In the future, the photodetector having both high gain and high bandwidth could be expected. By combining the operating mechanism of the DNW-based photodiode, the spatially modulated photodiode (SMPD), and the phototransistor (PT), a device structure named DNW-based spatially modulated phototransistor (SMPT) is proposed.
The top view and cross section are depicted in Figure 6-1. Gi, Si, and Di respectively represent the gate, source, and drain of the phototransistor that provides the relatively immediate photocurrent; Gd, Sd, and Dd respectively represent the gate, source, and drain of the phototransistor that provides the relatively deferred photocurrent; B and R represent the common ‡oating bulk and the common outer ring, respectively.
The operating mechanism of this SMPT is described as follows. (i) By connecting the DNW to a positive supply voltage, the slowly di¤usive carriers generated in Psub can be decoupled from the photocurrent. (ii) By subtracting the deferred portion from the immediate portion of the photocurrent, the slowly di¤usive e¤ect in Pwell can be alleviated.
(iii) Through the internal transistor action under moderate bias, the phototransistor can have a photocurrent ampli…cation. Therefore, the SMPT would be an attractive candidate to achieve a high speed and a high responsivity at the same time.
Figure 6-1: The top view and cross section of the proposed SMPT to have a high gain and a high bandwidth.
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Theoretical Derivation of the Photocurrent
Appendix
1 Basic Equations
For the unshaded area, the incident photon ‡ux density in the frequncy domain (s = jw) is given by
0(s) = Popt(s)
A hc(1 R); (1)
where Popt(s) is the input optical power, A is the device area, is the wavelength of the incident light, h is the Plank’s constant, c is the speed of light, and R is the re‡ectance.
The electron-hole generation rate from optical excitation is given by
G(x; s) = 0(s)e x; (2)
where is the absorption coe¢ cient. The total photocurrent is contributed from two di¤erent regions: the depletion regions and the neutral regions. In a depletion region, the photocurrent density is mainly contributed by the drift current density, given by
Jdr(s) = q Z
G(x; s)dr: (3)
Then the drift current can be obtained by taking surface integrals as
Idr(s) = Z
Jdr(s) ds: (4a)
In a neutral region, the electric …eld is negligible and thus the photocurrent density is mainly contributed by the di¤usion current density. Therefore, the continuity equations of these photogenerated carriers in the frequency domain can be written as
sNp = G Np
n
+ Dnr2Np; (5a)
sPn = G Pn
p
+ Dpr2Pn; (5b)
where Np is the electron concentration in the p-type material, and Pn is the hole concen-tration in teh n-type material; p and n are the carrier lifetimes for electrons and holes,
Light source
L
1D
1L
2Nwell neutral region
Depletion region
Psub neutral region
x y z
Figure 1: Cross section of a single photodiode.
respectively; Dn and Dp are the di¤usion constants for electrons and holes, respectively.
Combining the continuity equations in Eqs. (5a) and (5b) with the boundary conditions yields the minority carrier concentrations Np and Pn, and the electron and hole di¤usion current density can be obtained as
Jn(s) = qDnrNp; (6a)
Jp(s) = qDprPn: (6b)
Then the electron and hole di¤usion currents can be obtained by taking surface integrals as
In(s) = Z
Jn(s) ds; (7a)
Ip(s) = Z
Jp(s) ds: (7b)
2 Single Photodiode
Consider a single photodiode structure shown in Fig. 1. The generation rates of carriers per unit volume in the time-domain and frequency-domain are
g(x; t) = 0(t)e x; (8)
Figure 2: Waveform of f1(x)
G(x; s) = 0(s)e x: (9)
2.1 N-type Neutral Region
In the N-type neutral region, the continuity equations for holes in the time-domain and frequency-domain are
@pn(x; t)
@t = Dp@2pn(x; t)
@x2
pn(x; t)
p
+ g(x; t); (10)
sPn(x; s) = Dp@2Pn(x; s)
@x2
Pn(x; s)
p
+ G(x; s); (11)
and the boundary conditions are
@pn
@x x=0 = 0; pnjx=L1 = 0: (12)
A function f1(x)shown in Fig. 2 can satisfy the boundary conditions and is equal to e x for 0 x L1.
