Univ. of Inchon 6 pn Junction Diode : I-V Characteristics 반도체 소자 연구실 박 종 태

6 pn Junction Diode : I-V Characteristics 6.1 THE IDEAL DIODE EQUATION Qualitative Derivation

6 pn Junction Diode : I-V Characteristics

(6.1) Ideal diode equation

6 pn Junction Diode : I-V Characteristics Diode current at reverse bias - Generation current within depletion region

6 pn Junction Diode : I-V Characteristics Quantitative Solution Strategy General Considerations (1) The diode is being operation under steady state condition (2) A nondegenerately doped step junction models the doping profile (3) The diode is one-dimensional (4) Low-level injection prevails in the quasi-neutral region (5)There are no processes other than drift, diffusion, and thermal recombination-generation taking place inside the diode. Specifically, G L =0

6 pn Junction Diode : I-V Characteristics (6.2) (6.3) (6.4a) (6.4b) General relationships

6 pn Junction Diode : I-V Characteristics (6.5a) (6.5b) The condition for the use of the minority carrier diffusion equations

6 pn Junction Diode : I-V Characteristics Current due to diffusion ( ε ≈0 in the quasineutral regions) Depletion Region Considerations From continuity equations in the depletion regions (6.6a) (6.6b) (6.7a) (6.7b)

6 pn Junction Diode : I-V Characteristics Carrier current is constant throughout the depletion region Total current in the depletion region Boundary condition - Δn P in the p-side - Δp n in the n-side (6.8a) (6.8b) (6.9)

6 pn Junction Diode : I-V Characteristics At the Ohmic Contacts - There is no potential drop at p- and n- contact

6 pn Junction Diode : I-V Characteristics For wide-base diode, the contact is located at x=±∞ At the Depletion Region Edges From quasi-Fermi level formalism - F N -F P ≤ E Fn -E Fp =qV A - law of the junction (6.10a) (6.10b) (6.11) (6.12)

6 pn Junction Diode : I-V Characteristics at x=-x p or and Similarly (6.13) (6.14) (6.15) (6.16)

6 pn Junction Diode : I-V Characteristics or (6.17) and (6.18) Derivation Proper (6.19)

6 pn Junction Diode : I-V Characteristics From boundary condition where (6.20a) (6.21) (6.22) (6.20b)

6 pn Junction Diode : I-V Characteristics - x'→∞ : exp(x'/L P )→∞ - A 2 =0 - A 1 =Δp n (x'=0)

6 pn Junction Diode : I-V Characteristics and - On the quasineutral p-side of the junction and (6.26) (6.25) (6.24) (6.23)

6 pn Junction Diode : I-V Characteristics At the depletion edge or (6.27a) (6.27b) (6.28) (6.29) (6.30)

6 pn Junction Diode : I-V Characteristics Examination of Results Ideal I-V For forward biasing greater then a few KT/q (6.31)

6 pn Junction Diode : I-V Characteristics The Saturation Current and - As a general rule, the heavily doped side of an asymmetrical junction can be ignored in determining the electrical characteristics of the junction Example 6.1 (6.32a) (6.32b)

6 pn Junction Diode : I-V Characteristics Carrier Currents

6 pn Junction Diode : I-V Characteristics Carrier Concentrations

6 pn Junction Diode : I-V Characteristics Example 6.3

6 pn Junction Diode : I-V Characteristics Measured I-V plot of p-n diode 6.2 DEVIATIONS FROM THE IDEAL Ideal Theory Versus Experiment

6 pn Junction Diode : I-V Characteristics V BR is defined at the reverse voltage for I=1uA or 1mA V BR is dependent on the doping concentration of the bulk (6.33) Reverse-Bias Breakdown

6 pn Junction Diode : I-V Characteristics Avalanching - Electron hole pair generation within depletion region by input ionization

6 pn Junction Diode : I-V Characteristics - Multiplication factor An empirical fit to experimental data gives m=3~6 VBR dependence of doping concentration - From the electric field at x=0 (6.34) (6.35) (6.36)

6 pn Junction Diode : I-V Characteristics For asymmetrical doped junctions Zener Process - For heavily doped p-n junction - V BR ≃ 4.5V (6.37) (6.38) (6.39)

6 pn Junction Diode : I-V Characteristics The R-G Current Extra current arises from thermal carrier recombination-generation in the depletion region The thermal current (6.40) (6.41)

6 pn Junction Diode : I-V Characteristics

and For reverse biases greater than a few kT/q, n→0, p→0 where (6.42) (6.43) (6.44)

6 pn Junction Diode : I-V Characteristics The combined forward and reverse bias dependence of I R-G The diffusion current under forward biases Total forward bias current (6.45) (6.46) (6.47)

6 pn Junction Diode : I-V Characteristics VA→Vbi High-Current Phenomena Series Resistance Resistance in the quasineutral region Small contact resistance Junction voltage

6 pn Junction Diode : I-V Characteristics

(6.48) (6.49)

6 pn Junction Diode : I-V Characteristics The increased bias voltage gives rise to high-level injection I ∝ exp(q/2KT) Example 6.9 High-Level Injection

6 pn Junction Diode : I-V Characteristics Charge Control Approach Minority carrier excess in the n-side quasi-neutral region at given time t and a point x, x n ≤x≤∞ : ∆p n (x,t) Total excess hole charge : Q P The minority carrier diffusion equation with G L = 0 Since in a ≈0 region (6.50) (6.51) 6.3 SPECIAL CONSIDERATIONS

6 pn Junction Diode : I-V Characteristics we can alternatively write (6.53) (6.54) (6.55) (6.52)

6 pn Junction Diode : I-V Characteristics i DIFF : Hole current can flow into or out of the region : The excess charge can be modified by recombination- generation within the region In the steady state dQ p /dt =0, i DIFF =I DIFF From approximation of Q P in the diffusion length giving (6.59) (6.58) (6.57) (6.56)