A6525: Lec. 5 1 Solid State Detectors Astronomy 6525 Lecture 5 A6525 - Lecture 5 Solid State Detectors 2 Outline Semiconductor Models Pure Semiconductors Doped semiconductors Bohr model for impurities Expected spectral response Photoconductivity Unwanted impurities Photoelectron dynamics Photoconductive Gain Supplemental Material References Photovoltaic detectors
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A6525: Lec. 5
1
Solid State Detectors
Astronomy 6525
Lecture 5
A6525 - Lecture 5Solid State Detectors 2
Outline Semiconductor Models Pure Semiconductors Doped semiconductors Bohr model for impurities Expected spectral response Photoconductivity
Unwanted impurities Photoelectron dynamics Photoconductive Gain
Supplemental Material References Photovoltaic detectors
A6525: Lec. 5
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A6525 - Lecture 5Solid State Detectors 3
The Band Theory of Solids
Bring atoms together and the levels merge
The “valence states” and “conduction states” are analogous to the ground and excited states in the isolated atom.
BandGap
Tight binding approximation
Two levelAtoms
ConductionBand
ValenceBand
Metal, Insulator,or Semiconductor
A6525 - Lecture 5Solid State Detectors 4
Examples: H and He
Suppose we start with atomic hydrogen It forms a metallic solid since there are N e- and 2 N
levels for them in the 1s state.
An electron can migrate from one atom (proton) to the next with no additional energy.
If we start w/ helium The “broadened” 1s level is full because of the 2, 1s
electrons are present.
The e- cannot move an insulator
To move the e- must move up to the next (2s) level (Band)
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A6525 - Lecture 5Solid State Detectors 5
Semiconductors and Insulators
Valence Band
Band Gap
Conduction Band
Ev
Ec
Eg
Valence Band
Eg
Ec
Band Gap
Conduction Band
Ev Valence States
Conduction States
In a semiconductor or insulator, there is a threshold excitation requirement, Eg, for the e- to attain the conduction band
The filled band is called the valence band, while the unfilled one is called the conduction band The bandgap energy, Eg is the energy between the highest energy levels in the
valence band, and the lowest energy level in the conduction band For room temperature semiconductors: 0 < Eg < 3.5 eV
“metal”“semiconductor”
“insulator”
A6525 - Lecture 5Solid State Detectors 6
Band Gap
Si, Ge, InSb are “insulators” Have Eg = Eband gap ~ 20 kTroom
Thermal fluctuations (phonons) can excite an electron across the band gap.
Because there are many free (empty) levels, the electron and the hole left by it are free to move.
E
Valence Band
Band Gap Eg
Conduction Band
e-
hole (+)
ThermalExcitations
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A6525 - Lecture 5Solid State Detectors 7
Pure Semiconductors Pure semiconductors, i.e. Si and Ge, are called Intrinsic.
For quasi-monochromatic radiation P/hν = # photons/sec (P = power)
If we have one electron per photon Current = (# e-/sec)·e = e·P/hν
Responsivity [Amps/Watt] Rmax = e / hν = 0.81·λ(μm) in Amps/Watt
The actual responsivity will be
R = ηG ·Rmax η = Quantum Efficiency
G = Photoconductive Gain
A6525 - Lecture 5Solid State Detectors 18
What is the spectral response?
No (or little) response for hν < EB.
Peak response for hν ~ EB.
Decreasing response for hν > EB. Ionization cross-section decreases for hν > EB.
(σν ∝ ν -3 like H-atom)
Only one e-/photon but more energy per photon
increases asdown goes watt
sec/ of No. ν−
e
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A6525 - Lecture 5Solid State Detectors 19
Expected spectral responsePeak
Cut-off wavelength
∝ ν -4
log λ
log
R (
amps
/wat
t)
For an optically thin detector
A6525 - Lecture 5Solid State Detectors 20
Absorption cross-sections of impurity dopants in Si and Ge
Peak optical absorption cross sections vs. cutoff wavelengths of impurity dopants.
After Rieke (1996)10 100
Si: Acceptors
Si: Donors
Ge: Acceptors
Ge: Donors
Pea
k ab
sorp
tion
cro
ss-s
ecti
on (
cm2 )
10-13
10-14
10-15
10-16
10-17
10-18
λCO (μm)
CuBe
In
GaAl Cu
As
SbBe Ga
SbAs
P
PB
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A6525 - Lecture 5Solid State Detectors 21
Photoconductivity
Photoconductor The electrical conductivity of
a semiconductor is increased by photons which promote electrons into the conduction band.
Photoconductors can be either intrinsic or extrinsic.
Expect the (photo)current, id, to depend on the photon flux.
