dominant factor giving the intrinsic 3dB bandwidth.

A multiplication layer structure can be designed almost
independently from the light absorbing layer and it can be considered that the carrier
transit time in the multiplication layer is commonly added. Thus, a bandwidth when
taking only by the light absorbing layer into account is considered here. A saturation
velocity (V_{h} = 5 × 10^{6} cm/s) of holes is far smaller
than that of electrons. Therefore, when it is approximated that the carrier transit
time t_{D} in a structure (light absorbing layer thickness W_{AD})
where all the light absorbing layers are depleted, is determined by v_{h},
according to a charge control model, Formula (1) can be obtained.

$${\mathrm{t}}_{\mathrm{D}}={\mathrm{W}}_{\mathrm{A}\mathrm{D}}/3{\mathrm{v}}_{\mathrm{h}}$$

Moreover, 3dB bandwidth (f_{3dB}) is given by Formula
(2).

$${\mathrm{f}}_{3\mathrm{\hspace{0.17em}}\mathrm{dB},\mathrm{D}}=1/\left[2\mathrm{\&pgr;}{\mathrm{t}}_{\mathrm{D}}\right]=\left[1/{\mathrm{W}}_{\mathrm{A}\mathrm{D}}\mathrm{\hspace{0.17em}}\left(\mathrm{\&mgr;m}\right)\right]\times 24\mathrm{\hspace{0.17em}}\mathrm{GHz}$$

For example, when considering a margin in device design,
W_{AD} needs to be approximately 1.2 µm since f_{3dB,D} = 20GHz
is a measure for the 3dB bandwidth of APDs receiving 10Gbit/s signals. In order
to maintain the hole saturation velocity throughout the entire region of this W_{AD},
the electric field intensity needs to be 50 kV/cm or higher, in other words, a voltage
needs to be at least 6 V or higher. Accordingly, since the electric field intensity
of the light absorbing layer at the bias voltage for the avalanche multiplication
is normally designed to be approximately 100 kV/cm, a voltage drop over the light
absorbing layer part becomes 12 V, which is considerably large.

On the other hand, when the light absorbing part is only
of a p-type neutral layer (with a constant concentration and a thickness of W_{AN}),
the carrier transit time &tgr;_{N} is determined by a diffusion time of
electrons. Since holes generated in the p-type light absorbing layer are majority
carriers, they respond in order to maintain charge neutrality not as hole motion
but as a hole current. Hence, a hole transport does not participate directly in
a response speed. Assuming a diffusion coefficient of electrons to be D_{e},
the carrier transit time (t_{N}) is derived by Formula (3).

$${\mathrm{t}}_{\mathrm{N}}={{\mathrm{W}}_{\mathrm{AN}}}^{2}/3{\mathrm{D}}_{\mathrm{e}}$$

The 3dB bandwidth (f_{3dB}) is approximated by
Formula (4).

$${\mathrm{f}}_{3\mathrm{\hspace{0.17em}}\mathrm{dB},\mathrm{N}}=1/\left[2\mathrm{\&pgr;}{\mathrm{t}}_{\mathrm{N}}\right]$$

When InGaAs with a doping concentration of 3 × 10^{17}
cm^{3} is used for the light absorbing layer, an electron mobility is 6,000
cm^{2}/V_{S} and a diffusion coefficient is approximately 150 cm^{2}/s.
Then the following formula is established.

$${\mathrm{f}}_{3\mathrm{\hspace{0.17em}}\mathrm{dB},\mathrm{N}}=\left[1/{{\mathrm{W}}_{\mathrm{AN}}}^{2}\mathrm{\hspace{0.17em}}\left({\mathrm{\&mgr;m}}^{2}\right)\right]\times 7.2\mathrm{\hspace{0.17em}}\mathrm{GHz}$$

In a similar way, when considering f_{3dB,N} =
20 GHz as a measure, W_{AN} needs to be approximately 0.6 µm or lower.
When the p-type neutral light absorbing layer is used, it is advantageous for reducing
an APD operating voltage since the voltage for a carrier transit is not required.
On the other hand, since the light absorbing layer thickness is relatively thin
being 0.6 µm, which is about a half of that of the depleted light absorbing
layer, a quantum efficiency of 1.5 µm band remains 50 % or less and it becomes
difficult to realize an APD with a high sensitivity.