Since the Fourier series coe¢ ceint Am can be evaluated as
Am = 2
e x can be expressed as
e x= X1 m=1
Amcos (2m 1)
2L1 x ; for 0 x L1; (14)
and then G(x; s) can be expressed as
G(x; s) = 0(s) where am can be evaluated as
am = Am
The di¤usion current in the N-type neutral region is then obtained as
Ip(s) = AqDp @Pn(x; s)
Figure 3: Waveform of f2(x0)
2.2 P-type Neutral Region
In the P-type neutral region, the continuity equation for electrons in the time-domain and frequency-domain are
@np(x0; t)
@t = Dn@2np(x0; t)
@x02
np(x0; t)
n
+ g(x0; t); (19)
sNp(x0; s) = Dn@2Np(x0; s)
@x02
Np(x0; s)
n
+ G(x0; s); (20)
and the boundary conditions are
npjx0=0 = 0; npjx0=L2 = 0; (21) where x0 = x (L1+ D1).
A function f2(x0)shown in Fig. 3 can satisfy the boundary conditions and is equal to e x0 for 0 x0 L2.
Since the Fourier series coe¢ ceint Bm can be evaluated as
Bm = 2 L2
Z L2
0
f2(x0) sin m L2
x dx0
= 2m 1 ( 1)me L2
( L2)2+ (m )2 ; (22)
e x0 can be expressed as where bm can be evaluated as
bm = Bm
The di¤usion current in the P-type neutral region is then obtained as
In(s) = AqDn @Np(x0; s)
In the depletion region, the drift current is
Idr(s) = A
Z L1+D1
L1
qG(x; s)dx
= Aq 0(s) e L1 e (L1+D1) : (28)
2.4 Total Current
The output current Io(s) is
Io(s) = Ip(s) + In(s) + Idr(s): (29)
3 Finger Photodiode
Consider a …ger photodiode shown in Fig. 4. The generation rates of carriers per unit volume in the time-domain and frequency-domain are
g(x; y; t) = 0(t)e xf (y); (30)
G(x; y; s) = 0(s)e xf (y): (31)
3.1 N-type Neutral Region
In the N-type neutral region, the continuity equations for holes in the time-domain and frequency-domain are
@pn(x; y; t)
@t = Dp
@2pn(x; y; t)
@x2 + Dp
@2pn(x; y; t)
@y2
pn(x; y; t)
p
+ g(x; y; t); (32)
sPn(x; y; s) = Dp@2Pn(x; y; s)
@x2 + Dp@2Pn(x; y; s)
@y2
Pn(x; y; s)
p
+ G(x; y; s); (33)
and the boundary conditions are
@pn
@x x=0 = 0; pnjx=L1 = 0; (34)
pnjy=0 = 0; pnjy=L0Y = 0, for 0 x L1: (35)
A function f3(y)shown in Fig. 5 can satisfy the boundary conditions for 0 x L1.Since
x
y light source
p-substrate n-well
z x y
z optical mask n-well
L′
YL
1LYP
L
YD1
L2
(a)
(b)
A B
p-substrate n-well
y
y
Figure 4: Finger photodiode, (a) top view, (b) cross section along line AB.
Figure 5: Waveform of f3(y)
the Fourier series coe¢ ceint An can be evaluated as
An = 2
and then G(x; y; s) can be expressed as
G(x; y; s) = 0(s) where amn can be evaluated as
amn= AmAn
The di¤usion current Ip(s) in the N-type neutral region is then obtained as
In the P-type neutral region, the boundary conditions are similar to the case in a single photodiode. Therefore, the di¤usion current in the P-type neutral region is obtained as
In the depletion region, the drift current Idr(s) is
Idr(s) = A 1
The output current Io(s) is
Io(s) = Ip(s) + In(s) + Idr(s): (43)
x y light source
p-substrate n-well
z x y
z optical mask n-well
L′Y
L1
LYP
LY
D1
L2
(a)
(b)
A B
Figure 6: Finger-shaped SMPD, (a) top view, (b) cross section along line AB.