Vb
id
id ∝ Nph (ph/sec)
C
V
A6525 - Lecture 5Solid State Detectors 22
Unwanted impurities
Real semiconductors have impurities both n-type (donors) and p-type (acceptors)
Consider a semiconductor with excess donors
C
V
Donors (some ionized)Acceptors (all ionized)
C
V
Which looks like
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A6525 - Lecture 5Solid State Detectors 23
Photoelectron dynamics
A photon can ionize one of the neutral donors.
C
V
Electron sits near its creation sight for some amount of time and then recombines with one of the D+s.
D+ holes are left by the ionization of donors by impurity acceptors in the detector.
A6525 - Lecture 5Solid State Detectors 24
Electron traps
The electron moves toward the positive electrode. It may be captured by any of the D+s and stop.
The presence of acceptors produces traps (D+s) that can terminate the motion of a photoelectron.
Applying an electric field, the e- drift toward the + end. The D+s stay in place since they cannot move.
-+
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A6525 - Lecture 5Solid State Detectors 25
Photoconductive Gain Photoconductive gain (G)
One typically defines the photoconductive gain by the product of the mobility, μe of the e- × lifetime of e- × electric field strength, εx, divided by the interelectrode spacing:
G = τe·μe·εx/d = vx·τe/d = e/d In practical terms this is the ratio of the distance traveled, e, to the
interelectrode spacing, d: G = e/d
If there are large numbers of acceptors (“dirty” semiconductor) then e << d and the detector is not very responsive. Note 1: The detector may still have a high quantum efficiency but
it just doesn’t produce any current. Note 2: G can be > 1 since electrons can leave the detector and be
replaced by e- from the - electrode. This will continue until the e-recombines with a D+.
A6525 - Lecture 5Solid State Detectors 26
Photoconductive detector model
Under the influence of an electric field, E, the electron-hole pair will each drift.
The drift velocities will be
vn = - μnEvp = μpE
where μn, μp = mobilities for negative and positive carriers.
At T ~ 290 K, μn ~ 102 - 104 cm2/V/sec and μp ~ μn/10
See Boyd, page 162
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A6525 - Lecture 5Solid State Detectors 27
PC Detector Model - (cont’d)
Suppose monochromatic light with power, P, at frequency, ν, falls onto the detector.
P
V i w
Let S be the surface density of conduction-band electrons (electrons/unit area of detector surface) due to both thermal & photo-electrons.
Let ΔS be the contribution from photo-excited electrons.
A6525 - Lecture 5Solid State Detectors 28
PC Detector Model - (cont’d)
τνη S
wh
P
t
S Δ−=ΔΔ
Let τ be the lifetime of the electron in the conduction band
Which in steady state giveswh
PS
ντη=Δ
If the bias voltage is V, then the drift velocity is
whereEnn μ−=v
VE =
νη
h
PGeweSi n =Δ−= vThe photocurrent is then
2
|v|
VG n μττ ==G, the photoconductive gain,
increases with applied voltage
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A6525 - Lecture 5Solid State Detectors 29
Limitations of Photoconductors Cannot dope too high because “dark current” increases due
to e- hopping towards + end (hopping current). ND ~ 1015 - 1016 cm-3
To get a high η must make this thick (> 100 μm) to geta high optical depth
aePabsτ−−= 1
For τa ~ 1 det ~ 100 μm
detDDa N στ =
ND = 1016 cm-3
σD = 10-14 cm-2
Show time constant effects (hook response, spiking, etc.)
Susceptible to ionizing radiation due to size
A6525 - Lecture 5Solid State Detectors 30
Blocked Impurity Band Detectors Many more donors than
moves towards the + end and can pass by the blocking layer.
No D+ to recombine with along the way so G = 1.
+
-
BIB is a “brand” name coined by Rockwell Inventor of the BIB (Rockwell/Boeing/DRS Tech)
IBC: Impurity Band Conduction Name used by other companies
A6525 - Lecture 5Solid State Detectors 32
BIB Advantages
High doping: good photon absorption
broader wavelength coverage
D+ depletion: good e- collection efficiency
Intrinsic layer: blocks dark current
Small size: easier to make arrays
less susceptible to ionizing radiation
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A6525 - Lecture 5Solid State Detectors 33
BIB Structure
Back-Illumination for arrays.
Si
TransparentContact
ReflectingContact
Intrinsic SiBlocking LayerIR Active
Region
Back-Illuminated Blocked-Impurity-Band -> BIBIB
A6525 - Lecture 5Solid State Detectors 34
Supplemental Info
References: Radiometry and the Detector of Optical Radiation (Boyd)
Excellent book on theory
Detection of light from UV to sub-mm (Rieke) detectors, readout, etc.