As described so far, when an attempt is made to realize
a reduction in the operating voltage, which is desired in APDs, by using p-type
a neutral light absorbing layer, a problem of a reduction in a quantum efficiency
of devices operating in a high speed of 10Gbit/s or higher arises.

Document 1:
Japanese Patent No. 3141847

DISCLOSURE OF THE INVENTION
The present invention is made in light of such problems
and its object is to provide an ultra high speed APD, which is capable of realizing
the reduction in an operating voltage and achieving a high quantum efficiency at
the same time.

In the present invention, in order to achieve such an object,
an invention according to a first aspect of the present invention is an APD comprising:
a stacked layer bady in which an n-type electrode layer, an avalanche multiplication
layer, an electric field control layer, a graded bandgap layer, a light absorbing
layer with a layer thickness of W_{A}, and a p-type electrode layer are
stacked sequentially, wherein the light absorbing layer has a junction of a p-type
layer with a layer thickness of W_{AN} located on the side of the p-type
electrode layer and a low concentration layer with a layer thickness of W_{AD}
located on the side of the graded bandgap layer , an each doping profile of the
p-type and the low concentration layers is determined under device operating conditions
so that a p-type neutral state is maintained for the p-type layer except a region
in a vicinity of an interface of the junction with the low concentration layer while
the low concentration layer is depleted, and a ratio between the layer thickness
W_{AN} of the p-type layer and the layer thickness W_{AD} of the
low concentration layer is determined so as to satisfy a next formula in a case
where t_{total} is a delay time of element response accompanying a transit
of carriers generated in the light absorbing layer by light absorption, t_{N2}
is a delay time caused by the p-type layer, t_{D1} is a delay time caused
by the low concentration layer, and t_{D} is a delay time when an entire
region of the light absorbing layer is the low concentration layer, under a condition
that a layer thickness W_{A} (= W_{AN} + W_{AD}) of the
light absorbing layer is constant.

$${\mathrm{t}}_{\mathrm{D}}>{\mathrm{t}}_{\mathrm{total}}=\left({\mathrm{W}}_{\mathrm{A}\mathrm{D}}\times {\mathrm{t}}_{\mathrm{D}1}+{\mathrm{W}}_{\mathrm{A}\mathrm{N}}\times {\mathrm{t}}_{\mathrm{N}2}\right)/{\mathrm{W}}_{\mathrm{A}}$$

In a second aspect of the present invention, according
to the first aspect of the present invention, the ratio between the layer thickness
W_{AN} of the p-type layer and the layer thickness W_{AD} of the
low concentration layer is determined so that a formula [(W_{AD} ×
t_{D1} + W_{AN} × t_{N2}) / W_{A}] takes on
a local minimum.

A third aspect of the present invention, according to the
first aspect of the present invention, the p-type layer and the low concentration
layer are formed of an InGaAsP mixed crystal semiconductor, and a depletion thickness
of the low concentration layer during the device operation is thicker than 0.3 µm
(W_{AD} > 0.3 µm).

According to the present invention, substantial reduction
in the operating voltage is possible compared to the conventional APDs and it is
possible to realize more reliable elements and a power reduction of a light receiver.
Moreover, the device design is possible for a required bandwidth so as to achieve
a maximum quantum efficiency (in other words, best receiver sensitivity).

As described so far, the present invention is the one to
provide the ultra high speed APD capable of realizing reduction in the operating
voltage and increase in the quantum efficiency in a bandwidth used at the same time,
and to contribute in a stable operation and enhanced performance of an ultra high
speed optical receiver including a 10 Gbit/s region for example.