4 Finger-Shaped SMPD
Consider a …nger-shaped SMPD shown in Fig. 6. The generation rates of carriers per unit volume in the time-domain and frequency-domain are
g(x; y; t) = 0(t)e xf (y); (44)
G(x; y; s) = 0(s)e xf (y): (45)
4.1 N-type Neutral Region
In the N-type neutral region, the boundary conditions are similar to the case in a
…nger photodiode. Therefore, the di¤usion current Ip(s) in the N-type neutral region is obtained as
In the P-type neutral region, the continuity equation for electrons in the time-domain and frequency-domain are
and the boundary conditions are
npjx0=0 = 0; npjx0=L2 = 0; (49) np(x0; y) = np(x0; y + LY P), for 0 x0 L2: (50)
A function f4(y) shown in Fig. 7 can satisfy the boundary conditions for 0 x0 L2. Since the Fourier series coe¢ ceint Bn can be evaluated as
Figure 7: Waveform of f4(y)
bm = Bm
In the P-type neutral region, the immediate di¤usion current JnI(s) (collected by the unblocked diode) and the deferred di¤usion current JnD(s) (collected by the blocked diode) are then obtained as
InI(s) = AqDn 1
4.3 Depletion Region
In the depletion region, the drift current Idr(s) is
Idr(s) = A 1
Therefore, the di¤erential output current Iod(s)is
Iod(s) = Ip(s) + InI(s) + Idr(s) InD(s): (59)
Consider a jag-type rectangle-shaped SMPD shown in Fig. 8. The generation rates of carriers per unit volume in the time-domain and frequency-domain are
g(x; y; z; t) = 0(t)e xf (y)f (z): (60)
G(x; y; z; s) = 0(s)e xf (y)f (z): (61)
A A’
LY' LY
Incident Light LYP
z x y
L1
D1
L2 x z y
LYP Nwell Metal
Psub
Metal
Nwell
LY LZ LZP
Dielectric Layers
(a)
(b)
Figure 8: Rectangle-shaped SMPD, (a) top view, (b) cross section along line AA0.
5.1 N-type Neutral Region
In the N-type neutral region, the continuity equations for holes in the time-domain and frequency-domain are and the boundary conditions are
@pn where amnk can be evaluated as
amnk= AmAnAk
L
recFigure 9: Boundary conditions in the P-type neutral region of rec-type SMPD.
The di¤usion current Ip(s) in the N-type neutral region is then obtained as
Ip(s) = AqDp
In the P-type neutral region, the boundary conditions can be approximated to the case in Line-type SML-detector, as shown in Fig. 9, except that LY P is substituded by Lrec = 2p
5LLY PLY P
Y P+4LY P:
Therefore, in the P-type neutral region, the immediate di¤usion current InI(s) (col-lected by the unblocked diode) and the deferred di¤usion current InD(s)(collected by the blocked diode) are obtained as
InI(s) = AqDn 0(s)e (L1+D1)m
In the depletion region, the drift current is
Idr(s) = A 1
Therefore, the di¤erential output current Iod(s)is
Iod(s) = Ip(s) + InI(s) + Idr(s) InD(s): (75)
6 Meshed SMPD
Consider a meshed SMPD shown in Fig. 10. The generation rates of carriers per unit volume in the time-domain and frequency-domain are
A A’
LY' LY Incident Light
LYP
z x y
L1 D1
L2 x z y
LYP
Nwell Metal
Psub
Metal
Nwell
LY
LZ LZP
Dielectric Layers
(a)
(b)
Figure 10: Meshed SMPD, (a) top view, (b) cross section along line AA0.
