Download Quantitative P-N Junction Diodes - Lecture Slides | ECE 3040 and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! ECE 3040 - Dr. Alan DoolittleGeorgia Tech Lecture 14 P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1 ECE 3040 - Dr. Alan DoolittleGeorgia Tech Quantitative p-n Diode Solution Assumptions: 1) steady state conditions 2) non- degenerate doping 3) one- dimensional analysis 4) low- level injection 5) no light (GL = 0) Current equations: J=Jp(x)+Jn(x) Jn =q µnnE +qDn(dn/dx) Jp = q µppE - qDp (dp/dx) VA Quasi-Neutral Regions Depletion Region p-type n-type ECE 3040 - Dr. Alan DoolittleGeorgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region -xp xn ∞ Application of the Minority Carrier Diffusion Equation ∞− ?)( : =−=∆ pp xxn ConditionBoundary ?)( : ==∆ nn xxp ConditionBoundary 0≠E0=E 0=E ( ) ( ) ( ) −==∆= −=−=∆ −=−=∆ =−= =−==−=−= =−=−= == − −− 1)(1)( )( )( )()()( )()( 22 2 2 2 2 kT qV D i nnn kT qV A i pp o kT qV A i pp kT qV A i pp kT qV iApppppp kT FF ipppp kT FE i kT EF i AA A A A PN PiiN e N n xxpxxatsimilarlyande N n xxn ne N n xxn e N n xxn enNxxnxxpxxn enxxpxxn enpandenn ECE 3040 - Dr. Alan DoolittleGeorgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region -xp xn∞− ∞ Application of the Current Continuity Equation ( ) dx dx dx p n po n nnn nd qD nnd qD dnDnq J ∆ = ∆+ = +Ε= µ ( ) dx p dx dx n p no p ppp dqD ppdqD dpDpq J ∆ −= ∆+ −= −Ε= µ 0≠E0=E 0=E ? ECE 3040 - Dr. Alan DoolittleGeorgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region -xp xn∞− ∞ No thermal recombination and generation implies Jn and Jp are constant throughout the depletion region. Thus, the total current can be define in terms of only the current at the depletion region edges. Application of the Current Continuity Equation: Depletion Region )()( nppn xJxJJ +−= x J q J q t n t nJ qt n N N etclightassuch processesotherAllGenerationncombinatioN ∂ ∂ = ⋅∇= ∂ ∂ + ∂ ∂ +⋅∇= ∂ ∂ − 10 10 1 ..., Re 0≠E0=E 0=E x J q J q t p t pJ qt p P P etclightassuch processesotherAllGenerationncombinatioP ∂ ∂ −= ⋅∇−= ∂ ∂ + ∂ ∂ +⋅∇−= ∂ ∂ − 10 10 1 ..., Re ECE 3040 - Dr. Alan DoolittleGeorgia Tech ( ) 0'1)'( /' 2 ≥ −=∆ − xforee N nxp P A LxkT qV D i n p-type n-type Quantitative p-n Diode Solution Depletion Region x’=0∞ ∞ 0≠E0=E 0=E x’’=0 ( ) 0'1 J dqD J /' 2 p n pp ≥ −= ∆ −= − xforee NL nD q dx p P A LxkT qV Dp ip ECE 3040 - Dr. Alan DoolittleGeorgia Tech ( ) 0''1)''( /'' 2 ≥ −=∆ − xforee N nxn n A LxkT qV A i p p-type n-type Quantitative p-n Diode Solution Depletion Region x’=0∞ ∞ 0≠E0=E 0=E x’’=0 ( ) 0''1 J d qD J /'' 2 n p nn ≥ −= ∆ −= − xforee NL nDq dx n n A LxkT qV An in Similarly for electrons on the p-side… ECE 3040 - Dr. Alan DoolittleGeorgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region 0≠E0=E 0=E pn JJJ += ( )nLx n eJ /''−∝ ( )pLx p eJ /'−∝ np JJJ −= pn JJJ −= Total on current is constant throughout the device. Thus, we can characterize the current flow components as… x’=0∞ ∞x’’=0 Recombination Recombination