BRIEF DESCRIPTION OF THE DRAWINGS

- Fig. 1 is a band diagram of a conventional typical avalanche photodiode (APD)
of electron injection type under operating conditions.
- Fig. 2 is a band diagram of an avalanche APD of electron injection type disclosed
in Document 1 under operating conditions.
- Fig. 3A is a schematic diagram of a cross sectional structure of an APD of the
present invention.
- Fig. 3B is a band diagram of the APD of the present invention under operating
conditions.
- Fig. 4 is a diagram for explaining a sample calculation of a delay time (t
_{total})
of element response accompanying a carrier transit and dependency of a 3dB bandwidth
on a thickness W_{AN} of a p-type neutral light absorbing layer.
- Fig 5A is a diagram for explaining variation in a carrier transit time and the
3dB bandwidth during a pin-PD operation of the APD of the present invention, and
for explaining a sample calculation of t
_{total} and f_{3dB} when
W_{A} = W_{AD} + W_{AN} = 0.8 µm, D_{e} = 150
cm^{2}/s, and V_{h} = 5 × 10^{6} cm/s.
- Fig 5B is a diagram for explaining variation in the carrier transit time and
the 3dB bandwidth during the pin-PD operation of the APD of the present invention
and for explaining a sample calculation of t
_{total} and f_{3dB}
when a structure is adopted where f_{3dB} = 80GHz when optimized.

BEST MODE FOR CARRYING OUT THE INVENTION
Embodiments of the present invention will be described
below by referring to the drawings.

(First Embodiment)
Figs 3A and 3B are diagrams for explaining a configuration
example of an APD of the present invention, and Fig 3A is a cross sectional view
and Fig. 3B is a band diagram during operation. In these figures, reference numerals
11, 12, 13, 14, 15, 16, 17, 18, and 19 denote an n-type electrode layer of n-type
InP, an InP avalanche multiplication layer, an InP electric field control layer,
an InGaAsP graded bandgap layer, a low concentration light absorbing layer of InGaAs
of low concentration, a p-type light absorbing layer of p-type InGaAs, a p-type
electrode layer of p-type InGaAsP, and metal electrodes (n electrode and p electrode),
respectively. Note that the p-type light absorbing layer 16 and the low concentration
light absorbing layer 15 can be formed as InGaAsP mixed crystal semiconductors and
are not limited to InGaAs.

In this APD, doping concentration distribution of each
of the light absorbing layers is determined so that a neutrality of p-type light
absorbing layer 16 (undepleted) is maintained except a part on the side of low concentration
light absorbing layer 15 and also the low concentration light absorbing layer 15
(depleted light absorbing layer) is depleted.

When light signals are given to the light absorbing layers,
electron/hole pairs are generated in the p-type light absorbing layer 16 and the
low concentration light absorbing layer 15. Electron flow from the p-type light
absorbing layer 16 into the electrode 19 is blocked by a potential barrier formed
in the p-type electrode layer 17 and diffuse into the depleted low concentration
light absorbing layer 15. At the same time, electrons and holes in the depleted
low concentration light absorbing layer 15 respectively drift in the opposite directions
by an electric field to flow to both sides of the low concentration light absorbing
layer 15. Electrons generated in these two light absorbing layer reach the avalanche
multiplication layer 12 via the graded bandgap layer 14 of InGaAsP and the electric
field control layer 13 of InP, and cause an impact ionisation (avalanche multiplication).

Only a depleted part of the low concentration light absorbing
layer 15 generates a voltage drop in the light absorbing layer. Accordingly, when
using a similar avalanche multiplication layer, a voltage required for an operation
is lowered compared to that of the conventional APDs where all the light absorbing
layers are depleted. For example, in order to ensure a sufficient quantum efficiency,
the voltage drop in the light absorbing layer is approximately 12 V in a conventional
typical structure where the light absorbing layer is depleted throughout its entire
region and a light absorbing layer thickness is 1.2 µm. On the other hand,
according to the APD of the present invention, when a layer thickness of the depleted
low concentration light absorbing layer 15 is W_{AD} = 0.7 µm and a
layer thickness of the p-type light absorbing layer 16 is W_{AN} = 0.5 µm,
by assuming an electric field of the light absorbing layer 100 kV/cm during operation
of avalanche multiplication, the voltage drop is 7 V and the required operating
voltage of the APD is reduced by 5V.

On the other hand, although a "structure of making the
light absorbing layer as p-type as much as possible" shown in Fig. 2 is suited for
the reduction in an operating voltage, it cannot avoid a constraint of reduction
in efficiency when ensuring an operating bandwidth above a certain level (for example
10 Gbit/s operation) as described above.

