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Greek letters in the thesis text. (The equations are presented as GIFs.)
List of Symbols
Symbol |
Meaning (common units) |
| αeff | effective ionization coefficient. (m-1) |
| αn | electron ionization coefficient. (m-1) |
| αp | hole ionization coefficient. (m-1) |
| Δx | the distance between xmj and xp0, see equation (5.15). (m) |
| Δx | a small distance. (μm) |
| ΔT | a temperature differential. (K) |
| ε | dielectric constant of silicon, approximately 11.8 ε0. (F/m) |
| φ | heat flux. (W/cm2) |
| κ | thermal conductivity. (W/cmK) |
| λ | a dopant diffusion length. (μm) |
| λ1 | a dopant diffusion length. (μm) |
| λ2 | a dopant diffusion length. (μm) |
| π | lightly doped p-type region. |
| ρ | density. (g/cm3) |
| τ | high-level ambipolar lifetime, defined by equation (2.3). (ns) |
| τEFF | effective carrier lifetime. Defined by equation (3.4). (ns) |
| τn0 | low-level electron lifetime. (ns) |
| τp0 | low-level hole lifetime. (ns) |
| τRC | RC time constant of the reverse-biased diode near breakdown. (ns) |
| τth | thermal time constant. (s) |
| μn | electron mobility. (cm2/Vs) |
| μp | hole mobility. (cm2/Vs) |
| ω | angular frequency. (rad/s) |
| A | diode cross-sectional area. (mm2) |
| A | a DC bias voltage applied to a diode in C-V measurements. (V) |
| a | effective ionization parameter, see equation (C.4). (m-1) |
| A0 | a constant defining the parabola in equation (5.14). |
| A1 | a constant defining the parabola in equation (5.14). |
| al | location of left sweeping-out boundary. (μm) |
| an | electron ionization parameter, see equation (C.1). (m-1) |
| ap | hole ionization parameter, see equation (C.1). (m-1) |
| ar | location of right sweeping-out boundary. (μm) |
| B | a mobility ratio: (μn - μp)/(μn + μp). |
| B | amplitude of a sine-wave voltage applied in C-V measurements. (V) |
| b | effective ionization parameter, see equation (C.1). (V/cm) |
| bn | electron ionization parameter, see equation (C.1). (V/cm) |
| bp | hole ionization parameter, see equation (C.1). (V/cm) |
| BVnon | breakdown voltage of a non-punch-through structure. (V) |
| BVpt | breakdown voltage of a punch-through structure. (V) |
| C | a capacitance. (F) |
| Cp | specific heat capacity. (J/gK) |
| Cth | thermal capacity. (J/K) |
| d | one-half of the width of the s (or i) middle layer. d = W/2. (μm) |
| D | ambipolar diffusion coefficient, defined by equation (2.5). (cm2/s) |
| Dd | dopant diffusion constant. (cm2/s) |
| DFn | designator for a diffused structure. |
| Dn | electron diffusion coefficient (cm2/s) |
| DP | hole diffusion coefficient. (cm2/s) |
| E | electric field. (V/cm) |
| Ebulk | the electric field in the bulk of the middle s-layer. (V/cm) |
| EC | critical electric field. Electric field at junction at breakdown. (V/cm) |
| EC0 | empirically determined constant in equation (4.10). (V/cm) |
| EPn | designator for an epitaxial structure. |
| f | defined by equation (8.22). |
| g | a unitless parameter defined by equation (5.4). |
| i | intrinsic region. |
| I | a current. (A) |
| I0 | the critical current, at which f = 1. (A) |
| IBIAS | forward bias current in a SRD or WFSRD. (A) |
| IF | forward bias current. (A) |
| IL | leakage current. (μA) |
| IR | reverse current during storage time. (A) |
| J0 | the critical current density, at which f = 1. (A/mm2) |
| Jdiff | diffusion current density. (A/mm2) |
| JF | forward bias current density, IF/A. (A/mm2) |
| Jn | electron current density. (A/mm2) |
| Jp | hole current density. (A/mm2) |
| JR | reverse current density. (A/mm2) |
| K | a constant, 4010 Vcm-5/8. |
| L | an inductance. (H) |
| L | thickness of a wafer. (μm) |