g(x; y; z; t) = 0(t)e xf (y)f (z): (76)
G(x; y; z; s) = 0(s)e xf (y)f (z): (77)
6.1 N-type Neutral Region
In the N-type neutral region, the continuity equations for holes in the time-domain and frequency-domain are and the boundary conditions are
@pn
Pn(x; y; z; s) = 0(s) where amnk can be evaluated as
amnk= AmAnAk
The di¤usion current Ip(s) in the N-type neutral region is then obtained as
Ip(s) = AqDp 1
In the P-type neutral region, the continuity equation for electrons in the time-domain and frequency-domain are
sNp(x0; y; s) = Dn@2Np(x0; y; s)
and the boundary conditions are
npjx0=0 = 0; npjx0=L2 = 0; (91) np(y = 0) = np(y = LY P), for 0 x0 L2; (92) np(z = 0) = np(z = LZP), for 0 x0 L2: (93)
The function f4(y) and f4(z)can satisfy the boundary conditions for 0 x0 L2. Since the Fourier series coe¢ ceints Bn and Bk can be evaluated as
Bn = 2
G(x0; y; s) = 0(s)e (L1+D1)
In the P-type neutral region, the immediate di¤usion current JnI(s) (collected by the unblocked diode) and the deferred di¤usion current JnD(s) (collected by the blocked
diode) are then obtained as
In the depletion region, the drift current is
Idr(s) = A 1
Therefore, the di¤erential output current Iod(s)is
Iod(s) = Ip(s) + InI(s) + Idr(s) InD(s): (104)
Abbreviations
AA ascorbic acid
ABTS 2,2’-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid) BER bit-error-rate
BW bandwidth
CMOS complementary metal-oxide-semiconductor Conc. concentration
DAO diamine oxidase ddH2O double distilled water
DMEM Dulbecco’s modified Eagle’s medium DMSO dimethyl sulfoxid
DNW deep-Nwell
EDTA ethylene-diamine-tetraacetic acid ELISA enzyme-linked immuno-sorbent assay FWHM full width at half maximum
GBW gain-bandwidth product GOx glucose oxidase
GPIB general purpose interface bus HRP horseradish peroxidase IC integrated circuits ICS interactive characterization software ImAA imidazole acetic acid incr. conc. increasing concentration MMF multimode fibers
MOSFET metal-oxide-semiconductor field-effect transistor
MTT 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyltetrazolium-bromide]
NMOS n-channel MOSFET OEIC optoelectronic integrated circuits PA post limiting amplifier
PASS passivation layers PBS phosphate buffered saline
PD photodiode PMOS p-channel MOSFET PP peak-to-peak PRBS pseudo-random binary sequence PT phototransistor RGC regulated cascode RMS root-mean-square SD standard deviation SMPD spatially modulated photodiode SMPT spatially modulated phototransistor TIA transimpedance amplifier TMB 3,3’,5,5’-tetramethyl-benzidine TSMC Taiwan semiconductor manufacturing company
生化名詞中英對照
ABTS, 2,2’-azino-bis(3-ethylbenzthiazoline-6-sulphonic acid)
2,2’-連氮基-雙(3-乙基苯並二氫噻唑啉-6-磺酸)
acetaminophen 乙醯胺酚
antibiotic 抗生素
ascorbic acid 抗壞血酸
DAO, diamine oxidase 二氨氧化酶
DMEM, Dulbecco’s modified Eagle’s medium 經 Dulbecco 改良之 Eagle 培養基 DMSO, dimethyl sulfoxid 二甲基亞碸
DOPA 多巴
dopaquinone 多巴醌
EDTA, ethylene-diamine-tetraacetic acid 乙二胺四乙酸 ELISA, enzyme-linked immuno-sorbent assay 酶聯免疫吸附分析 fetal bovine serum 胎牛血清
formazan 甲臘
GOx, glucose oxidase 葡萄糖氧化酶
Gluconic Acid 葡萄糖酸
glucose 葡萄糖
histamine 組織胺
HRP, horseradish peroxidase 辣根過氧化酶 ImAA, imidazole acetic acid 咪唑醋酸
kojic acid 麴酸
lactate 乳酸
melanin 黑色素
melanocyte 黑素細胞
melanogenesis 黑素生成
mitochondrial enzyme 線粒體酶
MTT, 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyltetrazolium-bromide]
3-(4,5-二甲基-2-噻唑基)-2,5-二苯基四氮唑溴鹽 murine melanoma cells 小鼠黑色素瘤細胞
PBS 磷酸鹽緩衝劑
sodium bicarbonate 重碳酸鈉
TMB, 3,3’,5,5’-tetramethyl-benzidine 3,3’,5,5’-四甲基聯苯胺
trypsin 胰蛋白酶
tyrosinase 酪氨酸酶
uric acid 尿酸
簡 歷
一、基本資料
姓 名：張 育 維 英文姓名：Chang, Yu-Wei 姓 別：男
出生日期：民國六十九年三月九日 籍 貫：台灣
二、主要學歷
國立交通大學電子工程學系 1998/09－2002/06 國立陽明大學生醫光電研究所碩士班 2002/09－2004/06 國立交通大學電子研究所博士班 2004/09－2009/07
國立交通大學電子工程學系 1998/09－2002/06 國立陽明大學生醫光電研究所碩士班 2002/09－2004/06 國立交通大學電子研究所博士班 2004/09－2009/07