Photovoltaic Device See slides
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A6525 - Lecture 5Solid State Detectors 35
InSb Photoconductors: the Problem
For InSb it is not possible to simultaneously achieve both high G, and large resistance If G is small, signals are small likely dominated by
amplifier noise
If the resistance is small, the system will be dominated by Johnson noise (more later)
The situation is identical for Hg1-xCdxTe detectors, which are an alternative type in the near-IR
The situation is ameliorated by using the InSb or Hg1-xCdxTe materials as photodiodes
A6525 - Lecture 5Solid State Detectors 36
InSb Photoconductors: the Problem
Consider construction of an InSb intrinsic photoconductor for the 1-5 μm region The carrier lifetime, τe ≈ 10-7 s, μe ≈ 105 cm2V-1s-1
So that:G = τe·μe·εx/ ≈ 10-2 V/2
The breakdown voltage for InSb is small can only make G ~ 1 by making the physical size of
the device, , small. However, the detector resistance is:
Rd = /(σwd), where σ =qn0 μe Since the electron mobility in InSb is ~ 100 times that
of silicon, it is not possible to achieve high R, with small
Not shown in class
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A6525 - Lecture 5Solid State Detectors 37
Photovoltaic Detectors
Photovoltaic devices produce a photocurrent (or voltage) w/o a external bias.
C
V
p-type n-type
EF = Fermi level
EFdonors
acceptors
At room temperature most of the impurities will be ionized. (Fermi level => 1/2 occupancy)
E
p-n junction photodiode:
A6525 - Lecture 5Solid State Detectors 38
Photovoltaic Detectors When the two materials are brought into electrical contact,
the electrons and holes can diffuse: recombination occurs.
Depleted ofmobile charge
Not neutral
CB
VB
Depletion Region
Space Charge Region
EDevelopment of E-fieldstops diffusion.
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A6525 - Lecture 5Solid State Detectors 39
PV Detectors (cont’d) The electric field creates a potential difference, Vo,
between the p- and n-type materials.
current flows easilycurrent must overcome Vo
Electrons flow between the materials until the Fermi levels are in equilibrium
A diode
Vo
E
p-type n-typeCB
VB
A6525 - Lecture 5Solid State Detectors 40
Diode behavior – Reverse Bias
If we add to the contact potential (+ voltage applied to n-type material) this is termed reversed bias
The voltage drop appears across the depletion layer because this region has a large resistance (due to the depletion of mobile charges) The increased V increases the width of the
depletion zone, and Rjunction
Eventually the junction breaks down and becomes highly conducting
can occurs via tunneling: If the conduction band in the n-type is
brought below the energy level of the valence band in the p-type material, and the width of the depletion region is small enough that the electron’s wave function can extend across it.
At high reverse biases, breakdown occurs by avalanching: The strong field accelerates a free
electron in the p-type region so strongly that it then can create additional conduction electrons through collisions Figure 4.3 in Reike:
tunneling through a junction
Not shown in class
A6525 - Lecture 5Solid State Detectors 42
Diode behavior – Forward Bias
If we subtract from the contact potential (+ voltage applied to the p-type material), this is termed forward bias This decreases the width of the depletion zone If the bias voltage is larger than Vo, then the
junction becomes strongly conducting.