Fig. 4 is a diagram for explaining a sample calculation
of a delay time (t_{total}) of element response accompanying the carrier
transit and dependency of the 3dB bandwidth on the thickness W_{AN} of the
p-type light absorbing layer of the APD of the present invention in a case where
a total thickness of the light absorbing layer is 1.2 µm. From this diagram,
it can be interpreted that a similar level of performance to that of the conventional
APD can be realized in terms of the operation bandwidth, with the assumption that
W_{AD} = 0.7 µm and W_{AN} = 0.5 µm.

After all, according to the present invention, the operating
voltage can be reduced by 5 V while maintaining the same quantum efficiency and
an operating speed as those of the conventional APDs. In terms of an operating speed,
note that as will be described in detail in the next "second embodiment", a "structure
combining the depleted light absorbing layer and the p-type light absorbing layer
under a condition of a constant light absorbing layer thickness" always give a parameter
range where realization of a higher bandwidth compared to that of the conventional
APDs is possible.

Differences between the APD described in Document 1 and
that of the present invention here is described as follows. That is, the aim of
the APD in Document 1 is to improve "deterioration of a dark current with time"
while that of the present invention is "realization of compatibility between voltage
reduction and quantum efficiency enhancement."

In the APD in Document 1, for achieving such purpose, the
layer thickness of the depleted light absorbing layer is made thin enough to enhance
the effect of surface area minimization. The effect results in suppressing deterioration
of the dark current with time. Therefore, the APD described in Document 1 is able
to realize stable dark current characteristics/high reliability. On the other hand,
the present invention is enabling "realization of compatibility between voltage
reduction and quantum efficiency enhancement" by "determining the thicknesses of
depleted and undepleted regions so that the total carrier transit time takes on
a local minimum."

As a result of such differences in the configuration, thicknesses
of the depleted and undepleted regions are set independently in the APD described
in Document 1. On the other hand, thicknesses of the depleted and undepleted regions
are determined (optimized) so that the total carrier transit time takes on the local
minimum under a condition that the total thickness of the light absorbing layer
constituted by these regions is constant in the present invention.

Note that when comparing a level of the dark current of
the APD with the structure shown in Fig. 2, since the depleted light absorbing layer
of the APD of the present invention is thicker, this thickness of the depleted light
absorbing layer can become a cause of increase in the dark current. However, such
dark current can be avoided as an APD provided with a guard ring structure in order
to lower an electric field intensity on a device surface.

(Second Embodiment) When the carrier transit time, which
is independent in each layer (in the depleted light absorbing layer and the p-type
light absorbing layer), in the bandwidth during the pin-PD operation of the APD
of the present invention is determined, basically following Formulae (1) and (3).
First, t_{N} = W_{AN}
^{2} / 3D_{e} is obtained as the carrier transit time in the p-type
light absorbing layer. Moreover, since a layer thickness of an avalanche layer is
thin, when ignoring influences of the part, t_{D} = W_{AD} / 3v_{h}
is obtained as the carrier transit time in the depleted light absorbing layer.

In accordance with a definition in a charge control model,
a relationship between charge variation (&Dgr;Q_{D} and &Dgr;Q_{N}
in the depleted and the p-type light absorbing layers, respectively) and current
variation (&Dgr;I_{D} and &Dgr;I_{N} in the depleted and the
p-type light absorbing layers, respectively) in respective layers is described by
the following formula.

$${\mathrm{t}}_{\mathrm{D}}=\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{D}}/\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{D}},\mathrm{\hspace{0.17em}}{\mathrm{t}}_{\mathrm{N}}=\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{N}}/\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{N}}$$

By setting the total thickness of the light absorbing layer
W_{A} = W_{AD} + W_{AN}, when carriers are generated at
the same time in each layer, generally, the total carrier transit time t_{total}
is not a simple sum (t_{D} + t_{N}). This is because in a general
structure, since carriers generated in a depleted layer "D1" and a neutral layer
"N2" affect charge density in each other's region, terms of charge increment (&Dgr;Q_{N1}
and &Dgr;Q_{D2}) in each other's region are added. After all, the relationship
between the charge variation (&Dgr;Q_{D1} + &Dgr;Q_{N1} and
&Dgr;Q_{N2} + &Dgr;Q_{D2}) and the current variation (&Dgr;I_{D}
and &Dgr;I_{N}) due to carrier generation in the depleted layer "D1" and
the neutral layer "N2" is given by the following formula.

$${\mathrm{t}}_{\mathrm{D}1}=\left(\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{D}1}+\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{N}1}\right)/\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{D}},\mathrm{\hspace{0.17em}}{\mathrm{t}}_{\mathrm{N}2}=\left(\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{N}2}+\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{D}2}\right)/\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{N}}$$

Note here the relationships t_{D1} ≥ t_{D}
and t_{N2} ≥ t_{N}.

