微电子学-伯克利lecture4
合集下载
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
??where12????????????pdpnanisvvstotlndlndqnjejjtd0000????????xdiffnxdiffpxdriftnxdriftptotjjjjj??120???tdvvnainxdiffnelnnqdj??120???tdvvpdipxdiffpelnnqdjee105fall2011lecture4slide10prof
EE105 Fall 2011
Lecture 4, Slide 5
Prof. Salahuddin, UC Berkeley
Mathematical description of current flow in a p-n junction diode
EE105 Fall 2011
Lecture 4, Slide 6
Minority Carrier Concentrations at the Edges of the Depletion Region
• The minority-carrier concentrations at the edges of qV / kT V e e the depletion region are changed by the factor
EE105 Fall 2010 Lecture 4, Slide 1 Prof. Salahuddin, UC Berkeley
Energy Band Description
EE105 Fall 2011
Lecture 4, Slide 2
Prof. Salahuddin, UC Berkeley
– The carriers which diffuse across the junction become minority carriers in the quasi-neutral regions; they recombine with majority carriers, “dying out” with distance.
“Ideal diode” equation:
I D I S eVD /VT 1
2 i
Dn Dp I S AJ S Aqn N L N L D p A n
EE105 Fall 2011
Lecture 4, Slide 11
Prof. Salahuddin, UC Berkeley
Dp – If the P side is much more heavily doped, I S Aqni L N p D
2
Dn – If the N side is much more heavily doped, I S Aqni L N n A
n p ( x) n p 0 Dn p ( x) Dn p ( x) n e
2 i
VD / VT
1
NA
e
x / Ln
Notation: Ln electron diffusion length (cm)
J n,diff
x'
EE105 Fall 2011
dnp qDn ni2 VD /VT qDn e 1 e x / Ln dx N A Ln
EE105 Fall 2011
Lecture 4, Slide 3
Prof. Salahuddin, UC Berkeley
Energy Band Description
EE105 Fall 2011
Lecture 4, Slide 4
Prof. Salahuddin, UC Berkeley
I-V characteristic from energy band description
Practical PN Junctions
• Typically, pn junctions in IC devices are formed by counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if
VD (V)
Lecture 4, Slide 12 Prof. Salahuddin, UC Berkeley
EE105 Fall 2011
Parallel PN Junctions
• Since the current flowing across a PN junction is proportional to its cross-sectional area, two identical PN junctions connected in parallel act effectively as a single PN junction with twice the cross-sectional area, hence twice the current.
EE105 Fall 2011
Lecture 4, Slide 13
Prof. Salahuddin, UC Berkeley
Diode Saturation Current IS
Dn Dp I S Aqni L N L N n A p D
2
• IS can vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant concentrations.
Prof. Salahuddin, UC Berkeley
Minority Carrier Injection under Forward Bias
• The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.
Lecture 4, Slide 9
Prof. Salahuddin, UC Berkeley
Current Components under Forward Bias
• For a fixed bias voltage, Jtot is constant throughout the diode, but Jn(x) and Jp(x) vary with position.
PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens.
– NA net acceptor doping on p-side (NA-ND)p-side – ND net donor doping on n-side (ND-NA)n-side
I D I S (eqVD
ID (A)
2
kT
1)
Dn Dp I S Aqni L N L N n A p D
Jtot
-b
0
a
x
EE105 Fall 2011
Lecture 4, Slide 10
Prof. Salahuddin, UC Berkeley
I-V Characteristic of a PN Junction
• Current increases exponentially with applied forward bias voltage, and “saturates” at a relatively small negative current level for reverse bias voltages.
np(x)
np0 x'
edge of depletion region
x'
0
Equilbrium concentration of electrons on the P side:
Lecture 4, Slide 7
np0
ni2 NA
EE105 Fall 2011
Prof. Salahuddin, UC Berkeley
J n,diff
x 0
qDn ni2 VD /VT e 1 N A Ln
J p ,diff
2 i
x 0
qDp ni2 N D Lp
e
VD / VT
1
J tot J S e
EE105 Fall 2011
VD / VT
Dn Dp 1 where J S qn N L N L D p A n
Wdep
2 si q
1 1 N N V0 VR D A
Lecture 4, Slide 15 Prof. Salahuddin, UC Berkeley
EE105 Fall 2011
PN Junction Small-Signal Capacitancee is an excess concentration (Dpn, Dnp) of minority carriers in the quasi-neutral regions, under forward bias.
• Within the quasi-neutral regions, the excess minoritycarrier concentrations decay exponentially with distance from the depletion region, to zero:
Prof. Salahuddin, UC Berkeley
Lecture 4, Slide 8
Diode Current under Forward Bias
• The current flowing across the junction is comprised of hole diffusion and electron diffusion components:
– typical range of values for Si PN diodes: 10-14 to 10-17 A/mm2
• In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:
Lecture 4
OUTLINE • PN Junction Diodes
– Electrostatics – Capacitance – I/V – Reverse Breakdown – Large and Small signal models Reading: Chapter 2.2-2.3,3.2-3.4
2
EE105 Fall 2011 Lecture 4, Slide 14 Prof. Salahuddin, UC Berkeley
PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens.