Vo - VaC
V
breakdown
reverse bias forward biasp
n
i
Va
Va
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A6525 - Lecture 5Solid State Detectors 43
PV Depletion Region Size
Poisson’s eq’n:
)( 2 VEV −∇=−=∇ερ
Assume 1) junction at x = 02) NA = constant, x < 03) ND = constant, x > 0
Depletion Region
CB
VB
Space Charge Region
We also have
and
np xxdx
dVE ≥−≤=−= , 0
aopn VVVV −=−− )()(
NA = acceptor densityND = donor densityp = width of acceptor regionn = width of donor region
A6525 - Lecture 5Solid State Detectors 44
PV Depletion region size (cont’d)
=2
2
dx
Vd
0 << x-eN
pA
ε
nD x
eN<<− 0
εotherwise 0
Poisson’s Eq’nis then:
Solving gives:
=V( ) 0 2
22 <<+ x-xx
eNpp
A ε
( ) nnD xxx
eN <<−− 0 2
22
ε
( )2/1
/2
−
+= ao
DA
ADp VV
NN
NN
e
ε ( )
2/1/2
−
+= ao
DA
DAn VV
NN
NN
e
ε
where
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A6525 - Lecture 5Solid State Detectors 45
PV Depletion region size (cont’d)
nDpA NN =
Since the overall charge is neutral
The total width of the region is (p + n):
( )2/1
2
−+= ao
DA
DA VVNN
NN
ew
ε
Differentiating the voltage to get the electric field gives
=E
( ) 0 <<+− x-xeN
ppA
ε
( ) nnD xx
eN <<−− 0
ε
A6525 - Lecture 5Solid State Detectors 46
Plots of PV junction Parms
x
ρ(x)
ND
-NA
x
E(x)
p
-n
x
V(x)
( )w
VVE ao −−= 2
max
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A6525 - Lecture 5Solid State Detectors 47
Junction Capacitance Photodiodes have relatively high capacitance since the
distribution of oppositely charged particles across the junction forms a parallel plate capacitor with a small separation between the plates
This large capacitance limits the frequency response of the photodiode, and thereby drives the limiting noise of the readout electronics. Also, V = Q/C, higher C => lower voltage for a given charge. So
for a given voltage noise of the output amplifier (detector), this results in a higher (photoelectron) “read noise” [Q = CVoutput_noise]
A faster junction is a PIN diode p-type – intrinsic (insulator) – n-type junction
A6525 - Lecture 5Solid State Detectors 48
Junction Capacitance Stored charge per unit area
Q = eNAp in p-type region
-Q in n-type region
The p-n junction has a junction capacitance, which changes with voltage
For junction area, A, the differential capacitance is
w
A
VVNN
NNeA
dV
dAeN
dV
dQAC
aoDA
DA
pA
εε =
−+
=
==
2/11
2
Note that the capacitance decreases for an increasing negative bias.
Change of size of depletion region with bias change C
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A6525 - Lecture 5Solid State Detectors 49
Current flow through the p-n junction
Diffusion current, ind, electrons that enter the junction in the CB of the n-type material
with sufficient energy to overcome the potential barrier
kTeVondnd
aeii /,=
ind,o = electron diffusion current w/ no applied bias (Va)
ipd
Vo - VaCB
VB
p-type n-type
ind
A6525 - Lecture 5Solid State Detectors 50
Current flow through the p-n junction
Generation current, ing, that are generated via thermal excitation from the VB to the CB in
the p-type material.
There are analogous contributions from the motion of the positive carriers (holes).
Vo - VaCB
VB
p-type n-type
ing
ipg
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A6525 - Lecture 5Solid State Detectors 51
( ) ( )ngpgkTeV
ondopd
ngpgndpd
iieii
iiiii
a +−+=
−−+=/
,,
So that
Current flow (cont’d) The total current is the sum of each contribution
When the bias is zero, there can’t be any current flowing through the junction (isat = saturation current).
sat
ondopdngpg
i
iiii
≡
+=+ ,,
( )1/ −= kTeVsat
aeii
isat depends upon1) area of junction2) carrier mobilities3) recombination rates4) temperature
Typical isat ~ 10-7-10-9 A for Si photodiodes at room temp.
A6525 - Lecture 5Solid State Detectors 52
Adding photons
If hν > EB (band gap energy), the a photon will generate an electron-hole pair.
( )1/ −+−= kTeVsat
aeih
ePi
νη
Vo - VaCB
VB
p-type n-type
E
Want to keep isat small => less noise
Best to lower T rather than apply negative bias (keep small)
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A6525 - Lecture 5Solid State Detectors 53
Photodetection in a diode
Free carriers that are generated or recombine in either the n or the p-type regions produce little net current because of the low R in these regions
One needs creation of a charge carrier within or very near to a unbiased, or reverse-biased junction, so that it can be driven across the junction by the junction field to produce a net current
Charge carriers can be produced thermally or by photons –we presume that we can freeze out thermal electrons by cooling the device
Not shown in class
A6525 - Lecture 5Solid State Detectors 54
Photodetection in a diode – 2 The photodetection process is
illustrated to the right (Rieke F4.5): A photon is absorbed and excites and
e-/hole pair The hole drifts towards the negative
electrode or recombines The e- diffuses through the material
(remember the field drop only occurs across the depletion zone)
If it enters the depletion zone, it is accelerated across the region by the junction potential, creating the photocurrent
The process is the same if the n-type material is illuminated (with e-/hole role reversal)
Not shown in class
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A6525 - Lecture 5Solid State Detectors 55
Modes of operation
Photoconductive mode Bias detector negative so that the current is linear with photon flux. This is the usual mode: use constant voltage across the diode, and measure
the current If the voltage across the detector is held at zero, this suppresses certain
types of low frequency noise. Method – transimpedance amplifier – more later
i
VaDarkP0
P1
P0 < P1
P0,1 = incident power
Photovoltaic mode (no bias applied) Measure the output voltage at