However, in an electron ejection structure using an InP
semiconductor with extremely different velocities of electrons and holes, the total
carrier transit time is approximated by the following formula when the transit time
of layers other than the light absorbing layers is ignored.

$${\mathrm{t}}_{\mathrm{total}}=\left({\mathrm{W}}_{\mathrm{A}\mathrm{D}}\times {\mathrm{t}}_{\mathrm{D}1}+{\mathrm{W}}_{\mathrm{A}\mathrm{N}}\times {\mathrm{t}}_{\mathrm{N}2}\right)/\mathrm{W}$$

The formula described above is in a form of sum of t_{D1}
and t_{N1} proportionally weighted by the layer thickness.

The reason why it can be simplified as Formula (8) is as
follows. When the electron velocity is sufficiently larger than the hole velocity,
electron charge injected from the p-type light absorbing layer to the depleted light
absorbing layer changes a charge state (determined mostly by holes) only slightly
in the depleted layer. On the other hand, when the holes generated in the depleted
light absorbing layer flow into the p-type light absorbing layer, charges are not
induced since the p-type light absorbing layer is neutral. Accordingly, a condition
of &Dgr;Q_{N1} = &Dgr;Q_{D2} = 0 is established and a total
charge variation is approximated as &Dgr;Q_{D1} + &Dgr;Q_{N2}.
A transit time for the total charge is described by the following formula by taking
a sum (= &Dgr;I_{D} + &Dgr;I_{N}) of amount of current variation.

$${\mathrm{t}}_{\mathrm{total}}=\left(\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{D}1}+\mathrm{\&Dgr;}{\mathrm{Q}}_{\mathrm{N}2}\right)/\left(\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{D}}+\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{N}}\right)$$

Furthermore, since &Dgr;I_{D} and &Dgr;I_{N}
are proportional to the corresponding layer thicknesses W_{AD} and W_{AN},
the following formula is derived from Formulae (8) and (9).

$${\mathrm{t}}_{\mathrm{total}}\fallingdotseq \left(\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{D}}\times {\mathrm{t}}_{\mathrm{D}1}+\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{N}}\times {\mathrm{t}}_{\mathrm{N}2}\right)/\left(\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{D}}+\mathrm{\&Dgr;}{\mathrm{I}}_{\mathrm{N}}\right)\fallingdotseq \left({\mathrm{W}}_{\mathrm{A}\mathrm{D}1}\times {\mathrm{t}}_{\mathrm{D}}+{\mathrm{W}}_{\mathrm{A}\mathrm{N}}\times {\mathrm{t}}_{\mathrm{N}}\right)/\left({\mathrm{W}}_{\mathrm{A}\mathrm{D}}+{\mathrm{W}}_{\mathrm{A}\mathrm{N}}\right)=\left({{\mathrm{W}}_{\mathrm{AD}}}^{2}/3{\mathrm{v}}_{\mathrm{h}}+{{\mathrm{W}}_{\mathrm{AN}}}^{3}/3{\mathrm{D}}_{\mathrm{e}}\right)/{\mathrm{W}}_{\mathrm{A}}=\left[{\left(\mathrm{W}-{\mathrm{W}}_{\mathrm{A}\mathrm{N}}\right)}^{2}/3{\mathrm{v}}_{\mathrm{h}}+{{\mathrm{W}}_{\mathrm{AN}}}^{3}/3{\mathrm{D}}_{\mathrm{e}}\right]/{\mathrm{W}}_{\mathrm{A}}$$

Since the bandwidth is approximated by f_{3dB}
= 1 / [2&pgr;t_{total}], by setting W_{AD} and W_{AN}
so that t_{total} in Formula (10) becomes minimum, the bandwidth of the
APD of the present invention can be maximized.