| Ld | characteristic diffusion length of injected charge carriers. (μm) |
| M | empirically determined constant in equation (4.10). (unitless) |
| M | ionization multiplication factor. |
| N | doping of the s (or i) middle layer. (cm-3) |
| n(x) | electron density. (cm-3) |
| n+ | heavily-doped n-type region. |
| N1 | doping profile to the left of the junction. (cm-3) |
| N2 | doping profile to the right of the junction. (cm-3) |
| NA | acceptor density. (cm-3) |
| NA+ | ionized acceptor density. (cm-3) |
| navg | average carrier density in intrinsic layer. (cm-3) |
| NB | background doping. (cm-3) |
| ND | donor density. (cm-3) |
| ND+ | ionized donor density. (cm-3) |
| Neff | an effective doping, as defined by equation (3.2). (cm-3) |
| NS | surface doping. (cm-3) |
| NS1 | left surface doping. (cm-3) |
| NS2 | right surface doping. (cm-3) |
| p(x) | hole density. (cm-3) |
| p+ | heavily-doped p-type region. |
| p0 | mobile hole density in the space-charge region. (cm-3) |
| Pavg | average dissipated power. (W) |
| q | electron charge. (C) |
| Q | integrated charge density. (C/m2) |
| Q | quality factor. |
| Q- | charge removed by reverse bias. (C) |
| Q+ | charge stored by forward bias. (C) |
| Qimpl | dose of ion-implanted impurities. (cm-2) |
| QN | net charge density at x = x0. (C/m3) |
| Qn | a transistor. |
| R | a resistance. (Ω) |
| RL | load resistance, usually 50 Ω. |
| RT | thermal resistance. (K/W) |
| s | lightly-doped region, either p or n type. |
| s | the Laplace s-coordinate variable |
| t | time. (ns) |
| T | time normalized to τ. |
| T | temperature. (K) |
| tdi | the time at which double injection begins. (ns) |
| tEFF | predicted switching speed for a WFSRD. (ns) |
| tF | pulse width of the forward bias pulse, for a DSRD. (ns) |
| tR | switching time and/or rise time. (ns) |
| tRR | reverse recovery time, tS + tR. (ns) |
| tS | storage time. (ns) |
| tT | diode transit time. (ns) |
| V1 | empirically determined constant in equation (4.10). (V) |
| Vbias | a circuit voltage, see Figure 3.1. (V) |
| VBR | breakdown voltage. (V) |
| VBR0 | first iteration result when calculating VBR. (V) |
| VCEsatn | collector-emitter saturation voltage. (V) |
| Vd | diode voltage. |
| VF | forward bias applied across a diode and load. (V) |
| VIN | maximum positive input voltage to a pulse-sharpening circuit. (V) |
| Vmax | a circuit voltage, see Figure 3.1. (V) |
| VOP | operating voltage. Maximum reverse bias applied by a circuit to a SRD. (V) |
| VR | reverse bias applied across a diode and load. (V) |
| vR | charge removal velocity. (cm/s) |
| VRAMP | diode voltage immediately before the fast transient starts. (V) |
| vS | saturation velocity of electrons and holes, approximately 107 cm/s for silicon. |
| VT | thermal voltage, kT/q. (V) |
| W | width of the s (or i) middle layer. W = 2d. (μm) |
| WDR | width of the depletion region. (μm) |
| WF | width factor, W normalized to the width of the depletion region at VBR in a non-punchthrough structure. |
| WL | width of the s (or i) middle layer normalized to L. |
| WQ | distance between the p+n junction and the meeting point of the sweeping-out boundaries. (μm) |
| X | distance normalized to L. |
| x' | dummy integration variable. (μm) |
| x0 | the location of the apex of the parabola defined in equation (5.14). (μm) |
| x1 | location of the left edge of the depletion region. (μm) |
| x2 | location of the right edge of the depletion region. (μm) |
| xa | location of high-low junction, defined by equation (4.14). (μm) |
| xmj | location of the metallurgical junction. (μm) |
| xp0 | the location of the high-low junction. (μm) |
| z | dummy variable. |
| ZOUT | output impedance of a voltage source. (Ω) |
