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US 7,735,034 B2Granted
Simulation model for a semiconductor device describing a quasi-static density of a carrier as a non-quasi-static model
AssigneeSemiconductor Technology Academic Research Center
InventorsMitiko Miura, Noriaki Nakayama
Life of this patent
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Abstract
There is disclosed a simulation model and method for designing a semiconductor device being used for a simulation apparatus for designing a semiconductor device that includes using assuming units as to carrier transient density and current flow of electrodes along with a non-quasi-static model describing unit of the simulation apparatus. A simulation apparatus and computer readable medium with a simulation program for executing the method are also included.
Claims24
A simulation model for designing a semiconductor device being used for a simulation apparatus for designing a semiconductor device, comprising:
- assuming that, with respect to at least one semiconductor element having at least two first and second electrodes, a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- and
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit included in the simulation apparatus.
3 more elements
A simulation apparatus for designing a semiconductor device, comprising:
- a first assuming unit which assumes that, with respect to at least one semiconductor element having at least two first and second electrodes, a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming unit which assumes that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing unit which substitutes said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
3 more elements
A simulation method for designing a semiconductor device being executed by a simulation apparatus for designing a semiconductor device, comprising:
- assuming that, with respect to at least one semiconductor element having at least two first and second electrodes, a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit included in the simulation apparatus;
- and
- analyzing electric characteristics of the semiconductor element using the non-quasi-static model, and this process is processed by the simulation apparatus.
4 more elements
A computer-readable recording medium recording a simulation program for designing a semiconductor device being used for a simulation apparatus for designing a semiconductor device, the program allowing a computer as the simulation apparatus to execute:
- a first assuming process processed by a first assuming unit included in the simulation apparatus of assuming that, with respect to at least one semiconductor element having at least two first and second electrodes, a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming process processed by a second assuming unit included in the simulation apparatus of assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing process processed by a non-quasi-static model describing unit included in the simulation apparatus of substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
3 more elements
A semiconductor device comprising:
- at least one semiconductor element having at least two first and second electrodes, at least one of designing and inspecting of the semiconductor element being performed using a simulation model for designing the semiconductor device being used for a simulation apparatus for designing a semiconductor device,
- the simulation model for designing the semiconductor device, comprising:
- assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- and
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit included in the simulation apparatus.
5 more elements
A semiconductor device comprising:
- at least one semiconductor element having at least two first and second electrodes, at least one of designing and inspecting of the semiconductor element being performed using a simulation apparatus for designing the semiconductor device,
- the simulation apparatus for designing the semiconductor device, comprising:
- a first assuming unit which assumes that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming unit which assumes that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing unit which substitutes said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
5 more elements
A semiconductor device comprising:
- at least one semiconductor element having at least two first and second electrodes, at least one of designing and inspecting of the semiconductor element being performed by a simulation method for designing the semiconductor device being executed by a simulation apparatus for designing a semiconductor device,
- the simulation method for designing the semiconductor device, comprising:
- assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit included in the simulation apparatus;
- and
- analyzing electric characteristics of the semiconductor element using the non-quasi-static model, and this process is processed by the simulation apparatus.
6 more elements
A semiconductor device comprising:
- at least one semiconductor element having at least two first and second electrodes, at least one of designing and inspecting of the semiconductor element being performed by a computer operating based on a simulation program for designing the semiconductor device being used for a simulation apparatus for designing a semiconductor device as the computer, which is read from a computer-readable recording medium,
- the recording medium recording the simulation program for designing the semiconductor device, which allows the computer to execute:
- a first assuming process processed by a first assuming unit included in the simulation apparatus of assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming process processed by a second assuming unit included in the simulation apparatus of assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing process processed by a non-quasi-static model describing unit included in the simulation apparatus of substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
5 more elements
A method of manufacturing a semiconductor device, comprising:
- performing at least one of designing and inspecting with respect to at least one semiconductor element having at least two first and second electrodes using a simulation model for designing the semiconductor device being used for a simulation apparatus for designing a semiconductor device,
- the simulation model for designing the semiconductor device, comprising:
- assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- and
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit including in the simulation apparatus.
5 more elements
A method of manufacturing a semiconductor device, comprising:
- performing at least one of designing and inspecting with respect to at least one semiconductor element having at least two first and second electrodes using a simulation apparatus for designing the semiconductor device,
- the simulation apparatus for designing the semiconductor device, comprising:
- a first assuming unit which assumes that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming unit which assumes that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing unit which substitutes said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
5 more elements
A method of manufacturing a semiconductor device, comprising:
- performing at least one of designing and inspecting with respect to at least one semiconductor element having at least two first and second electrodes using a simulation method for designing the semiconductor device being executed by a simulation apparatus for designing a semiconductor device,
- the simulation method for designing the semiconductor device, comprising:
- assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti) and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)], and these processes are processed by a first assuming unit included in the simulation apparatus;
- assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt, and these processes are processed by a second assuming unit included in the simulation apparatus;
- substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model, and this process is processed by a non-quasi-static model describing unit included in the simulation apparatus;
- and
- analyzing electric characteristics of the semiconductor element using the non-quasi-static model, and this process is processed by the simulation apparatus.
6 more elements
A method of manufacturing a semiconductor device, comprising:
- performing at least one of designing and inspecting with respect to at least one semiconductor element having at least two first and second electrodes by a computer operating based on a simulation program for designing the semiconductor device being used for a simulation apparatus for designing a semiconductor device as the computer, which is read from a computer-readable recording medium,
- the recording medium recording the simulation program for designing the semiconductor device, which allows the computer to execute:
- a first assuming process processed by a first assuming unit included in the simulation apparatus of assuming that a transient density of a carrier at a predetermined time ti including a delay of the carrier running between the first and second electrodes is q(ti), a transient density of the carrier at a predetermined time ti-1 before the time ti is q(ti-1), a density of the carrier between the first and second electrodes in a quasi-static state assumed at the time ti is Q(ti), further a time required for the carrier to reach the other electrode from one of the first and second electrodes is τ, and said q(ti), q(ti-1), Q(ti), and τ satisfy the following first equation for a time (ti−ti-1) from the time ti-1 until the time ti:
- q(ti)=q(ti-1)+(ti−ti-1)/τ[Q(ti)−q(ti-1)];
- a second assuming process processed by a second assuming unit included in the simulation apparatus of assuming that a current flowing between the first and second electrodes at the time ti is I(ti), a quasi-static conduction current between the first and second electrodes, determined by the voltage applied at the time ti, is IDC, further a displacement current flowing between the first and second electrodes is dq(ti)/dt, and said I(ti), IDC, and dq(ti)/dt satisfy the following second equation at the time ti:
- I(ti)=IDC+dq(ti)/dt;
- and
- a non-quasi-static model describing process processed by a non-quasi-static model describing unit included in the simulation apparatus of substituting said q(ti) obtained from the first equation into the second equation to thereby describe said Q(ti) as a non-quasi-static model.
5 more elements
Dependencies are inferred from the claim text.