J tot J p ,drift
x 0
J n ,drift
x 0
J p ,diff
x 0
J n,diff
x 0
• Assuming that the diffusion current components are constant within the depletion region (i.e. no recombination occurs in the depletion region):
EE105 Fall 2011
Lecture 4, Slide 5
Prof. Salahuddin, UC Berkeley
Mathematical description of current flow in a p-n junction diode
EE105 Fall 2011
Lecture 4, Slide 6
Minority Carrier Concentrations at the Edges of the Depletion Region
• The minority-carrier concentrations at the edges of qV / kT V e e the depletion region are changed by the factor
EE105 Fall 2010 Lecture 4, Slide 1 Prof. Salahuddin, UC Berkeley
Energy Band Description
EE105 Fall 2011
Lecture 4, Slide 2
Prof. Salahuddin, UC Berkeley
– The carriers which diffuse across the junction become minority carriers in the quasi-neutral regions; they recombine with majority carriers, “dying out” with distance.
“Ideal diode” equation:
I D I S eVD /VT 1
2 i
Dn Dp I S AJ S Aqn N L N L D p A n
EE105 Fall 2011
Lecture 4, Slide 11
Prof. Salahuddin, UC Berkeley
Dp – If the P side is much more heavily doped, I S Aqni L N p D
2
Dn – If the N side is much more heavily doped, I S Aqni L N n A
n p ( x) n p 0 Dn p ( x) Dn p ( x) n e
2 i
VD / VT
1
NA
e
x / Ln
Notation: Ln electron diffusion length (cm)
J n,diff
x'
EE105 Fall 2011
dnp qDn ni2 VD /VT qDn e 1 e x / Ln dx N A Ln
EE105 Fall 2011
Lecture 4, Slide 3
Prof. Salahuddin, UC Berkeley
Energy Band Description
EE105 Fall 2011
Lecture 4, Slide 4
Prof. Salahuddin, UC Berkeley
I-V characteristic from energy band description
Practical PN Junctions
• Typically, pn junctions in IC devices are formed by counter-doping. The equations provided in class (and in the textbook) can be readily applied to such diodes if
VD (V)
Lecture 4, Slide 12 Prof. Salahuddin, UC Berkeley
EE105 Fall 2011
Parallel PN Junctions
• Since the current flowing across a PN junction is proportional to its cross-sectional area, two identical PN junctions connected in parallel act effectively as a single PN junction with twice the cross-sectional area, hence twice the current.
EE105 Fall 2011
Lecture 4, Slide 13
Prof. Salahuddin, UC Berkeley
Diode Saturation Current IS
Dn Dp I S Aqni L N L N n A p D
2
• IS can vary by orders of magnitude, depending on the diode area, semiconductor material, and net dopant concentrations.
Prof. Salahuddin, UC Berkeley
Minority Carrier Injection under Forward Bias
• The potential barrier to carrier diffusion is decreased by a forward bias; thus, carriers diffuse across the junction.
Lecture 4, Slide 9
Prof. Salahuddin, UC Berkeley
Current Components under Forward Bias
• For a fixed bias voltage, Jtot is constant throughout the diode, but Jn(x) and Jp(x) vary with position.
PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens.
– NA net acceptor doping on p-side (NA-ND)p-side – ND net donor doping on n-side (ND-NA)n-side
I D I S (eqVD
ID (A)
2
kT
1)
Dn Dp I S Aqni L N L N n A p D
Jtot
-b
0
a
x
EE105 Fall 2011
Lecture 4, Slide 10
Prof. Salahuddin, UC Berkeley
I-V Characteristic of a PN Junction
• Current increases exponentially with applied forward bias voltage, and “saturates” at a relatively small negative current level for reverse bias voltages.
np(x)
np0 x'
edge of depletion region
x'
0
Equilbrium concentration of electrons on the P side:
Lecture 4, Slide 7
np0
ni2 NA
EE105 Fall 2011
Prof. Salahuddin, UC Berkeley
J n,diff
x 0
qDn ni2 VD /VT e 1 N A Ln
J p ,diff
2 i
x 0
qDp ni2 N D Lp
e
VD / VT
1
J tot J S e
EE105 Fall 2011
VD / VT
Dn Dp 1 where J S qn N L N L D p A n
Wdep
2 si q
1 1 N N V0 VR D A
Lecture 4, Slide 15 Prof. Salahuddin, UC Berkeley
EE105 Fall 2011
PN Junction Small-Signal Capacitancee is an excess concentration (Dpn, Dnp) of minority carriers in the quasi-neutral regions, under forward bias.
• Within the quasi-neutral regions, the excess minoritycarrier concentrations decay exponentially with distance from the depletion region, to zero:
Prof. Salahuddin, UC Berkeley
Lecture 4, Slide 8
Diode Current under Forward Bias
• The current flowing across the junction is comprised of hole diffusion and electron diffusion components:
– typical range of values for Si PN diodes: 10-14 to 10-17 A/mm2
• In an asymmetrically doped PN junction, the term associated with the more heavily doped side is negligible:
Lecture 4
OUTLINE • PN Junction Diodes
– Electrostatics – Capacitance – I/V – Reverse Breakdown – Large and Small signal models Reading: Chapter 2.2-2.3,3.2-3.4
2
EE105 Fall 2011 Lecture 4, Slide 14 Prof. Salahuddin, UC Berkeley
PN Junction under Reverse Bias
• A reverse bias increases the potential drop across the junction. As a result, the magnitude of the electric field in the depletion region increases and the width of the depletion region widens.
J tot J p ,drift
x 0
J n ,drift
x 0
J p ,diff
x 0
J n,diff
x 0
• Assuming that the diffusion current components are constant within the depletion region (i.e. no recombination occurs in the depletion region):