When W_{A} is constant, Formula (10) takes on the
local minimum at:

$${\mathrm{W}}_{\mathrm{A}\mathrm{N}}=\left[-2{\mathrm{D}}_{\mathrm{e}}/3{\mathrm{v}}_{\mathrm{h}}+\left[{\left(2{\mathrm{D}}_{\mathrm{e}}/3{\mathrm{v}}_{\mathrm{h}}\right)}^{2}+8\mathrm{W}{\mathrm{D}}_{\mathrm{e}}/3{\mathrm{v}}_{\mathrm{h}}\right]{\mathrm{n}}^{0.5}\right]/2.$$

When being deviated from this, t_{total} increases
and f_{3dB} decreases.

An important point here is that the bandwidth increases
by adopting the combined structure of the depleted and p-type light absorbing layers
under a condition that the total thickness of the light absorbing layer W_{A}
= W_{AD} + W_{AN} is constant. Moreover, since a local minimum point
of t_{total} is clearly a monotonically increasing function of W, it is
understood that a combination of W_{AD} and W_{AN} giving the local
minimum point of t_{total} gives a maximum value of W_{A}, i.e.
a maximum point of the quantum efficiency for a constant t_{total} or f_{3dB}.

(Third Embodiment)

The combination of W_{AD1} and W_{AN} where the bandwidth f_{3dB}
becomes maximum in a specific structure of the APD of the present invention will
be described below. Here, an APD of 40 Gbis/s is considered as a structure example.

Fig. 5A is a diagram for explaining sample calculations
of t_{total} and f_{3dB} by setting W_{A} = W_{AD}
+ W_{AN} = 0.8 µm, D_{e} = 150 cm^{2}/s, V_{h}
= 5 × 10^{6} cm/s. When the thickness of the p-type light absorbing
layer is W_{AN} = 0.31 µm and the thickness of the depleted light absorbing
layer is W_{AD} = 0.49 µm, t_{total} takes on a minimum value
of 2.8 ps and f_{3dB} takes on a maximum value of 55 GHz. In other words,
when compared to f_{3dB} (11 GHz) in a structure configured only by the
p-type light absorbing layer or f_{3dB} (30 GHz) in a structure configured
only by the depleted light absorbing layer, a dramatic increase in bandwidth can
be expected.

An operation of the APD is restricted by a gain-bandwidth
product and its limit is considered to be approximately 200 GHz. A bandwidth capable
of obtaining a meaningful avalanche multiplication gain M (for example M = 2.5)
is approximately 80 GHz at a maximum.

Fig. 5B is a diagram for explaining sample calculations
of t_{total} and f_{3dB} in a case of a structure in which a constant
thickness of the light absorbing layer 0.6 µm, and f_{3dB} = 80 GHz
are set when optimized. From this diagram, W_{AN} = 0.26 µm and W_{AD}
= 0.34 µm are obtained as thicknesses of the p-type and the depleted light
absorbing layers giving maximum f_{3dB}. After all, the design method in
the present invention indicates that the thickness of the depleted light absorbing
layer of the avalanche photodiode which is practically meaningful is within a range
of W_{AD} > 0.3 µm, and an optimal thickness of the depleted light
absorbing layer tends to increase in APDs with a lower operating speed than that
handled in Fig. 3B.

Note that although explanations are made based on the charge
control model in the above described second and third embodiments in order to avoid
complications in the explanation, it is needless to say that methods other than
the charge control model can be applied for executing the present invention. For
example, by using a method based on continuous formulae using velocity-electric
field characteristics of carriers in devices or by a method of Monte Carlo calculation,
structure optimization with higher precision is possible without adding any changes
to a guideline related to a configuration method of the APD, which forms a base
of the present invention.

Moreover, although an electron transport in the p-type
light absorbing layer is treated based on a diffusion mechanism, a structure provided
with a quasi electric field by bandgap grading is also effective in reducing the
carrier transit time. Although an optimal ratio between W_{AN} and W_{AD}
when adopting this structure is different from that when the electron transport
in the p-type light absorbing layer is only diffusion, a device design is possible
based on a principle of "making the total carrier transit time a local minimum",
which is a basic principle of the present invention.

INDUSTRIAL APPLICABILITY
The present invention enables to provide an ultra high
speed APD capable of realizing operating voltage reduction and quantum efficiency
enhancement at the same time.